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Diffstat (limited to 'modules/linear_algebra/help')
252 files changed, 28980 insertions, 0 deletions
diff --git a/modules/linear_algebra/help/en_US/addchapter.sce b/modules/linear_algebra/help/en_US/addchapter.sce new file mode 100755 index 000000000..a33120d03 --- /dev/null +++ b/modules/linear_algebra/help/en_US/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Linear Algebra",SCI+"/modules/linear_algebra/help/en_US",%T); + diff --git a/modules/linear_algebra/help/en_US/eigen/CHAPTER b/modules/linear_algebra/help/en_US/eigen/CHAPTER new file mode 100755 index 000000000..88f8bc42b --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/CHAPTER @@ -0,0 +1,2 @@ +title = Eigenvalue and Singular Value + diff --git a/modules/linear_algebra/help/en_US/eigen/balanc.xml b/modules/linear_algebra/help/en_US/eigen/balanc.xml new file mode 100755 index 000000000..3f79b79c8 --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/balanc.xml @@ -0,0 +1,106 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="balanc"> + <refnamediv> + <refname>balanc</refname> + <refpurpose>matrix or pencil balancing</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Ab,X]=balanc(A) + [Eb,Ab,X,Y]=balanc(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A: </term> + <listitem> + <para>a real square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X: </term> + <listitem> + <para>a real square invertible matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>E: </term> + <listitem> + <para> + a real square matrix (same dimension as <literal>A</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y: </term> + <listitem> + <para>a real square invertible matrix.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Balance a square matrix to improve + its condition number. + </para> + <para> + <literal>[Ab,X] = balanc(A)</literal> finds a similarity transformation + <literal>X</literal> such that + </para> + <para> + <literal>Ab = inv(X)*A*X</literal> has approximately equal row and column norms. + </para> + <para> + For matrix pencils,balancing is done for improving the + generalized eigenvalue problem. + </para> + <para> + <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> returns left and right transformations <literal>X</literal> and <literal>Y</literal> + such that <literal>Eb=inv(X)*E*Y, Ab=inv(X)*A*Y</literal> + </para> + </refsection> + <refsection> + <title>Remark</title> + <para> + Balancing is made in the functions <literal>bdiag</literal> and <literal>spec</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=[1/2^10,1/2^10;2^10,2^10]; +[Ab,X]=balanc(A); +norm(A(1,:))/norm(A(2,:)) +norm(Ab(1,:))/norm(Ab(2,:)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/bdiag.xml b/modules/linear_algebra/help/en_US/eigen/bdiag.xml new file mode 100755 index 000000000..4cc6433e8 --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/bdiag.xml @@ -0,0 +1,106 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="bdiag"> + <refnamediv> + <refname>bdiag</refname> + <refpurpose>block diagonalization, generalized eigenvectors</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rmax</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ab</term> + <listitem> + <para>real or complex square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex non-singular matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>bs</term> + <listitem> + <para>vector of integers</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <programlisting role=""><![CDATA[ +[Ab [,X [,bs]]]=bdiag(A [,rmax]) + ]]></programlisting> + <para> + performs the block-diagonalization of matrix <literal>A</literal>. bs + gives the structure of the blocks (respective sizes of the + blocks). <literal>X</literal> is the change of basis i.e + <literal>Ab = inv(X)*A*X</literal>is block diagonal. + </para> + <para> + <literal>rmax</literal> controls the conditioning of <literal>X</literal>; the + default value is the l1 norm of <literal>A</literal>. + </para> + <para> + To get a diagonal form (if it exists) choose a large value for + <literal>rmax</literal> (<literal>rmax=1/%eps</literal> for example). + Generically (for real random A) the blocks are (1x1) and (2x2) and + <literal>X</literal> is the matrix of eigenvectors. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//Real case: 1x1 and 2x2 blocks +a=rand(5,5);[ab,x,bs]=bdiag(a);ab + +//Complex case: complex 1x1 blocks +[ab,x,bs]=bdiag(a+%i*0);ab + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="schur">schur</link> + </member> + <member> + <link linkend="sylv">sylv</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="sysdiag">sysdiag</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/gschur.xml b/modules/linear_algebra/help/en_US/eigen/gschur.xml new file mode 100755 index 000000000..2c9d2ae15 --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/gschur.xml @@ -0,0 +1,99 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" scilab:needs-examples="no" xml:id="gschur"> + <refnamediv> + <refname>gschur</refname> + <refpurpose> + generalized Schur form. <emphasis role="bold">This function is obsolete.</emphasis> + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[As,Es]=gschur(A,E) + [As,Es,Q,Z]=gschur(A,E) + [As,Es,Z,dim] = gschur(A,E,flag) + [As,Es,Z,dim]= gschur(A,E,extern) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Description</title> + <para> + This function is obsolete and is now included in the <literal>schur</literal> + function. In most cases the <literal>gschur</literal> function will still work as + before, but it will be removed in the future release. + </para> + <para> + The first three syntaxes can be replaced by + </para> + <programlisting role=""><![CDATA[ +[As,Es]=schur(A,E) +[As,Es,Q,Z]=schur(A,E);Q=Q' //NOTE THE TRANPOSITION HERE +[As,Es,Z,dim] = schur(A,E,flag) + ]]></programlisting> + <para> + The last syntax requires little more adaptations: + </para> + <variablelist> + <varlistentry> + <term>if</term> + <listitem> + <para>extern is a scilab function the new calling sequence + should be <literal>[As,Es,Z,dim]= schur(A,E,Nextern)</literal> with + Nextern defined as follow: + </para> + <programlisting role=""><![CDATA[ +function t=Nextern(R) +if R(2)==0 then + t=extern([1,R(1),R(3)])==1 +else + c=(R(1)+%i*R(2))/R(3) + t=extern([2,real(c+c'),real(c*c')])==1 +end +endfunction + ]]></programlisting> + </listitem> + </varlistentry> + <varlistentry> + <term>if</term> + <listitem> + <para>extern is the name of an external function coded in Fortran or C + the new calling sequence should be <literal>[As,Es,Z,dim]= schur(A,E,'nextern')</literal> with nextern defined as follow: + </para> + </listitem> + </varlistentry> + </variablelist> + <programlisting role=""><![CDATA[ +logical function nextern(ar,ai,beta) +double precision ar,ai,beta +integer r,extern +if (ai.eq.0.0d0) then + r=extern(1,ar,beta,0.0d0,0.0d0) +else + r=extern(2,0.0d0,0.0d0,2.0d0*ar,ar*ar+ai*ai) +endif +nextern=r.eq.1 +end + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="external">external</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/gspec.xml b/modules/linear_algebra/help/en_US/eigen/gspec.xml new file mode 100755 index 000000000..a5c5043a0 --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/gspec.xml @@ -0,0 +1,45 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" scilab:needs-examples="no" xml:id="gspec"> + <refnamediv> + <refname>gspec</refname> + <refpurpose> + eigenvalues of matrix pencil. <emphasis role="bold">This function is obsolete.</emphasis> + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[al,be]=gspec(A,E) + [al,be,Z]=gspec(A,E) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Description</title> + <para> + This function is now included in the <literal>spec</literal> function. + the calling syntax must be replaced by + </para> + <programlisting role=""><![CDATA[ +[al,be]=spec(A,E) +[al,be,Z]=spec(A,E) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/hess.xml b/modules/linear_algebra/help/en_US/eigen/hess.xml new file mode 100755 index 000000000..5f6add49f --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/hess.xml @@ -0,0 +1,97 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="hess"> + <refnamediv> + <refname>hess</refname> + <refpurpose>Hessenberg form</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>H = hess(A) + [U,H] = hess(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>H</term> + <listitem> + <para>real or complex square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>orthogonal or unitary square matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[U,H] = hess(A)</literal> produces a unitary matrix + <literal>U</literal> and a Hessenberg matrix <literal>H</literal> so that + <literal>A = U*H*U'</literal> and <literal>U'*U</literal> = + Identity. By itself, <literal>hess(A)</literal> returns <literal>H</literal>. + </para> + <para> + The Hessenberg form of a matrix is zero below the first + subdiagonal. If the matrix is symmetric or Hermitian, the form is + tridiagonal. + </para> + </refsection> + <refsection> + <title>References</title> + <para> + hess function is based on the Lapack routines + DGEHRD, DORGHR for real matrices and ZGEHRD, ZORGHR for the complex case. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);[U,H]=hess(A); +and( abs(U*H*U'-A)<1.d-10 ) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="contr">contr</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + <literal>hess</literal> function is based on the Lapack routines + DGEHRD, DORGHR for real matrices and ZGEHRD, ZORGHR for the + complex case. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/pbig.xml b/modules/linear_algebra/help/en_US/eigen/pbig.xml new file mode 100755 index 000000000..0d7f8a772 --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/pbig.xml @@ -0,0 +1,125 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="pbig"> + <refnamediv> + <refname>pbig</refname> + <refpurpose>eigen-projection</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>thres</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + character string (<literal>'c'</literal> or <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>real matrices</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Projection on eigen-subspace associated with eigenvalues with real + part >= <literal>thres</literal> (<literal>flag='c'</literal>) or + with magnitude >= <literal>thres</literal> + (<literal>flag='d'</literal>). + </para> + <para> + The projection is defined by <literal>Q*M</literal>, <literal>Q</literal> is + full column rank, <literal>M</literal> is full row rank and + <literal>M*Q=eye</literal>. + </para> + <para> + If <literal>flag='c'</literal>, the eigenvalues of + <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with real part + >= <literal>thres</literal>. + </para> + <para> + If <literal>flag='d'</literal>, the eigenvalues of + <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with magnitude + >= <literal>thres</literal>. + </para> + <para> + If <literal>flag='c'</literal> and if <literal>[Q1,M1]</literal> = + full rank factorization (<literal>fullrf</literal>) of + <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> = + eigenvalues of <literal>A</literal> with real part < + <literal>thres</literal>. + </para> + <para> + If <literal>flag='d'</literal> and if <literal>[Q1,M1]</literal> = + full rank factorization (<literal>fullrf</literal>) of + <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> = + eigenvalues of <literal>A</literal> with magnitude < + <literal>thres</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; +[Q,M]=pbig(A,1.5,'d'); +spec(M*A*Q) +[Q1,M1]=fullrf(eye()-Q*M); +spec(M1*A*Q1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="psmall">psmall</link> + </member> + <member> + <link linkend="projspec">projspec</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + <literal>pbig</literal> is based on the ordered schur form (scilab + function <literal>schur</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/projspec.xml b/modules/linear_algebra/help/en_US/eigen/projspec.xml new file mode 100755 index 000000000..d79f4573f --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/projspec.xml @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="projspec"> + <refnamediv> + <refname>projspec</refname> + <refpurpose>spectral operators</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[S,P,D,i]=projspec(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>S, P, D</term> + <listitem> + <para>square matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>i</term> + <listitem> + <para> + integer (index of the zero eigenvalue of <literal>A</literal>). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Spectral characteristics of <literal>A</literal> at 0. + </para> + <para> + <literal>S</literal> = reduced resolvent at 0 (<literal>S</literal> = -Drazin_inverse(<literal>A</literal>)). + </para> + <para> + <literal>P</literal> = spectral projection at 0. + </para> + <para> + <literal>D</literal> = nilpotent operator at 0. + </para> + <para> + <literal>index</literal> = index of the 0 eigenvalue. + </para> + <para> + One has <literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...</literal> + around the singularity s=0. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end') +A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7); +A=X*A*inv(X); +[S,P,D,index]=projspec(A); +index //size of J-block +trace(P) //sum of dimensions of J-blocks +A*S-(eye()-P) +norm(D^index,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="coff">coff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/psmall.xml b/modules/linear_algebra/help/en_US/eigen/psmall.xml new file mode 100755 index 000000000..c3823df65 --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/psmall.xml @@ -0,0 +1,122 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="psmall"> + <refnamediv> + <refname>psmall</refname> + <refpurpose>spectral projection</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,M]=psmall(A,thres,flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>thres</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + character string (<literal>'c'</literal> or <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>real matrices</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Projection on eigen-subspace associated with eigenvalues with real + part < <literal>thres</literal> (<literal>flag='c'</literal>) or + with modulus < <literal>thres</literal> + (<literal>flag='d'</literal>). + </para> + <para> + The projection is defined by <literal>Q*M</literal>, <literal>Q</literal> is + full column rank, <literal>M</literal> is full row rank and + <literal>M*Q=eye</literal>. + </para> + <para> + If <literal>flag='c'</literal>, the eigenvalues of + <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with real part + < <literal>thres</literal>. + </para> + <para> + If <literal>flag='d'</literal>, the eigenvalues of + <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with magnitude + < <literal>thres</literal>. + </para> + <para> + If <literal>flag='c'</literal> and if <literal>[Q1,M1]</literal> = + full rank factorization (<literal>fullrf</literal>) of + <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> = + eigenvalues of <literal>A</literal> with real part >= + <literal>thres</literal>. + </para> + <para> + If <literal>flag='d'</literal> and if <literal>[Q1,M1]</literal> = + full rank factorization (<literal>fullrf</literal>) of + <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> = + eigenvalues of <literal>A</literal> with magnitude >= + <literal>thres</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; +[Q,M]=psmall(A,2.5,'d'); +spec(M*A*Q) +[Q1,M1]=fullrf(eye()-Q*M); +spec(M1*A*Q1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="pbig">pbig</link> + </member> + <member> + <link linkend="proj">proj</link> + </member> + <member> + <link linkend="projspec">projspec</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + This function is based on the ordered schur form (scilab + function <literal>schur</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/schur.xml b/modules/linear_algebra/help/en_US/eigen/schur.xml new file mode 100755 index 000000000..fe17a979c --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/schur.xml @@ -0,0 +1,386 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="schur"> + <refnamediv> + <refname>schur</refname> + <refpurpose>[ordered] Schur decomposition of matrix and pencils</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[U,T] = schur(A) + [U,dim [,T] ]=schur(A,flag) + [U,dim [,T] ]=schur(A,extern1) + + [As,Es [,Q,Z]]=schur(A,E) + [As,Es [,Z,dim]] = schur(A,E,flag) + [Z,dim] = schur(A,E,flag) + [As,Es [,Z,dim]]= schur(A,E,extern2) + [Z,dim]= schur(A,E,extern2) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex square matrix.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para> + real or complex square matrix with same dimensions as <literal> A</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + character string (<literal>'c'</literal> or <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>extern1</term> + <listitem> + <para>an ``external'', see below</para> + </listitem> + </varlistentry> + <varlistentry> + <term>extern2</term> + <listitem> + <para>an ``external'', see below</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>orthogonal or unitary square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>orthogonal or unitary square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z</term> + <listitem> + <para>orthogonal or unitary square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>T</term> + <listitem> + <para>upper triangular or quasi-triangular square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>As</term> + <listitem> + <para>upper triangular or quasi-triangular square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Es</term> + <listitem> + <para>upper triangular square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para>integer</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Schur forms, ordered Schur forms of matrices and pencils + </para> + <variablelist> + <varlistentry> + <term>MATRIX SCHUR FORM</term> + <listitem> + <variablelist> + <varlistentry> + <term>Usual schur form:</term> + <listitem> + <para> + <literal>[U,T] = schur(A)</literal> produces a Schur matrix + <literal>T</literal> and a unitary matrix <literal>U</literal> so that + <literal>A = U*T*U'</literal> and <literal>U'*U = eye(U)</literal>. By itself, schur(<literal>A</literal>) returns + <literal>T</literal>. If <literal>A</literal> is complex, the Complex + Schur Form is returned in matrix + <literal>T</literal>. The Complex Schur Form is upper triangular with + the eigenvalues of <literal>A</literal> on the diagonal. If + <literal>A</literal> is real, the Real Schur Form is returned. The Real + Schur Form has the real eigenvalues on the diagonal and the + complex eigenvalues in 2-by-2 blocks on the diagonal. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ordered Schur forms</term> + <listitem> + <para> + <literal>[U,dim]=schur(A,'c')</literal> returns an unitary + matrix <literal>U</literal> which transforms <literal>A</literal> into schur + form. In addition, the dim first columns of <literal>U</literal> make + a basis of the eigenspace of <literal>A</literal> associated with + eigenvalues with negative real parts (stable "continuous + time" eigenspace). + </para> + <para> + <literal>[U,dim]=schur(A,'d')</literal> returns an unitary + matrix <literal>U</literal> which transforms <literal>A</literal> into schur + form. In addition, the <literal>dim</literal> first columns of + <literal>U</literal> span a basis of the eigenspace of <literal>A</literal> + associated with eigenvalues with magnitude lower than 1 (stable + "discrete time" eigenspace). + </para> + <para> + <literal>[U,dim]=schur(A,extern1)</literal> returns an unitary matrix + <literal>U</literal> which transforms <literal>A</literal> into schur form. + In addition, the <literal>dim</literal> first columns of + <literal>U</literal> span a basis of the eigenspace of <literal>A</literal> + associated with the eigenvalues which are selected by the + external function <literal>extern1</literal> (see external for + details). This external can be described by a Scilab function + or by C or Fortran procedure: + </para> + <variablelist> + <varlistentry> + <term>a Scilab function</term> + <listitem> + <para> + If <literal>extern1</literal> is described by a Scilab function, it + should have the following calling sequence: + <literal>s=extern1(Ev)</literal>, where <literal>Ev</literal> is an eigenvalue and + <literal>s</literal> a boolean. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>a C or Fortran procedure</term> + <listitem> + <para> + If <literal>extern1</literal> is described by a C or Fortran function it + should have the following calling sequence: + <literal>int extern1(double *EvR, double *EvI)</literal> + where <literal>EvR</literal> and <literal>EvI</literal> are eigenvalue real and complex parts. + a true or non zero returned value stands for selected eigenvalue. + </para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + <varlistentry> + <term>PENCIL SCHUR FORMS</term> + <listitem> + <variablelist> + <varlistentry> + <term>Usual Pencil Schur form</term> + <listitem> + <para> + <literal>[As,Es] = schur(A,E)</literal> produces a quasi triangular + <literal>As</literal> matrix and a triangular <literal>Es</literal> matrix + which are the generalized Schur form of the pair <literal>A, E</literal>. + </para> + <para> + <literal>[As,Es,Q,Z] = schur(A,E)</literal> + returns in addition two unitary matrices + <literal>Q</literal> and <literal>Z</literal> such that + <literal>As=Q'*A*Z</literal> and <literal>Es=Q'*E*Z</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ordered Schur forms:</term> + <listitem> + <para> + <literal>[As,Es,Z,dim] = schur(A,E,'c')</literal> + returns the real generalized + Schur form of the pencil <literal>s*E-A</literal>. In addition, the dim first columns + of <literal>Z</literal> span a basis of the right eigenspace associated with + eigenvalues with negative real parts (stable "continuous + time" generalized eigenspace). + </para> + <para> + <literal>[As,Es,Z,dim] = schur(A,E,'d')</literal> + </para> + <para> + returns the real generalized + Schur form of the pencil <literal>s*E-A</literal>. In addition, the dim first columns + of <literal>Z</literal> make a basis of the right eigenspace associated with + eigenvalues with magnitude lower than 1 (stable "discrete + time" generalized eigenspace). + </para> + <para> + <literal>[As,Es,Z,dim] = schur(A,E,extern2)</literal> + </para> + <para> + returns the real generalized Schur form of the pencil <literal>s*E-A</literal>. + In addition, the dim first columns + of <literal>Z</literal> make a basis of the right eigenspace associated with + eigenvalues of the pencil which are selected according to a + rule which is given by the function <literal>extern2</literal>. (see external + for details). This external can be described by a Scilab + function or by C or Fortran procedure: + </para> + <variablelist> + <varlistentry> + <term>A Scilab function</term> + <listitem> + <para> + If <literal>extern2</literal> is described by a Scilab function, it should + have the following calling sequence: + <literal>s=extern2(Alpha,Beta)</literal>, where <literal>Alpha</literal> and + <literal>Beta</literal> defines a generalized eigenvalue and + <literal>s</literal> a boolean. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>C or Fortran procedure</term> + <listitem> + <para> + if external <literal>extern2</literal> is described by a C or a + Fortran procedure, it should have the following calling + sequence: + </para> + <para> + <literal>int extern2(double *AlphaR, double *AlphaI, double *Beta)</literal> + </para> + <para> + if <literal>A</literal> and <literal>E</literal> are real and + </para> + <para> + <literal>int extern2(double *AlphaR, double *AlphaI, double *BetaR, double *BetaI)</literal> + </para> + <para> + if <literal>A</literal> or <literal>E</literal> are complex. + <literal>Alpha</literal>, and <literal>Beta</literal> defines the generalized eigenvalue. + a true or non zero returned value stands for selected generalized eigenvalue. + </para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>References</title> + <para> + Matrix schur form computations are based on the Lapack routines DGEES and ZGEES. + </para> + <para> + Pencil schur form computations are based on the Lapack routines DGGES and ZGGES. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//SCHUR FORM OF A MATRIX +//---------------------- +A=diag([-0.9,-2,2,0.9]);X=rand(A);A=inv(X)*A*X; +[U,T]=schur(A);T + +[U,dim,T]=schur(A,'c'); +T(1:dim,1:dim) //stable cont. eigenvalues + +function t=mytest(Ev),t=abs(Ev)<0.95,endfunction +[U,dim,T]=schur(A,mytest); +T(1:dim,1:dim) + +// The same function in C (a Compiler is required) +cd TMPDIR; +C=['int mytest(double *EvR, double *EvI) {' //the C code + 'if (*EvR * *EvR + *EvI * *EvI < 0.9025) return 1;' + 'else return 0; }';] +mputl(C,TMPDIR+'/mytest.c') + + +//build and link +lp=ilib_for_link('mytest','mytest.c',[],'c'); +link(lp,'mytest','c'); + +//run it +[U,dim,T]=schur(A,'mytest'); +//SCHUR FORM OF A PENCIL +//---------------------- +F=[-1,%s, 0, 1; + 0,-1,5-%s, 0; + 0, 0,2+%s, 0; + 1, 0, 0, -2+%s]; +A=coeff(F,0);E=coeff(F,1); +[As,Es,Q,Z]=schur(A,E); +Q'*F*Z //It is As+%s*Es + + +[As,Es,Z,dim] = schur(A,E,'c') +function t=mytest(Alpha,Beta),t=real(Alpha)<0,endfunction +[As,Es,Z,dim] = schur(A,E,mytest) + +//the same function in Fortran (a Compiler is required) +ftn=['integer function mytestf(ar,ai,b)' //the fortran code + 'double precision ar,ai,b' + 'mytestf=0' + 'if(ar.lt.0.0d0) mytestf=1' + 'end'] +mputl(' '+ftn,TMPDIR+'/mytestf.f') + +//build and link +lp=ilib_for_link('mytestf','mytestf.f',[],'F'); +link(lp,'mytestf','f'); + +//run it + +[As,Es,Z,dim] = schur(A,E,'mytestf') + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="ricc">ricc</link> + </member> + <member> + <link linkend="pbig">pbig</link> + </member> + <member> + <link linkend="psmall">psmall</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/spec.xml b/modules/linear_algebra/help/en_US/eigen/spec.xml new file mode 100755 index 000000000..4565a68fd --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/spec.xml @@ -0,0 +1,301 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spec" xml:lang="en"> + <refnamediv> + <refname>spec</refname> + <refpurpose>eigenvalues of matrices and pencils</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>evals=spec(A) + [R,diagevals]=spec(A) + + evals=spec(A,B) + [alpha,beta]=spec(A,B) + [alpha,beta,Z]=spec(A,B) + [alpha,beta,Q,Z]=spec(A,B) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>B</term> + <listitem> + <para>real or complex square matrix with same dimensions as + <literal> A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>evals</term> + <listitem> + <para>real or complex vector, the eigenvalues</para> + </listitem> + </varlistentry> + <varlistentry> + <term>diagevals</term> + <listitem> + <para>real or complex diagonal matrix (eigenvalues along the + diagonal) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>alpha</term> + <listitem> + <para>real or complex vector, al./be gives the eigenvalues</para> + </listitem> + </varlistentry> + <varlistentry> + <term>beta</term> + <listitem> + <para>real vector, al./be gives the eigenvalues</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para>real or complex invertible square matrix, matrix right + eigenvectors. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>L</term> + <listitem> + <para>real or complex invertible square matrix, pencil left + eigenvectors. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para>real or complex invertible square matrix, pencil right + eigenvectors. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term>evals=spec(A)</term> + <listitem> + <para> + returns in vector <literal>evals</literal> the + eigenvalues. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[R,diagevals] =spec(A)</term> + <listitem> + <para> + returns in the diagonal matrix <literal>evals</literal> the + eigenvalues and in <literal>R</literal> the right + eigenvectors. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>evals=spec(A,B)</term> + <listitem> + <para>returns the spectrum of the matrix pencil A - s B, i.e. the + roots of the polynomial matrix s B - A. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[alpha,beta] = spec(A,B)</term> + <listitem> + <para> + returns the spectrum of the matrix pencil <literal>A- s + B + </literal> + ,i.e. the roots of the polynomial matrix <literal>A - s + B + </literal> + .Generalized eigenvalues alpha and beta are so that the + matrix <literal>A - alpha./beta B</literal> is a singular matrix. + The eigenvalues are given by <literal>al./be</literal> and if + <literal>beta(i) = 0</literal> the ith eigenvalue is at infinity. + (For <literal>B = eye(A), alpha./beta</literal> is + <literal>spec(A)</literal>). It is usually represented as the pair + (alpha,beta), as there is a reasonable interpretation for beta=0, + and even for both being zero. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[alpha,beta,R] = spec(A,B)</term> + <listitem> + <para> + returns in addition the matrix <literal>R</literal> of + generalized right eigenvectors of the pencil. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[al,be,L,R] = spec(A,B)</term> + <listitem> + <para> + returns in addition the matrix <literal>L</literal> and + <literal>R</literal> of generalized left and right eigenvectors of + the pencil. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[al,be,Z] = spec(A,E)</term> + <listitem> + <para> + returns the matrix <literal>Z</literal> of right + generalized eigen vectors. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[al,be,Q,Z] = spec(A,E)</term> + <listitem> + <para> + returns the matrices <literal>Q</literal> + and <literal>Z</literal> of right and left generalized + eigen vectors. + </para> + </listitem> + </varlistentry> + </variablelist> + <para>For big full / sparse matrix, you can use the Arnoldi module.</para> + </refsection> + <refsection> + <title>References</title> + <para>Matrix eigenvalues computations are based on the Lapack + routines + </para> + <itemizedlist> + <listitem> + <para>DGEEV and ZGEEV when the matrix are not symmetric,</para> + </listitem> + <listitem> + <para>DSYEV and ZHEEV when the matrix are symmetric.</para> + </listitem> + </itemizedlist> + <para>A complex symmetric matrix has conjugate offdiagonal terms and real + diagonal terms. + </para> + <para>Pencil eigenvalues computations are based on the Lapack routines + DGGEV and ZGGEV. + </para> + </refsection> + <refsection> + <title>Real and complex matrices</title> + <para>It must be noticed that the type of the output variables, such as + evals or R for example, is not necessarily the same as the type of the + input matrices A and B. In the following paragraph, we analyse the type of + the output variables in the case where one computes the eigenvalues and + eigenvectors of one single matrix A. + </para> + <itemizedlist> + <listitem> + <para>Real A matrix</para> + <itemizedlist> + <listitem> + <para>Symetric</para> + <para>The eigenvalues and the eigenvectors are real.</para> + </listitem> + <listitem> + <para>Not symmetric</para> + <para>The eigenvalues and eigenvectors are complex.</para> + </listitem> + </itemizedlist> + </listitem> + <listitem> + <para>Complex A matrix</para> + <itemizedlist> + <listitem> + <para>Symetric</para> + <para>The eigenvalues are real but the eigenvectors are + complex. + </para> + </listitem> + <listitem> + <para>Not symmetric</para> + <para>The eigenvalues and the eigenvectors are complex.</para> + </listitem> + </itemizedlist> + </listitem> + </itemizedlist> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// MATRIX EIGENVALUES +A=diag([1,2,3]); +X=rand(3,3); +A=inv(X)*A*X; +spec(A) + +x=poly(0,'x'); +pol=det(x*eye()-A) +roots(pol) + +[S,X]=bdiag(A); +clean(inv(X)*A*X) + +// PENCIL EIGENVALUES +A=rand(3,3); +[al,be,R] = spec(A,eye(A)); +al./be +clean(inv(R)*A*R) //displaying the eigenvalues (generic matrix) +A=A+%i*rand(A); +E=rand(A); +roots(det(A-%s*E)) //complex case + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="dsaupd">dsaupd</link> + </member> + <member> + <link linkend="dnaupd">dnaupd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/sva.xml b/modules/linear_algebra/help/en_US/eigen/sva.xml new file mode 100755 index 000000000..4fd62c45c --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/sva.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="sva"> + <refnamediv> + <refname>sva</refname> + <refpurpose>singular value approximation</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[U,s,V]=sva(A,k) + [U,s,V]=sva(A,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>integer</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>nonnegative real number</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Singular value approximation. + </para> + <para> + <literal>[U,S,V]=sva(A,k)</literal> with <literal>k</literal> an integer + >=1, returns <literal>U,S</literal> and <literal>V</literal> such that + <literal>B=U*S*V'</literal> is the best L2 approximation of + <literal>A</literal> with rank(<literal>B</literal>)=<literal>k</literal>. + </para> + <para> + <literal>[U,S,V]=sva(A,tol)</literal> with <literal>tol</literal> a real + number, returns <literal>U,S</literal> and <literal>V</literal> such that + <literal>B=U*S*V'</literal> such that L2-norm of <literal>A-B</literal> + is at most <literal>tol</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,4)*rand(4,5); +[U,s,V]=sva(A,2); +B=U*s*V'; +svd(A) +svd(B) +clean(svd(A-B)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/eigen/svd.xml b/modules/linear_algebra/help/en_US/eigen/svd.xml new file mode 100755 index 000000000..24c626e38 --- /dev/null +++ b/modules/linear_algebra/help/en_US/eigen/svd.xml @@ -0,0 +1,126 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="svd"> + <refnamediv> + <refname>svd</refname> + <refpurpose>singular value decomposition</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>s=svd(X) + [U,S,V]=svd(X) + [U,S,V]=svd(X,0) (obsolete) + [U,S,V]=svd(X,"e") + [U,S,V,rk]=svd(X [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>a real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>s</term> + <listitem> + <para>real vector (singular values)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>S</term> + <listitem> + <para>real diagonal matrix (singular values)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U,V</term> + <listitem> + <para>orthogonal or unitary square matrices (singular vectors).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[U,S,V] = svd(X)</literal> produces a diagonal matrix + <literal>S</literal> , of the same dimension as <literal>X</literal> and with + nonnegative diagonal elements in decreasing order, and unitary + matrices <literal>U</literal> and <literal>V</literal> so that <literal>X = U*S*V'</literal>. + </para> + <para> + <literal>[U,S,V] = svd(X,0)</literal> produces the "economy + size" decomposition. If <literal>X</literal> is m-by-n with m > + n, then only the first n columns of <literal>U</literal> are computed + and <literal>S</literal> is n-by-n. + </para> + <para> + <literal>s= svd(X)</literal> by itself, returns a vector <literal>s</literal> + containing the singular values. + </para> + <para> + <literal>[U,S,V,rk]=svd(X,tol)</literal> gives in addition <literal>rk</literal>, the numerical rank of <literal>X</literal> i.e. the number of + singular values larger than <literal>tol</literal>. + </para> + <para> + The default value of <literal>tol</literal> is the same as in <literal>rank</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +X=rand(4,2)*rand(2,4) +svd(X) +sqrt(spec(X*X')) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="sva">sva</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + svd decompositions are based on the Lapack routines DGESVD for + real matrices and ZGESVD for the complex case. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/factorization/CHAPTER b/modules/linear_algebra/help/en_US/factorization/CHAPTER new file mode 100755 index 000000000..e6daeb8eb --- /dev/null +++ b/modules/linear_algebra/help/en_US/factorization/CHAPTER @@ -0,0 +1,2 @@ +title = Factorization + diff --git a/modules/linear_algebra/help/en_US/factorization/givens.xml b/modules/linear_algebra/help/en_US/factorization/givens.xml new file mode 100755 index 000000000..355899ae0 --- /dev/null +++ b/modules/linear_algebra/help/en_US/factorization/givens.xml @@ -0,0 +1,86 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="givens"> + <refnamediv> + <refname>givens</refname> + <refpurpose>Givens transformation</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>U=givens(xy) + U=givens(x,y) + [U,c]=givens(xy) + [U,c]=givens(x,y) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x,y</term> + <listitem> + <para>two real or complex numbers</para> + </listitem> + </varlistentry> + <varlistentry> + <term>xy</term> + <listitem> + <para> real or complex size 2 column vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>2x2 unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>c</term> + <listitem> + <para> real or complex size 2 column vector</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>U= givens(x, y)</literal> or <literal>U = givens(xy)</literal> with <literal>xy = [x;y]</literal> + returns a <literal>2</literal>x<literal>2</literal> unitary matrix <literal>U</literal> such that: + </para> + <para> + <literal>U*xy=[r;0]=c</literal>. + </para> + <para> + <note> + Note that <literal>givens(x,y)</literal> and <literal>givens([x;y])</literal> are equivalent. + </note> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=[3,4;5,6]; +U=givens(A(:,1)); +U*A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/factorization/householder.xml b/modules/linear_algebra/help/en_US/factorization/householder.xml new file mode 100755 index 000000000..c664395a9 --- /dev/null +++ b/modules/linear_algebra/help/en_US/factorization/householder.xml @@ -0,0 +1,70 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="householder"> + <refnamediv> + <refname>householder</refname> + <refpurpose>Householder orthogonal reflexion matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>u=householder(v [,w])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>v</term> + <listitem> + <para>real or complex column vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>w</term> + <listitem> + <para> + real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>u</term> + <listitem> + <para>real or complex column vector</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary + column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>. + <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix . + </para> + <para> + <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the + vector <literal> eye(v)*norm(v)</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="givens">givens</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/factorization/sqroot.xml b/modules/linear_algebra/help/en_US/factorization/sqroot.xml new file mode 100755 index 000000000..e248970f3 --- /dev/null +++ b/modules/linear_algebra/help/en_US/factorization/sqroot.xml @@ -0,0 +1,62 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="sqroot"> + <refnamediv> + <refname>sqroot</refname> + <refpurpose>W*W' hermitian factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>sqroot(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>symmetric non negative definite real or complex matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + returns W such that <literal>X=W*W'</literal> (uses SVD). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +X=rand(5,2)*rand(2,5);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) + +X=rand(5,2)+%i*rand(5,2);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="chol">chol</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/kernel/CHAPTER b/modules/linear_algebra/help/en_US/kernel/CHAPTER new file mode 100755 index 000000000..be67920e1 --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/CHAPTER @@ -0,0 +1,2 @@ +title = Kernel + diff --git a/modules/linear_algebra/help/en_US/kernel/colcomp.xml b/modules/linear_algebra/help/en_US/kernel/colcomp.xml new file mode 100755 index 000000000..7d658352e --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/colcomp.xml @@ -0,0 +1,106 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="colcomp"> + <refnamediv> + <refname>colcomp</refname> + <refpurpose>column compression, kernel, nullspace</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para>character string</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>W</term> + <listitem> + <para>square non-singular matrix (change of basis)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + integer (rank of <literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Column compression of <literal>A</literal>: <literal>Ac = A*W</literal> is + column compressed i.e + </para> + <para> + <literal>Ac=[0,Af]</literal> with <literal>Af</literal> full column rank, + rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>. + </para> + <para> + <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> + or <literal>'svd'</literal> (default is <literal>'svd'</literal>). + </para> + <para> + <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value). + </para> + <para> + The <literal>ma-rk</literal> first columns of <literal>W</literal> span the kernel of <literal>A</literal> + when <literal>size(A)=(na,ma)</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[X,r]=colcomp(A); +norm(A*X(:,1:$-r),1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="kernel">kernel</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/kernel/fullrf.xml b/modules/linear_algebra/help/en_US/kernel/fullrf.xml new file mode 100755 index 000000000..0343f81dc --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/fullrf.xml @@ -0,0 +1,101 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="fullrf"> + <refnamediv> + <refname>fullrf</refname> + <refpurpose>full rank factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>real number (threshold for rank determination)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + integer (rank of <literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Full rank factorization : <literal>fullrf</literal> returns <literal>Q</literal> and <literal>M</literal> such + that <literal>A = Q*M</literal> + with range(<literal>Q</literal>)=range(<literal>A</literal>) and ker(<literal>M</literal>)=ker(<literal>A</literal>), + <literal>Q</literal> full column rank , <literal>M</literal> full row rank, + <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>. + </para> + <para> + <literal>tol</literal> is an optional real parameter (default value is <literal>sqrt(%eps)</literal>). + The rank <literal>rk</literal> of <literal>A</literal> is defined as the number of singular values + larger than <literal>norm(A)*tol</literal>. + </para> + <para> + If A is symmetric, <literal>fullrf</literal> returns <literal>M=Q'</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[Q,M]=fullrf(A); +norm(Q*M-A,1) +[X,d]=rowcomp(A);Y=X'; +svd([A,Y(:,1:d),Q]) //span(Q) = span(A) = span(Y(:,1:2)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/kernel/fullrfk.xml b/modules/linear_algebra/help/en_US/kernel/fullrfk.xml new file mode 100755 index 000000000..f060add2e --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/fullrfk.xml @@ -0,0 +1,74 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="fullrfk"> + <refnamediv> + <refname>fullrfk</refname> + <refpurpose>full rank factorization of A^k</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>integer</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Bk,Ck</term> + <listitem> + <para>real or complex matrices</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + This function computes the full rank factorization of <literal>A^k</literal> i.e. + <literal>Bk*Ck=A^k</literal> where <literal>Bk</literal> is full column rank and <literal>Ck</literal> full row rank. + One has range(<literal>Bk</literal>)=range(<literal>A^k</literal>) and ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>). + </para> + <para> + For <literal>k=1</literal>, <literal>fullrfk</literal> is equivalent to <literal>fullrf</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3); +norm(Bk*Ck-A^3,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="range">range</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/kernel/im_inv.xml b/modules/linear_algebra/help/en_US/kernel/im_inv.xml new file mode 100755 index 000000000..2e288855e --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/im_inv.xml @@ -0,0 +1,107 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="im_inv"> + <refnamediv> + <refname>im_inv</refname> + <refpurpose>inverse image</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[X,dim]=im_inv(A,B [,tol]) + [X,dim,Y]=im_inv(A,B, [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A,B</term> + <listitem> + <para>two real or complex matrices with equal number of columns</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para> + orthogonal or unitary square matrix of order equal to the number of columns of <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para>integer (dimension of subspace)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para> + orthogonal matrix of order equal to the number of rows of <literal>A</literal> and <literal>B</literal>. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[X,dim]=im_inv(A,B)</literal> computes <literal>(A^-1)(B)</literal> + i.e vectors whose image through <literal>A</literal> are in + range(<literal>B</literal>) + </para> + <para> + The <literal>dim</literal> first columns of <literal>X</literal> span + <literal>(A^-1)(B)</literal> + </para> + <para> + <literal>tol</literal> is a threshold used to test if subspace inclusion; + default value is <literal>tol = 100*%eps</literal>. + If <literal>Y</literal> is returned, then <literal>[Y*A*X,Y*B]</literal> is partitioned as follows: + <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal> + </para> + <para> + where <literal>B1</literal> has full row rank (equals + <literal>rank(B)</literal>) and <literal>A22</literal> has full column rank + and has <literal>dim</literal> columns. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)]; +W=rand(5,5);A=W*A;B=W*B; +[X,dim]=im_inv(A,B) +svd([A*X(:,1:dim),B]) //vectors A*X(:,1:dim) belong to range(B) +[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B] + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="spaninter">spaninter</link> + </member> + <member> + <link linkend="spanplus">spanplus</link> + </member> + <member> + <link linkend="linsolve">linsolve</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/kernel/kernel.xml b/modules/linear_algebra/help/en_US/kernel/kernel.xml new file mode 100755 index 000000000..f891512d1 --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/kernel.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="kernel"> + <refnamediv> + <refname>kernel</refname> + <refpurpose>kernel, null space</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>W=kernel(A [,tol,[,flag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>full real or complex matrix or real sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + character string <literal>'svd'</literal> (default) or <literal>'qr'</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>W</term> + <listitem> + <para>full column rank matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>W=kernel(A)</literal> returns the kernel (null space) of <literal>A</literal>, and <literal>size(W,2)</literal> is the nullity of A. + If A has full column rank then an empty matrix [] is returned. + </para> + <para> + <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> + or <literal>'svd'</literal> (default is <literal>'svd'</literal>). + </para> + <para> + <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,1)*rand(1,3); +A*kernel(A) +A=sparse(A); +clean(A*kernel(A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="linsolve">linsolve</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/kernel/range.xml b/modules/linear_algebra/help/en_US/kernel/range.xml new file mode 100755 index 000000000..b8def609f --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/range.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="range"> + <refnamediv> + <refname>range</refname> + <refpurpose>range (span) of A^k</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[X,dim]=range(A,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>integer</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>orthonormal real matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para>integer (dimension of subspace)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Computation of Range <literal>A^k</literal> ; the first dim rows of <literal>X</literal> span the + range of <literal>A^k</literal>. The last rows of <literal>X</literal> span the + orthogonal complement of the range. <literal>X*X'</literal> is the Identity matrix + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(4,2)*rand(2,4); // 4 column vectors, 2 independent. +[X,dim]=range(A,1);dim // compute the range + +y1=A*rand(4,1); //a vector which is in the range of A +y2=rand(4,1); //a vector which is not in the range of A +norm(X(dim+1:$,:)*y1) //the last entries are zeros, y1 is in the range of A +norm(X(dim+1:$,:)*y2) //the last entries are not zeros + +I=X(1:dim,:)' //I is a basis of the range +coeffs=X(1:dim,:)*y1 // components of y1 relative to the I basis + +norm(I*coeffs-y1) //check + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + The <literal>range</literal> function is based on the <link linkend="rowcomp">rowcomp</link> function + which uses the <link linkend="svd">svd</link> decomposition. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/kernel/rowcomp.xml b/modules/linear_algebra/help/en_US/kernel/rowcomp.xml new file mode 100755 index 000000000..f012c21f6 --- /dev/null +++ b/modules/linear_algebra/help/en_US/kernel/rowcomp.xml @@ -0,0 +1,123 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rowcomp"> + <refnamediv> + <refname>rowcomp</refname> + <refpurpose>row compression, range</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[W,rk]=rowcomp(A [,flag [,tol]])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para>optional character string, with possible values + <literal>'svd'</literal> or <literal>'qr'</literal>. The default value is <literal>'svd'</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>optional real non negative number. The default value is + <literal>sqrt(%eps)*norm(A,1)</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>W</term> + <listitem> + <para>square non-singular matrix (change of basis)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + integer (rank of <literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Row compression of <literal>A</literal>. <literal>Ac = W*A</literal> is a row compressed matrix: i.e. + <literal>Ac=[Af;0]</literal> with <literal>Af</literal> full row rank. + </para> + <para> + <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag='qr'</literal> + or <literal>'svd'</literal> (default <literal>'svd'</literal>). + </para> + <para> + <literal>tol</literal> is a tolerance parameter. + </para> + <para> + The <literal>rk</literal> first columns of <literal>W'</literal> span the range of + <literal>A</literal>. + </para> + <para> + The <literal>rk</literal> first (top) rows of <literal>W</literal> span the row + range of <literal>A</literal>. + </para> + <para> + A non zero vector <literal>x</literal> belongs to range(<literal>A</literal>) iff + <literal>W*x</literal> is row compressed in accordance with <literal>Ac</literal> + i.e the norm of its last components is small w.r.t its first + components. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); // 4 col. vectors, 2 independent. +[X,dim]=rowcomp(A);Xp=X'; +svd([Xp(:,1:dim),A]) //span(A) = span(Xp(:,1:dim) +x=A*rand(4,1); //x belongs to span(A) +y=X*x +norm(y(dim+1:$))/norm(y(1:dim)) // small + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + The <literal>rowcomp</literal> function is based on the <link linkend="svd">svd</link> or + <link linkend="qr">qr</link> decompositions. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/CHAPTER b/modules/linear_algebra/help/en_US/linear/CHAPTER new file mode 100755 index 000000000..7d9d9cf49 --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/CHAPTER @@ -0,0 +1,2 @@ +title = Linear Equations + diff --git a/modules/linear_algebra/help/en_US/linear/aff2ab.xml b/modules/linear_algebra/help/en_US/linear/aff2ab.xml new file mode 100755 index 000000000..756469256 --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/aff2ab.xml @@ -0,0 +1,150 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="aff2ab"> + <refnamediv> + <refname>aff2ab</refname> + <refpurpose>linear (affine) function to A,b conversion</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[A,b]=aff2ab(afunction,dimX,D [,flag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>afunction</term> + <listitem> + <para> + a scilab function <literal> Y =fct(X,D) </literal> where <literal>X, D, Y</literal> are <literal>list</literal> of matrices + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dimX</term> + <listitem> + <para> + a p x 2 integer matrix (<literal>p</literal> is the number of matrices in <literal>X</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para> + a <literal>list</literal> of real matrices (or any other valid Scilab object). + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + optional parameter (<literal>flag='f'</literal> or <literal>flag='sp'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>a real matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para> + a real vector having same row dimension as <literal>A</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>aff2ab</literal> returns the matrix representation of an affine + function (in the canonical basis). + </para> + <para> + <literal>afunction</literal> is a function with imposed syntax: + <literal> Y=afunction(X,D) </literal> where <literal> X=list(X1,X2,...,Xp) </literal> is + a list of p real matrices, and <literal> Y=list(Y1,...,Yq) </literal> is + a list of q real real matrices which depend linearly of + the <literal> Xi</literal>'s. The (optional) input <literal> D</literal> contains + parameters needed to compute Y as a function of X. + (It is generally a list of matrices). + </para> + <para> + <literal> dimX</literal> is a p x 2 matrix: <literal>dimX(i)=[nri,nci]</literal> + is the actual number of rows and columns of matrix <literal>Xi</literal>. + These dimensions determine <literal>na</literal>, the column dimension of + the resulting matrix <literal>A</literal>: <literal>na=nr1*nc1 +...+ nrp*ncp</literal>. + </para> + <para> + If the optional parameter <literal>flag='sp'</literal> the resulting <literal>A</literal> + matrix is returned as a sparse matrix. + </para> + <para> + This function is useful to solve a system of linear equations + where the unknown variables are matrices. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// Lyapunov equation solver (one unknown variable, one constraint) +deff('Y=lyapunov(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q)') +A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3]; +[Aly,bly]=aff2ab(lyapunov,dimX,D); +[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); lyapunov(Xv,D) +Xm=Xv(:); A'*Xm+Xm*A-Q + +// Lyapunov equation solver with redundant constraint X=X' +// (one variable, two constraints) D is global variable +deff('Y=ly2(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q,Xm''-Xm)') +A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3]; +[Aly,bly]=aff2ab(ly2,dimX,D); +[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); ly2(Xv,D) + +// Francis equations +// Find matrices X1 and X2 such that: +// A1*X1 - X1*A2 + B*X2 -A3 = 0 +// D1*X1 -D2 = 0 +deff('Y=bruce(X,D)','[A1,A2,A3,B,D1,D2]=D(:),... +[X1,X2]=X(:);Y=list(A1*X1-X1*A2+B*X2-A3,D1*X1-D2)') +A1=[-4,10;-1,2];A3=[1;2];B=[0;1];A2=1;D1=[0,1];D2=1; +D=list(A1,A2,A3,B,D1,D2); +[n1,m1]=size(A1);[n2,m2]=size(A2);[n3,m3]=size(B); +dimX=[[m1,n2];[m3,m2]]; +[Af,bf]=aff2ab(bruce,dimX,D); +[Xf,KerAf]=linsolve(Af,bf);Xsol=vec2list(Xf,dimX) +bruce(Xsol,D) + +// Find all X which commute with A +deff('y=f(X,D)','y=list(D(:)*X(:)-X(:)*D(:))') +A=rand(3,3);dimX=[3,3];[Af,bf]=aff2ab(f,dimX,list(A)); +[Xf,KerAf]=linsolve(Af,bf);[p,q]=size(KerAf); +Xsol=vec2list(Xf+KerAf*rand(q,1),dimX); +C=Xsol(:); A*C-C*A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="linsolve">linsolve</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/chol.xml b/modules/linear_algebra/help/en_US/linear/chol.xml new file mode 100755 index 000000000..a0a37f1de --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/chol.xml @@ -0,0 +1,81 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="chol"> + <refnamediv> + <refname>chol</refname> + <refpurpose>Cholesky factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[R]=chol(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>a symmetric positive definite real or complex matrix.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + If <literal>X</literal> is positive definite, then <literal>R = chol(X)</literal> produces an upper + triangular matrix <literal>R</literal> such that <literal>R'*R = X</literal>. + </para> + <para> + <literal>chol(X)</literal> uses only the diagonal and upper triangle of <literal>X</literal>. + The lower triangular is assumed to be the (complex conjugate) + transpose of the upper. + </para> + </refsection> + <refsection> + <title>References</title> + <para> + Cholesky decomposition is based on the Lapack routines + DPOTRF for real matrices and ZPOTRF for the complex case. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +W=rand(5,5)+%i*rand(5,5); +X=W*W'; +R=chol(X); +norm(R'*R-X) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spchol">spchol</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/inv.xml b/modules/linear_algebra/help/en_US/linear/inv.xml new file mode 100755 index 000000000..1589972e7 --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/inv.xml @@ -0,0 +1,105 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="inv"> + <refnamediv> + <refname>inv</refname> + <refpurpose>matrix inverse</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>inv(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex square matrix, polynomial matrix, rational matrix in transfer or state-space representation.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>inv(X)</literal> is the inverse of the square matrix <literal>X</literal>. A warning + message is printed if <literal>X</literal> is badly scaled or nearly singular. + </para> + <para> + For polynomial matrices or rational matrices in transfer representation, + <literal>inv(X)</literal> is equivalent to <literal>invr(X)</literal>. + </para> + <para> + For linear systems in state-space representation (<literal>syslin</literal> list), + <literal>invr(X)</literal> is equivalent to <literal>invsyslin(X)</literal>. + </para> + </refsection> + <refsection> + <title>References</title> + <para> + <literal>inv</literal> function for matrices of numbers is based on the Lapack routines + DGETRF, DGETRI for real matrices and ZGETRF, ZGETRI for the complex case. + For polynomial matrix and rational function matrix <literal>inv</literal> is based on the <literal>invr</literal> + Scilab function. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);inv(A)*A + +x=poly(0,'x'); +A=[x,1,x;x^2,2,1+x;1,2,3];inv(A)*A + +A=[1/x,2;2+x,2/(1+x)] +inv(A)*A + +A=ssrand(2,2,3); +W=inv(A)*A +clean(ss2tf(W)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="slash">slash</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="coff">coff</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/linsolve.xml b/modules/linear_algebra/help/en_US/linear/linsolve.xml new file mode 100755 index 000000000..01df2dc47 --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/linsolve.xml @@ -0,0 +1,121 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="linsolve"> + <refnamediv> + <refname>linsolve</refname> + <refpurpose>linear equation solver</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para> + a <literal>na x ma</literal> real matrix (possibly sparse) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para> + a <literal>na x 1</literal> vector (same row dimension as <literal>A</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x0</term> + <listitem> + <para>a real vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>kerA</term> + <listitem> + <para> + a <literal>ma x k</literal> real matrix + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>linsolve</literal> computes all the solutions to <literal> A*x+b=0</literal>. + </para> + <para> + <literal>x0</literal> is a particular solution (if any) and <literal> kerA= </literal>nullspace + of <literal>A</literal>. Any <literal>x=x0+kerA*w</literal> with arbitrary <literal>w</literal> satisfies + <literal> A*x+b=0</literal>. + </para> + <para> + If compatible <literal>x0</literal> is given on entry, <literal>x0</literal> is returned. If not + a compatible <literal>x0</literal>, if any, is returned. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,8); +b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b //compatible b +b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b //uncompatible b +A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b //x is unique + +// Benchmark with other linear sparse solver: +[A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa"); + +b = zeros(size(A,1),1); + +tic(); +res = umfpack(A,'\',b); +mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc()); + +tic(); +res = linsolve(A,b); +mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc()); + +tic(); +res = A\b; +mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc()); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="inv">inv</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="im_inv">im_inv</link> + </member> + <member> + <link linkend="umfpack">umfpack</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/lsq.xml b/modules/linear_algebra/help/en_US/linear/lsq.xml new file mode 100755 index 000000000..1060d605b --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/lsq.xml @@ -0,0 +1,113 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="lsq"> + <refnamediv> + <refname>lsq</refname> + <refpurpose>linear least square problems. </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>X=lsq(A,B [,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>Real or complex (m x n) matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>B</term> + <listitem> + <para>real or complex (m x p) matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>positive scalar, used to determine the effective rank of A + (defined as the order of the largest leading triangular + submatrix R11 in the QR factorization with pivoting of A, + whose estimated condition number <= 1/tol. The tol default value is + set to <literal>sqrt(%eps)</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex (n x p) matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>X=lsq(A,B)</literal> computes the minimum norm least square solution of + the equation <literal>A*X=B</literal>, while <literal>X=A \ B</literal> compute a least square + solution with at at most <literal>rank(A)</literal> nonzero components per column. + </para> + </refsection> + <refsection> + <title>References</title> + <para> + <literal>lsq</literal> function is based on the LApack functions DGELSY for + real matrices and ZGELSY for complex matrices. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//Build the data +x=(1:10)'; + +y1=3*x+4.5+3*rand(x,'normal'); +y2=1.8*x+0.5+2*rand(x,'normal'); +plot2d(x,[y1,y2],[-2,-3]) +//Find the linear regression +A=[x,ones(x)];B=[y1,y2]; +X=lsq(A,B); + +y1e=X(1,1)*x+X(2,1); +y2e=X(1,2)*x+X(2,2); +plot2d(x,[y1e,y2e],[2,3]) + +//Difference between lsq(A,b) and A\b +A=rand(4,2)*rand(2,3);//a rank 2 matrix +b=rand(4,1); +X1=lsq(A,b) +X2=A\b +[A*X1-b, A*X2-b] //the residuals are the same + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="rank">rank</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/lu.xml b/modules/linear_algebra/help/en_US/linear/lu.xml new file mode 100755 index 000000000..2da9ad568 --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/lu.xml @@ -0,0 +1,154 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2009 - Digiteo - Michael Baudin + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="lu"> + <refnamediv> + <refname>lu</refname> + <refpurpose>LU factorization with pivoting</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[L,U]= lu(A) + [L,U,E]= lu(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix (m x n).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>L</term> + <listitem> + <para> real or complex matrices (m x min(m,n)).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>real or complex matrices (min(m,n) x n ).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>a (n x n) permutation matrix.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[L,U]= lu(A)</literal> produces two matrices <literal>L</literal> and + <literal>U</literal> such that <literal>A = L*U</literal> with <literal>U</literal> + upper triangular and <literal>L</literal> a general matrix without any particular + structure. In fact, the matrix <literal>A</literal> is factored as <literal>E*A=B*U</literal> + where the matrix <literal>B</literal> is lower triangular + and the matrix <literal>L</literal> is computed from <literal>L=E'*B</literal>. + </para> + <para> + If <literal>A</literal> has rank <literal>k</literal>, rows <literal>k+1</literal> to + <literal>n</literal> of <literal>U</literal> are zero. + </para> + <para> + <literal>[L,U,E]= lu(A)</literal> produces three matrices <literal>L</literal>, <literal>U</literal> and + <literal>E</literal> such that <literal>E*A = L*U</literal> with + <literal>U</literal> upper triangular and <literal>E*L</literal> lower + triangular for a permutation matrix <literal>E</literal>. + </para> + <para> + If <literal>A</literal> is a real matrix, using the function + <literal>lufact</literal> and <literal>luget</literal> it is possible to obtain + the permutation matrices and also when <literal>A</literal> is not full + rank the column compression of the matrix <literal>L</literal>. + </para> + </refsection> + <refsection> + <title>Example #1</title> + <para> + In the following example, we create the Hilbert matrix of size 4 and + factor it with A=LU. Notice that the matrix L is not lower triangular. + To get a lower triangular L matrix, we should have given the + output argument E to Scilab. + </para> + <programlisting role="example"><![CDATA[ +a = testmatrix("hilb",4); +[l,u]=lu(a) +norm(l*u-a) + ]]></programlisting> + </refsection> + <refsection> + <title>Example #2</title> + <para> + In the following example, we create the Hilbert matrix of size 4 and + factor it with EA=LU. Notice that the matrix L is lower triangular. + </para> + <programlisting role="example"><![CDATA[ +a = testmatrix("hilb",4); +[l,u,e]=lu(a) +norm(l*u-e*a) + ]]></programlisting> + </refsection> + <refsection> + <title>Example #3</title> + <para> + The following example shows how to use the lufact and luget functions. + </para> + <programlisting role="example"><![CDATA[ +a=rand(4,4); +[l,u]=lu(a) +norm(l*u-a) + +[h,rk]=lufact(sparse(a)) +[P,L,U,Q]=luget(h); +ludel(h) +P=full(P); +L=full(L); +U=full(U); +Q=full(Q); +norm(P*L*U*Q-a) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + lu decompositions are based on the Lapack routines DGETRF for real + matrices and ZGETRF for the complex case. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/pinv.xml b/modules/linear_algebra/help/en_US/linear/pinv.xml new file mode 100755 index 000000000..af87b920b --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/pinv.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="pinv"> + <refnamediv> + <refname>pinv</refname> + <refpurpose>pseudoinverse</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>pinv(A,[tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>X= pinv(A)</literal> produces a matrix <literal>X</literal> of the + same dimensions as <literal>A'</literal> such that: + </para> + <para> + <literal>A*X*A = A, X*A*X = X</literal> and both + <literal>A*X</literal> and <literal>X*A</literal> are Hermitian . + </para> + <para> + The computation is based on SVD and any singular values + lower than a tolerance are treated as zero: this tolerance + is accessed by <literal>X=pinv(A,tol)</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); +norm(A*pinv(A)*A-A,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + <literal>pinv</literal> function is based on the singular value decomposition + (Scilab function <literal>svd</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/qr.xml b/modules/linear_algebra/help/en_US/linear/qr.xml new file mode 100755 index 000000000..52b3bb433 --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/qr.xml @@ -0,0 +1,184 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="qr"> + <refnamediv> + <refname>qr</refname> + <refpurpose>QR decomposition</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,R]=qr(X [,"e"]) + [Q,R,E]=qr(X [,"e"]) + [Q,R,rk,E]=qr(X [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>nonnegative real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>square orthogonal or unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para> + matrix with same dimensions as <literal>X</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>permutation matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + integer (QR-rank of <literal>X</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term>[Q,R] = qr(X)</term> + <listitem> + <para> + produces an upper triangular matrix <literal>R</literal> of the same dimension as <literal>X</literal> and an orthogonal (unitary in the complex case) matrix <literal>Q</literal> so that <literal>X = Q*R</literal>. <literal>[Q,R] = qr(X,"e")</literal> produces an "economy size": If <literal>X</literal> is m-by-n with m > n, then only the first n columns of <literal>Q</literal> are computed as well as the first n rows of <literal>R</literal>. + </para> + <para> + From <literal>Q*R = X</literal> , it follows that + the kth column of the matrix <literal>X</literal>, is expressed as a linear combination + of the k first columns of <literal>Q</literal> (with coefficients <literal> R(1,k), ..., R(k,k) </literal>). The k first columns of <literal>Q</literal> make an orthogonal basis + of the subspace spanned by the k first comumns of <literal>X</literal>. If column <literal>k</literal> + of <literal>X</literal> (i.e. <literal>X(:,k)</literal> ) is a linear combination of the first + <literal>p</literal> columns of <literal>X</literal>, then the entries <literal>R(p+1,k), ..., R(k,k)</literal> + are zero. It this situation, <literal>R</literal> is upper trapezoidal. If <literal>X</literal> has + rank <literal>rk</literal>, rows <literal>R(rk+1,:), R(rk+2,:), ...</literal> are zeros. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[Q,R,E] = qr(X)</term> + <listitem> + <para> + produces a (column) permutation matrix <literal>E</literal>, an upper + triangular <literal>R</literal> with decreasing diagonal elements and an + orthogonal (or unitary) <literal>Q</literal> so that <literal>X*E = Q*R</literal>. + If <literal>rk</literal> is the rank of <literal>X</literal>, the + <literal>rk</literal> first entries along the main diagonal of + <literal>R</literal>, i.e. <literal>R(1,1), R(2,2), ..., R(rk,rk)</literal> + are all different from zero. <literal>[Q,R,E] = qr(X,"e")</literal> + produces an "economy size": + If <literal>X</literal> is m-by-n with m > n, then only the first n + columns of <literal>Q</literal> are computed as well as the first n + rows of <literal>R</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[Q,R,rk,E] = qr(X ,tol)</term> + <listitem> + <para> + returns <literal>rk</literal> = rank estimate of <literal>X</literal> i.e. <literal>rk</literal> is the number of diagonal elements in <literal>R</literal> which are larger than a given threshold <literal>tol</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[Q,R,rk,E] = qr(X) </term> + <listitem> + <para> + returns <literal>rk</literal> = rank estimate of <literal>X</literal> + i.e. <literal>rk</literal> is the number of diagonal elements in + <literal>R</literal> which are larger than + <literal>tol=R(1,1)*%eps*max(size(R))</literal>. See <literal>rankqr</literal> + for a rank revealing QR factorization, using the condition number + of <literal>R</literal>. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// QR factorization, generic case +// X is tall (full rank) +X=rand(5,2);[Q,R]=qr(X); [Q'*X R] + +//X is fat (full rank) +X=rand(2,3);[Q,R]=qr(X); [Q'*X R] + +//Column 4 of X is a linear combination of columns 1 and 2: +X=rand(8,5);X(:,4)=X(:,1)+X(:,2); [Q,R]=qr(X); R, R(:,4) + +//X has rank 2, rows 3 to $ of R are zero: +X=rand(8,2)*rand(2,5);[Q,R]=qr(X); R + +//Evaluating the rank rk: column pivoting ==> rk first +//diagonal entries of R are non zero : +A=rand(5,2)*rand(2,5); +[Q,R,rk,E] = qr(A,1.d-10); +norm(Q'*A-R) +svd([A,Q(:,1:rk)]) //span(A) =span(Q(:,1:rk)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rankqr">rankqr</link> + </member> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + qr decomposition is based the Lapack routines DGEQRF, DGEQPF, + DORGQR for the real matrices and ZGEQRF, ZGEQPF, ZORGQR for the + complex case. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/linear/rankqr.xml b/modules/linear_algebra/help/en_US/linear/rankqr.xml new file mode 100755 index 000000000..3532b3daa --- /dev/null +++ b/modules/linear_algebra/help/en_US/linear/rankqr.xml @@ -0,0 +1,150 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rankqr"> + <refnamediv> + <refname>rankqr</refname> + <refpurpose>rank revealing QR factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,R,JPVT,RANK,SVAL]=rankqr(A, [RCOND,JPVT])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>RCOND</term> + <listitem> + <para>real number used to determine the effective rank of + <literal>A</literal>, which is defined as the order of the largest leading + triangular submatrix <literal>R11</literal> in the QR factorization with + pivoting of<literal>A</literal>, whose estimated condition number < + <literal>1/RCOND</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>JPVT</term> + <listitem> + <para> + integer vector on entry, if <literal>JPVT(i)</literal> is not 0, the + <literal>i</literal>-th column of <literal> A</literal> is permuted to the front + of <literal>AP</literal>, otherwise column <literal>i</literal> is a free + column. On exit, if <literal>JPVT(i) = k</literal>, then the + <literal>i</literal>-th column of <literal>A*P</literal> was the + <literal>k</literal>-th column of <literal>A</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>RANK</term> + <listitem> + <para> + the effective rank of <literal>A</literal>, i.e., the order of the + submatrix <literal>R11</literal>. This is the same as the order of the + submatrix <literal>T1</literal> in the complete orthogonal factorization + of <literal>A</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>SVAL</term> + <listitem> + <para>real vector with 3 components; The estimates of some of the + singular values of the triangular factor <literal>R</literal>. + </para> + <para> + <literal>SVAL(1)</literal> is the largest singular value of + <literal>R(1:RANK,1:RANK)</literal>; + </para> + <para> + <literal>SVAL(2)</literal> is the + smallest singular value of <literal>R(1:RANK,1:RANK)</literal>; + </para> + <para> + <literal>SVAL(3)</literal> is the smallest singular value of + <literal>R(1:RANK+1,1:RANK+1)</literal>, if <literal>RANK</literal> < <literal>MIN(M,N)</literal>, + or of <literal>R(1:RANK,1:RANK)</literal>, otherwise. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + To compute (optionally) a rank-revealing QR factorization of a real + general M-by-N real or complex matrix <literal>A</literal>, which may be + rank-deficient, and estimate its effective rank using incremental + condition estimation. + </para> + <para> + The routine uses a QR factorization with column pivoting: + </para> + <programlisting role=""><![CDATA[ +A * P = Q * R, where R = [ R11 R12 ], + [ 0 R22 ] + ]]></programlisting> + <para> + with <literal>R11</literal> defined as the largest leading submatrix whose + estimated condition number is less than <literal>1/RCOND</literal>. The + order of <literal>R11</literal>, <literal>RANK</literal>, is the effective rank of + <literal>A</literal>. + </para> + <para> + If the triangular factorization is a rank-revealing one (which will be + the case if the leading columns were well- conditioned), then + <literal>SVAL(1)</literal> will also be an estimate for the largest singular + value of <literal>A</literal>, and <literal>SVAL(2)</literal> and + <literal>SVAL(3)</literal> will be estimates for the <literal>RANK</literal>-th + and <literal>(RANK+1)</literal>-st singular values of <literal>A</literal>, + respectively. + </para> + <para> + By examining these values, one can confirm that the + rank is well defined with respect to the chosen value of + <literal>RCOND</literal>. The ratio <literal>SVAL(1)/SVAL(2)</literal> is an + estimate of the condition number of <literal>R(1:RANK,1:RANK)</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,7); +[Q,R,JPVT,RANK,SVAL]=rankqr(A,%eps) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rank">rank</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para> + Slicot library routines MB03OD, ZB03OD. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/markov/CHAPTER b/modules/linear_algebra/help/en_US/markov/CHAPTER new file mode 100755 index 000000000..c29eb913c --- /dev/null +++ b/modules/linear_algebra/help/en_US/markov/CHAPTER @@ -0,0 +1,2 @@ +title = Markov Matrices + diff --git a/modules/linear_algebra/help/en_US/markov/classmarkov.xml b/modules/linear_algebra/help/en_US/markov/classmarkov.xml new file mode 100755 index 000000000..a80312508 --- /dev/null +++ b/modules/linear_algebra/help/en_US/markov/classmarkov.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="classmarkov"> + <refnamediv> + <refname>classmarkov</refname> + <refpurpose>recurrent and transient classes of Markov matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[perm,rec,tr,indsRec,indsT]=classmarkov(M)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>M</term> + <listitem> + <para>real N x N Markov matrix. Sum of entries in each row should add to one.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>perm</term> + <listitem> + <para>integer permutation vector.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rec, tr</term> + <listitem> + <para>integer vector, number (number of states in each recurrent classes, number of transient states).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>indsRec,indsT</term> + <listitem> + <para>integer vectors. (Indexes of recurrent and transient states).</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Returns a permutation vector <literal>perm</literal> such that + </para> + <programlisting role=""><![CDATA[ +M(perm,perm) = [M11 0 0 0 0 0] + [0 M22 0 0 0] + [0 0 M33 0] + [ ... ] + [0 0 Mrr 0] + [* * * Q] + ]]></programlisting> + <para> + Each <literal>Mii</literal> is a Markov matrix of dimension <literal>rec(i) i=1,..,r</literal>. + <literal>Q</literal> is sub-Markov matrix of dimension <literal>tr</literal>. + States 1 to sum(rec) are recurrent and states from r+1 to n + are transient. + One has <literal>perm=[indsRec,indsT]</literal> where indsRec is a vector of size sum(rec) + and indsT is a vector of size tr. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//P has two recurrent classes (with 2 and 1 states) 2 transient states +P=genmarkov([2,1],2,'perm') +[perm,rec,tr,indsRec,indsT]=classmarkov(P); +P(perm,perm) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="genmarkov">genmarkov</link> + </member> + <member> + <link linkend="eigenmarkov">eigenmarkov</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/markov/eigenmarkov.xml b/modules/linear_algebra/help/en_US/markov/eigenmarkov.xml new file mode 100755 index 000000000..950937188 --- /dev/null +++ b/modules/linear_algebra/help/en_US/markov/eigenmarkov.xml @@ -0,0 +1,81 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="eigenmarkov"> + <refnamediv> + <refname>eigenmarkov</refname> + <refpurpose>normalized left and right Markov eigenvectors</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[M,Q]=eigenmarkov(P)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>real N x N Markov matrix. Sum of entries in each row should add to one.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>M</term> + <listitem> + <para>real matrix with N columns.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>real matrix with N rows.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Returns normalized left and right eigenvectors + associated with the eigenvalue 1 of the Markov transition matrix P. + If the multiplicity of this eigenvalue is m and P + is N x N, M is a m x N matrix and Q a N x m matrix. + M(k,:) is the probability distribution vector associated with the kth + ergodic set (recurrent class). M(k,x) is zero if x is not in the + k-th recurrent class. + Q(x,k) is the probability to end in the k-th recurrent class starting + from x. If <literal>P^k</literal> converges for large <literal>k</literal> (no eigenvalues on the + unit circle except 1), then the limit is <literal>Q*M</literal> (eigenprojection). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//P has two recurrent classes (with 2 and 1 states) 2 transient states +P=genmarkov([2,1],2) +[M,Q]=eigenmarkov(P); +P*Q-Q +Q*M-P^20 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="genmarkov">genmarkov</link> + </member> + <member> + <link linkend="classmarkov">classmarkov</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/markov/genmarkov.xml b/modules/linear_algebra/help/en_US/markov/genmarkov.xml new file mode 100755 index 000000000..edf5baeeb --- /dev/null +++ b/modules/linear_algebra/help/en_US/markov/genmarkov.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="genmarkov"> + <refnamediv> + <refname>genmarkov</refname> + <refpurpose>generates random markov matrix with recurrent and transient classes</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>M=genmarkov(rec,tr) + M=genmarkov(rec,tr,flag) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>rec</term> + <listitem> + <para>integer row vector (its dimension is the number of recurrent classes).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tr</term> + <listitem> + <para>integer (number of transient states)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>M</term> + <listitem> + <para>real Markov matrix. Sum of entries in each row should add to one.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string <literal>'perm'</literal>. If given, a random permutation of the states is done. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Returns in M a random Markov transition probability matrix + with <literal>size(rec,1)</literal> recurrent classes with <literal>rec(1),...rec($)</literal> + entries respectively and tr transient states. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//P has two recurrent classes (with 2 and 1 states) 2 transient states +P=genmarkov([2,1],2,'perm') +[perm,rec,tr,indsRec,indsT]=classmarkov(P); +P(perm,perm) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="classmarkov">classmarkov</link> + </member> + <member> + <link linkend="eigenmarkov">eigenmarkov</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/matrix/CHAPTER b/modules/linear_algebra/help/en_US/matrix/CHAPTER new file mode 100755 index 000000000..bb89125cd --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/CHAPTER @@ -0,0 +1,2 @@ +title = Matrix Analysis + diff --git a/modules/linear_algebra/help/en_US/matrix/cond.xml b/modules/linear_algebra/help/en_US/matrix/cond.xml new file mode 100755 index 000000000..4c85c76c1 --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/cond.xml @@ -0,0 +1,158 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2012 - Scilab Enterprises - Adeline CARNIS + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="cond"> + <refnamediv> + <refname>cond</refname> + <refpurpose>condition number</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + c = cond(X) + c = cond(X, p) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex matrix. If c = cond(X, p), X must be real or complex square matrix.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>p</term> + <listitem> + <para>scalar or string (type of norm) (default value = 2).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>c</term> + <listitem> + <para>real scalar, the condition number.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term>c = cond(X)</term> + <listitem> + <para> + returns condition number in 2-norm.<literal>cond(X)</literal> is the ratio of the + largest singular value of <literal>X</literal> to the smallest. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>c = cond(X, p)</term> + <listitem> + <para> + returns condition number in p-norm : <literal>norm(X, p) * norm(inv(X), p)</literal>. + If <literal>p</literal> is specified, <literal>p</literal> can be equal to : + </para> + <itemizedlist> + <listitem> + <para> + p = 1. <literal>cond(X, p)</literal> returns condition number in 1-norm. + </para> + </listitem> + <listitem> + <para> + p = 2. <literal>cond(X, p)</literal> returns condition number in 2-norm. + </para> + </listitem> + <listitem> + <para> + p = %inf or 'inf'. <literal>cond(X, p)</literal> returns condition number in infinity norm. + </para> + </listitem> + <listitem> + <para> + p = 'fro'. <literal>cond(X, p)</literal> returns condition number in Frobenius norm. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"> + <![CDATA[ +A=testmatrix('hilb',6); +// condition number in 2-norm +cond(A) +cond(A, 2) + +// condition number in 1-norm +cond(A, 1) + +// condition number in infinity norm +cond(A, %inf) + +// condition number in Frobenius norm +cond(A, 'fro') + ]]> + </programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rcond">rcond</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="norm">norm</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revdescription> + <para> + Calling <literal>cond(X)</literal>, where <literal>X</literal> is + non square matrix, is now managed. For example: + </para> + <programlisting role=""> + <![CDATA[ +X = [1 0; 1 -1; 0 1]; +cond(X) + ]]> + </programlisting> + <para> + Calling <literal>cond(X, p)</literal> allows to calculate p-norm + condition number. For example: + </para> + <programlisting role=""> + <![CDATA[ +X = [1 -6 0; 1 0 -4;1 0 2]; +cond(X, 1) // condition number in 1-norm (p = 1) + ]]> + </programlisting> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/matrix/det.xml b/modules/linear_algebra/help/en_US/matrix/det.xml new file mode 100755 index 000000000..10d6965a0 --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/det.xml @@ -0,0 +1,104 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="det"> + <refnamediv> + <refname>det</refname> + <refpurpose>determinant</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>det(X) + [e,m]=det(X) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex square matrix, polynomial or rational matrix.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>m</term> + <listitem> + <para>real or complex number, the determinant base 10 mantissae</para> + </listitem> + </varlistentry> + <varlistentry> + <term>e</term> + <listitem> + <para>integer, the determinant base 10 exponent</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>det(X)</literal> ( <literal>m*10^e</literal> is the determinant of the square matrix <literal>X</literal>. + </para> + <para> + For polynomial matrix <literal>det(X)</literal> is equivalent to <literal>determ(X)</literal>. + </para> + <para> + For rational matrices <literal>det(X)</literal> is equivalent to <literal>detr(X)</literal>. + </para> + <para> + <important> + The <literal>det</literal> and <literal>detr</literal> functions don't use the same algorithm. + For a rational fraction, <literal>det(X)</literal> is overloaded by <literal>%r_det(X)</literal> which is based on the <literal>determ</literal> function. + <literal>detr()</literal> uses the Leverrier method. + </important> + <warning> + Sometimes the <literal>det</literal> and <literal>detr</literal> functions may return different values for rational matrices. + In such cases you should set rational simplification mode off by using <code>simp_mode(%f)</code> to get the same result. + </warning> + </para> + </refsection> + <refsection> + <title>References</title> + <para> + det computations are based on the Lapack routines + DGETRF for real matrices and ZGETRF for the complex case. + </para> + <para> + Concerning sparse matrices, the determinant is obtained from LU factorization of umfpack library. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +det([x,1+x;2-x,x^2]) +w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w) //zeros of linear system +A=rand(3,3); +det(A), prod(spec(A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="determ">determ</link> + </member> + <member> + <link linkend="simp_mode">simp_mode</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/matrix/orth.xml b/modules/linear_algebra/help/en_US/matrix/orth.xml new file mode 100755 index 000000000..a0c7c36eb --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/orth.xml @@ -0,0 +1,76 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="orth"> + <refnamediv> + <refname>orth</refname> + <refpurpose>orthogonal basis</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>Q=orth(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>Q=orth(A)</literal> returns <literal>Q</literal>, an orthogonal + basis for the span of <literal>A</literal>. Range(<literal>Q</literal>) = + Range(<literal>A</literal>) and <literal>Q'*Q=eye</literal>. + </para> + <para> + The number of columns of <literal>Q</literal> is the rank of + <literal>A</literal> as determined by the QR algorithm. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,4); +[X,dim]=rowcomp(A);X=X'; +svd([orth(A),X(:,1:dim)]) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="range">range</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/matrix/rank.xml b/modules/linear_algebra/help/en_US/matrix/rank.xml new file mode 100755 index 000000000..ec651a774 --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/rank.xml @@ -0,0 +1,87 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rank"> + <refnamediv> + <refname>rank</refname> + <refpurpose>rank</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[i]=rank(X) + [i]=rank(X,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>nonnegative real number</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>rank(X)</literal> is the numerical rank of <literal>X</literal> + i.e. the number of singular values of X that are larger than + <literal>norm(size(X),'inf') * norm(X) * %eps</literal>. + </para> + <para> + <literal>rank(X,tol)</literal> is the number of singular values of + <literal>X</literal> that are larger than <literal>tol</literal>. + </para> + <para> + <note> + Note that the default value of <literal>tol</literal> is proportional to + <literal>norm(X)</literal>. As a consequence + <literal>rank([1.d-80,0;0,1.d-80])</literal> is 2 !. + </note> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +rank([1.d-80,0;0,1.d-80]) +rank([1,0;0,1.d-80]) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="lu">lu</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/matrix/rcond.xml b/modules/linear_algebra/help/en_US/matrix/rcond.xml new file mode 100755 index 000000000..4d95cb28d --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/rcond.xml @@ -0,0 +1,82 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2010 - DIGITEO - Michael Baudin + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rcond"> + <refnamediv> + <refname>rcond</refname> + <refpurpose>inverse condition number</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>rcond(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex square matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>rcond(X)</literal> is an estimate for the reciprocal of the + condition of <literal>X</literal> in the 1-norm. + </para> + <para> + If <literal>X</literal> is well conditioned, <literal>rcond(X)</literal> is close to 1. + If not, <literal>rcond(X)</literal> is close to 0. + </para> + <para> + We compute the 1-norm of A with Lapack/DLANGE, compute its LU decomposition with Lapack/DGETRF + and finally estimate the condition with Lapack/DGECON. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=diag([1:10]); +rcond(A) +A(1,1)=0.000001; +rcond(A) + ]]></programlisting> + <para> + Estimating the 1-norm inverse condition number with <literal>rcond</literal> is + much faster than computing the 2-norm condition number with <literal>cond</literal>. + As a trade-off, <literal>rcond</literal> may be less reliable. + </para> + <programlisting role="example"><![CDATA[ + A=ones(1000,1000); + timer();cond(A);timer() + timer();1/rcond(A);timer() + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="cond">cond</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/matrix/rref.xml b/modules/linear_algebra/help/en_US/matrix/rref.xml new file mode 100755 index 000000000..d2d1f7774 --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/rref.xml @@ -0,0 +1,68 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rref"> + <refnamediv> + <refname>rref</refname> + <refpurpose>computes matrix row echelon form by lu transformations</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>R=rref(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para> m x n matrix with scalar entries</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para> m x n matrix,row echelon form of a</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>rref</literal> computes the row echelon form of the given matrix by left lu + decomposition. If ones need the transformation used just call + <literal>X=rref([A,eye(m,m)])</literal> the row echelon form <literal>R</literal> is <literal>X(:,1:n)</literal> and + the left transformation <literal>L</literal> is given by <literal>X(:,n+1:n+m)</literal> such as <literal>L*A=R</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=[1 2;3 4;5 6]; +X=rref([A,eye(3,3)]); +R=X(:,1:2) +L=X(:,3:5);L*A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="lu">lu</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/matrix/trace.xml b/modules/linear_algebra/help/en_US/matrix/trace.xml new file mode 100755 index 000000000..84ba1e20c --- /dev/null +++ b/modules/linear_algebra/help/en_US/matrix/trace.xml @@ -0,0 +1,57 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="trace"> + <refnamediv> + <refname>trace</refname> + <refpurpose>trace</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>trace(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex square matrix, polynomial or rational matrix.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>trace(X)</literal> is the trace of the matrix <literal>X</literal>. + </para> + <para> + Same as <literal>sum(diag(X))</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3); +trace(A)-sum(spec(A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/CHAPTER b/modules/linear_algebra/help/en_US/pencil/CHAPTER new file mode 100755 index 000000000..86d1da116 --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/CHAPTER @@ -0,0 +1,2 @@ +title = Matrix Pencil + diff --git a/modules/linear_algebra/help/en_US/pencil/companion.xml b/modules/linear_algebra/help/en_US/pencil/companion.xml new file mode 100755 index 000000000..0509be671 --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/companion.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="companion"> + <refnamediv> + <refname>companion</refname> + <refpurpose>companion matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>A=companion(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>polynomial or vector of polynomials</para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>square matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Returns a matrix <literal>A</literal> with characteristic polynomial equal + to <literal>p</literal> if <literal>p</literal> is monic. If <literal>p</literal> is not monic + the characteristic polynomial of <literal>A</literal> is equal to + <literal>p/c</literal> where <literal>c</literal> is the coefficient of largest degree + in <literal>p</literal>. + </para> + <para> + If <literal>p</literal> is a vector of monic polynomials, <literal>A</literal> is block diagonal, + and the characteristic polynomial of the ith block is <literal>p(i)</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=poly([1,2,3,4,1],'s','c') +det(s*eye()-companion(p)) +roots(p) +spec(companion(p)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="randpencil">randpencil</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/ereduc.xml b/modules/linear_algebra/help/en_US/pencil/ereduc.xml new file mode 100755 index 000000000..40a83b693 --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/ereduc.xml @@ -0,0 +1,114 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="ereduc"> + <refnamediv> + <refname>ereduc</refname> + <refpurpose>computes matrix column echelon form by qz transformations</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>m x n matrix with real entries.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>real positive scalar.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>column echelon form matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>m x m unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z</term> + <listitem> + <para>n x n unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>stair</term> + <listitem> + <para>vector of indexes,</para> + <variablelist> + <varlistentry> + <term>* </term> + <listitem> + <para> + <literal>ISTAIR(i) = + j</literal> if the boundary element <literal>E(i,j)</literal> is a corner point. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>* </term> + <listitem> + <para> + <literal>ISTAIR(i) = - j</literal> if the boundary element <literal>E(i,j)</literal> is not a corner point. + </para> + </listitem> + </varlistentry> + </variablelist> + <para> + <literal>(i=1,...,M)</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para>integer, estimated rank of the matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Given an <literal>m x n</literal> matrix <literal>X</literal> (not necessarily regular) the function + ereduc computes a unitary transformed matrix <literal>E=Q*X*Z</literal> which is in + column echelon form (trapezoidal form). Furthermore the rank of + matrix <literal>X</literal> is determined. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +X=[1 2 3;4 5 6] +[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="fstair">fstair</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/fstair.xml b/modules/linear_algebra/help/en_US/pencil/fstair.xml new file mode 100755 index 000000000..9d43f915b --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/fstair.xml @@ -0,0 +1,157 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="fstair"> + <refnamediv> + <refname>fstair</refname> + <refpurpose>computes pencil column echelon form by qz transformations</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>m x n matrix with real entries.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>real positive scalar.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>column echelon form matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>m x m unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z</term> + <listitem> + <para>n x n unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>stair</term> + <listitem> + <para>vector of indexes (see ereduc)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para>integer, estimated rank of the matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>AE</term> + <listitem> + <para>m x n matrix with real entries.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>EE</term> + <listitem> + <para>column echelon form matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>QE</term> + <listitem> + <para>m x m unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ZE</term> + <listitem> + <para>n x n unitary matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>nblcks</term> + <listitem> + <para> + is the number of submatrices having full row rank >= 0 detected in matrix <literal>A</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>muk: </term> + <listitem> + <para>integer array of dimension (n). Contains the column dimensions mu(k) (k=1,...,nblcks) of the submatrices having full column rank in the pencil sE(eps)-A(eps)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>nuk: </term> + <listitem> + <para>integer array of dimension (m+1). Contains the row dimensions nu(k) (k=1,...,nblcks) of the submatrices having full row rank in the pencil sE(eps)-A(eps)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>muk0: </term> + <listitem> + <para>integer array of dimension (n). Contains the column dimensions mu(k) (k=1,...,nblcks) of the submatrices having full column rank in the pencil sE(eps,inf)-A(eps,inf)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>nuk: </term> + <listitem> + <para>integer array of dimension (m+1). Contains the row dimensions nu(k) (k=1,...,nblcks) of the submatrices having full row rank in the pencil sE(eps,inf)-A(eps,inf)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>mnei: </term> + <listitem> + <para>integer array of dimension (4). mnei(1) = row dimension of sE(eps)-A(eps)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Given a pencil <literal>sE-A</literal> where matrix <literal>E</literal> is in column echelon form the + function <literal>fstair</literal> computes according to the wishes of the user a + unitary transformed pencil <literal>QE(sEE-AE)ZE</literal> which is more or less similar + to the generalized Schur form of the pencil <literal>sE-A</literal>. + The function yields also part of the Kronecker structure of + the given pencil. + </para> + <para> + <literal>Q,Z</literal> are the unitary matrices used to compute the pencil where E + is in column echelon form (see ereduc) + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="quaskro">quaskro</link> + </member> + <member> + <link linkend="ereduc">ereduc</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/glever.xml b/modules/linear_algebra/help/en_US/pencil/glever.xml new file mode 100755 index 000000000..cd3d577df --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/glever.xml @@ -0,0 +1,118 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="glever"> + <refnamediv> + <refname>glever</refname> + <refpurpose>inverse of matrix pencil</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>E, A</term> + <listitem> + <para>two real square matrices of same dimensions</para> + </listitem> + </varlistentry> + <varlistentry> + <term>s</term> + <listitem> + <para> + character string (default value '<literal>s</literal>') + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Bfs,Bis</term> + <listitem> + <para>two polynomial matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>chis</term> + <listitem> + <para>polynomial</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Computation of + </para> + <para> + <literal>(s*E-A)^-1</literal> + </para> + <para> + by generalized Leverrier's algorithm for a matrix pencil. + </para> + <programlisting role=""><![CDATA[ +(s*E-A)^-1 = (Bfs/chis) - Bis. + ]]></programlisting> + <para> + <literal>chis</literal> = characteristic polynomial (up to a multiplicative constant). + </para> + <para> + <literal>Bfs</literal> = numerator polynomial matrix. + </para> + <para> + <literal>Bis</literal> + = polynomial matrix ( - expansion of <literal>(s*E-A)^-1</literal> at infinity). + </para> + <para> + Note the - sign before <literal>Bis</literal>. + </para> + </refsection> + <refsection> + <title>Caution</title> + <para> + This function uses <literal>cleanp</literal> to simplify <literal>Bfs,Bis</literal> and <literal>chis</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1]; +[Bfs,Bis,chis]=glever(F) +inv(F)-((Bfs/chis) - Bis) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rowshuff">rowshuff</link> + </member> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/kroneck.xml b/modules/linear_algebra/help/en_US/pencil/kroneck.xml new file mode 100755 index 000000000..68488e0e7 --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/kroneck.xml @@ -0,0 +1,159 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="kroneck"> + <refnamediv> + <refname>kroneck</refname> + <refpurpose>Kronecker form of matrix pencil</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F) + [Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>F</term> + <listitem> + <para> + real matrix pencil <literal>F=s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E,A</term> + <listitem> + <para>two real matrices of same dimensions</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,Z</term> + <listitem> + <para>two square orthogonal matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Qd,Zd</term> + <listitem> + <para>two vectors of integers</para> + </listitem> + </varlistentry> + <varlistentry> + <term>numbeps,numeta</term> + <listitem> + <para>two vectors of integers</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Kronecker form of matrix pencil: <literal>kroneck</literal> computes two + orthogonal matrices <literal>Q, Z</literal> which put the pencil <literal>F=s*E -A</literal> into + upper-triangular form: + </para> + <programlisting role=""><![CDATA[ + | sE(eps)-A(eps) | X | X | X | + |----------------|----------------|------------|---------------| + | O | sE(inf)-A(inf) | X | X | +Q(sE-A)Z = |---------------------------------|----------------------------| + | | | | | + | 0 | 0 | sE(f)-A(f) | X | + |--------------------------------------------------------------| + | | | | | + | 0 | 0 | 0 | sE(eta)-A(eta)| + ]]></programlisting> + <para> + The dimensions of the four blocks are given by: + </para> + <para> + <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x Zd(2)</literal>, + <literal>f = Qd(3) x Zd(3)</literal>, <literal>eta=Qd(4)xZd(4)</literal> + </para> + <para> + The <literal>inf</literal> block contains the infinite modes of + the pencil. + </para> + <para> + The <literal>f</literal> block contains the finite modes of + the pencil + </para> + <para> + The structure of epsilon and eta blocks are given by: + </para> + <para> + <literal>numbeps(1)</literal> = <literal>#</literal> of eps blocks of size 0 x 1 + </para> + <para> + <literal>numbeps(2)</literal> = <literal>#</literal> of eps blocks of size 1 x 2 + </para> + <para> + <literal>numbeps(3)</literal> = <literal>#</literal> of eps blocks of size 2 x 3 etc... + </para> + <para> + <literal>numbeta(1)</literal> = <literal>#</literal> of eta blocks of size 1 x 0 + </para> + <para> + <literal>numbeta(2)</literal> = <literal>#</literal> of eta blocks of size 2 x 1 + </para> + <para> + <literal>numbeta(3)</literal> = <literal>#</literal> of eta blocks of size 3 x 2 etc... + </para> + <para> + The code is taken from T. Beelen (Slicot-WGS group). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +F=randpencil([1,1,2],[2,3],[-1,3,1],[0,3]); +Q=rand(17,17);Z=rand(18,18);F=Q*F*Z; +//random pencil with eps1=1,eps2=1,eps3=1; 2 J-blocks @ infty +//with dimensions 2 and 3 +//3 finite eigenvalues at -1,3,1 and eta1=0,eta2=3 +[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F); +[Qd(1),Zd(1)] //eps. part is sum(epsi) x (sum(epsi) + number of epsi) +[Qd(2),Zd(2)] //infinity part +[Qd(3),Zd(3)] //finite part +[Qd(4),Zd(4)] //eta part is (sum(etai) + number(eta1)) x sum(etai) +numbeps +numbeta + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gschur">gschur</link> + </member> + <member> + <link linkend="gspec">gspec</link> + </member> + <member> + <link linkend="systmat">systmat</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="randpencil">randpencil</link> + </member> + <member> + <link linkend="trzeros">trzeros</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/lyap.xml b/modules/linear_algebra/help/en_US/pencil/lyap.xml new file mode 100755 index 000000000..46874bc8e --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/lyap.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="lyap"> + <refnamediv> + <refname>lyap</refname> + <refpurpose>Lyapunov equation</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[X]=lyap(A,C,'c') + [X]=lyap(A,C,'d') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A, C</term> + <listitem> + <para> + real square matrices, <literal>C</literal> must be symmetric + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>X= lyap(A,C,flag)</literal> solves the continuous time or + discrete time matrix Lyapunov matrix equation: + </para> + <programlisting role=""><![CDATA[ +A'*X + X*A = C ( flag='c' ) +A'*X*A - X = C ( flag='d' ) + ]]></programlisting> + <para> + <note> + Note that a unique solution exist if and only if an eigenvalue of <literal>A</literal> is + not an eigenvalue of <literal>-A</literal> (<literal>flag='c'</literal>) or 1 over an eigenvalue of <literal>A</literal> + (<literal>flag='d'</literal>). + </note> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(4,4);C=rand(A);C=C+C'; +X=lyap(A,C,'c'); +A'*X + X*A -C +X=lyap(A,C,'d'); +A'*X*A - X -C + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sylv">sylv</link> + </member> + <member> + <link linkend="ctr_gram">ctr_gram</link> + </member> + <member> + <link linkend="obs_gram">obs_gram</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/pencan.xml b/modules/linear_algebra/help/en_US/pencil/pencan.xml new file mode 100755 index 000000000..77a19a64e --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/pencan.xml @@ -0,0 +1,105 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="pencan"> + <refnamediv> + <refname>pencan</refname> + <refpurpose>canonical form of matrix pencil</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,M,i1]=pencan(Fs) + [Q,M,i1]=pencan(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para> + a regular pencil <literal>s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E,A</term> + <listitem> + <para>two real square matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>two non-singular real matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>i1</term> + <listitem> + <para>integer</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Given the regular pencil <literal>Fs=s*E-A</literal>, <literal>pencan</literal> returns matrices <literal>Q</literal> + and <literal>M</literal> + such than <literal>M*(s*E-A)*Q</literal> is in "canonical" form. + </para> + <para> + <literal>M*E*Q</literal> is a block matrix + </para> + <programlisting role=""><![CDATA[ +[I,0; + 0,N] + ]]></programlisting> + <para> + with <literal>N</literal> nilpotent and <literal>i1</literal> = size of the <literal>I</literal> matrix above. + </para> + <para> + <literal>M*A*Q</literal> is a block matrix: + </para> + <programlisting role=""><![CDATA[ +[Ar,0; + 0,I] + ]]></programlisting> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +F=randpencil([],[1,2],[1,2,3],[]); +F=rand(6,6)*F*rand(6,6); +[Q,M,i1]=pencan(F); +W=clean(M*F*Q) +roots(det(W(1:i1,1:i1))) +det(W($-2:$,$-2:$)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + <member> + <link linkend="rowshuff">rowshuff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/penlaur.xml b/modules/linear_algebra/help/en_US/pencil/penlaur.xml new file mode 100755 index 000000000..00392641b --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/penlaur.xml @@ -0,0 +1,114 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="penlaur"> + <refnamediv> + <refname>penlaur</refname> + <refpurpose>Laurent coefficients of matrix pencil</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Si,Pi,Di,order]=penlaur(Fs) + [Si,Pi,Di,order]=penlaur(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para> + a regular pencil <literal>s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E, A</term> + <listitem> + <para>two real square matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Si,Pi,Di</term> + <listitem> + <para>three real square matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>order</term> + <listitem> + <para>integer</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>penlaur</literal> computes the first Laurent coefficients of <literal>(s*E-A)^-1</literal> at + infinity. + </para> + <para> + <literal>(s*E-A)^-1 = ... + Si/s - Pi - s*Di + ...</literal> at <literal>s</literal> = infinity. + </para> + <para> + <literal>order</literal> = order of the singularity (order=index-1). + </para> + <para> + The matrix pencil <literal>Fs=s*E-A</literal> should be invertible. + </para> + <para> + For a index-zero pencil, <literal>Pi, Di,...</literal> are zero and <literal>Si=inv(E)</literal>. + </para> + <para> + For a index-one pencil (order=0),<literal>Di</literal> =0. + </para> + <para> + For higher-index pencils, the terms <literal> -s^2 Di(2), -s^3 Di(3),... </literal> are given by: + </para> + <para> + <literal> Di(2)=Di*A*Di</literal>, <literal> Di(3)=Di*A*Di*A*Di</literal> (up + to <literal>Di(order)</literal>). + </para> + </refsection> + <refsection> + <title>Remark</title> + <para> + Experimental version: troubles when bad conditioning of <literal>so*E-A</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +F=randpencil([],[1,2],[1,2,3],[]); +F=rand(6,6)*F*rand(6,6);[E,A]=pen2ea(F); +[Si,Pi,Di]=penlaur(F); +[Bfs,Bis,chis]=glever(F); +norm(coeff(Bis,1)-Di,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="rowshuff">rowshuff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/quaskro.xml b/modules/linear_algebra/help/en_US/pencil/quaskro.xml new file mode 100755 index 000000000..d16e81dcd --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/quaskro.xml @@ -0,0 +1,134 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="quaskro"> + <refnamediv> + <refname>quaskro</refname> + <refpurpose>quasi-Kronecker form</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F) + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A) + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F,tol) + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>F</term> + <listitem> + <para> + real matrix pencil <literal>F=s*E-A</literal> (<literal>s=poly(0,'s')</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E,A</term> + <listitem> + <para>two real matrices of same dimensions</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>a real number (tolerance, default value=1.d-10)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,Z</term> + <listitem> + <para>two square orthogonal matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Qd,Zd</term> + <listitem> + <para>two vectors of integers</para> + </listitem> + </varlistentry> + <varlistentry> + <term>numbeps</term> + <listitem> + <para>vector of integers</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Quasi-Kronecker form of matrix pencil: <literal>quaskro</literal> computes two + orthogonal matrices <literal>Q, Z</literal> which put the pencil <literal>F=s*E -A</literal> into + upper-triangular form: + </para> + <programlisting role=""><![CDATA[ + | sE(eps)-A(eps) | X | X | + |----------------|----------------|------------| + | O | sE(inf)-A(inf) | X | +Q(sE-A)Z = |=================================|============| + | | | + | O | sE(r)-A(r) | + ]]></programlisting> + <para> + The dimensions of the blocks are given by: + </para> + <para> + <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x Zd(2)</literal>, + <literal>r = Qd(3) x Zd(3)</literal> + </para> + <para> + The <literal>inf</literal> block contains the infinite modes of + the pencil. + </para> + <para> + The <literal>f</literal> block contains the finite modes of + the pencil + </para> + <para> + The structure of epsilon blocks are given by: + </para> + <para> + <literal>numbeps(1)</literal> = <literal>#</literal> of eps blocks of size 0 x 1 + </para> + <para> + <literal>numbeps(2)</literal> = <literal>#</literal> of eps blocks of size 1 x 2 + </para> + <para> + <literal>numbeps(3)</literal> = <literal>#</literal> of eps blocks of size 2 x 3 etc... + </para> + <para> + The complete (four blocks) Kronecker form is given by + the function <literal>kroneck</literal> which calls <literal>quaskro</literal> on + the (pertransposed) pencil <literal>sE(r)-A(r)</literal>. + </para> + <para> + The code is taken from T. Beelen + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="kroneck">kroneck</link> + </member> + <member> + <link linkend="gschur">gschur</link> + </member> + <member> + <link linkend="gspec">gspec</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/randpencil.xml b/modules/linear_algebra/help/en_US/pencil/randpencil.xml new file mode 100755 index 000000000..c60dd7a9a --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/randpencil.xml @@ -0,0 +1,110 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="randpencil"> + <refnamediv> + <refname>randpencil</refname> + <refpurpose>random pencil</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>F=randpencil(eps,infi,fin,eta)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>eps</term> + <listitem> + <para>vector of integers</para> + </listitem> + </varlistentry> + <varlistentry> + <term>infi</term> + <listitem> + <para>vector of integers</para> + </listitem> + </varlistentry> + <varlistentry> + <term>fin</term> + <listitem> + <para>real vector, or monic polynomial, or vector of monic polynomial</para> + </listitem> + </varlistentry> + <varlistentry> + <term>eta</term> + <listitem> + <para>vector of integers</para> + </listitem> + </varlistentry> + <varlistentry> + <term>F</term> + <listitem> + <para> + real matrix pencil <literal>F=s*E-A</literal> (<literal>s=poly(0,'s')</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Utility function. + <literal>F=randpencil(eps,infi,fin,eta)</literal> returns a random pencil <literal>F</literal> + with given Kronecker structure. The structure is given by: + <literal>eps=[eps1,...,epsk]</literal>: structure of epsilon blocks (size eps1x(eps1+1),....) + <literal>fin=[l1,...,ln]</literal> set of finite eigenvalues (assumed real) (possibly []) + <literal>infi=[k1,...,kp]</literal> size of J-blocks at infinity + <literal>ki>=1</literal> (infi=[] if no J blocks). + <literal>eta=[eta1,...,etap]</literal>: structure ofeta blocks (size eta1+1)xeta1,...) + </para> + <para> + <literal>epsi</literal>'s should be >=0, <literal>etai</literal>'s should be >=0, <literal>infi</literal>'s should + be >=1. + </para> + <para> + If <literal>fin</literal> is a (monic) polynomial, the finite block admits the roots of + <literal>fin</literal> as eigenvalues. + </para> + <para> + If <literal>fin</literal> is a vector of polynomial, they are the finite elementary + divisors of <literal>F</literal> i.e. the roots of <literal>p(i)</literal> are finite + eigenvalues of <literal>F</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +F=randpencil([0,1],[2],[-1,0,1],[3]); +[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F); +Qd, Zd +s=poly(0,'s'); +F=randpencil([],[1,2],s^3-2,[]); //regular pencil +det(F) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="kroneck">kroneck</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/rowshuff.xml b/modules/linear_algebra/help/en_US/pencil/rowshuff.xml new file mode 100755 index 000000000..713c0a70f --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/rowshuff.xml @@ -0,0 +1,103 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rowshuff"> + <refnamediv> + <refname>rowshuff</refname> + <refpurpose>shuffle algorithm</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Ws,Fs1]=rowshuff(Fs, [alfa])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para> + square real pencil <literal>Fs = s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ws</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Fs1</term> + <listitem> + <para> + square real pencil <literal>F1s = s*E1 -A1</literal> with <literal>E1</literal> non-singular + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>alfa</term> + <listitem> + <para> + real number (<literal>alfa = 0</literal> is the default value) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Shuffle algorithm: Given the pencil <literal>Fs=s*E-A</literal>, returns Ws=W(s) + (square polynomial matrix) such that: + </para> + <para> + <literal> Fs1 = s*E1-A1 = W(s)*(s*E-A) </literal> is a pencil with non singular <literal>E1</literal> matrix. + </para> + <para> + This is possible iff the pencil <literal>Fs = s*E-A</literal> is regular (i.e. invertible). + The degree of <literal>Ws</literal> is equal to the index of the pencil. + </para> + <para> + The poles at infinity of <literal>Fs</literal> are put to <literal>alfa</literal> and the zeros of <literal>Ws</literal> are at <literal>alfa</literal>. + </para> + <para> + Note that <literal>(s*E-A)^-1 = (s*E1-A1)^-1 * W(s) = (W(s)*(s*E-A))^-1 *W(s)</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +F=randpencil([],[2],[1,2,3],[]); +F=rand(5,5)*F*rand(5,5); // 5 x 5 regular pencil with 3 evals at 1,2,3 +[Ws,F1]=rowshuff(F,-1); +[E1,A1]=pen2ea(F1); +svd(E1) //E1 non singular +roots(det(Ws)) +clean(inv(F)-inv(F1)*Ws,1.d-7) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/pencil/sylv.xml b/modules/linear_algebra/help/en_US/pencil/sylv.xml new file mode 100755 index 000000000..4b6d85939 --- /dev/null +++ b/modules/linear_algebra/help/en_US/pencil/sylv.xml @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="sylv"> + <refnamediv> + <refname>sylv</refname> + <refpurpose>Sylvester equation.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>sylv(A, B, C, flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A,B,C</term> + <listitem> + <para>three real matrices of appropriate dimensions.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + character string (<literal>'c'</literal> or <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>X= sylv(A, B, C, 'c')</literal> computes <literal>X</literal>, solution + of the "continuous time" Sylvester equation + </para> + <programlisting role=""><![CDATA[ +A*X+X*B = C + ]]></programlisting> + <para> + <literal>X=sylv(A, B, C, 'd')</literal> computes <literal>X</literal>, solution + of the modified "discrete time" Sylvester equation + </para> + <programlisting role=""><![CDATA[ +A*X*B+X = C + ]]></programlisting> + <para> + <literal>X=-sylv(-A, B, C, 'd')</literal> computes <literal>X</literal>, solution + of the real "discrete time" Sylvester equation + </para> + <programlisting role=""><![CDATA[ +A*X*B-X = C + ]]></programlisting> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// Continuous time Sylvester equation: +A = rand(4, 4); C = rand(4, 3); B = rand(3, 3); +X = sylv(A, B, C, 'c'); +norm(A*X+X*B-C) + +// Modified Discrete time Sylvester equation: +X = sylv(A, B, C, 'd'); +norm(A*X*B+X-C) + +// Real Discrete time Sylvester equation: +X = -sylv(-A, B, C, 'd'); +norm(A*X*B-X-C) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="lyap">lyap</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/proj.xml b/modules/linear_algebra/help/en_US/proj.xml new file mode 100755 index 000000000..0797774a1 --- /dev/null +++ b/modules/linear_algebra/help/en_US/proj.xml @@ -0,0 +1,72 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="proj"> + <refnamediv> + <refname>proj</refname> + <refpurpose>projection</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>P = proj(X1,X2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X1,X2</term> + <listitem> + <para>two real matrices with equal number of columns</para> + </listitem> + </varlistentry> + <varlistentry> + <term>P</term> + <listitem> + <para> + real projection matrix (<literal>P^2=P</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>P</literal> is the projection on <literal>X2</literal> parallel to <literal>X1</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +X1=rand(5,2);X2=rand(5,3); +P=proj(X1,X2); +norm(P^2-P,1) +trace(P) // This is dim(X2) +[Q,M]=fullrf(P); +svd([Q,X2]) // span(Q) = span(X2) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="projspec">projspec</link> + </member> + <member> + <link linkend="orth">orth</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/state_space/CHAPTER b/modules/linear_algebra/help/en_US/state_space/CHAPTER new file mode 100755 index 000000000..a0b62cdee --- /dev/null +++ b/modules/linear_algebra/help/en_US/state_space/CHAPTER @@ -0,0 +1,2 @@ +title = State-Space Matrices + diff --git a/modules/linear_algebra/help/en_US/state_space/coff.xml b/modules/linear_algebra/help/en_US/state_space/coff.xml new file mode 100755 index 000000000..2944ddac1 --- /dev/null +++ b/modules/linear_algebra/help/en_US/state_space/coff.xml @@ -0,0 +1,97 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="coff"> + <refnamediv> + <refname>coff</refname> + <refpurpose>resolvent (cofactor method) </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[N,d]=coff(M [,var])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>M</term> + <listitem> + <para>square real matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>var</term> + <listitem> + <para>character string</para> + </listitem> + </varlistentry> + <varlistentry> + <term>N</term> + <listitem> + <para> + polynomial matrix (same size as <literal>M</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>d</term> + <listitem> + <para> + polynomial (characteristic polynomial <literal>poly(A,'s')</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>coff</literal> computes R=<literal>(s*eye()-M)^-1</literal> for <literal>M</literal> a real matrix. + R is given by <literal>N/d</literal>. + </para> + <para> + <literal>N</literal> = numerator polynomial matrix. + </para> + <para> + <literal>d</literal> = common denominator. + </para> + <para> + <literal>var</literal> character string ('<literal>s</literal>' if omitted) + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +M=[1,2;0,3]; +[N,d]=coff(M) +N/d +inv(%s*eye()-M) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="ss2tf">ss2tf</link> + </member> + <member> + <link linkend="nlev">nlev</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/state_space/nlev.xml b/modules/linear_algebra/help/en_US/state_space/nlev.xml new file mode 100755 index 000000000..5d8bd89ad --- /dev/null +++ b/modules/linear_algebra/help/en_US/state_space/nlev.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="nlev"> + <refnamediv> + <refname>nlev</refname> + <refpurpose>Leverrier's algorithm</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[num,den]=nlev(A,z [,rmax])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>real square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>z</term> + <listitem> + <para>character string</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rmax</term> + <listitem> + <para> + optional parameter (see <literal>bdiag</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[num,den]=nlev(A,z [,rmax])</literal> computes + <literal>(z*eye()-A)^(-1)</literal> + </para> + <para> + by block diagonalization of A followed by Leverrier's algorithm + on each block. + </para> + <para> + This algorithm is better than the usual leverrier algorithm but + still not perfect! + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);x=poly(0,'x'); +[NUM,den]=nlev(A,'x') +clean(den-poly(A,'x')) +clean(NUM/den-inv(x*eye()-A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="coff">coff</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="ss2tf">ss2tf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/subspaces/CHAPTER b/modules/linear_algebra/help/en_US/subspaces/CHAPTER new file mode 100755 index 000000000..d87d9ca5e --- /dev/null +++ b/modules/linear_algebra/help/en_US/subspaces/CHAPTER @@ -0,0 +1,3 @@ +title = Subspaces + + diff --git a/modules/linear_algebra/help/en_US/subspaces/spaninter.xml b/modules/linear_algebra/help/en_US/subspaces/spaninter.xml new file mode 100755 index 000000000..650b9dba2 --- /dev/null +++ b/modules/linear_algebra/help/en_US/subspaces/spaninter.xml @@ -0,0 +1,91 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="spaninter"> + <refnamediv> + <refname>spaninter</refname> + <refpurpose>subspace intersection</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[X,dim]=spaninter(A,B [,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A, B</term> + <listitem> + <para>two real or complex matrices with equal number of rows</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>orthogonal or unitary square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para> + integer, dimension of subspace range(<literal>A</literal>) inter range(<literal>B</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + computes the intersection of range(<literal>A</literal>) and range(<literal>B</literal>). + </para> + <para> + The first <literal>dim</literal> columns of <literal>X</literal> span this intersection i.e. + <literal>X(:,1:dim)</literal> is an orthogonal basis for + </para> + <para> + range(<literal>A</literal>) inter range(<literal>B</literal>) + </para> + <para> + In the <literal>X</literal> basis <literal>A</literal> and <literal>B</literal> are respectively represented by: + </para> + <para> + <literal>X'*A</literal> and <literal>X'*B</literal>. + </para> + <para> + <literal>tol</literal> is a threshold (<literal>sqrt(%eps)</literal> is the default value). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,4); // A is 5 x 4, rank=3 +B=[A(:,2),rand(5,1)]*rand(2,2); +[X,dim]=spaninter(A,B); +X1=X(:,1:dim); //The intersection +svd(A),svd([X1,A]) // X1 in span(A) +svd(B),svd([B,X1]) // X1 in span(B) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spanplus">spanplus</link> + </member> + <member> + <link linkend="spantwo">spantwo</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/subspaces/spanplus.xml b/modules/linear_algebra/help/en_US/subspaces/spanplus.xml new file mode 100755 index 000000000..276ccdb50 --- /dev/null +++ b/modules/linear_algebra/help/en_US/subspaces/spanplus.xml @@ -0,0 +1,100 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="spanplus"> + <refnamediv> + <refname>spanplus</refname> + <refpurpose>sum of subspaces</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[X,dim,dima]=spanplus(A,B[,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A, B</term> + <listitem> + <para>two real or complex matrices with equal number of rows</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>orthogonal or unitary square matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim, dima</term> + <listitem> + <para>integers, dimension of subspaces</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>nonnegative real number</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + computes a basis X such that: + </para> + <para> + the first <literal>dima</literal> columns of <literal>X</literal> span Range(<literal>A</literal>) + and the following (<literal>dim-dima</literal>) columns make a basis of <literal>A+B</literal> + relative to <literal>A</literal>. + </para> + <para> + The <literal>dim</literal> first columns of <literal>X</literal> make a basis for <literal>A+B</literal>. + </para> + <para> + One has the following canonical form for <literal>[A,B]</literal>: + </para> + <programlisting role=""><![CDATA[ + [*,*] (dima rows) +X'*[A,B]=[0,*] (dim-dima rows) + [0,0] + ]]></programlisting> + <para> + <literal>tol</literal> is an optional argument (see function code). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=rand(6,2)*rand(2,5); // rank(A)=2 +B=[A(:,1),rand(6,2)]*rand(3,3); //two additional independent vectors +[X,dim,dimA]=spanplus(A,B); +dimA +dim + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spaninter">spaninter</link> + </member> + <member> + <link linkend="im_inv">im_inv</link> + </member> + <member> + <link linkend="spantwo">spantwo</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/en_US/subspaces/spantwo.xml b/modules/linear_algebra/help/en_US/subspaces/spantwo.xml new file mode 100755 index 000000000..7be745d6d --- /dev/null +++ b/modules/linear_algebra/help/en_US/subspaces/spantwo.xml @@ -0,0 +1,110 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="spantwo"> + <refnamediv> + <refname>spantwo</refname> + <refpurpose>sum and intersection of subspaces</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Xp,dima,dimb,dim]=spantwo(A,B, [tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A, B</term> + <listitem> + <para>two real or complex matrices with equal number of rows</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Xp</term> + <listitem> + <para>square non-singular matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>dima, dimb, dim</term> + <listitem> + <para>integers, dimension of subspaces</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>nonnegative real number</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Given two matrices <literal>A</literal> and <literal>B</literal> with same number of rows, + returns a square matrix <literal>Xp</literal> (non singular but not necessarily orthogonal) + such that : + </para> + <programlisting role=""><![CDATA[ + [A1, 0] (dim-dimb rows) +Xp*[A,B]=[A2,B2] (dima+dimb-dim rows) + [0, B3] (dim-dima rows) + [0 , 0] + ]]></programlisting> + <para> + The first <literal>dima</literal> columns of <literal>inv(Xp)</literal> span range(<literal>A</literal>). + </para> + <para> + Columns <literal>dim-dimb+1</literal> to <literal>dima</literal> of <literal>inv(Xp)</literal> span the + intersection of range(A) and range(B). + </para> + <para> + The <literal>dim</literal> first columns of <literal>inv(Xp)</literal> span + range(<literal>A</literal>)+range(<literal>B</literal>). + </para> + <para> + Columns <literal>dim-dimb+1</literal> to <literal>dim</literal> of <literal>inv(Xp)</literal> span + range(<literal>B</literal>). + </para> + <para> + Matrix <literal>[A1;A2]</literal> has full row rank (=rank(A)). Matrix <literal>[B2;B3]</literal> has + full row rank (=rank(B)). Matrix <literal>[A2,B2]</literal> has full row rank (=rank(A inter B)). Matrix <literal>[A1,0;A2,B2;0,B3]</literal> has full row rank (=rank(A+B)). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=[1,0,0,4; + 5,6,7,8; + 0,0,11,12; + 0,0,0,16]; +B=[1,2,0,0]';C=[4,0,0,1]; +Sl=ss2ss(syslin('c',A,B,C),rand(A)); +[no,X]=contr(Sl('A'),Sl('B'));CO=X(:,1:no); //Controllable part +[uo,Y]=unobs(Sl('A'),Sl('C'));UO=Y(:,1:uo); //Unobservable part +[Xp,dimc,dimu,dim]=spantwo(CO,UO); //Kalman decomposition +Slcan=ss2ss(Sl,inv(Xp)); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spanplus">spanplus</link> + </member> + <member> + <link linkend="spaninter">spaninter</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/addchapter.sce b/modules/linear_algebra/help/fr_FR/addchapter.sce new file mode 100755 index 000000000..6da99e965 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Algèbre Lineaire",SCI+"/modules/linear_algebra/help/fr_FR",%T); + diff --git a/modules/linear_algebra/help/fr_FR/eigen/CHAPTER b/modules/linear_algebra/help/fr_FR/eigen/CHAPTER new file mode 100755 index 000000000..88f8bc42b --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/CHAPTER @@ -0,0 +1,2 @@ +title = Eigenvalue and Singular Value + diff --git a/modules/linear_algebra/help/fr_FR/eigen/bdiag.xml b/modules/linear_algebra/help/fr_FR/eigen/bdiag.xml new file mode 100755 index 000000000..a7dc9f342 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/bdiag.xml @@ -0,0 +1,111 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="bdiag"> + <refnamediv> + <refname>bdiag</refname> + <refpurpose>bloc-diagonalisation, vecteurs propres généralisés </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice carrée réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rmax </term> + <listitem> + <para>nombre réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ab </term> + <listitem> + <para>matrice carrée réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice régulière, réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>bs </term> + <listitem> + <para>vecteur d'entiers + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <programlisting role=""><![CDATA[ +[Ab [,X [,bs]]]=bdiag(A [,rmax]) + ]]></programlisting> + <para> + <literal>[Ab [,X [,bs]]]=bdiag(A [,rmax])</literal> calcule la forme + bloc-diagonale de <literal>A</literal>. bs précise la structure des + blocs (tailles respectives des blocs). <literal>X</literal> est la + matrice de changement de base, c'est à dire que <literal>Ab = + inv(X)*A*X + </literal> + est bloc-diagonale. + </para> + <para> + <literal>rmax</literal> contrôle le conditionnement de <literal>X</literal>; + la valeur par défaut est la norme l1 de <literal>A</literal>. + </para> + <para> + Pour obtenir une forme diagonale (si celle-ci existe) choisissez + une valeur élevée de <literal>rmax</literal> (<literal>rmax=1/%eps</literal> + par exemple). Pour une matrice réelle quelconque, les blocs sont + de taille (1x1) ou (2x2) et <literal>X</literal> est la matrice des + vecteurs propres. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +// Cas réel: blocs 1x1 et 2x2 +a=rand(5,5);[ab,x,bs]=bdiag(a);ab +// Cas complexe : blocs complexes 1x1 +[ab,x,bs]=bdiag(a+%i*0);ab + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="schur">schur</link> + </member> + <member> + <link linkend="sylv">sylv</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/eigen/gspec.xml b/modules/linear_algebra/help/fr_FR/eigen/gspec.xml new file mode 100755 index 000000000..d7e856080 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/gspec.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="gspec"> + <refnamediv> + <refname>gspec</refname> + <refpurpose>valeurs propres d'un faisceau de matrices (obsolete) </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[al,be]=gspec(A,E) + [al,be,Z]=gspec(A,E) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A, E </term> + <listitem> + <para>matrices carrées réelles de mêmes dimensions + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>al, be </term> + <listitem> + <para>vecteurs réels + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z </term> + <listitem> + <para>matrice carrée régulière + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Cette fonction est maintenant un cas particulier de la fonction + <literal>spec</literal>. La syntaxe d'appel doit être remplacée par + </para> + <programlisting role=""><![CDATA[ +[al,be]=spec(A,E) +[al,be,Z]=spec(A,E) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/eigen/hess.xml b/modules/linear_algebra/help/fr_FR/eigen/hess.xml new file mode 100755 index 000000000..6ae439c64 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/hess.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="hess"> + <refnamediv> + <refname>hess</refname> + <refpurpose>Forme de Hessenberg </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>H = hess(A) + [U,H] = hess(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice carrée réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>H </term> + <listitem> + <para>matrice carrée réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U </term> + <listitem> + <para>matrice carrée unitaire + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[U,H] = hess(A)</literal> Calcule une matrice unitaire <literal>U</literal> + et une matrice de Hessenberg <literal>H</literal> telles que <literal>A = + U*H*U' + </literal> + et <literal>U'*U</literal> = Identité. La syntaxe + <literal>H=hess(A)</literal> ne renvoie que la matrice de Hessenberg. + </para> + <para> + Les coefficients d'une matrice sous forme de Hessenberg sont nuls + sous la première sous-diagonale. Si la matrice est symétrique ou + hermitienne, la forme est tridiagonale. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);[U,H]=hess(A); +and( abs(U*H*U'-A)<1.d-10 ) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="contr">contr</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + Le calcul de la forme de Hessenberg determinant est basé sur les routines Lapack : + DGEHRD, DORGHR pour les matrices réelles et ZGEHRD, ZORGHR pour le cas complexe. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/eigen/pbig.xml b/modules/linear_algebra/help/fr_FR/eigen/pbig.xml new file mode 100755 index 000000000..724cf59f4 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/pbig.xml @@ -0,0 +1,128 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="pbig"> + <refnamediv> + <refname>pbig</refname> + <refpurpose>projection sur des sous-espaces propres </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle carrée + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>thres </term> + <listitem> + <para>nombre réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para> + chaîne de caractères (<literal>'c'</literal> ou <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M </term> + <listitem> + <para>matrices réelles + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Projection sur des sous-espaces propres de A associés aux valeurs + propres avec partie réelle >= <literal>thres</literal> + (<literal>flag='c'</literal>) ou avec module >= + <literal>thres</literal> (<literal>flag='d'</literal>). + </para> + <para> + La projection est définie par <literal>Q*M</literal>, où <literal>Q</literal> + est de rang maximal, les lignes de <literal>M</literal> sont + linéairement indépendantes et <literal>M*Q=eye</literal>. + </para> + <para> + Si <literal>flag='c'</literal>, les valeurs propres de + <literal>M*A*Q</literal> = valeurs propres de <literal>A</literal> avec partie + réelle >= <literal>thres</literal>. + </para> + <para> + Si <literal>flag='d'</literal>, les valeurs propres de + <literal>M*A*Q</literal> = valeurs propres de <literal>A</literal> avec module + >= <literal>thres</literal>. + </para> + <para> + Si <literal>flag='c'</literal> et si <literal>[Q1,M1]</literal> = + factorisation de rang maximal (<literal>fullrf</literal>) de + <literal>eye()-Q*M</literal> alors les valeurs propres de + <literal>M1*A*Q1</literal> = valeurs propres de <literal>A</literal> avec + partie réelle < <literal>thres</literal>. + </para> + <para> + Si <literal>flag='d'</literal> et si <literal>[Q1,M1]</literal> = + factorisation de rang maximal (<literal>fullrf</literal>) de + <literal>eye()-Q*M</literal> alors les valeurs propres de + <literal>M1*A*Q1</literal> = valeurs propres de <literal>A</literal> avec + module < <literal>thres</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; +[Q,M]=pbig(A,1.5,'d'); +spec(M*A*Q) +[Q1,M1]=fullrf(eye()-Q*M); +spec(M1*A*Q1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="psmall">psmall</link> + </member> + <member> + <link linkend="projspec">projspec</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + <literal>pbig</literal> est basée sur la forme de Schur ordonnée + (fonction Scilab <literal>schur</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/eigen/spec.xml b/modules/linear_algebra/help/fr_FR/eigen/spec.xml new file mode 100755 index 000000000..de3027bc2 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/spec.xml @@ -0,0 +1,211 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="spec"> + <refnamediv> + <refname>spec</refname> + <refpurpose>valeurs propres d'une matrice </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>evals=spec(A) + [X,diagevals]=spec(A) + + evals=spec(A,E) + [al,be]=spec(A,E) + [al,be,Z]=spec(A,E) + [al,be]=spec(A,E) + [al,be,Q,Z]=spec(A,E) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice carrée réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E </term> + <listitem> + <para> + matrice carrée réelle ou complexe de même dimensions que <literal> A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>evals </term> + <listitem> + <para>vecteur réel ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>diagevals </term> + <listitem> + <para> matrice carrée diagonale réelle ou complexe (les éléments + diagonaux sont les valeurs propres) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>al </term> + <listitem> + <para>vecteur réel ou complexe, al./be donnes les valeurs propres + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>be </term> + <listitem> + <para>vecteur réel ou complexe, al./be donnes les valeurs propres + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice carrée inversible réelle ou complexe, matrices des + vecteurs propres. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q </term> + <listitem> + <para>matrice carrée inversible réelle ou complexe, matrices des + vecteurs propres à gauche. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z </term> + <listitem> + <para>atrice carrée inversible réelle ou complexe, matrices des + vecteurs propres à droite. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term>spec(A)</term> + <listitem> + <para> + <literal> evals=spec(A)</literal> retourne dans le vecteur + <literal>evals</literal> les valeurs propres de <literal>A</literal>. + </para> + <para> + <literal> [evals,X] =spec(A)</literal> retourne de plus les vecteurs + propres (s'ils existent). Voir Aussi <literal>bdiag</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>spec(A,B)</term> + <listitem> + <para> + <literal>evals=spec(A,E)</literal> retourne le spectre du faisceau + <literal>s E - A</literal>, c'est à dire les racines du déterminant de + la matrice de polynômes <literal>s E - A</literal>. + </para> + <para> + <literal>[al,be] = spec(A,E)</literal> retourne le spectre du faisceau + <literal>s E - A</literal>, c'est à dire les racines du déterminant de + la matrice de polynômes <literal>s E - A</literal>. Les valeurs propres + sont données par <literal>al./be</literal>. Si <literal>be(i) = 0</literal> la + <literal>i</literal>ième valeur propres est à l'infini. (Pour <literal>E = + eye(A), al./be + </literal> + est <literal>spec(A)</literal>). + </para> + <para> + <literal> [al,be,Z] = spec(A,E)</literal> retourne de plus la matrice + <literal>Z</literal> des vecteurs propres généralisés à droite. + </para> + <para> + <literal> [al,be,Q,Z] = spec(A,E)</literal> retourne de plus les matrices + <literal>Q</literal> et <literal>Z</literal> des vecteurs propres généralisés à + droite et à gauche. + </para> + <para>Pour les grosses matrices pleines / creuses, vous + pouvez utiliser le module Arnoldi. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +// MATRIX EIGENVALUES +A=diag([1,2,3]);X=rand(3,3);A=inv(X)*A*X; +spec(A) + +x=poly(0,'x'); +pol=det(x*eye()-A) +roots(pol) + +[S,X]=bdiag(A); +clean(inv(X)*A*X) + +// PENCIL EIGENVALUES +A=rand(3,3); +[al,be,Z] = spec(A,eye(A));al./be +clean(inv(Z)*A*Z) //displaying the eigenvalues (generic matrix) +A=A+%i*rand(A);E=rand(A); +roots(det(%s*E-A)) //complex case + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="gspec">gspec</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="dsaupd">dsaupd</link> + </member> + <member> + <link linkend="dnaupd">dnaupd</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + Le calcul des valeurs propres des matrices est basé sur les + routines Lapack DGEEV and ZGEEV. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/eigen/sva.xml b/modules/linear_algebra/help/fr_FR/eigen/sva.xml new file mode 100755 index 000000000..91c66ed91 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/sva.xml @@ -0,0 +1,87 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="sva"> + <refnamediv> + <refname>sva</refname> + <refpurpose>approximation de valeurs singulières </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[U,s,V]=sva(A,k) + [U,s,V]=sva(A,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k </term> + <listitem> + <para>entier + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel positif + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Approximation de valeurs singulières. + </para> + <para> + <literal>[U,S,V]=sva(A,k)</literal> avec <literal>k</literal> un entier + >=1, renvoie <literal>U,S</literal> et <literal>V</literal> telles que + <literal>B=U*S*V'</literal> est la meilleure approximation au sens + l_2 de <literal>A</literal> avec rang(<literal>B</literal>)=<literal>k</literal>. + </para> + <para> + <literal>[U,S,V]=sva(A,tol)</literal> où <literal>tol</literal> est un réel + positif, renvoie <literal>U,S</literal> et <literal>V</literal> tels que + <literal>B=U*S*V'</literal> et la norme l_2 de <literal>A-B</literal> est + inférieure à <literal>tol</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,4)*rand(4,5); +[U,s,V]=sva(A,2); +B=U*s*V'; +svd(A) +svd(B) +clean(svd(A-B)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/eigen/svd.xml b/modules/linear_algebra/help/fr_FR/eigen/svd.xml new file mode 100755 index 000000000..a78b9dda0 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/eigen/svd.xml @@ -0,0 +1,132 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="svd"> + <refnamediv> + <refname>svd </refname> + <refpurpose>décomposition en valeurs singulières </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>s=svd(X) + [U,S,V]=svd(X) + [U,S,V]=svd(X,0) (obsolete) + [U,S,V]=svd(X,"e") + [U,S,V,rk]=svd(X [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>s </term> + <listitem> + <para>vecteur réel (valeurs singulières) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>S </term> + <listitem> + <para>matrice réelle diagonale (valeurs singulières sur la diagonale) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U,V </term> + <listitem> + <para>matrices carrées unitaires (vecteurs singuliers). + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel positif + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[U,S,V]=svd(X)</literal> renvoie une matrice diagonale <literal>S</literal>, de même + dimension que <literal>X</literal> avec des éléments diagonaux positifs classés + par ordre décroissant, ainsi que deux matrices unitaires <literal>U</literal> + et <literal>V</literal> telles que + <literal>X = U*S*V'</literal>.<literal>[U,S,V]=svd(X,"e")</literal> + renvoie la décomposition réduite : si <literal>X</literal> est une + matrice <literal>m x n </literal> et que <literal>m > n </literal> alors + seulement les n premières colonnes de <literal>U</literal> sont + calculées et <literal>S</literal> est <literal>n x n </literal>. + </para> + <para> + <literal>s=svd(X)</literal> renvoie un vecteur <literal>s</literal> contenant + les valeurs singulières. + </para> + <para> + <literal>[U,S,V,rk]=svd(X [,tol])</literal> renvoie de plus + <literal>rk</literal>, le rang "numérique" de <literal>X</literal> + c'est à dire le nombre de valeurs singulières plus grandes + que <literal>tol</literal>. + </para> + <para> + La valeur par défaut de <literal>tol</literal> est la même que pour la fonction <literal>rank</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +X=rand(4,2)*rand(2,4) +svd(X) +sqrt(spec(X*X')) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="sva">sva</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + la décomposition svd est basée sur les routines DGESVD pour les + matrices réelles et ZGESVD pour le cas complexe. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/factorization/CHAPTER b/modules/linear_algebra/help/fr_FR/factorization/CHAPTER new file mode 100755 index 000000000..e6daeb8eb --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/factorization/CHAPTER @@ -0,0 +1,2 @@ +title = Factorization + diff --git a/modules/linear_algebra/help/fr_FR/factorization/givens.xml b/modules/linear_algebra/help/fr_FR/factorization/givens.xml new file mode 100755 index 000000000..233d0cd94 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/factorization/givens.xml @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="givens"> + <refnamediv> + <refname>givens</refname> + <refpurpose>Transformation de Givens </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>U=givens(xy) + U=givens(x,y) + [U,c]=givens(xy) + [U,c]=givens(x,y) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x,y </term> + <listitem> + <para>deux nombres réels ou complexes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>xy </term> + <listitem> + <para> vecteur colonne réel ou complexe à deux composantes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U </term> + <listitem> + <para>matrice unitaire 2 x 2 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>c </term> + <listitem> + <para> vecteur colonne réel ou complexe à deux composantes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>U= givens(x, y)</literal> ou <literal>U = givens(xy)</literal> avec <literal>xy = [x;y]</literal> + renvoie <literal>U</literal> une matrice unitaire <literal>2</literal>x<literal>2</literal> telle que : + </para> + <para> + <literal>U*xy=[r;0]=c</literal>. + </para> + <para> + <note> + Notez que <literal>givens(x,y)</literal> et <literal>givens([x;y])</literal> sont équivalents. + </note> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=[3,4;5,6]; +U=givens(A(:,1)); +U*A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/factorization/householder.xml b/modules/linear_algebra/help/fr_FR/factorization/householder.xml new file mode 100755 index 000000000..f81b8b9ad --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/factorization/householder.xml @@ -0,0 +1,71 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="householder"> + <refnamediv> + <refname>householder</refname> + <refpurpose>Matrice de Householder </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>u=householder(v [,w])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>v </term> + <listitem> + <para>vecteur colonne réel ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>w </term> + <listitem> + <para> + vecteur colonne réel ou complexe de même taille que <literal>v</literal> (la valeur par défaut est <literal>eye(v)</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>u </term> + <listitem> + <para>vecteur colonne réel ou complexe + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Etant donnés deux vecteurs colonnes <literal>v</literal> et <literal>w</literal> de même taille, <literal>householder(v,w)</literal> renvoie un vecteur normé <literal>u</literal>, tel que + <literal>(eye()-2*u*u')*v</literal> est colinéaire à <literal>w</literal>. + <literal>(eye()-2*u*u')</literal> est la matrice de la transformation de Householder correspondante. + </para> + <para> + La valeur par défaut de <literal>w</literal> est <literal> eye(v)</literal>. Dans ce cas le vecteur <literal> (eye()-2*u*u')*v</literal> est égal à <literal> eye(v)*norm(v)</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="givens">givens</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/factorization/sqroot.xml b/modules/linear_algebra/help/fr_FR/factorization/sqroot.xml new file mode 100755 index 000000000..55f751b12 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/factorization/sqroot.xml @@ -0,0 +1,63 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="sqroot"> + <refnamediv> + <refname>sqroot</refname> + <refpurpose>factorisation hermitienne W*W' </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>sqroot(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice complexe ou réelle, symétrique définie non-négative + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + renvoie W telle que <literal>X=W*W'</literal> (en utilisant svd). + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +X=rand(5,2)*rand(2,5);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) + +X=rand(5,2)+%i*rand(5,2);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="chol">chol</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/kernel/CHAPTER b/modules/linear_algebra/help/fr_FR/kernel/CHAPTER new file mode 100755 index 000000000..be67920e1 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/kernel/CHAPTER @@ -0,0 +1,2 @@ +title = Kernel + diff --git a/modules/linear_algebra/help/fr_FR/kernel/colcomp.xml b/modules/linear_algebra/help/fr_FR/kernel/colcomp.xml new file mode 100755 index 000000000..4f674ac87 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/kernel/colcomp.xml @@ -0,0 +1,108 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="colcomp"> + <refnamediv> + <refname>colcomp</refname> + <refpurpose>compression de colonnes, noyau </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para>chaîne de caractères + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>W </term> + <listitem> + <para>matrice carré régulière (matrice de changement de base) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para> + entier (rang de"<literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Compression des colonnes de <literal>A</literal> : <literal>Ac = A*W</literal> est à colonnes compressées, c'est à dire + </para> + <para> + <literal>Ac=[0,Af]</literal> et <literal>Af</literal> est de rang maximal + rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>. + </para> + <para> + <literal>flag</literal> et <literal>tol</literal> sont des paramètres optionnels : <literal>flag = 'qr'</literal> + ou <literal>'svd'</literal> (<literal>'svd'</literal> par défaut). + </para> + <para> + <literal>tol</literal> = paramètre de tolérance (de l'ordre de <literal>%eps</literal> par défaut). + </para> + <para> + Les <literal>ma-rk</literal> premières colonnes de <literal>W</literal> forment une base du noyau de <literal>A</literal> quand <literal>size(A)=[na,ma]</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[X,r]=colcomp(A); +norm(A*X(:,1:$-r),1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="kernel">kernel</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/kernel/fullrf.xml b/modules/linear_algebra/help/fr_FR/kernel/fullrf.xml new file mode 100755 index 000000000..07b037630 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/kernel/fullrf.xml @@ -0,0 +1,102 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="fullrf"> + <refnamediv> + <refname>fullrf</refname> + <refpurpose>factorisation de rang plein </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel (tolérance pour le calcul du rang) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M </term> + <listitem> + <para>matrices réelles ou complexes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para> + entier (rang de <literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Cette fonction calcule la factorisation de rang plein de <literal>A</literal> : <literal>fullrf</literal> renvoie <literal>Q</literal> et <literal>M</literal> telles que <literal>A = Q*M</literal> + avec Im(<literal>Q</literal>)=Im(<literal>A</literal>) et ker(<literal>M</literal>)=ker(<literal>A</literal>), + <literal>Q</literal> de rang maximal, et les lignes de <literal>M</literal> sont linéairement indépendantes, + <literal>rk</literal> = rank(<literal>A</literal>) = nombre de colonnes de <literal>Q</literal> = nombre de lignes de <literal>M</literal>. + </para> + <para> + <literal>tol</literal> = paramètre de tolérance (de l'ordre de <literal>%eps</literal> par défaut). + Le rang <literal>rk</literal> de <literal>A</literal> est considéré égal au nombre de ses valeurs singulières plus grandes que <literal>norm(A)*tol</literal>. + </para> + <para> + Si A est symétrique, <literal>fullrf</literal> renvoie <literal>M=Q'</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[Q,M]=fullrf(A); +norm(Q*M-A,1) +[X,d]=rowcomp(A);Y=X'; +svd([A,Y(:,1:d),Q]) // Im(Q) = Im(A) = Im(Y(:,1:2)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/kernel/fullrfk.xml b/modules/linear_algebra/help/fr_FR/kernel/fullrfk.xml new file mode 100755 index 000000000..12336d7bb --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/kernel/fullrfk.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="fullrfk"> + <refnamediv> + <refname>fullrfk</refname> + <refpurpose>factorisation de rang plein de A^k </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Q,M]=fullrfk(A,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k </term> + <listitem> + <para>entier + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M </term> + <listitem> + <para>matrices réelles ou complexes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Cette fonction calcule la factorisation de rang plein de <literal>A^k</literal> : <literal>fullrfk</literal> renvoie <literal>Q</literal> et <literal>M</literal> telles que <literal>A^k = Q*M</literal> + avec Im(<literal>Q</literal>)=Im(<literal>A^k</literal>) et ker(<literal>M</literal>)=ker(<literal>A^k</literal>), + <literal>Q</literal> de rang maximal, et les lignes de <literal>M</literal> sont linéairement indépendantes, + </para> + <para> + Pour <literal>k=1</literal>, <literal>fullrfk</literal> est équivalent à <literal>fullrf</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3); +norm(Bk*Ck-A^3,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="range">range</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/kernel/kernel.xml b/modules/linear_algebra/help/fr_FR/kernel/kernel.xml new file mode 100755 index 000000000..9cf413739 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/kernel/kernel.xml @@ -0,0 +1,96 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="kernel"> + <refnamediv> + <refname>kernel</refname> + <refpurpose>noyau</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>W=kernel(A [,tol,[,flag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe (pleine ou creuse) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para>chaîne de caractères + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>W </term> + <listitem> + <para>matrice régulière + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>W=kernel(A)</literal> calcule le noyau de <literal>A</literal>, et <literal>size(W,2)</literal> est la nullité de A. + Les colonnes de <literal>W</literal> forment une base du noyau de <literal>A</literal>. + Si A est régulière, alors W=[]. + </para> + <para> + <literal>flag</literal> et <literal>tol</literal> sont des paramètres optionnels : <literal>flag = 'qr'</literal> + or <literal>'svd'</literal> (<literal>'svd'</literal> par défaut). + </para> + <para> + <literal>tol</literal> = paramètre de tolérance (de l'ordre de <literal>%eps</literal> par défaut). + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,1)*rand(1,3); +A*kernel(A) +A=sparse(A); +clean(A*kernel(A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="linsolve">linsolve</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/kernel/range.xml b/modules/linear_algebra/help/fr_FR/kernel/range.xml new file mode 100755 index 000000000..e7b6aa6ef --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/kernel/range.xml @@ -0,0 +1,95 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="range"> + <refnamediv> + <refname>range</refname> + <refpurpose>Image de A^k </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[X,dim]=range(A,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle carrée</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k </term> + <listitem> + <para>entier non négatif, La valeur par défaut est 1</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice réelle orthonormale.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para>entier (dimension du sous-espace image)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Calcul de l'image de <literal>A^k</literal>; les <literal>dim</literal> + premières colonnes de <literal>X</literal> forment une base de + <literal>A^k</literal>. Les dernières lignes de <literal>X</literal> forment une + base de l'orthogonal de l'image. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(4,2)*rand(2,4); // Matrice de rang 2. +[X,dim]=range(A,1);dim // Calcul de l'image + +y1=A*rand(4,1); // un vecteur dans l'image de A +y2=rand(4,1); // un vecteur qui n'est pas dans l'image +norm(X(dim+1:$,:)*y1) // les derniéres composante sont nulles, y1 est dans l'image +norm(X(dim+1:$,:)*y2) // Les dernieres composantes ne sont pas nulles + +I=X(1:dim,:)' // I une base de l'image +coeffs=X(1:dim,:)*y1 // les composante de y1 dans la base I + +norm(I*coeffs-y1) // test + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + La fonction <literal>range</literal> est basée sue la fonction <link linkend="rowcomp">rowcomp</link> + qui utilise la décomposition <link linkend="svd">svd</link>. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/kernel/rowcomp.xml b/modules/linear_algebra/help/fr_FR/kernel/rowcomp.xml new file mode 100755 index 000000000..bb071feae --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/kernel/rowcomp.xml @@ -0,0 +1,124 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="rowcomp"> + <refnamediv> + <refname>rowcomp</refname> + <refpurpose>compression de lignes, image </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[W,rk]=colcomp(A [,flag [,tol]])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para>chaîne de caractères optionnelle qui peut prendre les valeurs + <literal>'svd'</literal> ou <literal>'qr'</literal>. La valeur par + défaut est <literal>sqrt(%eps)*norm(A,1)</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel non négatif. La valeur par + défaut est <literal>sqrt(%eps)*norm(A,1)</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>W </term> + <listitem> + <para>matrice carrée régulière (matrice de changement de base) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para> + entier (rang de"<literal>A</literal>). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Compression des colonnes de <literal>A</literal>. <literal>Ac = W*A</literal> est à + lignes compressées, c'est à dire + <literal>Ac=[Af;0]</literal> et les lignes de <literal>Af</literal> sont linéairement + indépendantes. + </para> + <para> + <literal>flag</literal> et <literal>tol</literal> sont des paramètres optionnels : + <literal>flag = 'qr'</literal> ou <literal>'svd'</literal> + (<literal>'svd'</literal> par défaut). + </para> + <para> + <literal>tol</literal> = paramètre de tolérance (de l'ordre de + <literal>%eps</literal> par défaut). + </para> + <para> + Les <literal>rk</literal> premières colonnes de <literal>W'</literal> forment + une base de l'image de <literal>A</literal>. + </para> + <para> + Un vecteur non nul <literal>x</literal> appartient à Im(<literal>A</literal>) si + <literal>W*x</literal> est à lignes compressées en accord avec <literal>Ac</literal> + c'est à dire que la norme de ses dernières composantes est nulle (à + la précision machine) par rapport à ses rk premières composantes. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); // 4 vecteurs colonne dont 2 indépendants +[X,dim]=rowcomp(A);Xp=X'; +svd([Xp(:,1:dim),A]) // Im(A) = Im(Xp(:,1:dim) +x=A*rand(4,1); // x appartient à Im(A) +y=X*x +norm(y(dim+1:$))/norm(y(1:dim)) // la norme est petite + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + La fonction <literal>rowcomp</literal> est basée sur les décompositions + <link linkend="svd">svd</link> ou <link linkend="qr">qr</link>. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/linear/CHAPTER b/modules/linear_algebra/help/fr_FR/linear/CHAPTER new file mode 100755 index 000000000..7d9d9cf49 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/linear/CHAPTER @@ -0,0 +1,2 @@ +title = Linear Equations + diff --git a/modules/linear_algebra/help/fr_FR/linear/chol.xml b/modules/linear_algebra/help/fr_FR/linear/chol.xml new file mode 100755 index 000000000..f155bb42c --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/linear/chol.xml @@ -0,0 +1,80 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="chol"> + <refnamediv> + <refname>chol</refname> + <refpurpose>Factorisation de Cholesky </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[R]=chol(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Si <literal>X</literal> est hermitienne (symétrique dans le cas réel) définie positive, alors <literal>R = chol(X)</literal> renvoie une matrice triangulaire supérieure <literal>R</literal> telle que <literal>R'*R = X</literal>. + </para> + <para> + <literal>chol(X)</literal> utilise uniquement la partie triangulaire supérieure de <literal>X</literal> dont la + partie triangulaire inférieure est supposée être la transposée (transposée conjuguée dans le cas complexe). + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +W=rand(5,5)+%i*rand(5,5); +X=W*W'; +R=chol(X); +norm(R'*R-X) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="spchol">spchol</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + La décomposition de Cholesky est basée sur les routines Lapack + DPOTRF pour les matrices réelles et ZPOTRF pour le cas complexe. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/linear/inv.xml b/modules/linear_algebra/help/fr_FR/linear/inv.xml new file mode 100755 index 000000000..2441ede3a --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/linear/inv.xml @@ -0,0 +1,112 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="inv"> + <refnamediv> + <refname>inv</refname> + <refpurpose>inverse d'une matrice </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>inv(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice carrée réelle, complexe, polynomiale ou rationnelle, + liste de type "syslin" + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>inv(X)</literal> est l'inverse de la matrice carrée + <literal>X</literal>. Un message de mise en garde est affiché si <literal>X</literal> + est mal équilibrée (termes très petits et termes très grands) ou + singulière à la précision machine. + </para> + <para> + Pour les matrices polynomiales ou rationnelles, <literal>inv(X)</literal> est + équivalent à <literal>invr(X)</literal>. + </para> + <para> + Pour les systèmes dynamiques linéaires sous forme de leur représentation + d'état (liste de type <literal>syslin</literal>), <literal>inv(X)</literal> est + équivalent à <literal>invsyslin(X)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);inv(A)*A + +x=poly(0,'x'); +A=[x,1,x;x^2,2,1+x;1,2,3];inv(A)*A + +A=[1/x,2;2+x,2/(1+x)] +inv(A)*A + +A=ssrand(2,2,3); +W=inv(A)*A +clean(ss2tf(W)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="slash">slash</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="coff">coff</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + La fonction <literal>inv</literal> pour les matrices de nombres est basée + sur les routines Lapack : + DGETRF, DGETRI pour les matrices réelles et ZGETRF, ZGETRI pour le + cas complexe. + Pour les matrices de polynomes et de fractions rationnelles + <literal>inv</literal> est basée sur la fonction Scilab <literal>invr</literal>. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/linear/linsolve.xml b/modules/linear_algebra/help/fr_FR/linear/linsolve.xml new file mode 100755 index 000000000..d7d5c3bc2 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/linear/linsolve.xml @@ -0,0 +1,121 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="linsolve"> + <refnamediv> + <refname>linsolve</refname> + <refpurpose>solveur d'équation linéaire </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para> + une matrice réelle <literal>na x ma</literal> (éventuellement creuse) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>b </term> + <listitem> + <para> + un vecteur <literal>na x 1</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x0 </term> + <listitem> + <para>un vecteur réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>kerA </term> + <listitem> + <para> + une matrice réelle <literal>ma x k </literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>linsolve</literal> donne toutes les solutions de <literal> A*x+b=0</literal>. + </para> + <para> + <literal>x0</literal> est une solution particulière (s'il en existe une) et <literal>kerA</literal> est le noyau de <literal>A</literal>. Tout vecteur de la forme <literal>x=x0+kerA*w</literal> avec <literal>w</literal> quelconque vérifie + <literal> A*x+b=0</literal>. + </para> + <para> + Si un <literal>x0</literal> compatible est donné en entrée, <literal>x0</literal> est renvoyé. Dans le cas contraire un <literal>x0</literal> compatible, s'il en existe un, est renvoyé. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,8); +b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b // b compatible +b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b // b incompatible +A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b // x est unique + +// Une comparaison des différentes méthode de résolution de systèmes linéaire creux + +[A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa"); + +b = zeros(size(A,1),1); + +tic(); +res = umfpack(A,'\',b); +mprintf('\ntemps nécessaire à la résolution du système avec umfpack: %.3f\n',toc()); + +tic(); +res = linsolve(A,b); +mprintf('\ntemps nécessaire à la résolution du système avec linsolve: %.3f\n',toc()); + +tic(); +res = A\b; +mprintf('\ntemps nécessaire à la résolution du système avec l''opérateur backslash: %.3f\n',toc()); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="inv">inv</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="im_inv">im_inv</link> + </member> + <member> + <link linkend="umfpack">umfpack</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/linear/lu.xml b/modules/linear_algebra/help/fr_FR/linear/lu.xml new file mode 100755 index 000000000..498ac9713 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/linear/lu.xml @@ -0,0 +1,119 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lu"> + <refnamediv> + <refname>lu</refname> + <refpurpose>factorisation LU </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[L,U]= lu(A) + [L,U,E]= lu(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice carrée réelle ou complexe (m x n). + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>L,U </term> + <listitem> + <para>matrices carrées réelles ou complexes (n x n). + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E </term> + <listitem> + <para>une matrice de permutation. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[L,U]= lu(A)</literal> calcule deux matrices <literal>L</literal> et + <literal>U</literal> telles que <literal>A = L*U</literal> avec <literal>U</literal> + triangulaire supérieure et <literal>L</literal> triangulaire inférieure + à une permutation des lignes près. + </para> + <para> + Si <literal>A</literal> est de rang <literal>k</literal>, les lignes + <literal>k+1</literal> à <literal>n</literal> de <literal>U</literal> sont nulles. + </para> + <para> + </para> + <para> + <literal>[L,U,E]= lu(A)</literal> calcule trois matrices <literal>L</literal>, + <literal>U</literal> et <literal>E</literal> telles que <literal>E*A = L*U</literal> + avec <literal>U</literal> triangulaire supérieure, <literal>L</literal> + triangulaire inférieure et <literal>E</literal> une matrice de + permutation. + </para> + <para> + Si <literal>A</literal> est une matrice réelle, il est possible en + utilisant <literal>lufact</literal> et <literal>luget</literal> + d'obtenir les matrices de permutations et quand + <literal>A</literal> n'est pas inversible la compression des + colonnes de la matrice <literal>L</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +a=rand(4,4); +[l,u]=lu(a) +norm(l*u-a) + +[h,rk]=lufact(sparse(a)) // lufact fonctionne avec des matrices creuses +[P,L,U,Q]=luget(h); +ludel(h) +P=full(P);L=full(L);U=full(U);Q=full(Q); +norm(P*L*U*Q-a) // P,Q sont des matrices de permutation + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para>La décomposition LU est basée sur les routines Lapack DGETRF pour + les matrices réelles et ZGETRF pour le cas complexe. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/linear/pinv.xml b/modules/linear_algebra/help/fr_FR/linear/pinv.xml new file mode 100755 index 000000000..70b1d11ec --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/linear/pinv.xml @@ -0,0 +1,85 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="pinv"> + <refnamediv> + <refname>pinv</refname> + <refpurpose>pseudo-inverse </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>pinv(A,[tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>X= pinv(A)</literal> renvoie une matrice <literal>X</literal> de mêmes dimensions que <literal>A'</literal> telle que : + </para> + <para> + <literal>A*X*A = A, X*A*X = X</literal> avec + <literal>A*X</literal> et <literal>X*A</literal> Hermitiennes. + </para> + <para> + Le calcul est basé sur une décomposition en valeurs singulières et + les valeurs singulières plus petites qu'une tolérance donnée + sont considérées comme nulles : pour cela utiliser la syntaxe + <literal>X=pinv(A,tol)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); +norm(A*pinv(A)*A-A,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + La fonction <literal>pinv</literal> est basée sur la decomposition en valeurs + singulières (fonction Scilab <literal>svd</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/linear/qr.xml b/modules/linear_algebra/help/fr_FR/linear/qr.xml new file mode 100755 index 000000000..3cb813d07 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/linear/qr.xml @@ -0,0 +1,194 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="qr"> + <refnamediv> + <refname>qr</refname> + <refpurpose>factorisation QR </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Q,R]=qr(X [,"e"]) + [Q,R,E]=qr(X [,"e"]) + [Q,R,rk,E]=qr(X [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel positif + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q </term> + <listitem> + <para>matrice carrée unitaire + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>R </term> + <listitem> + <para> + matrice de même dimensions que <literal>X</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E </term> + <listitem> + <para>matrice de permutation + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para> + entier (rang de <literal>X</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[Q,R] = qr(X)</literal> renvoie une matrice triangulaire supérieure + <literal>R</literal> de même + dimensions que <literal>X</literal> et une matrice carrée othogonale + (unitaire dans le cas complexe) <literal>Q</literal> telles que + <literal>X = Q*R</literal>. + + <literal>[Q,R] = qr(X,"e")</literal> renvoie une decomposition de + taille réduite: si <literal>X</literal> est une matrice <literal>m x + n + </literal> + avec <literal>m > n</literal> alors seulement les + <literal>n</literal> premières colonnes de <literal>Q</literal> sont calculées + ainsi que les <literal>n</literal> premières lignes de + <literal>R</literal>. + </para> + <para> + Il découle de <literal>Q*R = X</literal> que la + <literal>k</literal>ième colonne de <literal>X</literal> peut s'exprimer comme + une combinaison linéaire des <literal>k</literal> premieres colonnes de + <literal>Q</literal> (avec les coefficients <literal>R(1,k), ..., + R(k,k) + </literal> + .Les <literal>k</literal> premieres colonnes de + <literal>Q</literal> forment une base orthogonale du sous espace généré + par les Les <literal>k</literal> premieres colonnes de + <literal>X</literal>. Si la colonne <literal>k</literal> de <literal>X</literal> est + une combinaison linéaire des <literal>p</literal> premiéres colonnes de + <literal>X</literal> alors les éléments <literal>R(p+1,k), ..., + R(k,k) + </literal> + sont nuls. Dans cette situation <literal>R</literal> est + une matrice trapézoidale supérieure. Si <literal>X</literal> est de rang + <literal>rk</literal> alors les lignes <literal>R(rk+1,:), R(rk+2,:), + ... + </literal> + sont nulles. + + </para> + <para> + <literal>[Q,R,E] = qr(X)</literal> renvoie une matrice de permutations (de + colonnes) <literal>E</literal>, + une matrice triangulaire supérieure <literal>R</literal> dont les + éléments diagonaux sont classés par ordre décroissant et une + matrice unitaire <literal>Q</literal> telles que <literal>X*E = Q*R</literal>. + si <literal>rk</literal> est le rang de <literal>X</literal> les + <literal>rk</literal> premiers éléménts diagonaux de <literal>R</literal> sont + tous non nuls. <literal>[Q,R,E] = qr(X,"e")</literal> renvoie une decomposition de + taille réduite: si <literal>X</literal> est une matrice <literal>m x + n + </literal> + avec <literal>m > n</literal> alors seulement les + <literal>n</literal> premières colonnes de <literal>Q</literal> sont calculées + ainsi que les <literal>n</literal> premières lignes de + <literal>R</literal>. + </para> + <para> + <literal>[Q,R,rk,E] = qr(X [,tol])</literal>renvoie de plus + <literal>rk</literal> =rang estimé de <literal>X</literal>. + Plus précisément, + <literal>rk</literal> est le nombre d'éléments diagonaux de + <literal>R</literal> supérieurs à <literal>tol</literal>. La valeur par défaut + de <literal>tol</literal> est <literal>R(1,1)*%eps*max(size(R))</literal> + </para> + <para> + renvoie <literal>rk</literal> = rang estimé de <literal>X</literal>. Ici, + <literal>rk</literal> est le nombre d'éléments diagonaux de <literal>R</literal> + supérieurs à <literal>R(1,1)*%eps*max(size(R)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +// QR factorization, generic case +// X is tall (full rank) +X=rand(5,2);[Q,R]=qr(X); [Q'*X R] + +//X is fat (full rank) +X=rand(2,3);[Q,R]=qr(X); [Q'*X R] + +//Column 4 of X is a linear combination of columns 1 and 2: +X=rand(8,5);X(:,4)=X(:,1)+X(:,2); [Q,R]=qr(X); R, R(:,4) + +//X has rank 2, rows 3 to $ of R are zero: +X=rand(8,2)*rand(2,5);[Q,R]=qr(X); R + +//Evaluating the rank rk: column pivoting ==> rk first +//diagonal entries of R are non zero : +A=rand(5,2)*rand(2,5); +[Q,R,rk,E] = qr(A,1.d-10); +norm(Q'*A-R) +svd([A,Q(:,1:rk)]) //span(A) =span(Q(:,1:rk)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para>La décomposition QR est basée sur les routines Lapack DGEQRF, DGEQPF, + DORGQR pour les matrices réelles et ZGEQRF, ZGEQPF, ZORGQR pour le cas + complexe. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/markov/CHAPTER b/modules/linear_algebra/help/fr_FR/markov/CHAPTER new file mode 100755 index 000000000..deb78b04a --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/markov/CHAPTER @@ -0,0 +1,2 @@ +title = Matrices de Markov + diff --git a/modules/linear_algebra/help/fr_FR/matrix/CHAPTER b/modules/linear_algebra/help/fr_FR/matrix/CHAPTER new file mode 100755 index 000000000..bb89125cd --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/matrix/CHAPTER @@ -0,0 +1,2 @@ +title = Matrix Analysis + diff --git a/modules/linear_algebra/help/fr_FR/matrix/cond.xml b/modules/linear_algebra/help/fr_FR/matrix/cond.xml new file mode 100755 index 000000000..7c53f27ac --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/matrix/cond.xml @@ -0,0 +1,160 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2012 - Scilab Enterprises - Adeline CARNIS + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="cond"> + <refnamediv> + <refname>cond</refname> + <refpurpose>conditionnement </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis> + c = cond(X) + c = cond(X, p) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para> + matrice réelle ou complexe. Si c = cond(X, p), X doit être une matrice carrée réelle ou complexe. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>p</term> + <listitem> + <para>scalaire ou chaine de caractères (valeur par défaut p = 2).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>c</term> + <listitem> + <para>scalaire réel.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term>c = cond(X)</term> + <listitem> + <para> + retourne le conditionnement en norme 2.<literal>cond(X)</literal> est le quotient entre + la plus grande et la plus petite valeur singulière de <literal>X</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>c = cond(X, p)</term> + <listitem> + <para> + retourne le conditionnement en norme p : <literal>norm(X, p) * norm(inv(X), p)</literal>. + Si <literal>p</literal> est spécifié, <literal>p</literal> est égal soit à : + </para> + <itemizedlist> + <listitem> + <para> + p = 1. <literal>cond(X, p)</literal> retourne le conditionnement en norme 1. + </para> + </listitem> + <listitem> + <para> + p = 2. <literal>cond(X, p)</literal> retourne le conditionnement en norme 2. + </para> + </listitem> + <listitem> + <para> + p = %inf or 'inf'. <literal>cond(X, p)</literal> retourne le conditionnement en norme infinie. + </para> + </listitem> + <listitem> + <para> + p = 'fro'. <literal>cond(X, p)</literal> retourne le conditionnement en norme de Frobenius. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"> + <![CDATA[ +A=testmatrix('hilb',6); +// conditionnement en norme 2 +cond(A) +cond(A, 2) + +// conditionnement en norme 1 +cond(A, 1) + +// conditionnement en norme infinie +cond(A, %inf) + +// conditionnement en norme de Frobenius +cond(A, 'fro') + ]]> + </programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="rcond">rcond</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="norm">norm</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revdescription> + <para> + Appel de <literal>cond(X)</literal>, où <literal>X</literal> est une matrice non + carrée, est maintenant gérée. Par exemple : + </para> + <programlisting role=""> + <![CDATA[ +X = [1 0; 1 -1; 0 1]; +cond(X) + ]]> + </programlisting> + <para> + Appel de <literal>cond(X, p)</literal> permet de calculer le contionnement + en norme p. Par exemple : + </para> + <programlisting role=""> + <![CDATA[ +X = [1 -6 0; 1 0 -4;1 0 2]; +cond(X, 1) // conditionnement en norme 1 (p = 1) + ]]> + </programlisting> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/matrix/det.xml b/modules/linear_algebra/help/fr_FR/matrix/det.xml new file mode 100755 index 000000000..441b723c5 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/matrix/det.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="det"> + <refnamediv> + <refname>det </refname> + <refpurpose>déterminant </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>det(X) + [e,m]=det(X) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice carrée réelle ou complexe (creuse ou pleine), polynomiale ou rationnelle + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>m </term> + <listitem> + <para>nombre réel ou complexe, mantisse du déterminant en base 10 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>e </term> + <listitem> + <para>entier, exposant du déterminant en base 10 + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>det(X)</literal> ( <literal>m*10^e</literal> ) est le déterminant de la matrice carrée <literal>X</literal>. + </para> + <para> + Pour les matrices polynomiales <literal>det(X)</literal> est équivalent à <literal>determ(X)</literal>. + </para> + <para> + Pour les matrices rationnelles <literal>det(X)</literal> est équivalent à <literal>detr(X)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +det([x,1+x;2-x,x^2]) +w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w) // zéros du système linéaire +A=rand(3,3); +det(A), prod(spec(A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="determ">determ</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + Le calcul du determinant est basé sur les routines Lapack : + DGETRF pour les matrices réelles et ZGETRF pour le cas complexe. + </para> + <para> + Concernant le cas des matrices creuses, le calcul du déterminant est effectué + à partir de la décomposition LU de la librairie umfpack. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/matrix/orth.xml b/modules/linear_algebra/help/fr_FR/matrix/orth.xml new file mode 100755 index 000000000..1c190bc72 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/matrix/orth.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="orth"> + <refnamediv> + <refname>orth</refname> + <refpurpose>calcul d'une base orthogonale </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>Q=orth(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>Q=orth(A)</literal> renvoie <literal>Q</literal>, une base + orthogonale de l'image de <literal>A</literal>. Im(<literal>Q</literal>) + = Im(<literal>A</literal>) et <literal>Q'*Q = I</literal>. + </para> + <para> + Le nombre de colonnes de <literal>Q</literal> est égal au rang de + <literal>A</literal>, comme déterminé par l'algorithme QR. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,4); +[X,dim]=rowcomp(A);X=X'; +svd([orth(A),X(:,1:dim)]) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="range">range</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/matrix/rank.xml b/modules/linear_algebra/help/fr_FR/matrix/rank.xml new file mode 100755 index 000000000..06761fea1 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/matrix/rank.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="rank"> + <refnamediv> + <refname>rank</refname> + <refpurpose>rang </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[i]=rank(X) + [i]=rank(X,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol </term> + <listitem> + <para>nombre réel positif + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal> rank(X)</literal> calcule le rang "numérique" de + <literal>X</literal> c'est à dire le nombre de ses valeurs + singulières supérieures à <literal>norm(size(X),'inf') * + norm(X) * %eps + </literal> + . + </para> + <para> + <literal>rank(X,tol)</literal> est le nombre de valeurs singulières de + <literal>X</literal> supérieures à <literal>tol</literal>. + </para> + <para> + <note> + Notez que la valeur par défaut de <literal>tol</literal> est + proportionnelle à <literal>norm(X)</literal>. Par exemple + </note> + </para> + <para> + <literal>rank([1.d-80,0;0,1.d-80])</literal> vaut 2 !. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +rank([1.d-80,0;0,1.d-80]) +rank([1,0;0,1.d-80]) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="lu">lu</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/matrix/rcond.xml b/modules/linear_algebra/help/fr_FR/matrix/rcond.xml new file mode 100755 index 000000000..40f871b7f --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/matrix/rcond.xml @@ -0,0 +1,74 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="rcond"> + <refnamediv> + <refname>rcond</refname> + <refpurpose>estimation de l'inverse du conditionnement </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>rcond(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice carrée réelle ou complexe + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>rcond(X)</literal> est une estimation de l'inverse du conditionnement de <literal>X</literal> pour la norme l_1. + </para> + <para> + Si <literal>X</literal> est bien conditionnée, <literal>rcond(X)</literal> est proche 1. + Sinon, <literal>rcond(X)</literal> est proche de 0. + </para> + <para> + <literal>[r,z]=rcond(X)</literal> renvoie <literal>rcond(X)</literal> dans + <literal>r</literal> et renvoie aussi <literal>z</literal> tel que <literal>norm(X*z,1) = r*norm(X,1)*norm(z,1)</literal> + </para> + <para> + Ainsi, si <literal>rcond</literal> est très petit <literal>z</literal> est un vecteur se trouvant dans le noyau de X. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=diag([1:10]); +rcond(A) +A(1,1)=0.000001; +rcond(A) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="cond">cond</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/matrix/trace.xml b/modules/linear_algebra/help/fr_FR/matrix/trace.xml new file mode 100755 index 000000000..f37190fa4 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/matrix/trace.xml @@ -0,0 +1,58 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="trace"> + <refnamediv> + <refname>trace </refname> + <refpurpose>trace d'une matrice </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>trace(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice carrée, réelle, complexe, polynomiale ou rationnelle. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>trace(X)</literal> calcule la trace de <literal>X</literal>. + </para> + <para> + Identique à <literal>sum(diag(X))</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3); +trace(A)-sum(spec(A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/pencil/CHAPTER b/modules/linear_algebra/help/fr_FR/pencil/CHAPTER new file mode 100755 index 000000000..2c9344edc --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/pencil/CHAPTER @@ -0,0 +1,2 @@ +title = Matrice compagnon + diff --git a/modules/linear_algebra/help/fr_FR/pencil/companion.xml b/modules/linear_algebra/help/fr_FR/pencil/companion.xml new file mode 100755 index 000000000..80fc6d410 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/pencil/companion.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="companion"> + <refnamediv> + <refname>companion</refname> + <refpurpose>matrice compagnon </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>A=companion(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p </term> + <listitem> + <para>polynôme ou vecteur de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice carrée + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Renvoie une matrice <literal>A</literal> dont le polynôme caractéristique est + <literal>p</literal> si <literal>p</literal> est unitaire (le coefficient de plus haut degré est égal à un). Si <literal>p</literal> n'est pas unitaire + le polynôme caractéristique de <literal>A</literal> est égal à + <literal>p/c</literal> où <literal>c</literal> est le coefficient de plus haut degré de <literal>p</literal>. + </para> + <para> + Si <literal>p</literal> est un vecteur de polynômes unitaires, <literal>A</literal> est bloc-diagonale, + et le polynôme caractéristique du i-ème bloc est égal à <literal>p(i)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=poly([1,2,3,4,1],'s','c') +det(s*eye()-companion(p)) +roots(p) +spec(companion(p)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="randpencil">randpencil</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/pencil/glever.xml b/modules/linear_algebra/help/fr_FR/pencil/glever.xml new file mode 100755 index 000000000..784429a4f --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/pencil/glever.xml @@ -0,0 +1,123 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="glever"> + <refnamediv> + <refname>glever</refname> + <refpurpose>inverse d'un faisceau de matrices </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>E, A </term> + <listitem> + <para>matrices carrées réelles de même dimensions + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>s </term> + <listitem> + <para> + chaîne de caractères (indéterminée des polynômes, '<literal>s</literal>' par défaut ) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Bfs,Bis </term> + <listitem> + <para>deux matrices polynomiales + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>chis </term> + <listitem> + <para>polynôme + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Calcul de + </para> + <para> + (s*E-A)^-1 + </para> + <para> + par l'algorithme généralisé de Leverrier pour un faisceau de matrices. + </para> + <programlisting role=""><![CDATA[ +(s*E-A)^-1 = (Bfs/chis) - Bis. + ]]></programlisting> + <para> + <literal>chis</literal> = polynôme caractéristique (à une constante multiplicative près). + </para> + <para> + <literal>Bfs</literal> = matrice polynomiale de numérateurs + </para> + <para> + <literal>Bis</literal> + = matrice polynomiale ( - développement de <literal>(s*E-A)^-1</literal> à l'infini). + </para> + <para> + Noter le signe - devant <literal>Bis</literal>. + </para> + <para> + </para> + </refsection> + <refsection> + <title>Attention</title> + <para> + Cette fonction utilise <literal>cleanp</literal> pour simplifier <literal>Bfs,Bis</literal> et <literal>chis</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1]; +[Bfs,Bis,chis]=glever(F) +inv(F)-((Bfs/chis) - Bis) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="rowshuff">rowshuff</link> + </member> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/pencil/lyap.xml b/modules/linear_algebra/help/fr_FR/pencil/lyap.xml new file mode 100755 index 000000000..68e7a0eca --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/pencil/lyap.xml @@ -0,0 +1,82 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lyap"> + <refnamediv> + <refname>lyap </refname> + <refpurpose>Equation de Lyapunov </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[X]=lyap(A,C,flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A, C </term> + <listitem> + <para> + matrices réelles, <literal>C</literal> doit être symétrique + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para>chaîne de caractères, 'c' ou 'd' + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>X= lyap(A,C,flag)</literal> résout l'équation matricielle de + Lyapunov en temps continu ou discret + </para> + <programlisting role=""><![CDATA[ +A'*X + X*A = C ( flag = 'c' ) +A'*X*A - X = C ( flag = 'd' ) + ]]></programlisting> + <para> + Une solution unique existe si <literal>A</literal> n'a pas de valeur propre + sur l'axe imaginaire (<literal>flag='c'</literal>) ou si 1 n'est pas + valeur propre de <literal>A</literal> (<literal>flag='d'</literal>). + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(4,4);C=rand(A);C=C+C'; +X=lyap(A,C,'c'); +A'*X + X*A -C +X=lyap(A,C,'d'); +A'*X*A - X -C + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sylv">sylv</link> + </member> + <member> + <link linkend="ctr_gram">ctr_gram</link> + </member> + <member> + <link linkend="obs_gram">obs_gram</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/proj.xml b/modules/linear_algebra/help/fr_FR/proj.xml new file mode 100755 index 000000000..5bd02b507 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/proj.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="proj"> + <refnamediv> + <refname>proj</refname> + <refpurpose>projection </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>P = proj(X1,X2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X1,X2 </term> + <listitem> + <para>deux matrices réelles avec un nombre identique de colonnes. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P </term> + <listitem> + <para> + matrice réelle de projection (<literal>P^2=P</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>P</literal> est la projection sur <literal>X2</literal> parallèlement à <literal>X1</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +X1=rand(5,2);X2=rand(5,3); +P=proj(X1,X2); +norm(P^2-P,1) +trace(P) // il s'agit de dim(X2) +[Q,M]=fullrf(P); +svd([Q,X2]) // Im(Q) = Im(X2) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="projspec">projspec</link> + </member> + <member> + <link linkend="orth">orth</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/state_space/CHAPTER b/modules/linear_algebra/help/fr_FR/state_space/CHAPTER new file mode 100755 index 000000000..9f51d7351 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/state_space/CHAPTER @@ -0,0 +1 @@ +title = State-Space Matrices diff --git a/modules/linear_algebra/help/fr_FR/state_space/coff.xml b/modules/linear_algebra/help/fr_FR/state_space/coff.xml new file mode 100755 index 000000000..e69a389ef --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/state_space/coff.xml @@ -0,0 +1,99 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="coff"> + <refnamediv> + <refname>coff</refname> + <refpurpose>résolvante (méthode des cofacteurs) </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[N,d]=coff(M [,var])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>M </term> + <listitem> + <para>matrice carrée réelle + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>var </term> + <listitem> + <para>chaîne de caractères (indéterminée des polynômes) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>N </term> + <listitem> + <para> + matrice de polynômes (de même taille que <literal>M</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>d </term> + <listitem> + <para> + polynôme (polynôme caractéristique de M : <literal>poly(M,var)</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>coff</literal> calcule R=<literal>(s*eye()-M)^-1</literal> pour <literal>M</literal> une matrice réelle. + R est donnée par <literal>N/d</literal>. + </para> + <para> + <literal>N</literal> = matrice des numérateurs (polynômes). + </para> + <para> + <literal>d</literal> = dénominateur commun. + </para> + <para> + <literal>var</literal> chaîne de caractères (indéterminée des polynômes, '<literal>s</literal>' par défaut) + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +M=[1,2;0,3]; +[N,d]=coff(M) +N/d +inv(%s*eye()-M) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="ss2tf">ss2tf</link> + </member> + <member> + <link linkend="nlev">nlev</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/state_space/nlev.xml b/modules/linear_algebra/help/fr_FR/state_space/nlev.xml new file mode 100755 index 000000000..f309b8233 --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/state_space/nlev.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="nlev"> + <refnamediv> + <refname>nlev</refname> + <refpurpose>Algorithme de Leverrier </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[num,den]=nlev(A,z [,rmax])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle carrée + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>z </term> + <listitem> + <para>chaîne de caractères + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rmax </term> + <listitem> + <para> + paramètre optionnel (voir <literal>bdiag</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[num,den]=nlev(A,z [,rmax])</literal> calcule + <literal>(z*eye()-A)^(-1)</literal> par bloc diagonalisation de + <literal>A</literal> suivie de l'algorithme de Leverrier sur chaque + bloc. + </para> + <para> + Cet algorithme est plus efficace que l'algorithme de + Leverrier seul, mais il n'est toujours pas parfait ! + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);x=poly(0,'x'); +[NUM,den]=nlev(A,'x') +clean(den-poly(A,'x')) +clean(NUM/den-inv(x*eye()-A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="coff">coff</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="ss2tf">ss2tf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/fr_FR/subspaces/CHAPTER b/modules/linear_algebra/help/fr_FR/subspaces/CHAPTER new file mode 100755 index 000000000..90541a88e --- /dev/null +++ b/modules/linear_algebra/help/fr_FR/subspaces/CHAPTER @@ -0,0 +1,2 @@ +title = Sous-espaces + diff --git a/modules/linear_algebra/help/ja_JP/addchapter.sce b/modules/linear_algebra/help/ja_JP/addchapter.sce new file mode 100755 index 000000000..4b62a3ac7 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Linear Algebra",SCI+"/modules/linear_algebra/help/ja_JP",%T); + diff --git a/modules/linear_algebra/help/ja_JP/eigen/CHAPTER b/modules/linear_algebra/help/ja_JP/eigen/CHAPTER new file mode 100755 index 000000000..88f8bc42b --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/CHAPTER @@ -0,0 +1,2 @@ +title = Eigenvalue and Singular Value + diff --git a/modules/linear_algebra/help/ja_JP/eigen/balanc.xml b/modules/linear_algebra/help/ja_JP/eigen/balanc.xml new file mode 100755 index 000000000..b150c2ea6 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/balanc.xml @@ -0,0 +1,203 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="balanc"> + + <refnamediv> + + <refname>balanc</refname> + + <refpurpose>行列ã¾ãŸã¯ãƒšãƒ³ã‚·ãƒ«ã®å¹³è¡¡åŒ–</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Ab,X]=balanc(A) + + [Eb,Ab,X,Y]=balanc(E,A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A: </term> + + <listitem> + + <para>実数æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X: </term> + + <listitem> + + <para>å¯é€†ãªå®Ÿæ•°æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E: </term> + + <listitem> + + <para> + + 実数æ£æ–¹è¡Œåˆ— (<literal>A</literal>ã¨åŒã˜æ¬¡å…ƒ) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Y: </term> + + <listitem> + + <para>å¯é€†ãªå®Ÿæ•°æ£æ–¹è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + æ£æ–¹è¡Œåˆ—ã®æ¡ä»¶æ•°ã‚’改善ã™ã‚‹ãŸã‚ã«å¹³è¡¡åŒ–ã—ã¾ã™. + + </para> + + <para> + + <literal>[Ab,X] = balanc(A)</literal> ã¯, + + 以下ã®ã‚ˆã†ãªç›¸ä¼¼å¤‰æ›<literal>X</literal>を見ã¤ã‘ã¾ã™: + + </para> + + <para> + + <literal>Ab = inv(X)*A*X</literal>ãŒè¿‘似的ã«ç‰ã—ã„ + + 行ノルムãŠã‚ˆã³åˆ—ノルムを有ã™ã‚‹. + + </para> + + <para> + + 行列ペンシルã®å ´åˆ,平衡化ã¯ä¸€èˆ¬åŒ–固有値å•é¡Œã‚’改善ã™ã‚‹ã“ã¨ã«ã‚ˆã‚Š + + è¡Œã‚ã‚Œã¾ã™. + + </para> + + <para> + + <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> ã¯, + + <literal>Eb=inv(X)*E*Y, Ab=inv(X)*A*Y</literal> ã¨ãªã‚‹ã‚ˆã†ãª + + å·¦ãŠã‚ˆã³å³å¤‰æ› + + <literal>X</literal> ãŠã‚ˆã³ <literal>Y</literal> ã‚’è¿”ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>注æ„</title> + + <para> + + 平衡化ã¯é–¢æ•°<literal>bdiag</literal> ãŠã‚ˆã³ <literal>spec</literal> + + ã§è¡Œã‚ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=[1/2^10,1/2^10;2^10,2^10]; +[Ab,X]=balanc(A); +norm(A(1,:))/norm(A(2,:)) +norm(Ab(1,:))/norm(Ab(2,:)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="bdiag">bdiag</link> + + </member> + + <member> + + <link linkend="spec">spec</link> + + </member> + + <member> + + <link linkend="schur">schur</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/bdiag.xml b/modules/linear_algebra/help/ja_JP/eigen/bdiag.xml new file mode 100755 index 000000000..ba3a9117c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/bdiag.xml @@ -0,0 +1,189 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="bdiag"> + + <refnamediv> + + <refname>bdiag</refname> + + <refpurpose>ブãƒãƒƒã‚¯å¯¾è§’化, 一般化固有ベクトル</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rmax</term> + + <listitem> + + <para>実数</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Ab</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£å‰‡è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>bs</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <programlisting role=""><![CDATA[ +[Ab [,X [,bs]]]=bdiag(A [,rmax]) + ]]></programlisting> + + <para> + + ã¯,行列<literal>A</literal>ã®ãƒ–ãƒãƒƒã‚¯å¯¾è§’化を行ãªã„ã¾ã™. + + bs ã¯ãƒ–ãƒãƒƒã‚¯ã®æ§‹é€ (個々ã®ãƒ–ãƒãƒƒã‚¯ã®å¤§ãã•)を出力ã—ã¾ã™. + + <literal>X</literal> ã¯åŸºåº•å¤‰æ›ã§ã™. + + ã™ãªã‚ã¡, <literal>Ab = inv(X)*A*X</literal> ã¯ãƒ–ãƒãƒƒã‚¯å¯¾è§’ã§ã™. + + </para> + + <para> + + <literal>rmax</literal> ã¯<literal>X</literal>ã® + + æ¡ä»¶æ•°ã‚’制御ã—ã¾ã™; + + デフォルト値㯠<literal>A</literal> ã® l1ノルムã§ã™. + + </para> + + <para> + + (å˜åœ¨ã™ã‚‹å ´åˆ,)対角形å¼ã‚’å¾—ã‚‹ã«ã¯<literal>rmax</literal>ã« + + 大ããªå€¤ã‚’指定ã—ã¾ã™(例ãˆã°,<literal>rmax=1/%eps</literal>). + + 一般ã«(ランダムãªå®Ÿæ•°ã® Aã®å ´åˆ) ブãƒãƒƒã‚¯ã¯ (1x1) ãŠã‚ˆã³ (2x2) ã§, + + <literal>X</literal> ã¯å›ºæœ‰å€¤ã®è¡Œåˆ—ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +//実数ã®å ´åˆ: 1x1 ãŠã‚ˆã³ 2x2 ブãƒãƒƒã‚¯ +a=rand(5,5);[ab,x,bs]=bdiag(a);ab +//è¤‡ç´ æ•°ã®å ´åˆ: è¤‡ç´ æ•° 1x1 ブãƒãƒƒã‚¯ +[ab,x,bs]=bdiag(a+%i*0);ab + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="schur">schur</link> + + </member> + + <member> + + <link linkend="sylv">sylv</link> + + </member> + + <member> + + <link linkend="spec">spec</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/gschur.xml b/modules/linear_algebra/help/ja_JP/eigen/gschur.xml new file mode 100755 index 000000000..2f42eb262 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/gschur.xml @@ -0,0 +1,180 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="gschur"> + + <refnamediv> + + <refname>gschur</refname> + + <refpurpose> + + 一般化Schur分解. + + <emphasis role="bold">ã“ã®é–¢æ•°ã¯å»ƒæ¢ã•ã‚Œã¾ã—ãŸ.</emphasis> + + </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[As,Es]=gschur(A,E) + + [As,Es,Q,Z]=gschur(A,E) + + [As,Es,Z,dim] = gschur(A,E,flag) + + [As,Es,Z,dim]= gschur(A,E,extern) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>説明</title> + + <para> + + ã“ã®é–¢æ•°ã¯å»ƒæ¢ã•ã‚Œã¦ãŠã‚Š, <literal>schur</literal>関数ã«çµ±åˆã•ã‚Œã¦ã„ã¾ã™. + + 多ãã®å ´åˆ, <literal>gschur</literal>関数ã¯ä»¥å‰ã¨åŒæ§˜ã«å‹•ä½œã—ã¾ã™ãŒ, + + å°†æ¥ã®ãƒªãƒªãƒ¼ã‚¹ã§ã¯å‰Šé™¤ã•ã‚Œã‚‹äºˆå®šã§ã™. + + </para> + + <para> + + 最åˆã®3ã¤ã®æ§‹æ–‡ã¯ä»¥ä¸‹ã®ã‚ˆã†ã«ç½®ãæ›ãˆã‚‹ã“ã¨ãŒã§ãã¾ã™ + + </para> + + <programlisting role=""><![CDATA[ +[As,Es]=schur(A,E) +[As,Es,Q,Z]=schur(A,E);Q=Q' //NOTE THE TRANPOSITION HERE +[As,Es,Z,dim] = schur(A,E,flag) + ]]></programlisting> + + <para> + + 最後ã®æ§‹æ–‡ã¯ã•ã‚‰ã«è‹¥å¹²ã®èª¿æ•´ãŒå¿…è¦ã§ã™: + + </para> + + <variablelist> + + <varlistentry> + + <term>ã‚‚ã—,</term> + + <listitem> + + <para> + + extern ãŒã€€Scilab関数ã®å ´åˆ, + + Nextern を以下ã®ã‚ˆã†ã«å®šç¾©ã™ã‚‹ã¨, + + æ–°ã—ã„呼ã³å‡ºã—æ‰‹é †ã¯, + + <literal>[As,Es,Z,dim]= schur(A,E,Nextern)</literal> + + ã¨ãªã‚Šã¾ã™: + + </para> + + <programlisting role=""><![CDATA[ +function t=Nextern(R) +if R(2)==0 then + t=extern([1,R(1),R(3)])==1 +else + c=(R(1)+%i*R(2))/R(3) + t=extern([2,real(c+c'),real(c*c')])==1 +end +endfunction + ]]></programlisting> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ã‚‚ã—,</term> + + <listitem> + + <para> + + extern ã¯,Fortran ã¾ãŸã¯ Cã§è¨˜è¿°ã•ã‚ŒãŸå¤–部関数ã®åå‰ã®å ´åˆ, + + nextern を以下ã®ã‚ˆã†ã«å®šç¾©ã™ã‚‹ã¨ + + æ–°ã—ã„呼ã³å‡ºã—æ‰‹é †ã¯, + + <literal>[As,Es,Z,dim]= schur(A,E,'nextern')</literal> + + ã®ã‚ˆã†ã«ãªã‚Šã¾ã™: + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + <programlisting role=""><![CDATA[ +logical function nextern(ar,ai,beta) +double precision ar,ai,beta +integer r,extern +if (ai.eq.0.0d0) then + r=extern(1,ar,beta,0.0d0,0.0d0) +else + r=extern(2,0.0d0,0.0d0,2.0d0*ar,ar*ar+ai*ai) +endif +nextern=r.eq.1 +end + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="external">external</link> + + </member> + + <member> + + <link linkend="schur">schur</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/gspec.xml b/modules/linear_algebra/help/ja_JP/eigen/gspec.xml new file mode 100755 index 000000000..fffb2f624 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/gspec.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="gspec"> + + <refnamediv> + + <refname>gspec</refname> + + <refpurpose> + + 行列ペンシルã®å›ºæœ‰å€¤. + + <emphasis role="bold">ã“ã®é–¢æ•°ã¯å»ƒæ¢ã•ã‚Œã¾ã—ãŸ.</emphasis> + + </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[al,be]=gspec(A,E) + + [al,be,Z]=gspec(A,E) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>説明</title> + + <para> + + ã“ã®é–¢æ•°ã¯ç¾åœ¨ã§ã¯ <literal>spec</literal> 関数ã«çµ±åˆã•ã‚Œã¦ã„ã¾ã™. + + 呼ã³å‡ºã—æ‰‹é †ã¯ä»¥ä¸‹ã®ã‚ˆã†ã«ç½®ãæ›ã‚‰ã‚Œã¦ã„ã¾ã™ + + </para> + + <programlisting role=""><![CDATA[ +[al,be]=spec(A,E) +[al,be,Z]=spec(A,E) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spec">spec</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/hess.xml b/modules/linear_algebra/help/ja_JP/eigen/hess.xml new file mode 100755 index 000000000..9ffb1de41 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/hess.xml @@ -0,0 +1,179 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="hess"> + + <refnamediv> + + <refname>hess</refname> + + <refpurpose>ヘッセンベルク形å¼</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>H = hess(A) + + [U,H] = hess(A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>H</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>U</term> + + <listitem> + + <para>直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>[U,H] = hess(A)</literal> ã¯, + + <literal>A = U*H*U'</literal> ãŠã‚ˆã³ <literal>U'*U</literal> =å˜ä½è¡Œåˆ— ã¨ãªã‚‹ã‚ˆã†ãª + + ユニタリ行列<literal>U</literal> ãŠã‚ˆã³ãƒ˜ãƒƒã‚»ãƒ³ãƒ™ãƒ«ã‚¯è¡Œåˆ—<literal>H</literal>を出力ã—ã¾ã™. + + ã“ã‚Œã«ã‚ˆã‚Š, <literal>hess(A)</literal> 㯠<literal>H</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + <para>行列ã®ãƒ˜ãƒƒã‚»ãƒ³ãƒ™ãƒ«ã‚¯å½¢å¼ã¯æœ€åˆã®å‰¯å¯¾è§’線以下ã§ã¯ 0ã¨ãªã‚Šã¾ã™. + + ã“ã®è¡Œåˆ—ãŒå¯¾ç§°ã¾ãŸã¯ã‚¨ãƒ«ãƒŸãƒ¼ãƒˆè¡Œåˆ—ã®å ´åˆ, + + å½¢ã¯3é‡å¯¾è§’ã¨ãªã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>リファレンス</title> + + <para> + + hess 関数㯠Lapack ルーãƒãƒ³ + + DGEHRD, DORGHR (実数行列ã®å ´åˆ) ãŠã‚ˆã³ ZGEHRD, ZORGHR (è¤‡ç´ æ•°è¡Œåˆ—ã®å ´åˆ)ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(3,3);[U,H]=hess(A); +and( abs(U*H*U'-A)<1.d-10 ) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="contr">contr</link> + + </member> + + <member> + + <link linkend="schur">schur</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + <literal>hess</literal> 関数ã¯Lapack ルーãƒãƒ³ + + DGEHRD, DORGHR (実数行列ã®å ´åˆ) ãŠã‚ˆã³ ZGEHRD, ZORGHR (è¤‡ç´ æ•°è¡Œåˆ—ã®å ´åˆ)ã« + + 基ã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/pbig.xml b/modules/linear_algebra/help/ja_JP/eigen/pbig.xml new file mode 100755 index 000000000..feaaa4c4c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/pbig.xml @@ -0,0 +1,234 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="pbig"> + + <refnamediv> + + <refname>pbig</refname> + + <refpurpose>固有投影</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>thres</term> + + <listitem> + + <para>実数</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para> + + æ–‡å—列 (<literal>'c'</literal> ã¾ãŸã¯ <literal>'d'</literal>) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q,M</term> + + <listitem> + + <para>実数行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 実部>= <literal>thres</literal> (<literal>flag='c'</literal>) + + ã¾ãŸã¯ + + 大ãã•>= <literal>thres</literal>(<literal>flag='d'</literal>) + + ã®å›ºæœ‰å€¤ã‚’有ã™ã‚‹å›ºæœ‰å€¤-部分空間ã¸ã®æŠ•å½±. + + </para> + + <para> + + 投影ã¯<literal>Q*M</literal>ã«ã‚ˆã‚Šå®šç¾©ã•ã‚Œ,<literal>Q</literal> + + ã¯åˆ—フルランク, <literal>M</literal>ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯ãŠã‚ˆã³ + + <literal>M*Q=eye</literal>. + + </para> + + <para> + + <literal>flag='c'</literal>ã®å ´åˆ, + + <literal>M*A*Q</literal>ã®å›ºæœ‰å€¤ = 実部>= <literal>thres</literal> + + ã®<literal>A</literal>ã®å›ºæœ‰å€¤ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>flag='d'</literal>ã®å ´åˆ, + + <literal>M*A*Q</literal>ã®å›ºæœ‰å€¤ = 大ãã•>= <literal>thres</literal>ã® + + <literal>A</literal>ã®å›ºæœ‰å€¤ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>flag='c'</literal> ã®å ´åˆ,ãã—㦠+ + <literal>[Q1,M1]</literal> = <literal>eye()-Q*M</literal>ã® + + フルランク分解 (<literal>fullrf</literal>)ã®å ´åˆ, + + <literal>M1*A*Q1</literal>ã®å›ºæœ‰å€¤ = + + 実部 < <literal>thres</literal>ã®<literal>A</literal>ã®å›ºæœ‰å€¤ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>flag='d'</literal>ã®å ´åˆ,ãã—㦠<literal>[Q1,M1]</literal> = + + <literal>eye()-Q*M</literal>ã®ãƒ•ãƒ«ãƒ©ãƒ³ã‚¯åˆ†è§£ (<literal>fullrf</literal>)ã®å ´åˆ, + + <literal>M1*A*Q1</literal>ã®å›ºæœ‰å€¤ =大ãã• <<literal>thres</literal>ã® + + <literal>A</literal>ã®å›ºæœ‰å€¤ã¨ãªã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; +[Q,M]=pbig(A,1.5,'d'); +spec(M*A*Q) +[Q1,M1]=fullrf(eye()-Q*M); +spec(M1*A*Q1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="psmall">psmall</link> + + </member> + + <member> + + <link linkend="projspec">projspec</link> + + </member> + + <member> + + <link linkend="fullrf">fullrf</link> + + </member> + + <member> + + <link linkend="schur">schur</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + <literal>pbig</literal> 㯠+ + ソートã•ã‚ŒãŸ Schur å½¢å¼ã«åŸºã¥ã„ã¦ã„ã¾ã™ + + (Scilab関数 <literal>schur</literal>). + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/projspec.xml b/modules/linear_algebra/help/ja_JP/eigen/projspec.xml new file mode 100755 index 000000000..351331f8e --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/projspec.xml @@ -0,0 +1,165 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="projspec"> + + <refnamediv> + + <refname>projspec</refname> + + <refpurpose>スペクトル演算å</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[S,P,D,i]=projspec(A)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>S, P, D</term> + + <listitem> + + <para>sæ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>i</term> + + <listitem> + + <para> + + æ•´æ•° (<literal>A</literal>ã®ã‚¼ãƒå›ºæœ‰å€¤ã®æ·»å—). + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>A</literal>ã®0ã«ãŠã‘るスペクトル特性. + + </para> + + <para> + + <literal>S</literal> = 0ã«ãŠã‘る縮å°ãƒ¬ã‚¾ãƒ«ãƒ™ãƒ³ãƒˆ + + (<literal>S</literal> = -Drazin_inverse(<literal>A</literal>)). + + </para> + + <para> + + <literal>P</literal> = 0ã«ãŠã‘るスペクトル投影. + + </para> + + <para> + + <literal>D</literal> = 0ã«ãŠã‘る冪零演算å. + + </para> + + <para> + + <literal>index</literal> = 0固有値ã®æ·»å—. + + </para> + + <para> + + 特異点s=0ã®å‘¨ã‚Šã§ã® + + <literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...</literal> + + ãŒå‡ºåŠ›ã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end') +A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7); +A=X*A*inv(X); +[S,P,D,index]=projspec(A); +index //J-ブãƒãƒƒã‚¯ã®å¤§ãã• +trace(P) //J-ブãƒãƒƒã‚¯ã®æ¬¡å…ƒã®åˆè¨ˆ +A*S-(eye()-P) +norm(D^index,1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="coff">coff</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/psmall.xml b/modules/linear_algebra/help/ja_JP/eigen/psmall.xml new file mode 100755 index 000000000..e67b13bdf --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/psmall.xml @@ -0,0 +1,232 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="psmall"> + + <refnamediv> + + <refname>psmall</refname> + + <refpurpose>スペクトル投影</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,M]=psmall(A,thres,flag)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã®æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>thres</term> + + <listitem> + + <para>実数</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para> + + æ–‡å—列 (<literal>'c'</literal> ã¾ãŸã¯ <literal>'d'</literal>) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q,M</term> + + <listitem> + + <para>実数行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 実部 < <literal>thres</literal> (<literal>flag='c'</literal>) + + ã¾ãŸã¯çµ¶å¯¾å€¤ < <literal>thres</literal>(<literal>flag='d'</literal>) + + ã¨ãªã‚‹å›ºæœ‰å€¤-部分空間ã¸ã®æŠ•å½±. + + </para> + + <para> + + ã“ã®æŠ•å½±ã¯<literal>Q*M</literal>ã«ã‚ˆã‚Šå®šç¾©ã•ã‚Œã¾ã™. + + ã“ã“ã§, + + <literal>Q</literal>ã¯åˆ—フルランク,<literal>M</literal>ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯, + + ãã—ã¦<literal>M*Q=eye</literal>ã§ã™. + + </para> + + <para> + + <literal>flag='c'</literal>ã®å ´åˆ, + + <literal>M*A*Q</literal>ã®å›ºæœ‰å€¤ = + + 実部< <literal>thres</literal>ã®<literal>A</literal>ã®å›ºæœ‰å€¤. + + </para> + + <para> + + <literal>flag='d'</literal>ã®å ´åˆ, + + <literal>M*A*Q</literal>ã®å›ºæœ‰å€¤ = + + 大ãã• < <literal>thres</literal>ã®<literal>A</literal>ã®å›ºæœ‰å€¤. + + </para> + + <para> + + <literal>flag='c'</literal>ã®å ´åˆ, + + <literal>[Q1,M1]</literal> = <literal>eye()-Q*M</literal>ã® + + フルランク分解(<literal>fullrf</literal>)ã®å ´åˆ, + + <literal>M1*A*Q1</literal>ã®å›ºæœ‰å€¤ =実部>= + + <literal>thres</literal>ã® + + <literal>A</literal>ã®å›ºæœ‰å€¤ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>flag='d'</literal>ã®å ´åˆ, + + <literal>[Q1,M1]</literal> =<literal>eye()-Q*M</literal> + + ã®ãƒ•ãƒ«ãƒ©ãƒ³ã‚¯åˆ†è§£(<literal>fullrf</literal>)ã®å ´åˆ, + + <literal>M1*A*Q1</literal>ã®å›ºæœ‰å€¤ = + + 大ãã•>=<literal>thres</literal>ã® + + <literal>A</literal>ã®å›ºæœ‰å€¤. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; +[Q,M]=psmall(A,2.5,'d'); +spec(M*A*Q) +[Q1,M1]=fullrf(eye()-Q*M); +spec(M1*A*Q1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="pbig">pbig</link> + + </member> + + <member> + + <link linkend="proj">proj</link> + + </member> + + <member> + + <link linkend="projspec">projspec</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + ã“ã®é–¢æ•°ã¯ã‚½ãƒ¼ãƒˆã•ã‚ŒãŸ Schurå½¢å¼(scilab + + 関数 <literal>schur</literal>)ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/schur.xml b/modules/linear_algebra/help/ja_JP/eigen/schur.xml new file mode 100755 index 000000000..be68d6eed --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/schur.xml @@ -0,0 +1,711 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="schur"> + + <refnamediv> + + <refname>schur</refname> + + <refpurpose>行列ãŠã‚ˆã³ãƒšãƒ³ã‚·ãƒ«ã®[ソートã•ã‚ŒãŸ] Schur 分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[U,T] = schur(A) + + [U,dim [,T] ]=schur(A,flag) + + [U,dim [,T] ]=schur(A,extern1) + + + + [As,Es [,Q,Z]]=schur(A,E) + + [As,Es [,Q],Z,dim] = schur(A,E,flag) + + [Z,dim] = schur(A,E,flag) + + [As,Es [,Q],Z,dim]= schur(A,E,extern2) + + [Z,dim]= schur(A,E,extern2) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E</term> + + <listitem> + + <para> + + <literal>A</literal>ã¨åŒã˜æ¬¡å…ƒã®å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para> + + æ–‡å—列 (<literal>'c'</literal> ã¾ãŸã¯ <literal>'d'</literal>) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>extern1</term> + + <listitem> + + <para>an ``external'', 以下ã®å‚ç…§</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>extern2</term> + + <listitem> + + <para>an ``external'', 以下ã®å‚ç…§</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>U</term> + + <listitem> + + <para>直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q</term> + + <listitem> + + <para>直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Z</term> + + <listitem> + + <para>o直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>T</term> + + <listitem> + + <para>上三角ã¾ãŸã¯æº–三角æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>As</term> + + <listitem> + + <para>上三角ã¾ãŸã¯æº–三角æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Es</term> + + <listitem> + + <para>上三角æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>dim</term> + + <listitem> + + <para>æ•´æ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + Schur å½¢å¼, 行列ãŠã‚ˆã³ãƒšãƒ³ã‚·ãƒ«ã®ã‚½ãƒ¼ãƒˆã•ã‚ŒãŸ Schur å½¢å¼ + + </para> + + <variablelist> + + <varlistentry> + + <term>行列Schurå½¢å¼</term> + + <listitem> + + <variablelist> + + <varlistentry> + + <term>通常ã®Schurå½¢å¼:</term> + + <listitem> + + <para> + + <literal>[U,T] = schur(A)</literal> ã¯, + + <literal>A = U*T*U'</literal> ãŠã‚ˆã³ <literal>U'*U = eye(U)</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + Schur行列<literal>T</literal> ãŠã‚ˆã³ãƒ¦ãƒ‹ã‚¿ãƒªè¡Œåˆ— <literal>U</literal> + + を出力ã—ã¾ã™. + + Schur(<literal>A</literal>)ã¯,<literal>T</literal>ã‚’è¿”ã—ã¾ã™. + + <literal>A</literal> ãŒè¤‡ç´ æ•°ã®å ´åˆ, è¤‡ç´ Schurå½¢å¼ã¯,行列<literal>T</literal>ã«è¿”ã—ã¾ã™. + + è¤‡ç´ Schurå½¢å¼ã¯,<literal>A</literal>ã®å›ºæœ‰å€¤ã‚’å¯¾è§’é …ã«æœ‰ã™ã‚‹ä¸Šä¸‰è§’行列ã§ã™. + + <literal>A</literal> ãŒå®Ÿæ•°ã®å ´åˆ, 実数Schurå½¢å¼ãŒè¿”ã•ã‚Œã¾ã™. + + 実数Schurå½¢å¼ã¯,å¯¾è§’é …ã«å®Ÿæ•°å›ºæœ‰å€¤ã€è¤‡ç´ æ•°å›ºæœ‰å€¤ã‚’å¯¾è§’é …ã®2x2ブãƒãƒƒã‚¯ã« + + 有ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ソートã•ã‚ŒãŸSchurå½¢å¼</term> + + <listitem> + + <para> + + <literal>[U,dim]=schur(A,'c')</literal> ã¯, + + <literal>A</literal>ã‚’ Schur å½¢å¼ã«å¤‰æ›ã™ã‚‹ + + ユニタリ行列 <literal>U</literal> ã‚’è¿”ã—ã¾ã™. + + æ›´ã«,<literal>U</literal>ã®æœ€åˆã®åˆ— dim ã¯, + + 実部ãŒè² ã®å›ºæœ‰å€¤(安定ãª"連続時間"固有値空間) + + ã«é–¢é€£ã™ã‚‹<literal>A</literal>ã®å›ºæœ‰å€¤ç©ºé–“ + + ã®åŸºåº•ã‚’構æˆã—ã¾ã™. + + </para> + + <para> + + <literal>[U,dim]=schur(A,'d')</literal> ã¯, + + <literal>A</literal>ã‚’ Schur å½¢å¼ã«å¤‰æ›ã™ã‚‹ + + ユニタリ行列 <literal>U</literal> ã‚’è¿”ã—ã¾ã™. + + æ›´ã«,<literal>U</literal>ã®æœ€åˆã®åˆ— dim ã¯, + + 大ãã•ãŒ1未満ã®å›ºæœ‰å€¤(安定ãª"離散時間"固有値空間) + + ã«é–¢é€£ã™ã‚‹<literal>A</literal>ã®å›ºæœ‰å€¤ç©ºé–“ + + ã®åŸºåº•ã‚’構æˆã—ã¾ã™. + + </para> + + <para> + + <literal>[U,dim]=schur(A,extern1)</literal> ã¯, + + <literal>A</literal>ã‚’ Schur å½¢å¼ã«å¤‰æ›ã™ã‚‹ + + ユニタリ行列<literal>U</literal>ã‚’è¿”ã—ã¾ã™. + + æ›´ã«,<literal>U</literal>ã®æœ€åˆã®åˆ— dim ã¯, + + 外部関数 <literal>extern1</literal> (詳細㯠external å‚ç…§) + + ã«ã‚ˆã‚Šé¸æŠžã•ã‚ŒãŸå›ºæœ‰å€¤ã«é–¢é€£ã™ã‚‹<literal>A</literal>ã®å›ºæœ‰å€¤ç©ºé–“ + + ã®åŸºåº•ã‚’構æˆã—ã¾ã™. + + ã“ã® external ã¯Scilab関数ã¾ãŸã¯Cã¾ãŸã¯Fortranプãƒã‚·ãƒ¼ã‚¸ãƒ£ã«ã‚ˆã‚Š + + 次ã®ã‚ˆã†ã«è¨˜è¿°ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™: + + </para> + + <variablelist> + + <varlistentry> + + <term>Scilab関数</term> + + <listitem> + + <para> + + <literal>extern1</literal>㌠+ + Scilab関数ã«ã‚ˆã‚Šè¨˜è¿°ã•ã‚Œã‚‹å ´åˆ, + + 以下ã®å‘¼ã³å‡ºã—æ‰‹é †ã‚’æœ‰ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™: + + <literal>s=extern1(Ev)</literal>, ãŸã ã— <literal>Ev</literal> ã¯å›ºæœ‰å€¤, + + <literal>s</literal> ã¯è«–ç†å€¤ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>C ã¾ãŸã¯ Fortran プãƒã‚·ãƒ¼ã‚¸ãƒ£</term> + + <listitem> + + <para> + + <literal>extern1</literal> ãŒCã¾ãŸã¯Fortran関数ã«ã‚ˆã‚Š + + 記述ã•ã‚Œã‚‹å ´åˆ,以下ã®å‘¼ã³å‡ºã—æ‰‹é †ã‚’æœ‰ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™: + + <literal>int extern1(double *EvR, double *EvI)</literal> + + ãŸã ã— <literal>EvR</literal> ãŠã‚ˆã³ <literal>EvI</literal> 㯠+ + 固有値ã®å®Ÿéƒ¨ãŠã‚ˆã³è™šéƒ¨ã§ã™. + + trueã¾ãŸã¯ã‚¼ãƒã§ãªã„戻り値ã¯,é¸æŠžã•ã‚ŒãŸå›ºæœ‰å€¤ã‚’æ„味ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </listitem> + + </varlistentry> + + </variablelist> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ペンシルSchurå½¢å¼</term> + + <listitem> + + <variablelist> + + <varlistentry> + + <term>通常ã®ãƒšãƒ³ã‚·ãƒ«Schurå½¢å¼</term> + + <listitem> + + <para> + + <literal>[As,Es] = schur(A,E)</literal> ã¯, + + 対<literal>A, E</literal>ã®ä¸€èˆ¬åŒ–Schurå½¢å¼ã§ã‚ã‚‹ + + 準三角行列<literal>As</literal>行列ãŠã‚ˆã³ä¸‰è§’行列<literal>Es</literal> + + を出力ã—ã¾ã™. + + </para> + + <para> + + <literal>[As,Es,Q,Z] = schur(A,E)</literal>ã¯,æ›´ã« + + <literal>As=Q'*A*Z</literal> ãŠã‚ˆã³ <literal>Es=Q'*E*Z</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + 2ã¤ã®ãƒ¦ãƒ‹ã‚¿ãƒªè¡Œåˆ—<literal>Q</literal> ãŠã‚ˆã³ <literal>Z</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ソートã•ã‚ŒãŸSchurå½¢å¼:</term> + + <listitem> + + <para> + + <literal>[As,Es,Z,dim] = schur(A,E,'c')</literal>ã¯, + + ペンシル<literal>s*E-A</literal>ã®å®Ÿæ•°ä¸€èˆ¬åŒ–Schurå½¢å¼ã‚’è¿”ã—ã¾ã™. + + æ›´ã«, <literal>Z</literal>ã®æœ€åˆã®åˆ— dim ã¯, + + 実部ãŒè² ã®å›ºæœ‰å€¤ (安定ãª"連続時間"一般化固有値空間)ã«é–¢é€£ã™ã‚‹ + + 固有値空間ã®åŸºåº•ã‚’構æˆã—ã¾ã™. + + </para> + + <para> + + <literal>[As,Es,Z,dim] = schur(A,E,'d')</literal> + + </para> + + <para> + + ã¯,ペンシル<literal>s*E-A</literal>ã® + + 実数一般化Schurå½¢å¼ã‚’è¿”ã—ã¾ã™. + + æ›´ã«, <literal>Z</literal>ã®æœ€åˆã®åˆ— dim ã¯, + + 大ãã•1未満ã®å›ºæœ‰å€¤ (安定ãª"離散時間"一般化固有値空間)ã«é–¢é€£ã™ã‚‹ + + 固有値空間ã®åŸºåº•ã‚’構æˆã—ã¾ã™. + + </para> + + <para> + + <literal>[As,Es,Z,dim] = schur(A,E,extern2)</literal> + + </para> + + <para> + + ã¯,ペンシル<literal>s*E-A</literal>ã®å®Ÿä¸€èˆ¬åŒ–Schurå½¢å¼ã‚’è¿”ã—ã¾ã™. + + æ›´ã«, <literal>Z</literal>ã®æœ€åˆã®åˆ— dim ã¯, + + 関数<literal>extern2</literal>ã«ã‚ˆã‚ŠæŒ‡å®šã•ã‚ŒãŸè¦å‰‡ã«åŸºã¥ãé¸æŠžã•ã‚ŒãŸ + + ペンシルã®å›ºæœ‰å€¤ã«é–¢ã™ã‚‹å›ºæœ‰å€¤ç©ºé–“ã®åŸºåº•ã‚’構æˆã—ã¾ã™. + + (詳細㯠external å‚ç…§) + + ã“ã® external 㯠Scilab 関数ã¾ãŸã¯Cã¾ãŸã¯Fortranプãƒã‚·ãƒ¼ã‚¸ãƒ£ + + ã«ã‚ˆã‚Šæ¬¡ã®ã‚ˆã†ã«è¨˜è¿°ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™: + + </para> + + <variablelist> + + <varlistentry> + + <term>Scilab関数</term> + + <listitem> + + <para> + + <literal>extern2</literal>ãŒScilab関数ã«ã‚ˆã‚Šè¨˜è¿°ã•ã‚Œã‚‹å ´åˆ, + + 以下ã®å‘¼ã³å‡ºã—æ‰‹é †ã‚’æœ‰ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™: + + <literal>s=extern2(Alpha,Beta)</literal>, ãŸã ã— <literal>Alpha</literal> ãŠã‚ˆã³ + + <literal>Beta</literal> ã¯ä¸€èˆ¬åŒ–固有値ãŠã‚ˆã³è«–ç†å€¤ <literal>s</literal> + + を定義ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>C ã¾ãŸã¯Fortranプãƒã‚·ãƒ¼ã‚¸ãƒ£</term> + + <listitem> + + <para> + + if external <literal>extern2</literal> ãŒCã¾ãŸã¯Fortran関数ã«ã‚ˆã‚Š + + 記述ã•ã‚Œã‚‹å ´åˆ,以下ã®å‘¼ã³å‡ºã—æ‰‹é †ã‚’æœ‰ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™: + + </para> + + <para> + + <literal>int extern2(double *AlphaR, double *AlphaI, double *Beta)</literal> + + </para> + + <para> + + : <literal>A</literal> ãŠã‚ˆã³ <literal>E</literal> ãŒå®Ÿæ•°ã®å ´åˆ. + + </para> + + <para> + + <literal>int extern2(double *AlphaR, double *AlphaI, double *BetaR, double *BetaI)</literal> + + </para> + + <para> + + : <literal>A</literal> ãŠã‚ˆã³ <literal>E</literal> ãŒè¤‡ç´ æ•°ã®å ´åˆ. + + <literal>Alpha</literal>, ãŠã‚ˆã³ <literal>Beta</literal> ã¯ä¸€èˆ¬åŒ–固有値を定義ã—ã¾ã™. + + trueã¾ãŸã¯éžã‚¼ãƒã®æˆ»ã‚Šå€¤ã¯,é¸æŠžã•ã‚ŒãŸä¸€èˆ¬åŒ–固有値をæ„味ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </listitem> + + </varlistentry> + + </variablelist> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>å‚考</title> + + <para> + + 行列Schurå½¢å¼ã®è¨ˆç®—ã¯Lapackルーãƒãƒ³DGEES ãŠã‚ˆã³ ZGEESã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + <para> + + ペンシルSchurå½¢å¼ã®è¨ˆç®—ã¯Lapackルーãƒãƒ³DGGES ãŠã‚ˆã³ ZGGESã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +//行列Schurå½¢å¼ +//---------------------- +A=diag([-0.9,-2,2,0.9]);X=rand(A);A=inv(X)*A*X; +[U,T]=schur(A);T + +[U,dim,T]=schur(A,'c'); +T(1:dim,1:dim) //安定ãªé€£ç¶šæ™‚間固有値 + +function t=mytest(Ev),t=abs(Ev)<0.95,endfunction +[U,dim,T]=schur(A,mytest); +T(1:dim,1:dim) + +// Cã®åŒã˜é–¢æ•° (コンパイラãŒå¿…è¦) +cd TMPDIR; +C=['int mytest(double *EvR, double *EvI) {' //the C code + 'if (*EvR * *EvR + *EvI * *EvI < 0.9025) return 1;' + 'else return 0; }';] +mputl(C,TMPDIR+'/mytest.c') + + +//構築/リンク +lp=ilib_for_link('mytest','mytest.c',[],'c'); +link(lp,'mytest','c'); + +//実行 +[U,dim,T]=schur(A,'mytest'); +//ペンシルã®Schurå½¢å¼ +//---------------------- +F=[-1,%s, 0, 1; + 0,-1,5-%s, 0; + 0, 0,2+%s, 0; + 1, 0, 0, -2+%s]; +A=coeff(F,0);E=coeff(F,1); +[As,Es,Q,Z]=schur(A,E); +Q'*F*Z //ã“ã‚Œã¯As+%s*Esã§ã™ + + +[As,Es,Z,dim] = schur(A,E,'c') +function t=mytest(Alpha,Beta),t=real(Alpha)<0,endfunction +[As,Es,Z,dim] = schur(A,E,mytest) + +//Fortranã®åŒã˜é–¢æ•° (コンパイラãŒå¿…è¦) +ftn=['integer function mytestf(ar,ai,b)' //fortranコード + 'double precision ar,ai,b' + 'mytestf=0' + 'if(ar.lt.0.0d0) mytestf=1' + 'end'] +mputl(' '+ftn,TMPDIR+'/mytestf.f') + +//build and link +lp=ilib_for_link('mytestf','mytestf.f',[],'F'); +link(lp,'mytestf','f'); + +//実行 + +[As,Es,Z,dim] = schur(A,E,'mytestf') + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spec">spec</link> + + </member> + + <member> + + <link linkend="bdiag">bdiag</link> + + </member> + + <member> + + <link linkend="ricc">ricc</link> + + </member> + + <member> + + <link linkend="pbig">pbig</link> + + </member> + + <member> + + <link linkend="psmall">psmall</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/spec.xml b/modules/linear_algebra/help/ja_JP/eigen/spec.xml new file mode 100755 index 000000000..ad29f187a --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/spec.xml @@ -0,0 +1,522 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spec" xml:lang="ja"> + + <refnamediv> + + <refname>spec</refname> + + <refpurpose>行列ã¨ãƒšãƒ³ã‚·ãƒ«ã®å›ºæœ‰å€¤</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>evals=spec(A) + + [R,diagevals]=spec(A) + + + + evals=spec(A,B) + + [alpha,beta]=spec(A,B) + + [alpha,beta,Z]=spec(A,B) + + [alpha,beta,Q,Z]=spec(A,B) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>B</term> + + <listitem> + + <para> + + <literal> A</literal>ã¨åŒã˜æ¬¡å…ƒã®å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ£æ–¹è¡Œåˆ— + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>evals</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ ベクトル, 固有値</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>diagevals</term> + + <listitem> + + <para>実数ã¾ãŸã¯(å¯¾è§’é …ã«å›ºæœ‰å€¤ã‚’有ã™ã‚‹)è¤‡ç´ å¯¾è§’è¡Œåˆ— </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>alpha</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ ベクトル, al./be ã«ã‚ˆã‚Šå›ºæœ‰å€¤ãŒå¾—られã¾ã™</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>beta</term> + + <listitem> + + <para>実数ベクトル, al./be ã«ã‚ˆã‚Šå›ºæœ‰å€¤ãŒå¾—られã¾ã™</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>R</term> + + <listitem> + + <para>å¯é€†ãªå®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ£æ–¹è¡Œåˆ—, 行列å³å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>L</term> + + <listitem> + + <para>å¯é€†ãªå®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ£æ–¹è¡Œåˆ—,　ペンシル左固有ベクトル.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>R</term> + + <listitem> + + <para>å¯é€†ãªå®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ£æ–¹è¡Œåˆ—,　ペンシルå³å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«.</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <variablelist> + + <varlistentry> + + <term>evals=spec(A)</term> + + <listitem> + + <para> + + ベクトル<literal>evals</literal> ã«å›ºæœ‰å€¤ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[R,diagevals] =spec(A)</term> + + <listitem> + + <para> + + 対角行列r <literal>evals</literal> ã«å›ºæœ‰å€¤, + + <literal>R</literal>ã«å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>evals=spec(A,B)</term> + + <listitem> + + <para>行列ペンシル A - s B ã®ã‚¹ãƒšã‚¯ãƒˆãƒ«,ã™ãªã‚ã¡, + + å¤šé …å¼è¡Œåˆ— s B - Aã®æ ¹,ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[alpha,beta] = spec(A,B)</term> + + <listitem> + + <para> + + 行列ペンシル<literal>A- s B</literal>ã®ã‚¹ãƒšã‚¯ãƒˆãƒ«, + + ã™ãªã‚ã¡,å¤šé …å¼è¡Œåˆ— <literal>A - s B</literal>ã®æ ¹ã‚’è¿”ã—ã¾ã™. + + 一般化固有値 alpha 㨠beta ã¯è¡Œåˆ— + + <literal>A - alpha./beta B</literal> ãŒç‰¹ç•°è¡Œåˆ—ã¨ãªã‚‹å€¤ã§ã™. + + 固有値㯠<literal>al./be</literal> ã«ã‚ˆã‚ŠæŒ‡å®šã•ã‚Œ, + + <literal>beta(i) = 0</literal>ã®å ´åˆ,i番目ã®å›ºæœ‰å€¤ã¯ç„¡é™å¤§ã¨ãªã‚Šã¾ã™. + + (<literal>B = eye(A)</literal>ã®å ´åˆ, <literal>alpha./beta</literal>㯠+ + <literal>spec(A)</literal>ã¨ãªã‚Šã¾ã™). + + 通常,beta=0や両方ãŒã‚¼ãƒã®å ´åˆã«é–¢ã—ã¦éƒ½åˆãŒè‰¯ã„解釈ãŒå˜åœ¨ã™ã‚‹ãŸã‚, + + (alpha,beta)ã®çµ„ã¿åˆã‚ã›ã§è¡¨ã•ã‚Œã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[alpha,beta,R] = spec(A,B)</term> + + <listitem> + + <para>上記ã«åŠ ãˆã¦ãƒšãƒ³ã‚·ãƒ«ã®ä¸€èˆ¬åŒ–å³å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã¨ãªã‚‹ + + 行列 <literal>R</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[al,be,L,R] = spec(A,B)</term> + + <listitem> + + <para> + + 上記ã«åŠ ãˆã¦ãƒšãƒ³ã‚·ãƒ«ã®ä¸€èˆ¬åŒ–å³ãŠã‚ˆã³å·¦å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã§ã‚る行列 + + <literal>L</literal> ãŠã‚ˆã³<literal>R</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[al,be,Z] = spec(A,E)</term> + + <listitem> + + <para> + + 一般化å³å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã§ã‚る行列 <literal>Z</literal> ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[al,be,Q,Z] = spec(A,E)</term> + + <listitem> + + <para> + + 一般化å³ãŠã‚ˆã³å·¦å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã§ã‚る行列 <literal>Q</literal> + + ãŠã‚ˆã³ <literal>Z</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + <para>大ããªå®Œå…¨ / 疎行列ã®å ´åˆ, Arnoldi モジュールを使用ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™.</para> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <para>行列ã®å›ºæœ‰å€¤è¨ˆç®—㯠Lapack ルーãƒãƒ³ã«åŸºã¥ã„ã¦ã„ã¾ã™</para> + + <itemizedlist> + + <listitem> + + <para>行列ãŒå¯¾ç§°ã§ãªã„å ´åˆ, DGEEV ãŠã‚ˆã³ ZGEEV.</para> + + </listitem> + + <listitem> + + <para>行列ãŒå¯¾ç§°ã®å ´åˆ, DSYEV ãŠã‚ˆã³ ZHEEV.</para> + + </listitem> + + </itemizedlist> + + <para>è¤‡ç´ å¯¾è±¡è¡Œåˆ—ã¯è¤‡ç´ 共役ã®éžå¯¾è§’é …ã¨å®Ÿæ•°ã®å¯¾è§’é …ã‚’æœ‰ã—ã¾ã™.</para> + + <para>ペンシル固有値計算㯠Lapack ルーãƒãƒ³ + + DGGEV ãŠã‚ˆã³ ZGGEVã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>実数ãŠã‚ˆã³è¤‡ç´ 行列</title> + + <para> + + 例ãˆã° evals ã‚„ R ã®ã‚ˆã†ãªå‡ºåŠ›å¤‰æ•°ã®åž‹ã¯å…¥åŠ›è¡Œåˆ— A ãŠã‚ˆã³ B ã®åž‹ã¨ + + åŒã˜ã§ã‚ã‚‹å¿…è¦ã¯ãªã„ã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + + 以下ã®ãƒ‘ラグラフã§ã¯ã€è¡Œåˆ— A ã®å›ºæœ‰å€¤ãŠã‚ˆã³å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã‚’ + + 計算ã™ã‚‹éš›ã®å‡ºåŠ›å¤‰æ•°ã®åž‹ã‚’解æžã—ã¾ã™. + + </para> + + <itemizedlist> + + <listitem> + + <para>実数 A 行列</para> + + <itemizedlist> + + <listitem> + + <para>対称</para> + + <para>固有値ã¨å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã¯å®Ÿæ•°.</para> + + </listitem> + + <listitem> + + <para>éžå¯¾ç§°</para> + + <para>固有値ã¨å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã¯è¤‡ç´ æ•°.</para> + + </listitem> + + </itemizedlist> + + </listitem> + + <listitem> + + <para>è¤‡ç´ A 行列</para> + + <itemizedlist> + + <listitem> + + <para>対称</para> + + <para>固有値ã¯å®Ÿæ•°ã ãŒå›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã¯è¤‡ç´ æ•°.</para> + + </listitem> + + <listitem> + + <para>éžå¯¾ç§°</para> + + <para>固有値,固有ベクトルã¯è¤‡ç´ æ•°.</para> + + </listitem> + + </itemizedlist> + + </listitem> + + </itemizedlist> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +// MATRIX EIGENVALUES +A=diag([1,2,3]); +X=rand(3,3); +A=inv(X)*A*X; +spec(A) + +x=poly(0,'x'); +pol=det(x*eye()-A) +roots(pol) + +[S,X]=bdiag(A); +clean(inv(X)*A*X) + +// PENCIL EIGENVALUES +A=rand(3,3); +[al,be,R] = spec(A,eye(A)); +al./be +clean(inv(R)*A*R) //displaying the eigenvalues (generic matrix) +A=A+%i*rand(A); +E=rand(A); +roots(det(A-%s*E)) //complex case + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="poly">poly</link> + + </member> + + <member> + + <link linkend="det">det</link> + + </member> + + <member> + + <link linkend="schur">schur</link> + + </member> + + <member> + + <link linkend="bdiag">bdiag</link> + + </member> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + <member> + + <link linkend="dsaupd">dsaupd</link> + + </member> + + <member> + + <link linkend="dnaupd">dnaupd</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/sva.xml b/modules/linear_algebra/help/ja_JP/eigen/sva.xml new file mode 100755 index 000000000..64e9f801f --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/sva.xml @@ -0,0 +1,155 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="sva"> + + <refnamediv> + + <refname>sva</refname> + + <refpurpose>特異値近似</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[U,s,V]=sva(A,k) + + [U,s,V]=sva(A,tol) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>k</term> + + <listitem> + + <para>æ•´æ•°</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>éžè² ã®å®Ÿæ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 特異値近似. + + </para> + + <para> + + <literal>k</literal>ã‚’>=1ã®æ•´æ•°ã¨ã™ã‚‹ã¨ã, + + <literal>[U,S,V]=sva(A,k)</literal> ã¯, + + rank(<literal>B</literal>)=<literal>k</literal>ã¨ã—㦠+ + <literal>B=U*S*V'</literal>ãŒ<literal>A</literal>ã®æœ€è‰¯ã®L2è¿‘ä¼¼ã¨ãªã‚‹ + + よã†ãª + + <literal>U,S</literal> ãŠã‚ˆã³<literal>V</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + <para> + + 実数<literal>tol</literal>を指定ã—ãŸ<literal>[U,S,V]=sva(A,tol)</literal>ã¯, + + <literal>A-B</literal>ã®L2ノルムã§ã‚ã‚‹<literal>B=U*S*V'</literal>ã® + + 最大値ãŒ<literal>tol</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + <literal>U,S</literal> ãŠã‚ˆã³ <literal>V</literal> ã‚’è¿”ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,4)*rand(4,5); +[U,s,V]=sva(A,2); +B=U*s*V'; +svd(A) +svd(B) +clean(svd(A-B)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="svd">svd</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/eigen/svd.xml b/modules/linear_algebra/help/ja_JP/eigen/svd.xml new file mode 100755 index 000000000..d5e536a04 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/eigen/svd.xml @@ -0,0 +1,252 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="svd"> + + <refnamediv> + + <refname>svd</refname> + + <refpurpose>特異値分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>s=svd(X) + + [U,S,V]=svd(X) + + [U,S,V]=svd(X,0) (obsolete) + + [U,S,V]=svd(X,"e") + + [U,S,V,rk]=svd(X [,tol]) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ 行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>s</term> + + <listitem> + + <para>実数ベクトル (特異値)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>S</term> + + <listitem> + + <para>実数対角行列 (特異値)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>U,V</term> + + <listitem> + + <para>直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ—(特異値).</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>[U,S,V] = svd(X)</literal> 㯠+ + <literal>X</literal> ã¨åŒæ¬¡å…ƒã§ + + é™é †ã«éžè² ã®å¯¾è§’è¦ç´ を有ã™ã‚‹ + + 対角行列 <literal>S</literal>ãŠã‚ˆã³ + + <literal>X = U*S*V'</literal>ã¨ãªã‚‹ + + ユニタリ行列 <literal>U</literal> 㨠<literal>V</literal> + + を出力ã—ã¾ã™. + + </para> + + <para> + + <literal>[U,S,V] = svd(X,0)</literal> 㯠+ + "エコノミーサイズ"分解を出力ã—ã¾ã™. + + <literal>X</literal> ãŒmè¡Œn列 (m > n)ã®å ´åˆ, + + <literal>U</literal> ã®æœ€åˆã®n列ã®ã¿ãŒè¨ˆç®—ã•ã‚Œ, + + <literal>S</literal>㯠nè¡Œn列ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>s= svd(X)</literal> 㯠+ + 特異値をå«ã‚€ãƒ™ã‚¯ãƒˆãƒ«<literal>s</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + <para> + + <literal>[U,S,V,rk]=svd(X,tol)</literal> 㯠+ + <literal>rk</literal>ã«åŠ ãˆã¦, + + <literal>X</literal> ã®æ•°å€¤ãƒ©ãƒ³ã‚¯,ã™ãªã‚ã¡ + + <literal>tol</literal>より大ããªç‰¹ç•°å€¤ã®æ•°ã‚’出力ã—ã¾ã™. + + </para> + + <para> + + <literal>tol</literal>ã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã¯ + + <literal>rank</literal>ã¨åŒã˜ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +X=rand(4,2)*rand(2,4) +svd(X) +sqrt(spec(X*X')) + ]]></programlisting> + + </refsection> + + <refsection> + + <title>å‚考</title> + + <simplelist type="inline"> + + <member> + + <link linkend="rank">rank</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + <member> + + <link linkend="sva">sva</link> + + </member> + + <member> + + <link linkend="spec">spec</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + svd 分解ã¯Lapackã®ãƒ«ãƒ¼ãƒãƒ³ DGESVD (実数行列ã®å ´åˆ)ãŠã‚ˆã³ + + ZGESVD (è¤‡ç´ æ•°ã®å ´åˆ)ã«åŸºã¥ã„ã¦ã„ã‚‹. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/factorization/CHAPTER b/modules/linear_algebra/help/ja_JP/factorization/CHAPTER new file mode 100755 index 000000000..e6daeb8eb --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/factorization/CHAPTER @@ -0,0 +1,2 @@ +title = Factorization + diff --git a/modules/linear_algebra/help/ja_JP/factorization/givens.xml b/modules/linear_algebra/help/ja_JP/factorization/givens.xml new file mode 100755 index 000000000..7eae55a1e --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/factorization/givens.xml @@ -0,0 +1,162 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="givens"> + + <refnamediv> + + <refname>givens</refname> + + <refpurpose>ギブンス変æ›</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>U=givens(xy) + + U=givens(x,y) + + [U,c]=givens(xy) + + [U,c]=givens(x,y) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>x,y</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>xy</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¦ç´ æ•°2ã®åˆ—ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>U</term> + + <listitem> + + <para>2x2 ユニタリ行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>c</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¦ç´ æ•°2ã®åˆ—ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title><literal>xy = [x;y]</literal>ã¨ã—㦠+ + <para> + + <literal>U= givens(x, y)</literal> ã¾ãŸã¯ <literal>U = givens(xy)</literal> + + ã¯,次ã®ã‚ˆã†ãª<literal>2</literal>x<literal>2</literal> ã® + + ユニタリ行列 <literal>U</literal> ã‚’è¿”ã—ã¾ã™: + + </para> + + <para> + + <literal>U*xy=[r;0]=c</literal>. + + </para> + + <para> + + <note> + + <literal>givens(x,y)</literal> ãŠã‚ˆã³ <literal>givens([x;y])</literal> ã¯ç‰ä¾¡ã§ã‚ã‚‹ã“ã¨ã« + + 注æ„ã—ã¦ãã ã•ã„. + + </note> + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=[3,4;5,6]; +U=givens(A(:,1)); +U*A + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="qr">qr</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/factorization/householder.xml b/modules/linear_algebra/help/ja_JP/factorization/householder.xml new file mode 100755 index 000000000..9643f73ee --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/factorization/householder.xml @@ -0,0 +1,140 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="householder"> + + <refnamediv> + + <refname>householder</refname> + + <refpurpose>ãƒã‚¦ã‚¹ãƒ›ãƒ«ãƒ€ãƒ¼ç›´äº¤é¡æ˜ 行列</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>u=householder(v [,w])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>v</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®åˆ—ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>w</term> + + <listitem> + + <para> + + <literal>v</literal>ã¨åŒã˜å¤§ãã•ã®å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ•°ã®åˆ—ベクトル. + + デフォルト値ã¯<literal>eye(v)</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>u</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®åˆ—ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + åŒã˜å¤§ãã•ã®åˆ—ベクトル + + <literal>v</literal>, <literal> w</literal> を指定ã™ã‚‹ã¨, + + <literal>householder(v,w)</literal> ã¯, + + <literal> (eye()-2*u*u')*v</literal>ãŒ<literal>w</literal>ã«æ¯”例ã™ã‚‹ã‚ˆã†ãª + + ユニタリ列ベクトル<literal>u</literal>ã‚’è¿”ã—ã¾ã™. + + <literal>(eye()-2*u*u')</literal> ã¯ãƒã‚¦ã‚¹ãƒ›ãƒ«ãƒ€ãƒ¼ç›´äº¤é¡æ˜ 行列ã§ã™. + + </para> + + <para> + + <literal>w</literal> ã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã¯ <literal> eye(v)</literal>ã§ã™. + + ã“ã®å ´åˆ,ベクトル<literal> (eye()-2*u*u')*v</literal> ã¯ãƒ™ã‚¯ãƒˆãƒ« + + <literal> eye(v)*norm(v)</literal>ã§ã™. + + </para> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="givens">givens</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/factorization/sqroot.xml b/modules/linear_algebra/help/ja_JP/factorization/sqroot.xml new file mode 100755 index 000000000..0498d89f5 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/factorization/sqroot.xml @@ -0,0 +1,105 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="sqroot"> + + <refnamediv> + + <refname>sqroot</refname> + + <refpurpose>W*W' エルミート分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>sqroot(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>対称éžè² 定実ã¾ãŸã¯è¤‡ç´ 行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>X=W*W'</literal> ã¨ãªã‚‹ã‚ˆã†ãªWã‚’è¿”ã—ã¾ã™(SVDを使用). + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +X=rand(5,2)*rand(2,5);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) +X=rand(5,2)+%i*rand(5,2);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="chol">chol</link> + + </member> + + <member> + + <link linkend="svd">svd</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/kernel/CHAPTER b/modules/linear_algebra/help/ja_JP/kernel/CHAPTER new file mode 100755 index 000000000..be67920e1 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/CHAPTER @@ -0,0 +1,2 @@ +title = Kernel + diff --git a/modules/linear_algebra/help/ja_JP/kernel/colcomp.xml b/modules/linear_algebra/help/ja_JP/kernel/colcomp.xml new file mode 100755 index 000000000..31a6a6ba2 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/colcomp.xml @@ -0,0 +1,206 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="colcomp"> + + <refnamediv> + + <refname>colcomp</refname> + + <refpurpose>列圧縮,カーãƒãƒ«,ヌル空間</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para>æ–‡å—列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>W</term> + + <listitem> + + <para>æ£æ–¹æ£å‰‡è¡Œåˆ— (基底変æ›)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rk</term> + + <listitem> + + <para> + + æ•´æ•° (<literal>A</literal>ã®ãƒ©ãƒ³ã‚¯) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>A</literal>ã®åˆ—圧縮: <literal>Ac = A*W</literal> 㯠+ + 列圧縮,ã™ãªã‚ã¡ <literal>Ac=[0,Af]</literal> ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + ãŸã ã—, <literal>Af</literal> ã¯ãƒ•ãƒ«åˆ—ランクを有ã—ã¾ã™: + + rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>. + + </para> + + <para> + + <literal>flag</literal> ãŠã‚ˆã³ <literal>tol</literal> 㯠+ + オプションã®ãƒ‘ラメータ: <literal>flag = 'qr'</literal> + + ã¾ãŸã¯ <literal>'svd'</literal> (デフォルト㯠+ + <literal>'svd'</literal>)ã§ã™. + + </para> + + <para> + + <literal>tol</literal> = 許容誤差パラメータ (デフォルト値㯠+ + <literal>%eps</literal>ã®ã‚ªãƒ¼ãƒ€ãƒ¼). + + </para> + + <para> + + <literal>W</literal>ã®æœ€åˆã®<literal>ma-rk</literal>列ã¯, + + <literal>size(A)=(na,ma)</literal>ã¨ã™ã‚‹ã¨ã, + + <literal>A</literal>ã®ã‚«ãƒ¼ãƒãƒ«ã«åºƒãŒã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[X,r]=colcomp(A); +norm(A*X(:,1:$-r),1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + <member> + + <link linkend="fullrf">fullrf</link> + + </member> + + <member> + + <link linkend="fullrfk">fullrfk</link> + + </member> + + <member> + + <link linkend="kernel">kernel</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/kernel/fullrf.xml b/modules/linear_algebra/help/ja_JP/kernel/fullrf.xml new file mode 100755 index 000000000..6085443bb --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/fullrf.xml @@ -0,0 +1,198 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="fullrf"> + + <refnamediv> + + <refname>fullrf</refname> + + <refpurpose>フルランク分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数 (ランク定義時ã®é–¾å€¤)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q,M</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rk</term> + + <listitem> + + <para> + + æ•´æ•° (<literal>A</literal>ã®ãƒ©ãƒ³ã‚¯) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + フルランク分解 : <literal>fullrf</literal> ã¯, + + <literal>A = Q*M</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + <literal>Q</literal> ãŠã‚ˆã³ <literal>M</literal>ã‚’è¿”ã—ã¾ã™. + + ãŸã ã—, + + range(<literal>Q</literal>)=range(<literal>A</literal>) ãŠã‚ˆã³ + + ker(<literal>M</literal>)=ker(<literal>A</literal>), + + <literal>Q</literal> フル列ランク , <literal>M</literal> フル行ランク, + + <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>ã§ã™. + + </para> + + <para> + + <literal>tol</literal> ã¯ã‚ªãƒ—ションã®å®Ÿæ•°ãƒ‘ラメータã§ã™ + + (デフォルト値㯠<literal>sqrt(%eps)</literal>ã§ã™). + + <literal>A</literal>ã®ãƒ©ãƒ³ã‚¯<literal>rk</literal>㯠+ + <literal>norm(A)*tol</literal>より大ã㪠+ + 特異値ã®æ•°ã¨ã—ã¦å®šç¾©ã•ã‚Œã¾ã™. + + </para> + + <para> + + AãŒå¯¾ç§°ã®å ´åˆ, + + <literal>fullrf</literal> 㯠<literal>M=Q'</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[Q,M]=fullrf(A); +norm(Q*M-A,1) +[X,d]=rowcomp(A);Y=X'; +svd([A,Y(:,1:d),Q]) //span(Q) = span(A) = span(Y(:,1:2)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="svd">svd</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="fullrfk">fullrfk</link> + + </member> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/kernel/fullrfk.xml b/modules/linear_algebra/help/ja_JP/kernel/fullrfk.xml new file mode 100755 index 000000000..8ce763a2c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/fullrfk.xml @@ -0,0 +1,143 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="fullrfk"> + + <refnamediv> + + <refname>fullrfk</refname> + + <refpurpose>A^kã®ãƒ•ãƒ«ãƒ©ãƒ³ã‚¯åˆ†è§£</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>k</term> + + <listitem> + + <para>æ•´æ•°</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Bk,Ck</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + ã“ã®é–¢æ•°ã¯,<literal>A^k</literal>ã®ãƒ•ãƒ«ãƒ©ãƒ³ã‚¯åˆ†è§£, + + ã™ãªã‚ã¡, <literal>Bk*Ck=A^k</literal> を計算ã—ã¾ã™. + + ãŸã ã—, <literal>Bk</literal> ã¯åˆ—フルランク, + + <literal>Ck</literal>ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯ã§ã™. + + range(<literal>Bk</literal>)=range(<literal>A^k</literal>) + + ãŠã‚ˆã³ ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>)ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>k=1</literal>ã®å ´åˆ, <literal>fullrfk</literal> 㯠+ + <literal>fullrf</literal>ã¨ç‰ä¾¡ã«ãªã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3); +norm(Bk*Ck-A^3,1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="fullrf">fullrf</link> + + </member> + + <member> + + <link linkend="range">range</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/kernel/im_inv.xml b/modules/linear_algebra/help/ja_JP/kernel/im_inv.xml new file mode 100755 index 000000000..de6c340d7 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/im_inv.xml @@ -0,0 +1,202 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="im_inv"> + + <refnamediv> + + <refname>im_inv</refname> + + <refpurpose>原åƒ</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[X,dim]=im_inv(A,B [,tol]) + + [X,dim,Y]=im_inv(A,B, [,tol]) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A,B</term> + + <listitem> + + <para>åŒã˜åˆ—ã®æ•°ã‚’有ã™ã‚‹å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ 数行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para> + + 次数ãŒ<literal>A</literal>ã®åˆ—ã®æ•°ã«ç‰ã—ã„直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ— + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>dim</term> + + <listitem> + + <para>æ•´æ•° (部分空間ã®æ¬¡å…ƒ)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Y</term> + + <listitem> + + <para> + + 次数ãŒ<literal>A</literal>ãŠã‚ˆã³<literal>B</literal>ã®è¡Œã®æ•°ã«ç‰ã—ã„直交行列. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>[X,dim]=im_inv(A,B)</literal> 㯠<literal>(A^-1)(B)</literal>, + + ã™ãªã‚ã¡, <literal>A</literal>ã¸ã®åƒãŒ range(<literal>B</literal>) ã« + + ã‚るベクトルを計算ã—ã¾ã™. + + </para> + + <para> + + <literal>X</literal>ã®æœ€åˆã®åˆ— <literal>dim</literal> 㯠+ + <literal>(A^-1)(B)</literal>ã«åºƒãŒã£ã¦ã„ã¾ã™. + + </para> + + <para> + + <literal>tol</literal> ã¯éƒ¨åˆ†ç©ºé–“ã®å–ã‚Šè¾¼ã¿ã‚’確èªã™ã‚‹ãŸã‚ã« + + 閾値ãŒä½¿ç”¨ã•ã‚Œã¦ãŠã‚Š, + + ãã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã¯ <literal>tol = 100*%eps</literal> ã§ã™. + + <literal>Y</literal> ãŒè¿”ã•ã‚Œã‚‹æ™‚, + + <literal>[Y*A*X,Y*B]</literal> ã¯ä»¥ä¸‹ã®ã‚ˆã†ã«åˆ†å‰²ã•ã‚Œã¾ã™: + + <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal> + + </para> + + <para> + + ãŸã ã—, <literal>B1</literal>ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯ ( + + <literal>rank(B)</literal>ã«ç‰ã—ã„) ãã—㦠<literal>A22</literal> 㯠+ + 列フルランク㧠<literal>dim</literal> 列ã¨ãªã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)]; +W=rand(5,5);A=W*A;B=W*B; +[X,dim]=im_inv(A,B) +svd([A*X(:,1:dim),B]) //vectors A*X(:,1:dim) belong to range(B) +[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B] + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + <member> + + <link linkend="spaninter">spaninter</link> + + </member> + + <member> + + <link linkend="spanplus">spanplus</link> + + </member> + + <member> + + <link linkend="linsolve">linsolve</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/kernel/kernel.xml b/modules/linear_algebra/help/ja_JP/kernel/kernel.xml new file mode 100755 index 000000000..f46881733 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/kernel.xml @@ -0,0 +1,173 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="kernel"> + + <refnamediv> + + <refname>kernel</refname> + + <refpurpose>カーãƒãƒ«, ヌル空間</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>W=kernel(A [,tol,[,flag])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®ãƒ•ãƒ«è¡Œåˆ—ã¾ãŸã¯å®Ÿæ•°ç–Žè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para> + + æ–‡å—列 <literal>'svd'</literal> (デフォルト) ã¾ãŸã¯ <literal>'qr'</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>W</term> + + <listitem> + + <para>列フルランク行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>W=kernel(A)</literal> ã¯<literal>A</literal>ã®ã‚«ãƒ¼ãƒãƒ« (ヌル空間)ã‚’è¿”ã—ã¾ã™. + + A ãŒåˆ—フルランクã®å ´åˆ, 空ã®è¡Œåˆ— [] ãŒè¿”ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>flag</literal> ãŠã‚ˆã³ <literal>tol</literal> 㯠+ + オプションã®ãƒ‘ラメータã§ã™: <literal>flag = 'qr'</literal> + + ã¾ãŸã¯ <literal>'svd'</literal> (デフォルト㯠<literal>'svd'</literal>). + + </para> + + <para> + + <literal>tol</literal> = 許容誤差パラメータ (デフォルト値㯠<literal>%eps</literal> ã®ã‚ªãƒ¼ãƒ€). + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(3,1)*rand(1,3); +A*kernel(A) +A=sparse(A); +clean(A*kernel(A)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + <member> + + <link linkend="fullrf">fullrf</link> + + </member> + + <member> + + <link linkend="fullrfk">fullrfk</link> + + </member> + + <member> + + <link linkend="linsolve">linsolve</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/kernel/range.xml b/modules/linear_algebra/help/ja_JP/kernel/range.xml new file mode 100755 index 000000000..30905174c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/range.xml @@ -0,0 +1,173 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="range"> + + <refnamediv> + + <refname>range</refname> + + <refpurpose>A^kã®ç¯„囲</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[X,dim]=range(A,k)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>k</term> + + <listitem> + + <para>æ•´æ•°</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>直交実数行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>dim</term> + + <listitem> + + <para>æ•´æ•° (部分空間ã®æ¬¡å…ƒ)</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 範囲 <literal>A^k</literal>を計算ã—ã¾ã™ ; <literal>X</literal> ã® + + 最åˆã® dim è¡Œã¯, <literal>A^k</literal>ã®ç¯„囲ã«åºƒãŒã‚Šã¾ã™. + + <literal>X</literal>ã®æœ€å¾Œã®è¡Œã¯, + + ã“ã®ç›´äº¤ç›¸è£œãªç¯„囲ã«åºƒãŒã‚Šã¾ã™. + + <literal>X*X'</literal> ã¯å˜ä½è¡Œåˆ—ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(4,2)*rand(2,4); // 4 列ベクトル, 2 独立. +[X,dim]=range(A,1);dim // 範囲を計算 + +y1=A*rand(4,1); //Aã®ç¯„囲ã®ãƒ™ã‚¯ãƒˆãƒ« +y2=rand(4,1); //Aã®ç¯„囲ã«ãªã„ベクトル +norm(X(dim+1:$,:)*y1) //最後ã®ã‚¨ãƒ³ãƒˆãƒªã¯ã‚¼ãƒ, y1 ã¯Aã®ç¯„囲 +norm(X(dim+1:$,:)*y2) //最後ã®ã‚¨ãƒ³ãƒˆãƒªã¯éžã‚¼ãƒ + +I=X(1:dim,:)' //I ãŒç¯„囲ã®åŸºåº• +coeffs=X(1:dim,:)*y1 // 基底Iã«é–¢é€£ã™ã‚‹y1ã®è¦ç´ + +norm(I*coeffs-y1) //check + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="fullrfk">fullrfk</link> + + </member> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + <literal>range</literal> 関数ã¯, + + <link linkend="svd">svd</link>分解を使用ã™ã‚‹ + + <link linkend="rowcomp">rowcomp</link> 関数 + + ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/kernel/rowcomp.xml b/modules/linear_algebra/help/ja_JP/kernel/rowcomp.xml new file mode 100755 index 000000000..dc29889fb --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/kernel/rowcomp.xml @@ -0,0 +1,233 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rowcomp"> + + <refnamediv> + + <refname>rowcomp</refname> + + <refpurpose>行圧縮, 範囲</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[W,rk]=rowcomp(A [,flag [,tol]])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para>オプションã®æ–‡å—列, 指定å¯èƒ½ãªå€¤ã¯ + + <literal>'svd'</literal> ã¾ãŸã¯ <literal>'qr'</literal>ã§ã™. + + デフォルト値 <literal>'svd'</literal>ã¯ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>オプションã®éžè² ã®å®Ÿæ•°. デフォルト値㯠+ + <literal>sqrt(%eps)*norm(A,1)</literal>. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>W</term> + + <listitem> + + <para>æ£æ–¹æ£å‰‡è¡Œåˆ— (基底ã®å¤‰æ›´)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rk</term> + + <listitem> + + <para> + + æ•´æ•° (<literal>A</literal>ã®ãƒ©ãƒ³ã‚¯) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>A</literal>ã®è¡Œåœ§ç¸®. <literal>Ac = W*A</literal> ã¯è¡Œåœ§ç¸®ã•ã‚ŒãŸè¡Œåˆ—ã§ã™: ã™ãªã‚ã¡, + + <literal>Af</literal>を行フルランクã¨ã—㦠+ + <literal>Ac=[Af;0]</literal> ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>flag</literal> ãŠã‚ˆã³ <literal>tol</literal> ã¯ã‚ªãƒ—ションã®ãƒ‘ラメータã§ã™: <literal>flag='qr'</literal> + + ã¾ãŸã¯ <literal>'svd'</literal> (デフォルト <literal>'svd'</literal>). + + </para> + + <para> + + <literal>tol</literal> ã¯è¨±å®¹èª¤å·®ãƒ‘ラメータã§ã™. + + </para> + + <para> + + <literal>W'</literal>ã®æœ€åˆã®<literal>rk</literal> 列ã«ã¯, + + <literal>A</literal>ã®ç¯„囲ãŒåºƒãŒã‚Šã¾ã™. + + </para> + + <para> + + <literal>W</literal>ã®æœ€åˆã®(上å´ã®)<literal>rk</literal> è¡Œã«ã¯, + + <literal>A</literal>ã®è¡Œç¯„囲ãŒåºƒãŒã‚Šã¾ã™. + + </para> + + <para> + + éžã‚¼ãƒãƒ™ã‚¯ãƒˆãƒ« <literal>x</literal> ã¯, + + <literal>W*x</literal>ãŒ<literal>Ac</literal>ã«åŸºã¥ã行圧縮ã•ã‚ŒãŸå ´åˆ, + + ã™ãªã‚ã¡,ãã®æœ€å¾Œã®è¦ç´ ã®ãƒŽãƒ«ãƒ ãŒæœ€åˆã®è¦ç´ ã«å¯¾ã—ã¦å°ã•ã„å ´åˆã«é™ã‚Š, + + range(<literal>A</literal>)ã«å±žã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); // 4 列ベクトル, 2 ã¤ã¯ç‹¬ç«‹. +[X,dim]=rowcomp(A);Xp=X'; +svd([Xp(:,1:dim),A]) //span(A) = span(Xp(:,1:dim) +x=A*rand(4,1); //x 㯠span(A)ã«å±žã—ã¾ã™ +y=X*x +norm(y(dim+1:$))/norm(y(1:dim)) // å°ã•ã„ + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + <member> + + <link linkend="fullrf">fullrf</link> + + </member> + + <member> + + <link linkend="fullrfk">fullrfk</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + <literal>rowcomp</literal> 関数ã¯<link linkend="svd">svd</link> ã¾ãŸã¯ + + <link linkend="qr">qr</link> 分解d. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/CHAPTER b/modules/linear_algebra/help/ja_JP/linear/CHAPTER new file mode 100755 index 000000000..7d9d9cf49 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/CHAPTER @@ -0,0 +1,2 @@ +title = Linear Equations + diff --git a/modules/linear_algebra/help/ja_JP/linear/aff2ab.xml b/modules/linear_algebra/help/ja_JP/linear/aff2ab.xml new file mode 100755 index 000000000..f15783cf4 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/aff2ab.xml @@ -0,0 +1,258 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="aff2ab"> + + <refnamediv> + + <refname>aff2ab</refname> + + <refpurpose>ç·šå½¢ (アフィン)関数を A,b ã«å¤‰æ›</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[A,b]=aff2ab(afunction,dimX,D [,flag])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>afunction</term> + + <listitem> + + <para> + + scilab 関数 <literal> Y =fct(X,D) </literal> + + ãŸã ã—, <literal>X, D, Y</literal> ã¯è¡Œåˆ—ã®<literal>リスト</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>dimX</term> + + <listitem> + + <para> + + p x 2 整数行列 (<literal>p</literal> 㯠+ + <literal>X</literal>ã®è¡Œåˆ—ã®æ•°) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>D</term> + + <listitem> + + <para> + + 実数行列ã®<literal>list</literal> (ã¾ãŸã¯ä»»æ„ã®æœ‰åŠ¹ãªScilab オブジェクト). + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para> + + オプションã®ãƒ‘ラメータ (<literal>flag='f'</literal> + + ã¾ãŸã¯ <literal>flag='sp'</literal>) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>b</term> + + <listitem> + + <para> + + <literal>A</literal>ã¨åŒã˜è¡Œæ¬¡å…ƒã‚’有ã™ã‚‹å®Ÿæ•°ãƒ™ã‚¯ãƒˆãƒ« + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>aff2ab</literal>ã¯,アフィン関数ã®(æ£æº–å½¢å¼ã®)行列表ç¾ã‚’è¿”ã—ã¾ã™. + + </para> + + <para> + + <literal>afunction</literal> ã¯ä»¥ä¸‹ã®è¦å®šã®æ§‹æ–‡ã‚’有ã™ã‚‹é–¢æ•°ã§ã™: + + <literal> Y=afunction(X,D) </literal> + + ãŸã ã—, <literal> X=list(X1,X2,...,Xp) </literal> 㯠+ + p 個ã®å®Ÿæ•°è¡Œåˆ—ã®ãƒªã‚¹ãƒˆ,<literal> Y=list(Y1,...,Yq) </literal> 㯠+ + <literal> Xi</literal>ã«ç·šå½¢ã«ä¾å˜ã™ã‚‹q 個ã®å®Ÿæ•°è¡Œåˆ—ã®ãƒªã‚¹ãƒˆã§ã™. + + (オプションã®) 入力 <literal> D</literal> ã¯, X ã®é–¢æ•°ã¨ã—㦠+ + Yを計算ã™ã‚‹ãŸã‚ã«å¿…è¦ãªãƒ‘ラメータを有ã—ã¦ã„ã¾ã™. + + </para> + + <para> + + <literal> dimX</literal> 㯠p x 2 行列ã§ã™: <literal>dimX(i)=[nri,nci]</literal> + + ã¯è¡Œåˆ—<literal>Xi</literal>ã®è¡Œã¨åˆ—ã®å®Ÿéš›ã®æ•°ã§ã™. + + ã“れらã®æ¬¡å…ƒã¯,çµæžœã®è¡Œåˆ—<literal>A</literal>ã®åˆ—ã®æ¬¡å…ƒã§ã‚ã‚‹ + + <literal>na</literal> を以下ã®ã‚ˆã†ã«å®šç¾©ã—ã¾ã™: + + <literal>na=nr1*nc1 +...+ nrp*ncp</literal>. + + </para> + + <para> + + オプションã®ãƒ‘ラメータ <literal>flag='sp'</literal> ãŒæŒ‡å®šã•ã‚ŒãŸå ´åˆ, + + çµæžœã®è¡Œåˆ— <literal>A</literal>ã¯ç–Žè¡Œåˆ—ã¨ã—ã¦è¿”ã•ã‚Œã¾ã™. + + </para> + + <para> + + ã“ã®é–¢æ•°ã¯,未知変数ãŒè¡Œåˆ—ã§ã‚るよã†ãª + + 線形方程å¼ã®ã‚·ã‚¹ãƒ†ãƒ を解ããŸã‚ã«æœ‰ç”¨ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +// リアプノフ方程å¼ã‚½ãƒ«ãƒ (未知変数1ã¤, 拘æŸæ¡ä»¶1ã¤) +deff('Y=lyapunov(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q)') +A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3]; +[Aly,bly]=aff2ab(lyapunov,dimX,D); +[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); lyapunov(Xv,D) +Xm=Xv(:); A'*Xm+Xm*A-Q +// 冗長ãªæ‹˜æŸ t X=X'を有ã™ã‚‹ãƒªã‚¢ãƒ—ノフ方程å¼ã‚½ãƒ«ãƒ +// (変数1ã¤, 拘æŸæ¡ä»¶2ã¤t) D ã¯ã‚°ãƒãƒ¼ãƒãƒ«å¤‰æ•° +deff('Y=ly2(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q,Xm''-Xm)') +A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3]; +[Aly,bly]=aff2ab(ly2,dimX,D); +[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); ly2(Xv,D) +// ãƒ•ãƒ©ãƒ³ã‚·ã‚¹æ–¹ç¨‹å¼ +// 以下ã®ã‚ˆã†ãªè¡Œåˆ— X1 ãŠã‚ˆã³ X2 を見ã¤ã‘ã‚‹: +// A1*X1 - X1*A2 + B*X2 -A3 = 0 +// D1*X1 -D2 = 0 +deff('Y=bruce(X,D)','[A1,A2,A3,B,D1,D2]=D(:),... +[X1,X2]=X(:);Y=list(A1*X1-X1*A2+B*X2-A3,D1*X1-D2)') +A1=[-4,10;-1,2];A3=[1;2];B=[0;1];A2=1;D1=[0,1];D2=1; +D=list(A1,A2,A3,B,D1,D2); +[n1,m1]=size(A1);[n2,m2]=size(A2);[n3,m3]=size(B); +dimX=[[m1,n2];[m3,m2]]; +[Af,bf]=aff2ab(bruce,dimX,D); +[Xf,KerAf]=linsolve(Af,bf);Xsol=vec2list(Xf,dimX) +bruce(Xsol,D) +// Aを変æ›ã™ã‚‹å…¨ã¦ã®Xを見ã¤ã‘ã‚‹ +deff('y=f(X,D)','y=list(D(:)*X(:)-X(:)*D(:))') +A=rand(3,3);dimX=[3,3];[Af,bf]=aff2ab(f,dimX,list(A)); +[Xf,KerAf]=linsolve(Af,bf);[p,q]=size(KerAf); +Xsol=vec2list(Xf+KerAf*rand(q,1),dimX); +C=Xsol(:); A*C-C*A + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="linsolve">linsolve</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/chol.xml b/modules/linear_algebra/help/ja_JP/linear/chol.xml new file mode 100755 index 000000000..3838ddb87 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/chol.xml @@ -0,0 +1,149 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="chol"> + + <refnamediv> + + <refname>chol</refname> + + <refpurpose>コレスã‚ー分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[R]=chol(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£å®šå¯¾ç§°è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>X</literal> ãŒæ£å®šã®å ´åˆ, <literal>R = chol(X)</literal> ã¯, + + <literal>R'*R = X</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + 上三角行列<literal>R</literal>を出力ã—ã¾ã™. + + </para> + + <para> + + <literal>chol(X)</literal> ã¯<literal>X</literal>ã®å¯¾è§’é … + + ã¨ä¸Šä¸‰è§’部ã®ã¿ã‚’使用ã—ã¾ã™. + + 下三角部ã¯ä¸Šä¸‰è§’部ã®è»¢ç½®(è¤‡ç´ å…±å½¹)ã¨ã¿ãªã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>å‚考文献</title> + + <para> + + コレスã‚ー分解ã¯Lapackルーãƒãƒ³ DPOTRF (実数行列ã®å ´åˆ)ãŠã‚ˆã³ ZPOTRF (è¤‡ç´ è¡Œåˆ—ã®å ´åˆ) + + ã«åŸºã¥ãã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +W=rand(5,5)+%i*rand(5,5); +X=W*W'; +R=chol(X); +norm(R'*R-X) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spchol">spchol</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="svd">svd</link> + + </member> + + <member> + + <link linkend="bdiag">bdiag</link> + + </member> + + <member> + + <link linkend="fullrf">fullrf</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/inv.xml b/modules/linear_algebra/help/ja_JP/linear/inv.xml new file mode 100755 index 000000000..64e289d34 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/inv.xml @@ -0,0 +1,195 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="inv"> + + <refnamediv> + + <refname>inv</refname> + + <refpurpose>逆行列</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>inv(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—, å¤šé …å¼è¡Œåˆ—ãŠã‚ˆã³ + + ä¼é”関数ã¾ãŸã¯çŠ¶æ…‹ç©ºé–“表ç¾ã®æœ‰ç†è¡Œåˆ—. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>inv(X)</literal> ã¯,æ£æ–¹è¡Œåˆ— <literal>X</literal>ã®é€†è¡Œåˆ— + + ã¨ãªã‚Šã¾ã™. + + <literal>X</literal> ã®ã‚¹ã‚±ãƒ¼ãƒªãƒ³ã‚°ãŒ + + 悪ã„å ´åˆã‚„特異行列ã«è¿‘ã„å ´åˆã«ã¯è¦å‘Šã‚’出力ã—ã¾ã™. + + </para> + + <para> + + å¤šé …å¼è¡Œåˆ—ã¾ãŸã¯ä¼é”関数表ç¾ã®æœ‰ç†è¡Œåˆ—ã®å ´åˆ, + + <literal>inv(X)</literal> 㯠<literal>invr(X)</literal>ã«ç‰ã—ããªã‚Šã¾ã™. + + </para> + + <para> + + 状態空間表ç¾ã®ç·šå½¢ã‚·ã‚¹ãƒ†ãƒ (<literal>syslin</literal> リスト)ã®å ´åˆ, + + <literal>invr(X)</literal> 㯠<literal>invsyslin(X)</literal>ã«ç‰ã—ããªã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <para> + + 数値行列用ã®<literal>inv</literal> 関数㯠Lapack ルーãƒãƒ³ + + DGETRF, DGETRI (実数行列ã®å ´åˆ)ãŠã‚ˆã³ ZGETRF, ZGETRI + + (è¤‡ç´ æ•°ã®å ´åˆ)ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + å¤šé …å¼ãŠã‚ˆã³æœ‰ç†è¡Œåˆ—ã«é–¢ã™ã‚‹ <literal>inv</literal> 㯠+ + Scilab関数<literal>invr</literal>ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(3,3);inv(A)*A +x=poly(0,'x'); +A=[x,1,x;x^2,2,1+x;1,2,3];inv(A)*A +A=[1/x,2;2+x,2/(1+x)] +inv(A)*A +A=ssrand(2,2,3); +W=inv(A)*A +clean(ss2tf(W)) + ]]></programlisting> + + </refsection> + + <refsection> + + <title>å‚考</title> + + <simplelist type="inline"> + + <member> + + <link linkend="slash">slash</link> + + </member> + + <member> + + <link linkend="backslash">backslash</link> + + </member> + + <member> + + <link linkend="pinv">pinv</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="lufact">lufact</link> + + </member> + + <member> + + <link linkend="lusolve">lusolve</link> + + </member> + + <member> + + <link linkend="invr">invr</link> + + </member> + + <member> + + <link linkend="coff">coff</link> + + </member> + + <member> + + <link linkend="coffg">coffg</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/linsolve.xml b/modules/linear_algebra/help/ja_JP/linear/linsolve.xml new file mode 100755 index 000000000..f34d07ead --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/linsolve.xml @@ -0,0 +1,211 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="linsolve"> + + <refnamediv> + + <refname>linsolve</refname> + + <refpurpose>線形方程å¼ã‚½ãƒ«ãƒ</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para> + + a <literal>na x ma</literal> 実数行列 (疎行列ã®å ´åˆã‚‚ã‚ã‚Š) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>b</term> + + <listitem> + + <para> + + <literal>na x 1</literal>ベクトル (<literal>A</literal>ã®è¡Œã¨åŒã˜æ¬¡å…ƒ) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>x0</term> + + <listitem> + + <para>実数ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>kerA</term> + + <listitem> + + <para> + + <literal>ma x k</literal> 実数行列 + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>linsolve</literal> ã¯, + + <literal> A*x+b=0</literal>ã®è§£ã‚’å…¨ã¦è¨ˆç®—ã—ã¾ã™. + + </para> + + <para> + + <literal>x0</literal> ã¯ç‰¹è§£ (å˜åœ¨ã™ã‚‹å ´åˆ), + + <literal> kerA </literal> ã¯<literal>A</literal>ã®ãƒŒãƒ«ç©ºé–“ã§ã™. + + ä»»æ„ã®<literal>w</literal>ã«ã¤ã„ã¦<literal>x=x0+kerA*w</literal>ã¯, + + <literal> A*x+b=0</literal>を満ãŸã—ã¾ã™. + + </para> + + <para> + + 互æ›æ€§ã®ã‚ã‚‹ <literal>x0</literal> ãŒã‚¨ãƒ³ãƒˆãƒªã«æŒ‡å®šã•ã‚ŒãŸå ´åˆ, + + <literal>x0</literal>ãŒè¿”ã•ã‚Œã¾ã™. + + ãã†ã§ãªã„å ´åˆ,<literal>x0</literal>ã¨äº’æ›æ€§ã®ã‚ã‚‹ã‚‚ã®(å˜åœ¨ã™ã‚‹å ´åˆ)ãŒè¿”ã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,8); +b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b //compatible b +b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b //uncompatible b +A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b //x is unique +// Benchmark with other linear sparse solver: +[A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa"); +b = zeros(size(A,1),1); +tic(); +res = umfpack(A,'\',b); +mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc()); +tic(); +res = linsolve(A,b); +mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc()); +tic(); +res = A\b; +mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc()); + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="inv">inv</link> + + </member> + + <member> + + <link linkend="pinv">pinv</link> + + </member> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + <member> + + <link linkend="im_inv">im_inv</link> + + </member> + + <member> + + <link linkend="umfpack">umfpack</link> + + </member> + + <member> + + <link linkend="backslash">backslash</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/lsq.xml b/modules/linear_algebra/help/ja_JP/linear/lsq.xml new file mode 100755 index 000000000..51c55183d --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/lsq.xml @@ -0,0 +1,192 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="lsq"> + + <refnamediv> + + <refname>lsq</refname> + + <refpurpose>線形最å°äºŒä¹—å•é¡Œ. </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>X=lsq(A,B [,tol])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã® (m x n) 行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>B</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã® (m x p) 行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>Aã®å®ŸåŠ¹ãƒ©ãƒ³ã‚¯ã‚’定義ã™ã‚‹ãŸã‚ã«ä½¿ç”¨ã•ã‚Œã‚‹æ£ã®ã‚¹ã‚«ãƒ©ãƒ¼ + + (Aã®ãƒ”ボットæ“作付ãQR分解ã«ãŠã‘る最å‰éƒ¨ã«ã‚る部分三角行列R11ã®æ¬¡æ•°ã¨ã—㦠+ + 定義ã•ã‚Œ,æ¡ä»¶æ•°ã®æŽ¨å®šå€¤ã¯<= 1/tolã¨ãªã‚Šã¾ã™. + + tolã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã¯ <literal>sqrt(%eps)</literal>ã«è¨å®šã•ã‚Œã¾ã™ ) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã® (n x p) 行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>X=lsq(A,B)</literal> ã¯æ–¹ç¨‹å¼ <literal>A*X=B</literal>ã® + + 最å°äºŒä¹—解ã®æœ€å°ãƒŽãƒ«ãƒ を計算ã—ã¾ã™. + + 一方, <literal>X=A \ B</literal>㯠+ + å„列ã«æœ€å¤§<literal>rank(A)</literal>個ã®éžã‚¼ãƒè¦ç´ を有ã™ã‚‹æœ€å°äºŒä¹—解を計算ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>å‚考文献</title> + + <para> + + <literal>lsq</literal> 関数ã¯LApack 関数 DGELSY (実行列ã®å ´åˆ)ãŠã‚ˆã³ + + ZGELSY (è¤‡ç´ è¡Œåˆ—ã®å ´åˆ)ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +//Build the data +x=(1:10)'; +y1=3*x+4.5+3*rand(x,'normal'); +y2=1.8*x+0.5+2*rand(x,'normal'); +plot2d(x,[y1,y2],[-2,-3]) +//Find the linear regression +A=[x,ones(x)];B=[y1,y2]; +X=lsq(A,B); +y1e=X(1,1)*x+X(2,1); +y2e=X(1,2)*x+X(2,2); +plot2d(x,[y1e,y2e],[2,3]) +//Difference between lsq(A,b) and A\b +A=rand(4,2)*rand(2,3);//a rank 2 matrix +b=rand(4,1); +X1=lsq(A,b) +X2=A\b +[A*X1-b, A*X2-b] //the residuals are the same + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="backslash">backslash</link> + + </member> + + <member> + + <link linkend="inv">inv</link> + + </member> + + <member> + + <link linkend="pinv">pinv</link> + + </member> + + <member> + + <link linkend="rank">rank</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/lu.xml b/modules/linear_algebra/help/ja_JP/linear/lu.xml new file mode 100755 index 000000000..6ce19d0e3 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/lu.xml @@ -0,0 +1,299 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2009 - Digiteo - Michael Baudin + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="lu"> + + <refnamediv> + + <refname>lu</refname> + + <refpurpose>ピボットé¸æŠžä»˜ãã®LU 分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[L,U]= lu(A) + + [L,U,E]= lu(A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ— (m x n).</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>L</term> + + <listitem> + + <para> 実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ— (m x min(m,n)).</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>U</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ— (min(m,n) x n ).</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E</term> + + <listitem> + + <para>a (n x n) ç½®æ›è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>[L,U]= lu(A)</literal> ã¯, + + <literal>U</literal>を上三角行列, + + <literal>L</literal>を何らã‹ã®ç‰¹åˆ¥ãªæ§‹é€ ã‚’æŒãŸãªã„一般的ãªè¡Œåˆ—ã¨ã—ã¦, + + <literal>A = L*U</literal> ã¨ãªã‚‹ã‚ˆã†ãª + + 2ã¤ã®è¡Œåˆ— <literal>L</literal> ãŠã‚ˆã³ + + <literal>U</literal> を出力ã—ã¾ã™. + + 実際ã¯,行列<literal>A</literal>ã¯<literal>E*A=B*U</literal> + + ã®ã‚ˆã†ã«åˆ†è§£ã•ã‚Œã¾ã™. + + ãŸã ã—, 行列<literal>B</literal>ã¯ä¸‹ä¸‰è§’行列, + + 行列<literal>L</literal>ã¯<literal>L=E'*B</literal>ã‹ã‚‰è¨ˆç®—ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>A</literal> ãŒãƒ©ãƒ³ã‚¯ <literal>k</literal>を有ã—ã¦ã„ã‚‹å ´åˆ, + + <literal>U</literal>ã®è¡Œ <literal>k+1</literal> ã‹ã‚‰ + + <literal>n</literal> ã¾ã§ã¯ 0　ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + <literal>[L,U,E]= lu(A)</literal> ã¯, + + 上三角行列<literal>U</literal>ãŠã‚ˆã³ + + ç½®æ›è¡Œåˆ—ã‚’ <literal>E</literal>ã¨ã—ãŸä¸‹ä¸‰è§’行列 <literal>E*L</literal>, + + ã«ã‚ˆã‚Š<literal>E*A = L*U</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + 3ã¤ã®è¡Œåˆ— <literal>L</literal>, <literal>U</literal> ãŠã‚ˆã³ + + <literal>E</literal>を出力ã—ã¾ã™. + + </para> + + <para> + + <literal>A</literal> ãŒå®Ÿæ•°è¡Œåˆ—ã®å ´åˆ, + + 関数<literal>lufact</literal> ãŠã‚ˆã³ <literal>luget</literal>ã‚’ + + 用ã„ã‚‹ã“ã¨ã«ã‚ˆã‚Š, + + ç½®æ›è¡Œåˆ—ã‚’å¾—ã‚‹ã“ã¨ãŒã§ãã¾ã™. + + <literal>A</literal>ãŒãƒ•ãƒ«ãƒ©ãƒ³ã‚¯ã§ãªã„å ´åˆ,行列 <literal>L</literal> + + ã®åˆ—圧縮も得るã“ã¨ãŒã§ãã‚‹. + + </para> + + </refsection> + + <refsection> + + <title>例 #1</title> + + <para> + + 以下ã®ä¾‹ã§ã¯,大ãã•4ã®ãƒ’ルãƒãƒ¼ãƒˆè¡Œåˆ—を作æˆã—, + + A=LU ã¨åˆ†è§£ã—ã¾ã™. + + 行列 L ã¯ä¸‹ä¸‰è§’行列ã§ã¯ãªã„ã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + + 下三角行列Lã‚’å–å¾—ã™ã‚‹ã«ã¯, + + 出力引数 E ã‚’ Scilab ã«æŒ‡å®šã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +a = testmatrix("hilb",4); +[l,u]=lu(a) +norm(l*u-a) + ]]></programlisting> + + </refsection> + + <refsection> + + <title>例 #2</title> + + <para> + + 以下ã®ä¾‹ã§ã¯,大ãã•4ã®ãƒ’ルãƒãƒ¼ãƒˆè¡Œåˆ—を作æˆã—, + + EA=LU ã¨åˆ†è§£ã—ã¾ã™. + + 行列 L ã¯ä¸‹ä¸‰è§’行列ã§ã‚ã‚‹ã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + + </para> + + <programlisting role="example"><![CDATA[ +a = testmatrix("hilb",4); +[l,u,e]=lu(a) +norm(l*u-e*a) + ]]></programlisting> + + </refsection> + + <refsection> + + <title>例 #3</title> + + <para> + + 以下ã®ä¾‹ã§ã¯, lufact ãŠã‚ˆã³ luget 関数を使用ã™ã‚‹ + + 方法を示ã—ã¦ã„ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +a=rand(4,4); +[l,u]=lu(a) +norm(l*u-a) +[h,rk]=lufact(sparse(a)) +[P,L,U,Q]=luget(h); +ludel(h) +P=full(P); +L=full(L); +U=full(U); +Q=full(Q); +norm(P*L*U*Q-a) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="lufact">lufact</link> + + </member> + + <member> + + <link linkend="luget">luget</link> + + </member> + + <member> + + <link linkend="lusolve">lusolve</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="svd">svd</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã™ã‚‹é–¢æ•°</title> + + <para> + + lu 分解 Lapack ルーãƒãƒ³ DGETRF (実数行列ã®å ´åˆ) + + ãŠã‚ˆã³ ZGETRF (è¤‡ç´ æ•°ã®å ´åˆ) ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/pinv.xml b/modules/linear_algebra/help/ja_JP/linear/pinv.xml new file mode 100755 index 000000000..1b59ae16c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/pinv.xml @@ -0,0 +1,159 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="pinv"> + + <refnamediv> + + <refname>pinv</refname> + + <refpurpose>擬似逆行列</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>pinv(A,[tol])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>X= pinv(A)</literal> ã¯, + + <literal>A'</literal>ã¨åŒã˜æ¬¡å…ƒã®ä»¥ä¸‹ã®ã‚ˆã†ãª + + 行列<literal>X</literal>を出力ã—ã¾ã™: + + </para> + + <para> + + <literal>A*X*A = A, X*A*X = X</literal> ãã—㦠+ + <literal>A*X</literal> ãŠã‚ˆã³ <literal>X*A</literal> + + ã¯å…±ã«ã‚¨ãƒ«ãƒŸãƒ¼ãƒˆè¡Œåˆ—ã§ã™. + + </para> + + <para> + + 計算ã¯ç‰¹ç•°å€¤åˆ†è§£ã«åŸºã¥ã„ã¦ãŠã‚Š, + + 許容値よりもå°ã•ã„特異値㯠0 ã¨ã—ã¦æ‰±ã‚ã‚Œã¾ã™: + + ã“ã®è¨±å®¹èª¤å·®ã¯ <literal>X=pinv(A,tol)</literal> + + ã§ã‚¢ã‚¯ã‚»ã‚¹ã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); +norm(A*pinv(A)*A-A,1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="rank">rank</link> + + </member> + + <member> + + <link linkend="svd">svd</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + <literal>pinv</literal> 関数ã¯ç‰¹ç•°å€¤åˆ†è§£ã«åŸºã¥ã„ã¦ã„ã¾ã™ + + (Scilab関数 <literal>svd</literal>). + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/qr.xml b/modules/linear_algebra/help/ja_JP/linear/qr.xml new file mode 100755 index 000000000..d1b1acdad --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/qr.xml @@ -0,0 +1,378 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="qr"> + + <refnamediv> + + <refname>qr</refname> + + <refpurpose>QR 分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,R]=qr(X [,"e"]) + + [Q,R,E]=qr(X [,"e"]) + + [Q,R,rk,E]=qr(X [,tol]) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>éžè² ã®å®Ÿæ•°</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q</term> + + <listitem> + + <para>æ£æ–¹ç›´äº¤ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>R</term> + + <listitem> + + <para> + + <literal>X</literal>ã¨åŒã˜æ¬¡å…ƒã®è¡Œåˆ— + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E</term> + + <listitem> + + <para>ç½®æ›è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rk</term> + + <listitem> + + <para> + + æ•´æ•° (<literal>X</literal>ã®QRランク) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <variablelist> + + <varlistentry> + + <term>[Q,R] = qr(X)</term> + + <listitem> + + <para> + + <literal>X= Q*R</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + <literal>X</literal>ã¨åŒã˜æ¬¡å…ƒã® + + 上三角行列<literal>R</literal>ãŠã‚ˆã³ç›´äº¤(è¤‡ç´ æ•°ã®å ´åˆã¯ãƒ¦ãƒ‹ã‚¿ãƒª)行列 + + <literal>Q</literal>を出力ã—ã¾ã™. + + <literal>[Q,R] = qr(X,"e")</literal>ã¯æ¬¡ã«ã‚ˆã†ã« + + "エコノミーサイズ"ã§å‡ºåŠ›ã—ã¾ã™: + + <literal>X</literal> ㌠mè¡Œn列 (m > n)ã®å ´åˆ, + + <literal>Q</literal>ã®æœ€åˆã®n列ã®ã¿ãŒ + + <literal>R</literal>ã®æœ€åˆã®nè¡Œã¨åŒæ™‚ã«è¨ˆç®—ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>Q*R = X</literal> ã‹ã‚‰, + + 行列 <literal>X</literal>ã®k番目ã®åˆ—ã¯, + + (ä¿‚æ•° <literal> R(1,k), ..., R(k,k) </literal>を用ã„ã¦) + + <literal>Q</literal>ã®æœ€åˆã®k列ã®ç·šå½¢çµåˆã§è¡¨ã•ã‚Œã¾ã™. + + <literal>Q</literal>ã®æœ€åˆã®k列ã¯,<literal>X</literal>ã®æœ€åˆã®k列 + + ã«åºƒãŒã‚‹éƒ¨åˆ†ç©ºé–“ã®ç›´äº¤åŸºåº•ã‚’作æˆã—ã¾ã™. + + <literal>X</literal>ã®åˆ—<literal>k</literal>(ã™ãªã‚ã¡, <literal>X(:,k)</literal> ) + + ãŒ<literal>X</literal>ã®æœ€åˆã®<literal>p</literal>列ã®ç·šå½¢çµåˆã®å ´åˆ, + + エントリ<literal>R(p+1,k), ..., R(k,k)</literal>㯠0 ã¨ãªã‚Šã¾ã™. + + ã“ã®å ´åˆ,<literal>R</literal>ã¯ä¸Šå°å½¢ã¨ãªã‚Šã¾ã™. + + <literal>X</literal> ãŒãƒ©ãƒ³ã‚¯<literal>rk</literal>を有ã™ã‚‹å ´åˆ, + + è¡Œ <literal>R(rk+1,:), R(rk+2,:), ...</literal> 㯠0 ã¨ãªã‚Šã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[Q,R,E] = qr(X)</term> + + <listitem> + + <para> + + <literal>X*E = Q*R</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + (列)ç½®æ›è¡Œåˆ—<literal>E</literal>, + + é™é †ã®å¯¾è§’è¦ç´ を有ã™ã‚‹ä¸Šä¸‰è§’行列 <literal>R</literal>, + + 直交(ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒª)<literal>Q</literal> + + を出力ã—ã¾ã™. + + <literal>rk</literal>ãŒ<literal>X</literal>ã®ãƒ©ãƒ³ã‚¯ã®å ´åˆ, + + <literal>R</literal>ã®ä¸»å¯¾è§’é …ã«æ²¿ã£ãŸ + + 最åˆã®<literal>rk</literal>個ã®ã‚¨ãƒ³ãƒˆãƒª, + + ã™ãªã‚ã¡,<literal>R(1,1), R(2,2), ..., R(rk,rk)</literal>㯠+ + å…¨ã¦0以外ã¨ãªã‚Šã¾ã™. + + <literal>[Q,R,E] = qr(X,"e")</literal> 㯠+ + "エコノミーサイズ"ã§å‡ºåŠ›ã—ã¾ã™: + + <literal>X</literal> ㌠mè¡Œn列 (m > n)ã®å ´åˆ, + + <literal>Q</literal>ã®æœ€åˆã®n列ã®ã¿ãŒ + + <literal>R</literal>ã®æœ€åˆã®nè¡Œã¨åŒæ™‚ã«è¨ˆç®—ã•ã‚Œã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[Q,R,rk,E] = qr(X ,tol)</term> + + <listitem> + + <para> + + <literal>rk</literal> = <literal>X</literal>ã®ãƒ©ãƒ³ã‚¯ã®æŽ¨å®šå€¤ + + ã‚’è¿”ã—ã¾ã™. + + ã™ãªã‚ã¡, <literal>rk</literal>ã¯, + + 指定ã—ãŸé–¾å€¤<literal>tol</literal>より大ã㪠+ + <literal>R</literal>ã®å¯¾è§’è¦ç´ ã®æ•°ã¨ãªã‚Šã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>[Q,R,rk,E] = qr(X) </term> + + <listitem> + + <para> + + <literal>rk</literal> = <literal>X</literal>ã®ãƒ©ãƒ³ã‚¯ã®æŽ¨å®šå€¤ + + ã‚’è¿”ã—ã¾ã™. + + ã™ãªã‚ã¡,<literal>rk</literal> 㯠+ + <literal>tol=R(1,1)*%eps*max(size(R))</literal>より大ã㪠+ + <literal>R</literal>ã®å¯¾è§’è¦ç´ ã®æ•°ã¨ãªã‚Šã¾ã™. + + <literal>R</literal>ã®æ¡ä»¶æ•°ã‚’用ã„ã‚‹ + + ランク計算型ã®QR分解ã«ã¤ã„ã¦ã¯,<literal>rankqr</literal>ã‚’ + + å‚ç…§ã—ã¦ãã ã•ã„. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +// QR factorization, generic case +// X is tall (full rank) +X=rand(5,2);[Q,R]=qr(X); [Q'*X R] +//X is fat (full rank) +X=rand(2,3);[Q,R]=qr(X); [Q'*X R] +//Column 4 of X is a linear combination of columns 1 and 2: +X=rand(8,5);X(:,4)=X(:,1)+X(:,2); [Q,R]=qr(X); R, R(:,4) +//X has rank 2, rows 3 to $ of R are zero: +X=rand(8,2)*rand(2,5);[Q,R]=qr(X); R +//Evaluating the rank rk: column pivoting ==> rk first +//diagonal entries of R are non zero : +A=rand(5,2)*rand(2,5); +[Q,R,rk,E] = qr(A,1.d-10); +norm(Q'*A-R) +svd([A,Q(:,1:rk)]) //span(A) =span(Q(:,1:rk)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="rankqr">rankqr</link> + + </member> + + <member> + + <link linkend="rank">rank</link> + + </member> + + <member> + + <link linkend="svd">svd</link> + + </member> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã™ã‚‹é–¢æ•°</title> + + <para> + + qr 分解ã¯Lapack ルーãƒãƒ³ DGEQRF, DGEQPF, + + DORGQR (実数行列)ãŠã‚ˆã³ ZGEQRF, ZGEQPF, ZORGQR (è¤‡ç´ æ•°ã®å ´åˆ) + + ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/linear/rankqr.xml b/modules/linear_algebra/help/ja_JP/linear/rankqr.xml new file mode 100755 index 000000000..b6013b2fa --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/linear/rankqr.xml @@ -0,0 +1,290 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rankqr"> + + <refnamediv> + + <refname>rankqr</refname> + + <refpurpose>QR分解ã«åŸºã¥ã階数</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,R,JPVT,RANK,SVAL]=rankqr(A, [RCOND,JPVT])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>RCOND</term> + + <listitem> + + <para> + + <literal>A</literal>ã®å®ŸåŠ¹éšŽæ•°(ランク)を定義ã™ã‚‹ãŸã‚ã«ä½¿ç”¨ã•ã‚Œã‚‹å®Ÿæ•°ã§ã™. + + ã“ã®éšŽæ•°ã¯, + + <literal>A</literal>ã®ãƒ”ボットé¸æŠžä»˜ãã®QR分解ã®ä¸ã® + + 最大ã®å…ˆé ã®éƒ¨åˆ†ä¸‰è§’行列<literal>R11</literal>ã®æ¬¡æ•°ã¨ã—ã¦å®šç¾©ã•ã‚Œã¾ã™. + + ãã®æŽ¨å®šã•ã‚ŒãŸæ¡ä»¶æ•°ã¯ < <literal>1/RCOND</literal> ã¨ãªã‚Šã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>JPVT</term> + + <listitem> + + <para> + + エントリã®æ•´æ•°ãƒ™ã‚¯ãƒˆãƒ«, <literal>JPVT(i)</literal> ㌠0ã§ãªã„å ´åˆ, + + <literal> A</literal>ã®<literal>i</literal>列目㯠+ + <literal>AP</literal>ã®å…ˆé ã¨äº¤æ›ã•ã‚Œ, + + ãれ以外ã®å ´åˆ,<literal>i</literal>ã¯è‡ªç”±ãªåˆ—ã¨ãªã‚Šã¾ã™. + + 処ç†çµ‚了時ã«<literal>JPVT(i) = k</literal>ã®å ´åˆ, + + <literal>A*P</literal>ã®<literal>i</literal>列目ã¯, + + <literal>A</literal>ã®<literal>k</literal>列目ã¨ãªã£ã¦ã„ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>RANK</term> + + <listitem> + + <para> + + <literal>A</literal>ã®å®ŸåŠ¹ãƒ©ãƒ³ã‚¯,ã™ãªã‚ã¡, + + 部分行列<literal>R11</literal>ã®æ¬¡æ•°. + + ã“ã‚Œã¯,<literal>A</literal>ã®å®Œå…¨ãªç›´äº¤åˆ†è§£ã«ãŠã‘ã‚‹ + + 部分行列<literal>T1</literal>ã®æ¬¡æ•°ã¨åŒã˜ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>SVAL</term> + + <listitem> + + <para> + + 3ã¤ã®è¦ç´ を有ã™ã‚‹å®Ÿæ•°ãƒ™ã‚¯ãƒˆãƒ«;三角分解<literal>R</literal>ã® + + 特異値ã®æŽ¨å®šå€¤. + + </para> + + <para> + + <literal>SVAL(1)</literal> ã¯, + + <literal>R(1:RANK,1:RANK)</literal>ã®æœ€å¤§ç‰¹ç•°å€¤ã§ã™; + + </para> + + <para> + + <literal>SVAL(2)</literal> ã¯, + + <literal>R(1:RANK,1:RANK)</literal>ã®æœ€å°ç‰¹ç•°å€¤ã§ã™; + + </para> + + <para> + + <literal>SVAL(3)</literal> ã¯, + + <literal>RANK</literal> < <literal>MIN(M,N)</literal>ã®å ´åˆ, + + <literal>R(1:RANK+1,1:RANK+1)</literal>, + + ãã†ã§ãªã„å ´åˆ, <literal>R(1:RANK,1:RANK)</literal>ã®æœ€å°ç‰¹ç•°å€¤ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 実数ã¾ãŸã¯è¤‡ç´ æ•°ã®Mè¡ŒN列一般行列<literal>A</literal>ã®(オプションã§) + + ランク出力を伴ãªã†QR分解を計算ã—ã¾ã™. + + ランクãŒä¸å®Œå…¨ã«ãªã‚‹å¯èƒ½æ€§ãŒã‚ã‚Š,実効ランクをæ¡ä»¶æ•°ã®ã‚¤ãƒ³ã‚¯ãƒªãƒ¡ãƒ³ã‚¿ãƒ«æŽ¨å®šã«ã‚ˆã‚Š + + 推定ã—ã¾ã™. + + </para> + + <para> + + ã“ã®ãƒ«ãƒ¼ãƒãƒ³ã¯åˆ—ピボットé¸æŠžä»˜ãã®QR分解を使用ã—ã¾ã™: + + </para> + + <programlisting role=""><![CDATA[ +A * P = Q * R, where R = [ R11 R12 ], + [ 0 R22 ] + ]]></programlisting> + + <para> + + <literal>R11</literal>ã¯,æ¡ä»¶æ•°ã®æŽ¨å®šå€¤ãŒ<literal>1/RCOND</literal>未満ã¨ãªã‚‹ + + 最大ã®éƒ¨åˆ†è¡Œåˆ—ã¨ã—ã¦å®šç¾©ã•ã‚Œã¾ã™. + + <literal>R11</literal>, <literal>RANK</literal>ã®æ¬¡æ•°ã¯, + + <literal>A</literal>ã®å®ŸåŠ¹éšŽæ•°ã§ã™. + + </para> + + <para> + + 三角分解ãŒéšŽæ•°å‡ºåŠ›ã‚’ä¼´ãªã†å ´åˆ (ã“ã‚Œã¯å…ˆé ã®åˆ—ãŒå¥å…¨(well-conditioned)ãªå ´åˆã§ã™), + + <literal>SVAL(1)</literal>ã¯<literal>A</literal>ã®æœ€å¤§ç‰¹ç•°å€¤ã® + + 推定値ã¨ãªã‚Š,<literal>SVAL(2)</literal> ãŠã‚ˆã³ + + <literal>SVAL(3)</literal>ã¯,ãã‚Œãžã‚Œ <literal>A</literal>ã® + + <literal>RANK</literal>番目ãŠã‚ˆã³<literal>(RANK+1)</literal>番目㮠+ + 特異値ã®æŽ¨å®šå€¤ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + ã“れらã®å€¤ã‚’評価ã™ã‚‹ã“ã¨ã«ã‚ˆã‚Š,é¸æŠžã—ãŸ<literal>RCOND</literal>ã® + + 値ã«ã‚ˆã‚ŠéšŽæ•°ãŒè‰¯å¥½ã«å®šç¾©ã•ã‚Œã‚‹ã“ã¨ã‚’確èªã™ã‚‹ã“ã¨ãŒã§ãã¾ã™. + + 比 <literal>SVAL(1)/SVAL(2)</literal> ã¯, + + <literal>R(1:RANK,1:RANK)</literal>ã®æ¡ä»¶æ•°ã®æŽ¨å®šå€¤ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,7); +[Q,R,JPVT,RANK,SVAL]=rankqr(A,%eps) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="rank">rank</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>使用ã•ã‚Œã‚‹é–¢æ•°</title> + + <para> + + Slicot library routines MB03OD, ZB03OD. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/markov/CHAPTER b/modules/linear_algebra/help/ja_JP/markov/CHAPTER new file mode 100755 index 000000000..c29eb913c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/markov/CHAPTER @@ -0,0 +1,2 @@ +title = Markov Matrices + diff --git a/modules/linear_algebra/help/ja_JP/markov/classmarkov.xml b/modules/linear_algebra/help/ja_JP/markov/classmarkov.xml new file mode 100755 index 000000000..48055e45c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/markov/classmarkov.xml @@ -0,0 +1,176 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="classmarkov"> + + <refnamediv> + + <refname>classmarkov</refname> + + <refpurpose>マルコフ行列ã®å†å¸°çš„ã‹ã¤ä¸€æ™‚çš„ãªã‚¯ãƒ©ã‚¹</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[perm,rec,tr,indsRec,indsT]=classmarkov(M)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>M</term> + + <listitem> + + <para>実数 N x N マルコフ行列. å„è¡Œã®ã‚¨ãƒ³ãƒˆãƒªã®åˆè¨ˆã‚’ + + 1ã«åŠ ãˆãŸã‚‚ã® + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>perm</term> + + <listitem> + + <para>整数交æ›ãƒ™ã‚¯ãƒˆãƒ«.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rec, tr</term> + + <listitem> + + <para>整数ベクトル, 数値 (å„å†å¸°çš„クラスã«ãŠã‘る状態é‡ã®æ•°, + + 一時的ãªçŠ¶æ…‹é‡ã®æ•°). + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>indsRec,indsT</term> + + <listitem> + + <para>整数ベクトル. (å†å¸°çš„ãŠã‚ˆã³ä¸€æ™‚çš„ãªçŠ¶æ…‹é‡ã®æ·»å—).</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 以下ã®ã‚ˆã†ãªç½®æ›ãƒ™ã‚¯ãƒˆãƒ«<literal>perm</literal>ã‚’è¿”ã—ã¾ã™ + + </para> + + <programlisting role=""><![CDATA[ +M(perm,perm) = [M11 0 0 0 0 0] + [0 M22 0 0 0] + [0 0 M33 0] + [ ... ] + [0 0 Mrr 0] + [* * * Q] + ]]></programlisting> + + <para> + + å„ <literal>Mii</literal> ã¯<literal>rec(i) i=1,..,r</literal>次㮠+ + マルコフ行列ã§ã™. + + <literal>Q</literal>ã¯,<literal>tr</literal>次ã®ã‚µãƒ–マルコフ行列ã§ã™. + + 1 ã‹ã‚‰ sum(rec)ã®çŠ¶æ…‹é‡ã¯å†å¸°çš„ã§, + + r+1ã‹ã‚‰nã¯ä¸€æ™‚çš„ãªçŠ¶æ…‹é‡ã§ã™. + + <literal>perm=[indsRec,indsT]</literal>ã¨ãªã‚Šã¾ã™. + + ãŸã ã—, indsRec ã¯å¤§ãã• sum(rec)ã®ãƒ™ã‚¯ãƒˆãƒ«, + + indsT ã¯å¤§ãã• trã®ãƒ™ã‚¯ãƒˆãƒ«ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +//P ã¯2ã¤ã®å†å¸°çš„ãªã‚¯ãƒ©ã‚¹ (2ãŠã‚ˆã³1個ã®çŠ¶æ…‹é‡ã‚’有ã™ã‚‹) 2ã¤ã®ä¸€æ™‚çš„ãªçŠ¶æ…‹é‡ +P=genmarkov([2,1],2,'perm') +[perm,rec,tr,indsRec,indsT]=classmarkov(P); +P(perm,perm) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="genmarkov">genmarkov</link> + + </member> + + <member> + + <link linkend="eigenmarkov">eigenmarkov</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/markov/eigenmarkov.xml b/modules/linear_algebra/help/ja_JP/markov/eigenmarkov.xml new file mode 100755 index 000000000..11762fb51 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/markov/eigenmarkov.xml @@ -0,0 +1,150 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="eigenmarkov"> + + <refnamediv> + + <refname>eigenmarkov</refname> + + <refpurpose>æ£è¦åŒ–ã•ã‚ŒãŸå·¦ãŠã‚ˆã³å³ãƒžãƒ«ã‚³ãƒ•å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[M,Q]=eigenmarkov(P)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>P</term> + + <listitem> + + <para>実数 N x N マルコフ行列. 1ã«åŠ ãˆã‚‹å„è¡Œã®ã‚¨ãƒ³ãƒˆãƒªã®åˆè¨ˆ.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>M</term> + + <listitem> + + <para>N個ã®åˆ—を有ã™ã‚‹å®Ÿæ•°è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q</term> + + <listitem> + + <para>N個ã®è¡Œã‚’有ã™ã‚‹å®Ÿæ•°è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + マルコフ推移行列 P ã®å›ºæœ‰å€¤ 1 ã«é–¢é€£ã™ã‚‹ + + æ£è¦åŒ–ã•ã‚ŒãŸå·¦ãŠã‚ˆã³å³å›ºæœ‰ãƒ™ã‚¯ãƒˆãƒ«ã‚’è¿”ã—ã¾ã™. + + ã“ã®å›ºæœ‰å€¤ã®å¤šé‡åº¦ãŒ m　ã§, P㌠N x N ã®å ´åˆ, + + M 㯠m x N 行列㧠Q 㯠N x m 行列ã¨ãªã‚Šã¾ã™. + + M(k,:) ã¯k番目ã®ã‚¨ãƒ«ã‚´ãƒ¼ãƒ‰é›†åˆ(å†å¸°çš„クラス)ã«é–¢é€£ã™ã‚‹ + + 確率分布ベクトルã§ã™. + + M(k,x) ã¯ã€€x ㌠k番目ã®å†å¸°çš„クラスã«ãªã„å ´åˆã«ã¯ + + 0ã¨ãªã‚Šã¾ã™. + + Q(x,k) ã¯x ã‹ã‚‰å§‹ã¾ã‚‹ k 番目ã®å†å¸°çš„クラスã«æœ€çµ‚çš„ã«ã‚る確率ã§ã™. + + 大ããª<literal>k</literal>ã«é–¢ã—ã¦<literal>P^k</literal> ㌠+ + åŽæŸã™ã‚‹å ´åˆ(1以外ã«å˜ä½å††ä¸Šã«å›ºæœ‰å€¤ãŒãªã„), + + 極é™ã¯<literal>Q*M</literal>ã¨ãªã‚Šã¾ã™(固有投影). + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +//P ã¯2ã¤ã®å†å¸°çš„ãªã‚¯ãƒ©ã‚¹ (2ãŠã‚ˆã³1個ã®çŠ¶æ…‹é‡ã‚’有ã™ã‚‹) 2ã¤ã®ä¸€æ™‚çš„ãªçŠ¶æ…‹é‡ +P=genmarkov([2,1],2) +[M,Q]=eigenmarkov(P); +P*Q-Q +Q*M-P^20 + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="genmarkov">genmarkov</link> + + </member> + + <member> + + <link linkend="classmarkov">classmarkov</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/markov/genmarkov.xml b/modules/linear_algebra/help/ja_JP/markov/genmarkov.xml new file mode 100755 index 000000000..287e19b83 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/markov/genmarkov.xml @@ -0,0 +1,161 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="genmarkov"> + + <refnamediv> + + <refname>genmarkov</refname> + + <refpurpose> + + å†å¸°çš„ãŠã‚ˆã³ä¸€æ™‚çš„ãªã‚¯ãƒ©ã‚¹ã‚’有ã™ã‚‹ãƒ©ãƒ³ãƒ€ãƒ ãªãƒžãƒ«ã‚³ãƒ•è¡Œåˆ—を生æˆã™ã‚‹ + + </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>M=genmarkov(rec,tr) + + M=genmarkov(rec,tr,flag) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>rec</term> + + <listitem> + + <para>整数行ベクトル (次元ã¯å†å¸°çš„クラスã®æ•°).</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tr</term> + + <listitem> + + <para>æ•´æ•° (一時的ãªçŠ¶æ…‹é‡ã®æ•°)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>M</term> + + <listitem> + + <para>実数ã®ãƒžãƒ«ã‚³ãƒ•è¡Œåˆ—. + + 1ã«è¿½åŠ ã™ã‚‹å„è¡Œã®ã‚¨ãƒ³ãƒˆãƒªã®åˆè¨ˆ. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para> + + æ–‡å—列 <literal>'perm'</literal>. 指定ã—ãŸå ´åˆ, + + 状態é‡ã®ãƒ©ãƒ³ãƒ€ãƒ ãªç½®æ›ãŒè¡Œã‚ã‚Œã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + ãã‚Œãžã‚Œ<literal>rec(1),...rec($)</literal>個ã®ã‚¨ãƒ³ãƒˆãƒªã‚’有ã™ã‚‹ + + <literal>size(rec,1)</literal>個ã®å†å¸°çš„ãªã‚¯ãƒ©ã‚¹ã¨tr個ã®ä¸€æ™‚çš„ãªçŠ¶æ…‹é‡ã‚’有ã™ã‚‹ + + ランダムãªãƒžãƒ«ã‚³ãƒ•æŽ¨ç§»ç¢ºçŽ‡è¡Œåˆ—ã‚’Mã«è¿”ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +//P has two recurrent classes (with 2 and 1 states) 2 transient states +P=genmarkov([2,1],2,'perm') +[perm,rec,tr,indsRec,indsT]=classmarkov(P); +P(perm,perm) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="classmarkov">classmarkov</link> + + </member> + + <member> + + <link linkend="eigenmarkov">eigenmarkov</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/matrix/CHAPTER b/modules/linear_algebra/help/ja_JP/matrix/CHAPTER new file mode 100755 index 000000000..bb89125cd --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/CHAPTER @@ -0,0 +1,2 @@ +title = Matrix Analysis + diff --git a/modules/linear_algebra/help/ja_JP/matrix/cond.xml b/modules/linear_algebra/help/ja_JP/matrix/cond.xml new file mode 100755 index 000000000..874d2fd98 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/cond.xml @@ -0,0 +1,292 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="cond"> + + <refnamediv> + + <refname>cond</refname> + + <refpurpose>æ¡ä»¶æ•°</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis> + + c = cond(X) + + c = cond(X, p) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para> + + 実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—. c = cond(X, p)ã®å ´åˆ, Xã¯å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ•°ã® + + æ£æ–¹è¡Œåˆ—ã¨ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>c</term> + + <listitem> + + <para>実数スカラー, æ¡ä»¶æ•°.</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <variablelist> + + <varlistentry> + + <term>c = cond(X)</term> + + <listitem> + + <para> + + ã¯,2-ノルムã®æ¡ä»¶æ•°ã‚’è¿”ã—ã¾ã™. + + <literal>cond(X)</literal>ã¯<literal>X</literal>ã® + + 最大特異値ã¨æœ€å°ç‰¹ç•°å€¤ã®æ¯”ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>c = cond(X, p)</term> + + <listitem> + + <para> + + ã¯,p-ノルムã®æ¡ä»¶æ•°ã‚’è¿”ã—ã¾ã™ : + + <literal>norm(X, p) * norm(inv(X), p)</literal>. + + <literal>p</literal> ãŒæŒ‡å®šã•ã‚ŒãŸå ´åˆ, + + <literal>p</literal> ã¯ä»¥ä¸‹ã«ç‰ã—ããªã‚Šã¾ã™ : + + </para> + + <itemizedlist> + + <listitem> + + <para> + + p = 1. <literal>cond(X, p)</literal> ã¯,1-ノルムã®æ¡ä»¶æ•°ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + <listitem> + + <para> + + p = 2. <literal>cond(X, p)</literal> ã¯,1-ノルムã®æ¡ä»¶æ•°ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + <listitem> + + <para> + + p = %inf ã¾ãŸã¯ 'inf'. <literal>cond(X, p)</literal> + + ã¯,ç„¡é™å¤§ãƒŽãƒ«ãƒ ã®æ¡ä»¶æ•°ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + <listitem> + + <para> + + p = 'fro'. <literal>cond(X, p)</literal> + + ã¯ãƒ•ãƒãƒ™ãƒ‹ã‚¦ã‚¹ãƒŽãƒ«ãƒ ã®æ¡ä»¶æ•°ã‚’è¿”ã—ã¾ã™. + + </para> + + </listitem> + + </itemizedlist> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"> + + <![CDATA[ +A=testmatrix('hilb',6); +// 2-ノルムã®æ¡ä»¶æ•° +cond(A) +cond(A, 2) + +// 1-ノルムã®æ¡ä»¶æ•° +cond(A, 1) + +// ç„¡é™å¤§ãƒŽãƒ«ãƒ ã®æ¡ä»¶æ•° +cond(A, %inf) + +// フãƒãƒ™ãƒ‹ã‚¦ã‚¹ãƒŽãƒ«ãƒ ã®æ¡ä»¶æ•° +cond(A, 'fro') + ]]> + + </programlisting> + + </refsection> + + <refsection> + + <title>å‚考</title> + + <simplelist type="inline"> + + <member> + + <link linkend="rcond">rcond</link> + + </member> + + <member> + + <link linkend="svd">svd</link> + + </member> + + <member> + + <link linkend="norm">norm</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>å±¥æ´</title> + + <revhistory> + + <revision> + + <revnumber>5.4.0</revnumber> + + <revdescription> + + <para> + + éžæ£æ–¹è¡Œåˆ—ã®<literal>X</literal>を指定ã—ã¦, + + <literal>cond(X)</literal>をコールã—ã¦ã‚‚管ç†ã•ã‚Œã‚‹ã‚ˆã†ã«ãªã‚Šã¾ã—ãŸ. + + 例ãˆã°: + + </para> + + <programlisting role=""> + + <![CDATA[ +X = [1 0; 1 -1; 0 1]; +cond(X) + ]]> + + </programlisting> + + <para> + + <literal>cond(X, p)</literal>をコールã™ã‚‹ã“ã¨ã§ã€ + + p-ノルムæ¡ä»¶æ•°ã‚’計算ã§ãるよã†ã«ãªã‚Šã¾ã—ãŸ. + + 例ãˆã°: + + </para> + + <programlisting role=""> + + <![CDATA[ +X = [1 -6 0; 1 0 -4;1 0 2]; +cond(X, 1) // 1-ノルム(p = 1)ã®æ¡ä»¶æ•° + ]]> + + </programlisting> + + </revdescription> + + </revision> + + </revhistory> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/matrix/det.xml b/modules/linear_algebra/help/ja_JP/matrix/det.xml new file mode 100755 index 000000000..c7ea8f509 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/det.xml @@ -0,0 +1,212 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="det"> + + <refnamediv> + + <refname>det</refname> + + <refpurpose>行列å¼</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼出ã—æ‰‹é †</title> + + <synopsis>det(X) + + [e,m]=det(X) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ£æ–¹è¡Œåˆ—, å¤šé …å¼ã¾ãŸã¯æœ‰ç†è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>m</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°, 行列å¼ã® 10 を基底ã¨ã™ã‚‹ä»®æ•°</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>e</term> + + <listitem> + + <para>æ•´æ•°, 行列å¼ã® 10 を基底ã¨ã™ã‚‹æŒ‡æ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>det(X)</literal> (<literal>m*10^e</literal>)ã¯, + + æ£æ–¹è¡Œåˆ—<literal>X</literal>ã®è¡Œåˆ—å¼ã§ã™. + + </para> + + <para> + + å¤šé …å¼è¡Œåˆ—ã®å ´åˆ,<literal>det(X)</literal> 㯠+ + <literal>determ(X)</literal>ã¨ç‰ã—ããªã‚Šã¾ã™. + + </para> + + <para> + + 有ç†æ•°è¡Œåˆ—ã®å ´åˆ, <literal>det(X)</literal> 㯠+ + <literal>detr(X)</literal>ã¨ç‰ã—ããªã‚Šã¾ã™. + + </para> + + <para> + + <important> + + <literal>det</literal> ãŠã‚ˆã³ <literal>detr</literal> 関数㯠+ + åŒã˜ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ を使用ã—ã¾ã›ã‚“. + + 有ç†æ•°é–¢æ•°ã®å ´åˆ, <literal>det(X)</literal> 㯠+ + <literal>determ</literal>関数ã«åŸºã¥ã + + <literal>%r_det(X)</literal> ã§ã‚ªãƒ¼ãƒãƒ¼ãƒãƒ¼ãƒ‰ã•ã‚Œã¾ã™. + + <literal>detr()</literal> ã¯, Leverrier法を使用ã—ã¾ã™. + + </important> + + <warning> + + 時々, + + <literal>det</literal> ãŠã‚ˆã³ <literal>detr</literal> 関数㯠+ + 有ç†æ•°é–¢æ•°ã¨ç•°ãªã‚‹å€¤ã‚’è¿”ã™å¯èƒ½æ€§ãŒã‚ã‚Šã¾ã™. + + ã“ã®ã‚ˆã†ãªå ´åˆ,åŒã˜çµæžœã‚’å¾—ã‚‹ãŸã‚ã«, + + 有ç†æ•°ã¯<code>simp_mode(%f)</code>を使用ã™ã‚‹ã“ã¨ã«ã‚ˆã‚Š + + 有ç†æ•°ã‚’ç°¡å˜åŒ–ã™ã‚‹ãƒ¢ãƒ¼ãƒ‰ã‚’無効ã«ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + </warning> + + </para> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <para> + + det ã®è¨ˆç®—㯠Lapack ルーãƒãƒ³ DGETRF (実数行列ã®å ´åˆ) ãŠã‚ˆã³ + + ZGETRF (è¤‡ç´ æ•°ã®å ´åˆ)ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + <para> + + 疎行列ã®å ´åˆ, 行列å¼ã¯ umfpack ライブラリã®LU分解ã«ã‚ˆã‚Šå¾—られã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +det([x,1+x;2-x,x^2]) +w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w) //線形システムã®ã‚¼ãƒ +A=rand(3,3); +det(A), prod(spec(A)) + ]]></programlisting> + + </refsection> + + <refsection> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="detr">detr</link> + + </member> + + <member> + + <link linkend="determ">determ</link> + + </member> + + <member> + + <link linkend="simp_mode">simp_mode</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/matrix/orth.xml b/modules/linear_algebra/help/ja_JP/matrix/orth.xml new file mode 100755 index 000000000..c66862e31 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/orth.xml @@ -0,0 +1,144 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="orth"> + + <refnamediv> + + <refname>orth</refname> + + <refpurpose>直交基底</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>Q=orth(A)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>Q=orth(A)</literal> ã¯, + + <literal>A</literal>ã®ç¯„囲ã§ã®ç›´äº¤åŸºåº•ã§ã‚ã‚‹ + + <literal>Q</literal>ã‚’è¿”ã—ã¾ã™. + + Range(<literal>Q</literal>) = + + Range(<literal>A</literal>) ãŠã‚ˆã³ <literal>Q'*Q=eye</literal>. + + </para> + + <para> + + <literal>Q</literal>ã®åˆ—ã®æ•°ã¯, + + QRアルゴリズムã§å®šç¾©ã•ã‚ŒãŸ + + <literal>A</literal>ã®ãƒ©ãƒ³ã‚¯ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,4); +[X,dim]=rowcomp(A);X=X'; +svd([orth(A),X(:,1:dim)]) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + <member> + + <link linkend="range">range</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/matrix/rank.xml b/modules/linear_algebra/help/ja_JP/matrix/rank.xml new file mode 100755 index 000000000..cdbd5aee6 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/rank.xml @@ -0,0 +1,157 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rank"> + + <refnamediv> + + <refname>rank</refname> + + <refpurpose>階数</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[i]=rank(X) + + [i]=rank(X,tol) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>éžè² 実数</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>rank(X)</literal> ã¯, <literal>X</literal>ã®æ•°å€¤çš„ãªéšŽæ•°(ランク), + + ã™ãªã‚ã¡, <literal>norm(size(X),'inf') * norm(X) * %eps</literal> より大ã㪠+ + X ã®ç‰¹ç•°å€¤ã®æ•°ã§ã™. + + </para> + + <para> + + <literal>rank(X,tol)</literal> ã¯,<literal>tol</literal> + + より大ããª<literal>X</literal>ã®ç‰¹ç•°å€¤ã®æ•°ã§ã™. + + </para> + + <para> + + <literal>tol</literal> ã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã¯ + + <literal>norm(X)</literal>ã«æ¯”例ã™ã‚‹ã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + + çµæžœã¨ã—ã¦,<literal>rank([1.d-80,0;0,1.d-80])</literal> 㯠2 ã«ãªã‚Šã¾ã™!. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +rank([1.d-80,0;0,1.d-80]) +rank([1,0;0,1.d-80]) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="svd">svd</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + <member> + + <link linkend="rowcomp">rowcomp</link> + + </member> + + <member> + + <link linkend="colcomp">colcomp</link> + + </member> + + <member> + + <link linkend="lu">lu</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/matrix/rcond.xml b/modules/linear_algebra/help/ja_JP/matrix/rcond.xml new file mode 100755 index 000000000..e12e728b5 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/rcond.xml @@ -0,0 +1,145 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rcond"> + + <refnamediv> + + <refname>rcond</refname> + + <refpurpose>æ¡ä»¶æ•°ã®é€†æ•°</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>rcond(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>rcond(X)</literal> ã¯,1-ノルムã«ãŠã‘ã‚‹ + + <literal>X</literal>ã®æ¡ä»¶ã®é€†æ•°ã®æŽ¨å®šå€¤ã§ã™. + + </para> + + <para> + + <literal>X</literal>ãŒå¥å…¨ãªå ´åˆ, + + <literal>rcond(X)</literal> 㯠1 ã«è¿‘ããªã‚Šã¾ã™. + + ãã†ã§ãªã„å ´åˆ, <literal>rcond(X)</literal> 㯠0ã«è¿‘ããªã‚Šã¾ã™. + + </para> + + <para> + + Aã®1-ノルムを Lapack/DLANGEã§è¨ˆç®—, ãã®LU分解をLapack/DGETRFã§è¨ˆç®—, + + 最後ã«æ¡ä»¶ã‚’Lapack/DGECONã§æŽ¨å®šã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=diag([1:10]); +rcond(A) +A(1,1)=0.000001; +rcond(A) + ]]></programlisting> + + <para> + + <literal>rcond</literal>ã«ã‚ˆã‚‹1-ノルム逆æ¡ä»¶æ•°ã®æŽ¨å®šã¯, + + <literal>cond</literal>ã«ã‚ˆã‚‹2-ノルムæ¡ä»¶æ•°ã®è¨ˆç®—よりã¯ã‚‹ã‹ã«é«˜é€Ÿã§ã™. + + トレードオフã¨ã—ã¦,<literal>rcond</literal> ã¯è‹¥å¹²ä¿¡é ¼æ€§ãŒä½Žä¸‹ã™ã‚‹å¯èƒ½æ€§ãŒã‚ã‚Šã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ + A=ones(1000,1000); + timer();cond(A);timer() + timer();1/rcond(A);timer() + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="svd">svd</link> + + </member> + + <member> + + <link linkend="cond">cond</link> + + </member> + + <member> + + <link linkend="inv">inv</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/matrix/rref.xml b/modules/linear_algebra/help/ja_JP/matrix/rref.xml new file mode 100755 index 000000000..cf47e7b89 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/rref.xml @@ -0,0 +1,127 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rref"> + + <refnamediv> + + <refname>rref</refname> + + <refpurpose>LU分解ã«ã‚ˆã‚Šè¡Œã‚¨ã‚·ãƒ¥ãƒãƒ³å½¢å¼ã®è¡Œåˆ—を計算</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>R=rref(A)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>スカラーã®ã‚¨ãƒ³ãƒˆãƒªã‚’有ã™ã‚‹m x n 行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>R</term> + + <listitem> + + <para> Aã®è¡Œã‚¨ã‚·ãƒ¥ãƒãƒ³å½¢å¼ã®m x n行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>rref</literal> ã¯,å·¦LU分解ã«ã‚ˆã‚ŠæŒ‡å®šã—ãŸè¡Œåˆ— + + ã®è¡Œã‚¨ã‚·ãƒ¥ãƒãƒ³å½¢å¼ã‚’計算ã—ã¾ã™. + + <literal>X=rref([A,eye(m,m)])</literal>をコールã™ã‚‹éš›ã«ä½¿ç”¨ã—㟠+ + 変æ›ã ã‘ãŒå¿…è¦ãªå ´åˆ,行エシュãƒãƒ³å½¢å¼<literal>R</literal>㯠+ + <literal>X(:,1:n)</literal>ã¨ãªã‚Šã¾ã™. + + 左変æ›<literal>L</literal>ã¯,<literal>L*A=R</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + <literal>X(:,n+1:n+m)</literal> ã«ã‚ˆã‚Šå¾—ã‚‹ã“ã¨ãŒã§ãã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=[1 2;3 4;5 6]; +X=rref([A,eye(3,3)]); +R=X(:,1:2) +L=X(:,3:5);L*A + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="lu">lu</link> + + </member> + + <member> + + <link linkend="qr">qr</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/matrix/trace.xml b/modules/linear_algebra/help/ja_JP/matrix/trace.xml new file mode 100755 index 000000000..c3b6fd4ba --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/matrix/trace.xml @@ -0,0 +1,103 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="trace"> + + <refnamediv> + + <refname>trace</refname> + + <refpurpose>トレース</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>trace(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®æ£æ–¹è¡Œåˆ—, å¤šé …å¼ã¾ãŸã¯æœ‰ç†è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>trace(X)</literal>ã¯,行列<literal>X</literal>ã® + + トレースã§ã™. + + </para> + + <para> + + <literal>sum(diag(X))</literal>ã¨åŒã˜ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(3,3); +trace(A)-sum(spec(A)) + ]]></programlisting> + + </refsection> + + <refsection> + + <title>å‚考</title> + + <simplelist type="inline"> + + <member> + + <link linkend="det">det</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/CHAPTER b/modules/linear_algebra/help/ja_JP/pencil/CHAPTER new file mode 100755 index 000000000..86d1da116 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/CHAPTER @@ -0,0 +1,2 @@ +title = Matrix Pencil + diff --git a/modules/linear_algebra/help/ja_JP/pencil/companion.xml b/modules/linear_algebra/help/ja_JP/pencil/companion.xml new file mode 100755 index 000000000..93a9adcec --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/companion.xml @@ -0,0 +1,150 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="companion"> + + <refnamediv> + + <refname>companion</refname> + + <refpurpose>コンパニオン行列 </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>A=companion(p)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>p</term> + + <listitem> + + <para>å¤šé …å¼ã¾ãŸã¯å¤šé …å¼ã®ãƒ™ã‚¯ãƒˆãƒ«</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + ç‰¹æ€§å¤šé …å¼ã‚’有ã™ã‚‹ + + 行列<literal>A</literal>ã‚’è¿”ã—ã¾ã™. + + <literal>p</literal>ãŒãƒ¢ãƒ‹ãƒƒã‚¯ãªå ´åˆ,ç‰¹æ€§å¤šé …å¼ã¯ + + <literal>p</literal>ã«ç‰ã—ããªã‚Šã¾ã™. + + <literal>p</literal>ãŒãƒ¢ãƒ‹ãƒƒã‚¯ã§ãªã„å ´åˆ, + + <literal>A</literal>ã®ç‰¹æ€§æ–¹ç¨‹å¼ã¯ + + <literal>p/c</literal>ã«ç‰ã—ããªã‚Šã¾ã™. + + ãŸã ã—,<literal>c</literal>ã¯<literal>p</literal> + + ã®æœ€å¤§æ¬¡æ•°ã®ä¿‚æ•°ã§ã™. + + </para> + + <para> + + <literal>p</literal> ãŒãƒ¢ãƒ‹ãƒƒã‚¯ãªå¤šé …å¼ã®ãƒ™ã‚¯ãƒˆãƒ«ã®å ´åˆ, + + <literal>A</literal> ã¯ãƒ–ãƒãƒƒã‚¯å¯¾è§’ã¨ãªã‚Š, + + i番目ã®ç‰¹æ€§å¤šé …å¼ã¯ + + <literal>p(i)</literal>ã¨ãªã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=poly([1,2,3,4,1],'s','c') +det(s*eye()-companion(p)) +roots(p) +spec(companion(p)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spec">spec</link> + + </member> + + <member> + + <link linkend="poly">poly</link> + + </member> + + <member> + + <link linkend="randpencil">randpencil</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/ereduc.xml b/modules/linear_algebra/help/ja_JP/pencil/ereduc.xml new file mode 100755 index 000000000..b1d93ff64 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/ereduc.xml @@ -0,0 +1,223 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="ereduc"> + + <refnamediv> + + <refname>ereduc</refname> + + <refpurpose>QZ変æ›ã«ã‚ˆã‚Šåˆ—階段型行列を計算</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数エントリを有ã™ã‚‹m x n 行列.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数ã®æ£ã®ã‚¹ã‚«ãƒ©ãƒ¼.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E</term> + + <listitem> + + <para>列階段型行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q</term> + + <listitem> + + <para>m x m ユニタリ行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Z</term> + + <listitem> + + <para>n x n ユニタリ行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>stair</term> + + <listitem> + + <para>æ·»å—ベクトル,</para> + + <variablelist> + + <varlistentry> + + <term>* </term> + + <listitem> + + <para> + + 境界è¦ç´ <literal>E(i,j)</literal>ãŒç«¯ç‚¹ã®å ´åˆ, + + <literal>ISTAIR(i) = + j</literal>. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>* </term> + + <listitem> + + <para> + + 境界è¦ç´ <literal>E(i,j)</literal>ãŒç«¯ç‚¹ã§ãªã„å ´åˆ, + + <literal>ISTAIR(i) = - j</literal>. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + <para> + + <literal>(i=1,...,M)</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rk</term> + + <listitem> + + <para>æ•´æ•°, 行列ã®ãƒ©ãƒ³ã‚¯ã®æŽ¨å®šå€¤</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>mx n</literal>行列<literal>X</literal> (æ£å‰‡ã§ã‚ã‚‹ + + å¿…è¦ã¯ãªã„)を指定ã™ã‚‹ã¨, + + 関数ereducã¯,列階段型(å°å½¢)ã® + + ユニタリ変æ›è¡Œåˆ—<literal>E=Q*X*Z</literal> + + を計算ã—ã¾ã™. + + æ›´ã«è¡Œåˆ—<literal>X</literal>ã®ãƒ©ãƒ³ã‚¯ãŒå®šç¾©ã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +X=[1 2 3;4 5 6] +[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="fstair">fstair</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/fstair.xml b/modules/linear_algebra/help/ja_JP/pencil/fstair.xml new file mode 100755 index 000000000..7f82fe30d --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/fstair.xml @@ -0,0 +1,354 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="fstair"> + + <refnamediv> + + <refname>fstair</refname> + + <refpurpose>QZ変æ›ã«ã‚ˆã‚Šåˆ—階段型ペンシルを計算ã™ã‚‹</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数エントリを有ã™ã‚‹m x n行列.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数ã®æ£ã®ã‚¹ã‚«ãƒ©ãƒ¼.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E</term> + + <listitem> + + <para>列階段型行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q</term> + + <listitem> + + <para>m x m ユニタリ行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Z</term> + + <listitem> + + <para>n x n ユニタリ行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>stair</term> + + <listitem> + + <para>æ·»å—ベクトル (ereducå‚ç…§)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rk</term> + + <listitem> + + <para>æ•´æ•°, 行列ランクã®æŽ¨å®šå€¤</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>AE</term> + + <listitem> + + <para>実数エントリを有ã™ã‚‹m x n行列.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>EE</term> + + <listitem> + + <para>列階段型行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>QE</term> + + <listitem> + + <para>m x m ユニタリ行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ZE</term> + + <listitem> + + <para>n x n ユニタリ行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>nblcks</term> + + <listitem> + + <para> + + 行列<literal>A</literal>ã§æ¤œå‡ºã•ã‚ŒãŸ + + フル行ランクを有ã™ã‚‹ã‚µãƒ–行列ã®æ•°(>= 0). + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>muk: </term> + + <listitem> + + <para>次元 (n) ã®æ•´æ•°é…列. + + ペンシルsE(eps)-A(eps)ã«ãŠã„㦠+ + 列フルランクを有ã™ã‚‹ã‚µãƒ–行列ã®åˆ—次元 mu(k) (k=1,...,nblcks) ã‚’å«ã¿ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>nuk: </term> + + <listitem> + + <para> + + 次元 (m+1) ã®æ•´æ•°é…列. + + ペンシルsE(eps)-A(eps)ã«ãŠã„㦠+ + 行フルランクを有ã™ã‚‹ã‚µãƒ–行列ã®è¡Œæ¬¡å…ƒ nu(k) (k=1,...,nblcks) + + ã‚’å«ã¿ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>muk0: </term> + + <listitem> + + <para> + + 次元 (n) ã®æ•´æ•°é…列. + + ペンシルsE(eps,inf)-A(eps,inf)ã«ãŠã„㦠+ + 列フルランクを有ã™ã‚‹ã‚µãƒ–行列ã®åˆ—次元 mu(k) (k=1,...,nblcks) ã‚’å«ã¿ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>nuk: </term> + + <listitem> + + <para> + + 次元 (m+1) ã®æ•´æ•°é…列. + + ペンシルsE(eps,inf)-A(eps,inf)ã«ãŠã„㦠+ + 行フルランクを有ã™ã‚‹ã‚µãƒ–行列ã®è¡Œæ¬¡å…ƒ nu(k) (k=1,...,nblcks) + + ã‚’å«ã¿ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>mnei: </term> + + <listitem> + + <para>次元 (4) ã®æ•´æ•°é…列. + + mnei(1) = sE(eps)-A(eps)ã®è¡Œã®æ¬¡å…ƒ + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 行列 <literal>E</literal> を列階段形ã¨ã—ã¦, + + ペンシル <literal>sE-A</literal> を指定ã™ã‚‹ã¨, + + 関数<literal>fstair</literal>㯠+ + ユーザã®æŒ‡å®šã«åŸºã¥ã + + ユニタリ変æ›ã•ã‚ŒãŸãƒšãƒ³ã‚·ãƒ«<literal>QE(sEE-AE)ZE</literal>ã‚’ + + 計算ã—ã¾ã™. + + ã“ã®ãƒšãƒ³ã‚·ãƒ«ã¯, ã»ã¼ãƒšãƒ³ã‚·ãƒ«<literal>sE-A</literal> + + ã®ä¸€èˆ¬åŒ–Schurå½¢å¼ã§ã™. + + ã“ã®é–¢æ•°ã¯,指定ã—ãŸãƒšãƒ³ã‚·ãƒ«ã® + + クãƒãƒãƒƒã‚«ãƒ¼æ§‹é€ ã®éƒ¨åˆ†ã‚‚出力ã—ã¾ã™. + + </para> + + <para> + + <literal>Q,Z</literal> ã¯ãƒ¦ãƒ‹ã‚¿ãƒªè¡Œåˆ—ã§, + + ペンシルを計算ã™ã‚‹éš›ã«ä½¿ç”¨ã•ã‚Œã¾ã™. + + ãŸã ã—, E ã¯åˆ—階段形ã§ã™ (ereducå‚ç…§) + + </para> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="quaskro">quaskro</link> + + </member> + + <member> + + <link linkend="ereduc">ereduc</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/glever.xml b/modules/linear_algebra/help/ja_JP/pencil/glever.xml new file mode 100755 index 000000000..b51eac00e --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/glever.xml @@ -0,0 +1,220 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="glever"> + + <refnamediv> + + <refname>glever</refname> + + <refpurpose>行列ペンシルã®é€†</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>E, A</term> + + <listitem> + + <para>åŒã˜æ¬¡å…ƒã®æ£æ–¹å®Ÿè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>s</term> + + <listitem> + + <para> + + æ–‡å—列 (デフォルト値 '<literal>s</literal>') + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Bfs,Bis</term> + + <listitem> + + <para>å¤šé …å¼è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>chis</term> + + <listitem> + + <para>å¤šé …å¼</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para>一般化ã—ãŸLeverrierã®ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã«ã‚ˆã‚Šã‚る行列ペンシルã«ã¤ã„㦠+ + </para> + + <para> + + <literal>(s*E-A)^-1</literal> + + </para> + + <para> + + を計算ã—ã¾ã™. + + </para> + + <programlisting role=""><![CDATA[ +(s*E-A)^-1 = (Bfs/chis) - Bis. + ]]></programlisting> + + <para> + + <literal>chis</literal> = ç‰¹æ€§å¤šé …å¼ (乗法定数ã¾ã§). + + </para> + + <para> + + <literal>Bfs</literal> = 分åã®ç‰¹æ€§å¤šé …å¼è¡Œåˆ—. + + </para> + + <para> + + <literal>Bis</literal> + + = å¤šé …å¼è¡Œåˆ— ( - <literal>(s*E-A)^-1</literal> ã®ç„¡é™å¤§ã¾ã§ã®ç´šæ•°å±•é–‹). + + </para> + + <para> + + <literal>Bis</literal>ã®å‰ã« - 符å·ãŒã‚ã‚‹ã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + + </para> + + </refsection> + + <refsection> + + <title>注æ„</title> + + <para> + + ã“ã®é–¢æ•°ã¯,<literal>Bfs,Bis</literal> ãŠã‚ˆã³ <literal>chis</literal>ã‚’ + + ç°¡å˜åŒ–ã™ã‚‹ãŸã‚ã« <literal>cleanp</literal>を使用ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1]; +[Bfs,Bis,chis]=glever(F) +inv(F)-((Bfs/chis) - Bis) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="rowshuff">rowshuff</link> + + </member> + + <member> + + <link linkend="det">det</link> + + </member> + + <member> + + <link linkend="invr">invr</link> + + </member> + + <member> + + <link linkend="coffg">coffg</link> + + </member> + + <member> + + <link linkend="pencan">pencan</link> + + </member> + + <member> + + <link linkend="penlaur">penlaur</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/kroneck.xml b/modules/linear_algebra/help/ja_JP/pencil/kroneck.xml new file mode 100755 index 000000000..73cd277ef --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/kroneck.xml @@ -0,0 +1,281 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="kroneck"> + + <refnamediv> + + <refname>kroneck</refname> + + <refpurpose>行列ペンシルã®ã‚¯ãƒãƒãƒƒã‚«ãƒ¼å½¢å¼</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F) + + [Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(E,A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>F</term> + + <listitem> + + <para> + + 実数行列ペンシル <literal>F=s*E-A</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E,A</term> + + <listitem> + + <para>åŒã˜æ¬¡å…ƒã®å®Ÿæ•°è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q,Z</term> + + <listitem> + + <para>æ£æ–¹ç›´äº¤è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Qd,Zd</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>numbeps,numeta</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 行列ペンシルã®ã‚¯ãƒãƒãƒƒã‚«ãƒ¼å½¢å¼: <literal>kroneck</literal> ã¯, + + ペンシル<literal>F=s*E -A</literal>を以下ã®ã‚ˆã†ãªä¸Šä¸‰è§’å½¢å¼ã«å¤‰æ›ã™ã‚‹ + + 2ã¤ã®ç›´äº¤è¡Œåˆ—<literal>Q, Z</literal>を計算ã—ã¾ã™: + + </para> + + <programlisting role=""><![CDATA[ + | sE(eps)-A(eps) | X | X | X | + |----------------|----------------|------------|---------------| + | O | sE(inf)-A(inf) | X | X | +Q(sE-A)Z = |---------------------------------|----------------------------| + | | | | | + | 0 | 0 | sE(f)-A(f) | X | + |--------------------------------------------------------------| + | | | | | + | 0 | 0 | 0 | sE(eta)-A(eta)| + ]]></programlisting> + + <para> + + 4個ã®ãƒ–ãƒãƒƒã‚¯ã®æ¬¡å…ƒã¯ä»¥ä¸‹ã®ã‚ˆã†ã«æŒ‡å®šã•ã‚Œã¾ã™: + + </para> + + <para> + + <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x Zd(2)</literal>, + + <literal>f = Qd(3) x Zd(3)</literal>, <literal>eta=Qd(4)xZd(4)</literal> + + </para> + + <para> + + <literal>inf</literal>ブãƒãƒƒã‚¯ã«ã¯ãƒšãƒ³ã‚·ãƒ«ã®ç„¡é™å¤§ãƒ¢ãƒ¼ãƒ‰ãŒå«ã¾ã‚Œã¾ã™. + + </para> + + <para> + + <literal>f</literal> ブãƒãƒƒã‚¯ã«ã¯ãƒšãƒ³ã‚·ãƒ«ã®æœ‰é™ãƒ¢ãƒ¼ãƒ‰ãŒå«ã¾ã‚Œã¾ã™. + + </para> + + <para> + + イプシãƒãƒ³ã¨etaブãƒãƒƒã‚¯ã®æ§‹é€ ã¯ä»¥ä¸‹ã®ã‚ˆã†ã«æŒ‡å®šã•ã‚Œã¾ã™: + + </para> + + <para> + + <literal>numbeps(1)</literal> = 大ãã• 0 x 1ã®epsブãƒãƒƒã‚¯ã®ç•ªå· + + </para> + + <para> + + <literal>numbeps(2)</literal> = 大ãã• 1 x 2ã®epsブãƒãƒƒã‚¯ã®ç•ªå· + + </para> + + <para> + + <literal>numbeps(3)</literal> = 大ãã• 2 x 3ã®epsブãƒãƒƒã‚¯ã®ç•ªå· etc... + + </para> + + <para> + + <literal>numbeta(1)</literal> = 大ãã• 1 x 0ã®etaブãƒãƒƒã‚¯ã®ç•ªå· + + </para> + + <para> + + <literal>numbeta(2)</literal> = 大ãã• 2 x 1ã®etaブãƒãƒƒã‚¯ã®ç•ªå· + + </para> + + <para> + + <literal>numbeta(3)</literal> = 大ãã• 3 x 2ã®etaブãƒãƒƒã‚¯ã®ç•ªå· etc... + + </para> + + <para> + + ã“ã®ã‚³ãƒ¼ãƒ‰ã¯T. Beelen (Slicot-WGS group)ã«ã‚ˆã‚‹ã‚‚ã®ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +F=randpencil([1,1,2],[2,3],[-1,3,1],[0,3]); +Q=rand(17,17);Z=rand(18,18);F=Q*F*Z; +//random pencil with eps1=1,eps2=1,eps3=1; 2 J-blocks @ infty +//with dimensions 2 and 3 +//3 finite eigenvalues at -1,3,1 and eta1=0,eta2=3 +[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F); +[Qd(1),Zd(1)] //eps. part is sum(epsi) x (sum(epsi) + number of epsi) +[Qd(2),Zd(2)] //infinity part +[Qd(3),Zd(3)] //finite part +[Qd(4),Zd(4)] //eta part is (sum(etai) + number(eta1)) x sum(etai) +numbeps +numbeta + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="gschur">gschur</link> + + </member> + + <member> + + <link linkend="gspec">gspec</link> + + </member> + + <member> + + <link linkend="systmat">systmat</link> + + </member> + + <member> + + <link linkend="pencan">pencan</link> + + </member> + + <member> + + <link linkend="randpencil">randpencil</link> + + </member> + + <member> + + <link linkend="trzeros">trzeros</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/lyap.xml b/modules/linear_algebra/help/ja_JP/pencil/lyap.xml new file mode 100755 index 000000000..206c3f209 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/lyap.xml @@ -0,0 +1,143 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="lyap"> + + <refnamediv> + + <refname>lyap</refname> + + <refpurpose>リアプノフ方程å¼</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[X]=lyap(A,C,'c') + + [X]=lyap(A,C,'d') + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A, C</term> + + <listitem> + + <para> + + 実数æ£æ–¹è¡Œåˆ—, <literal>C</literal> ã¯å¯¾ç§°ã§ã‚ã‚‹ã“ã¨ãŒå¿…è¦ + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>X= lyap(A,C,flag)</literal> ã¯é€£ç¶šæ™‚é–“ã¾ãŸã¯é›¢æ•£æ™‚間行列 + + リアプノフ方程å¼ã‚’解ãã¾ã™: + + </para> + + <programlisting role=""><![CDATA[ +A'*X + X*A = C ( flag='c' ) +A'*X*A - X = C ( flag='d' ) + ]]></programlisting> + + <para> + + <note> + + <literal>A</literal>ã®å›ºæœ‰å€¤ãŒ<literal>-A</literal>ã® + + 固有値ã§ãªã„å ´åˆ(<literal>flag='c'</literal>) + + ã¾ãŸã¯<literal>A</literal>ã®å›ºæœ‰å€¤åˆ†ã®1ã®å ´åˆ + + (<literal>flag='d'</literal>)ã«ã®ã¿ãƒ¦ãƒ‹ãƒ¼ã‚¯ãª + + 解ãŒå¾—られるã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + + </note> + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(4,4);C=rand(A);C=C+C'; +X=lyap(A,C,'c'); +A'*X + X*A -C +X=lyap(A,C,'d'); +A'*X*A - X -C + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sylv">sylv</link> + + </member> + + <member> + + <link linkend="ctr_gram">ctr_gram</link> + + </member> + + <member> + + <link linkend="obs_gram">obs_gram</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/pencan.xml b/modules/linear_algebra/help/ja_JP/pencil/pencan.xml new file mode 100755 index 000000000..842d32110 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/pencan.xml @@ -0,0 +1,191 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="pencan"> + + <refnamediv> + + <refname>pencan</refname> + + <refpurpose>行列ペンシルã®æ£æº–å½¢</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,M,i1]=pencan(Fs) + + [Q,M,i1]=pencan(E,A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>Fs</term> + + <listitem> + + <para> + + 標準ペンシル <literal>s*E-A</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E,A</term> + + <listitem> + + <para>実数æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q,M</term> + + <listitem> + + <para>æ£å‰‡å®Ÿæ•°è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>i1</term> + + <listitem> + + <para>æ•´æ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 標準ペンシル <literal>Fs=s*E-A</literal>を指定ã™ã‚‹ã¨, + + <literal>pencan</literal> ã¯, + + <literal>M*(s*E-A)*Q</literal>ãŒ"æ£æº–"å½¢ã¨ãªã‚‹ã‚ˆã†ãª + + 行列<literal>Q</literal> ãŠã‚ˆã³<literal>M</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + <para> + + <literal>M*E*Q</literal> ã¯ãƒ–ãƒãƒƒã‚¯è¡Œåˆ—ã§ã™. + + </para> + + <programlisting role=""><![CDATA[ +[I,0; + 0,N] + ]]></programlisting> + + <para> + + ãŸã ã—,<literal>N</literal>ã¯å†ªé›¶è¡Œåˆ—<literal>N</literal>, + + <literal>i1</literal> = 行列<literal>I</literal>ã®å¤§ãã•ã§ã™. + + </para> + + <para> + + <literal>M*A*Q</literal> ã¯ä»¥ä¸‹ã®ã‚ˆã†ãªãƒ–ãƒãƒƒã‚¯è¡Œåˆ—ã§ã™: + + </para> + + <programlisting role=""><![CDATA[ +[Ar,0; + 0,I] + ]]></programlisting> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +F=randpencil([],[1,2],[1,2,3],[]); +F=rand(6,6)*F*rand(6,6); +[Q,M,i1]=pencan(F); +W=clean(M*F*Q) +roots(det(W(1:i1,1:i1))) +det(W($-2:$,$-2:$)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="glever">glever</link> + + </member> + + <member> + + <link linkend="penlaur">penlaur</link> + + </member> + + <member> + + <link linkend="rowshuff">rowshuff</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/penlaur.xml b/modules/linear_algebra/help/ja_JP/pencil/penlaur.xml new file mode 100755 index 000000000..33556c0e8 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/penlaur.xml @@ -0,0 +1,224 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="penlaur"> + + <refnamediv> + + <refname>penlaur</refname> + + <refpurpose>行列ペンシルã®ãƒãƒ¼ãƒ©ãƒ³ä¿‚æ•°</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Si,Pi,Di,order]=penlaur(Fs) + + [Si,Pi,Di,order]=penlaur(E,A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>Fs</term> + + <listitem> + + <para> + + 標準ペンシル <literal>s*E-A</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E, A</term> + + <listitem> + + <para>実数æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Si,Pi,Di</term> + + <listitem> + + <para>実数æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>order</term> + + <listitem> + + <para>æ•´æ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>penlaur</literal> ã¯,ç„¡é™å¤§ã«ãŠã‘ã‚‹ + + <literal>(s*E-A)^-1</literal>ã®ç¬¬ä¸€ãƒãƒ¼ãƒ©ãƒ³ä¿‚æ•°ã‚’ + + 計算ã—ã¾ã™. + + </para> + + <para> + + <literal>s</literal> = ç„¡é™å¤§ ã«ãŠã„ã¦, + + <literal>(s*E-A)^-1 = ... + Si/s - Pi - s*Di + ...</literal> + + </para> + + <para> + + <literal>order</literal> = 特異点ã®æ¬¡æ•° (order=index-1). + + </para> + + <para> + + 行列ペンシル <literal>Fs=s*E-A</literal> ã¯å¯é€†ã§ã‚ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + </para> + + <para> + + æ·»å—0ã®ãƒšãƒ³ã‚·ãƒ«ã®å ´åˆ, + + <literal>Pi, Di,...</literal> 㯠0,ãŠã‚ˆã³ <literal>Si=inv(E)</literal> + + ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + æ·»å—1ã®ãƒšãƒ³ã‚·ãƒ«(order=0)ã®å ´åˆ, + + <literal>Di</literal> =0 ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + より大ããªæ·»å—ã®ãƒšãƒ³ã‚·ãƒ«ã®å ´åˆ, + + é … <literal> -s^2 Di(2), -s^3 Di(3),... </literal> ã¯æ¬¡ã®ã‚ˆã†ã«æŒ‡å®šã•ã‚Œã¾ã™: + + </para> + + <para> + + <literal> Di(2)=Di*A*Di</literal>, <literal> Di(3)=Di*A*Di*A*Di</literal> (最大 <literal>Di(order)</literal>). + + </para> + + </refsection> + + <refsection> + + <title>注æ„</title> + + <para> + + 実験的ãªãƒãƒ¼ã‚¸ãƒ§ãƒ³: <literal>so*E-A</literal>ã®æ¡ä»¶æ•°ãŒæ‚ªã„å ´åˆã« + + å•é¡Œã‚’発生ã—ã¾ã™ + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +F=randpencil([],[1,2],[1,2,3],[]); +F=rand(6,6)*F*rand(6,6);[E,A]=pen2ea(F); +[Si,Pi,Di]=penlaur(F); +[Bfs,Bis,chis]=glever(F); +norm(coeff(Bis,1)-Di,1) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="glever">glever</link> + + </member> + + <member> + + <link linkend="pencan">pencan</link> + + </member> + + <member> + + <link linkend="rowshuff">rowshuff</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/quaskro.xml b/modules/linear_algebra/help/ja_JP/pencil/quaskro.xml new file mode 100755 index 000000000..cee463831 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/quaskro.xml @@ -0,0 +1,249 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="quaskro"> + + <refnamediv> + + <refname>quaskro</refname> + + <refpurpose>準クãƒãƒãƒƒã‚«ãƒ¼å½¢å¼</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F) + + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A) + + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F,tol) + + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A,tol) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>F</term> + + <listitem> + + <para> + + 実数行列ペンシル <literal>F=s*E-A</literal> (<literal>s=poly(0,'s')</literal>) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>E,A</term> + + <listitem> + + <para>åŒã˜æ¬¡å…ƒã®å®Ÿæ•°è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>実数 (許容誤差,デフォルト値=1.d-10)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q,Z</term> + + <listitem> + + <para>æ£æ–¹ç›´äº¤è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Qd,Zd</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>numbeps</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 行列ペンシルã®æº–クãƒãƒãƒƒã‚«ãƒ¼å½¢å¼: + + <literal>quaskro</literal>ã¯,ペンシル<literal>F=s*E -A</literal>を上三角行列形å¼ã«å¤‰æ›ã™ã‚‹ + + 直交行列 <literal>Q, Z</literal>を計算ã—ã¾ã™: + + </para> + + <programlisting role=""><![CDATA[ + | sE(eps)-A(eps) | X | X | + |----------------|----------------|------------| + | O | sE(inf)-A(inf) | X | +Q(sE-A)Z = |=================================|============| + | | | + | O | sE(r)-A(r) | + ]]></programlisting> + + <para> + + ブãƒãƒƒã‚¯ã®æ¬¡å…ƒã¯æ¬¡ã®ã‚ˆã†ã«æŒ‡å®šã•ã‚Œã¾ã™: + + </para> + + <para> + + <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x Zd(2)</literal>, + + <literal>r = Qd(3) x Zd(3)</literal> + + </para> + + <para> + + <literal>inf</literal> ブãƒãƒƒã‚¯ã«ã¯, ペンシルã®ç„¡é™å¤§ãƒ¢ãƒ¼ãƒ‰ãŒå«ã¾ã‚Œã¾ã™. + + </para> + + <para> + + <literal>f</literal> ブãƒãƒƒã‚¯ã«ã¯, ペンシルã®æœ‰é™ãƒ¢ãƒ¼ãƒ‰ãŒå«ã¾ã‚Œã¾ã™. + + </para> + + <para> + + epsilonブãƒãƒƒã‚¯ã®æ§‹é€ ã¯æ¬¡ã®ã‚ˆã†ã«æŒ‡å®šã•ã‚Œã¾ã™: + + </para> + + <para> + + <literal>numbeps(1)</literal> = 大ãã• 0 x 1ã®epsブãƒãƒƒã‚¯ã®æ•° + + </para> + + <para> + + <literal>numbeps(2)</literal> = 大ãã• 1 x 2ã®epsブãƒãƒƒã‚¯ã®æ•° + + </para> + + <para> + + <literal>numbeps(3)</literal> = 大ãã• 2 x 3ã®epsブãƒãƒƒã‚¯ã®æ•° etc... + + </para> + + <para> + + 完全ãª(4ブãƒãƒƒã‚¯ã®)クãƒãƒãƒƒã‚«ãƒ¼å½¢å¼ã¯, + + (pertransposed)ペンシル<literal>sE(r)-A(r)</literal>を指定ã—㦠+ + <literal>quaskro</literal>をコールã™ã‚‹ + + 関数<literal>kroneck</literal>ã«ã‚ˆã‚ŠæŒ‡å®šã•ã‚Œã¾ã™. + + </para> + + <para> + + ã“ã®ã‚³ãƒ¼ãƒ‰ T. Beelenã«ã‚ˆã‚‹ã‚‚ã®ã§ã™. + + </para> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="kroneck">kroneck</link> + + </member> + + <member> + + <link linkend="gschur">gschur</link> + + </member> + + <member> + + <link linkend="gspec">gspec</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/randpencil.xml b/modules/linear_algebra/help/ja_JP/pencil/randpencil.xml new file mode 100755 index 000000000..e83731339 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/randpencil.xml @@ -0,0 +1,207 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="randpencil"> + + <refnamediv> + + <refname>randpencil</refname> + + <refpurpose>ランダムãªãƒšãƒ³ã‚·ãƒ«</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>F=randpencil(eps,infi,fin,eta)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>eps</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>infi</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>fin</term> + + <listitem> + + <para>実数ベクトル, ã¾ãŸã¯ãƒ¢ãƒ‹ãƒƒã‚¯ãªå¤šé …å¼, ã¾ãŸã¯ãƒ¢ãƒ‹ãƒƒã‚¯ãªå¤šé …å¼ã®ãƒ™ã‚¯ãƒˆãƒ«</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>eta</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>F</term> + + <listitem> + + <para> + + 実数行列ペンシル <literal>F=s*E-A</literal> (<literal>s=poly(0,'s')</literal>) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + ユーティリティ関数. + + <literal>F=randpencil(eps,infi,fin,eta)</literal> ã¯,指定ã—ãŸã‚¯ãƒãƒãƒƒã‚«ãƒ¼æ§‹é€ を有ã™ã‚‹ + + ランダムãªãƒšãƒ³ã‚·ãƒ« <literal>F</literal>ã‚’è¿”ã—ã¾ã™. + + æ§‹é€ ã¯ä»¥ä¸‹ã®ã‚ˆã†ã«æŒ‡å®šã•ã‚Œã¾ã™: + + <literal>eps=[eps1,...,epsk]</literal>: epsilon ブãƒãƒƒã‚¯ã®æ§‹é€ (大ãã• eps1 x(eps1+1),....) + + <literal>fin=[l1,...,ln]</literal> 有é™ã®å›ºæœ‰å€¤ã®é›†åˆ (実数ã¨ä»®å®š)( []ã®å ´åˆã‚‚ã‚ã‚Šã¾ã™) + + <literal>infi=[k1,...,kp]</literal> ç„¡é™å¤§ã«ãŠã‘ã‚‹J-ブãƒãƒƒã‚¯ã®å¤§ãã• + + <literal>ki>=1</literal> (J ブãƒãƒƒã‚¯ãŒãªã„å ´åˆ: infi=[] ). + + <literal>eta=[eta1,...,etap]</literal>: ofeta ブãƒãƒƒã‚¯æ§‹é€ (大ãã• (eta1+1)x eta1,...) + + </para> + + <para> + + <literal>epsi</literal> >=0ã§ã‚ã‚‹å¿…è¦ãŒã‚ã‚Š, + + <literal>etai</literal> >=0ã§ã‚ã‚‹å¿…è¦ãŒã‚ã‚Š, <literal>infi</literal> + + >=1ã§ã‚ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + </para> + + <para> + + <literal>fin</literal> ㌠(モニックãª) å¤šé …å¼ã®å ´åˆ, + + 有é™ã®ãƒ–ãƒãƒƒã‚¯ã¯<literal>fin</literal>ã®æ ¹ã‚’固有値ã¨ã—ã¦è¨±å®¹ã—ã¾ã™. + + </para> + + <para> + + <literal>fin</literal> ãŒå¤šé …å¼ã®ãƒ™ã‚¯ãƒˆãƒ«ã®å ´åˆ, + + ã“れらã¯<literal>F</literal>ã®æœ‰é™å˜å› å,ã™ãªã‚ã¡,<literal>p(i)</literal>ã®æ ¹ã¯ + + <literal>F</literal>ã®æœ‰é™ãªå›ºæœ‰å€¤ã¨ãªã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +F=randpencil([0,1],[2],[-1,0,1],[3]); +[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F); +Qd, Zd +s=poly(0,'s'); +F=randpencil([],[1,2],s^3-2,[]); //通常ã®ãƒšãƒ³ã‚·ãƒ« +det(F) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="kroneck">kroneck</link> + + </member> + + <member> + + <link linkend="pencan">pencan</link> + + </member> + + <member> + + <link linkend="penlaur">penlaur</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/rowshuff.xml b/modules/linear_algebra/help/ja_JP/pencil/rowshuff.xml new file mode 100755 index 000000000..3f6b66c49 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/rowshuff.xml @@ -0,0 +1,196 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rowshuff"> + + <refnamediv> + + <refname>rowshuff</refname> + + <refpurpose>シャッフルアルゴリズム</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Ws,Fs1]=rowshuff(Fs, [alfa])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>Fs</term> + + <listitem> + + <para> + + æ£æ–¹å®Ÿæ•°ãƒšãƒ³ã‚·ãƒ« <literal>Fs = s*E-A</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Ws</term> + + <listitem> + + <para>å¤šé …å¼è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Fs1</term> + + <listitem> + + <para> + + æ£æ–¹å®Ÿæ•°ãƒšãƒ³ã‚·ãƒ« <literal>F1s = s*E1 -A1</literal>, + + ãŸã ã— <literal>E1</literal> ã¯æ£å‰‡ + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>alfa</term> + + <listitem> + + <para> + + 実数 (<literal>alfa = 0</literal> ãŒãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + シャッフルアルゴリズム: ペンシル <literal>Fs=s*E-A</literal>を指定ã™ã‚‹ã¨, + + 以下ã®ã‚ˆã†ãª(æ£æ–¹å¤šé …å¼è¡Œåˆ—) Ws=W(s) ã‚’è¿”ã—ã¾ã™: + + </para> + + <para> + + <literal> Fs1 = s*E1-A1 = W(s)*(s*E-A) </literal> ã¯, + + æ£å‰‡ãªãƒšãƒ³ã‚·ãƒ«è¡Œåˆ— <literal>E1</literal> ã§ã™. + + </para> + + <para> + + ã“ã‚Œã¯,ペンシル<literal>Fs = s*E-A</literal>ãŒæ£å‰‡ (ã™ãªã‚ã¡,å¯é€†)ã®å ´åˆã«é™ã‚Šå¯èƒ½ã§ã™. + + <literal>Ws</literal> ã®æ¬¡æ•°ã¯ãƒšãƒ³ã‚·ãƒ«ã®æ·»å—ã«ç‰ã—ããªã‚Šã¾ã™. + + </para> + + <para> + + <literal>Fs</literal>ã®ç„¡é™å¤§ã«ã‚る極ã¯<literal>alfa</literal>ã«é…ç½®ã•ã‚Œ, + + <literal>Ws</literal>ã®ã‚¼ãƒã¯<literal>alfa</literal>ã«é…ç½®ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>(s*E-A)^-1 = (s*E1-A1)^-1 * W(s) = (W(s)*(s*E-A))^-1 *W(s)</literal> + + ã¨ãªã‚‹ã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +F=randpencil([],[2],[1,2,3],[]); +F=rand(5,5)*F*rand(5,5); // 3ã¤ã®è©•ä¾¡ç‚¹ã‚’1,2,3ã«æœ‰ã™ã‚‹5 x 5 ã®æ£å‰‡ãƒšãƒ³ã‚·ãƒ« +[Ws,F1]=rowshuff(F,-1); +[E1,A1]=pen2ea(F1); +svd(E1) //E1 æ£å‰‡ +roots(det(Ws)) +clean(inv(F)-inv(F1)*Ws,1.d-7) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="pencan">pencan</link> + + </member> + + <member> + + <link linkend="glever">glever</link> + + </member> + + <member> + + <link linkend="penlaur">penlaur</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/pencil/sylv.xml b/modules/linear_algebra/help/ja_JP/pencil/sylv.xml new file mode 100755 index 000000000..185456e74 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/pencil/sylv.xml @@ -0,0 +1,132 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="sylv"> + + <refnamediv> + + <refname>sylv</refname> + + <refpurpose>シルベスタ方程å¼. </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>sylv(A, B, C, flag)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A,B,C</term> + + <listitem> + + <para>é©å½“ãªæ¬¡å…ƒã®å®Ÿæ•°è¡Œåˆ—.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <para> + + æ–‡å—列 (<literal>'c'</literal> ã¾ãŸã¯ <literal>'d'</literal>) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>X= sylv(A,B,C,'c')</literal> ã¯ä»¥ä¸‹ã® + + "連続時間" シルベスタ方程å¼ã®è§£<literal>X</literal>を計算ã—ã¾ã™, + + </para> + + <programlisting role=""><![CDATA[ +A*X+X*B=C + ]]></programlisting> + + <para> + + <literal>X=sylv(A,B,C,'d')</literal> ã¯ä»¥ä¸‹ã® + + "離散時間" シルベスタ方程å¼ã®è§£<literal>X</literal>を計算ã—ã¾ã™, + + </para> + + <programlisting role=""><![CDATA[ +A*X*B-X=C + ]]></programlisting> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A = rand(4, 4); C = rand(4, 3); B = rand(3, 3); +X = sylv(A, B, C, 'c'); +norm(A*X+X*B-C) +X = sylv(A, B, C, 'd'); +norm(A*X*B-X-C) + ]]></programlisting> + + </refsection> + + <refsection> + + <title>å‚考</title> + + <simplelist type="inline"> + + <member> + + <link linkend="lyap">lyap</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/proj.xml b/modules/linear_algebra/help/ja_JP/proj.xml new file mode 100755 index 000000000..6346f8afd --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/proj.xml @@ -0,0 +1,129 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="proj"> + + <refnamediv> + + <refname>proj</refname> + + <refpurpose>投影</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>P = proj(X1,X2)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X1,X2</term> + + <listitem> + + <para>åŒã˜åˆ—ã®æ•°ã‚’有ã™ã‚‹å®Ÿæ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>P</term> + + <listitem> + + <para> + + 実数ã®æŠ•å½±è¡Œåˆ— (<literal>P^2=P</literal>) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>P</literal> ã¯<literal>X1</literal>ã«å¹³è¡Œãª + + <literal>X2</literal>ã¸ã®æŠ•å½±ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +X1=rand(5,2);X2=rand(5,3); +P=proj(X1,X2); +norm(P^2-P,1) +trace(P) // This is dim(X2) +[Q,M]=fullrf(P); +svd([Q,X2]) // span(Q) = span(X2) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="projspec">projspec</link> + + </member> + + <member> + + <link linkend="orth">orth</link> + + </member> + + <member> + + <link linkend="fullrf">fullrf</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/state_space/CHAPTER b/modules/linear_algebra/help/ja_JP/state_space/CHAPTER new file mode 100755 index 000000000..a0b62cdee --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/state_space/CHAPTER @@ -0,0 +1,2 @@ +title = State-Space Matrices + diff --git a/modules/linear_algebra/help/ja_JP/state_space/coff.xml b/modules/linear_algebra/help/ja_JP/state_space/coff.xml new file mode 100755 index 000000000..ebf5b06cc --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/state_space/coff.xml @@ -0,0 +1,183 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="coff"> + + <refnamediv> + + <refname>coff</refname> + + <refpurpose>レゾルベント (ä½™å› å法) </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[N,d]=coff(M [,var])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>M</term> + + <listitem> + + <para>æ£æ–¹å®Ÿæ•°è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>var</term> + + <listitem> + + <para>æ–‡å—列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>N</term> + + <listitem> + + <para> + + å¤šé …å¼è¡Œåˆ— (<literal>M</literal>ã¨åŒã˜å¤§ãã•) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>d</term> + + <listitem> + + <para> + + å¤šé …å¼ (ç‰¹æ€§å¤šé …å¼ <literal>poly(A,'s')</literal>) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>coff</literal> ã¯, + + 実数行列 <literal>M</literal>ã«ã¤ã„㦠R=<literal>(s*eye()-M)^-1</literal> + + を計算ã—ã¾ã™. + + R 㯠<literal>N/d</literal>ã§æŒ‡å®šã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>N</literal> = å¤šé …å¼è¡Œåˆ—ã®åˆ†å. + + </para> + + <para> + + <literal>d</literal> = 共通分æ¯. + + </para> + + <para> + + <literal>var</literal> æ–‡å—列 (çœç•¥æ™‚ã¯'<literal>s</literal>') + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +M=[1,2;0,3]; +[N,d]=coff(M) +N/d +inv(%s*eye()-M) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="coffg">coffg</link> + + </member> + + <member> + + <link linkend="ss2tf">ss2tf</link> + + </member> + + <member> + + <link linkend="nlev">nlev</link> + + </member> + + <member> + + <link linkend="poly">poly</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/state_space/nlev.xml b/modules/linear_algebra/help/ja_JP/state_space/nlev.xml new file mode 100755 index 000000000..996d6e566 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/state_space/nlev.xml @@ -0,0 +1,161 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="nlev"> + + <refnamediv> + + <refname>nlev</refname> + + <refpurpose>Leverrierã®ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[num,den]=nlev(A,z [,rmax])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>実数æ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>z</term> + + <listitem> + + <para>æ–‡å—列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rmax</term> + + <listitem> + + <para> + + オプションã®ãƒ‘ラメータ (<literal>bdiag</literal>å‚ç…§) + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>[num,den]=nlev(A,z [,rmax])</literal> ã¯, + + <literal>(z*eye()-A)^(-1)</literal>を計算ã—ã¾ã™. + + </para> + + <para> + + 計算ã®éš›ã«ã¯,Aã®ãƒ–ãƒãƒƒã‚¯å¯¾è§’化ã®å¾Œã« + + Leverrierアルゴリズムをå„ブãƒãƒƒã‚¯ã«é©ç”¨ã—ã¾ã™. + + </para> + + <para> + + ã“ã®ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã¯é€šå¸¸ã® Leverrierアルゴリズム+ + より優れã¦ã„ã¾ã™ãŒ,ã¾ã 完全ã§ã¯ã‚ã‚Šã¾ã›ã‚“! + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(3,3);x=poly(0,'x'); +[NUM,den]=nlev(A,'x') +clean(den-poly(A,'x')) +clean(NUM/den-inv(x*eye()-A)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="coff">coff</link> + + </member> + + <member> + + <link linkend="coffg">coffg</link> + + </member> + + <member> + + <link linkend="glever">glever</link> + + </member> + + <member> + + <link linkend="ss2tf">ss2tf</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/subspaces/CHAPTER b/modules/linear_algebra/help/ja_JP/subspaces/CHAPTER new file mode 100755 index 000000000..d87d9ca5e --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/subspaces/CHAPTER @@ -0,0 +1,3 @@ +title = Subspaces + + diff --git a/modules/linear_algebra/help/ja_JP/subspaces/spaninter.xml b/modules/linear_algebra/help/ja_JP/subspaces/spaninter.xml new file mode 100755 index 000000000..0ec8c806c --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/subspaces/spaninter.xml @@ -0,0 +1,169 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="spaninter"> + + <refnamediv> + + <refname>spaninter</refname> + + <refpurpose>共通部分空間</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[X,dim]=spaninter(A,B [,tol])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A, B</term> + + <listitem> + + <para>åŒæ•°ã®è¡Œã‚’有ã™ã‚‹å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>dim</term> + + <listitem> + + <para> + + æ•´æ•°, range(<literal>A</literal>) ãŠã‚ˆã³ + + range(<literal>B</literal>)é–“ã®å…±é€šéƒ¨åˆ†ç©ºé–“ã®æ¬¡å…ƒ + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + range(<literal>A</literal>) ãŠã‚ˆã³ range(<literal>B</literal>)ã® + + 共通部分を計算ã—ã¾ã™. + + </para> + + <para> + + <literal>X</literal>ã®æœ€åˆã®<literal>dim</literal>列ã¯,ã“ã®å…±é€šéƒ¨åˆ†ã«å±•é–‹ã—ã¾ã™. + + ã™ãªã‚ã¡,<literal>X(:,1:dim)</literal>ã¯, + + range(<literal>A</literal>) 㨠range(<literal>B</literal>)ã®é–“ã®ç›´äº¤åŸºåº•ã§ã™. + + </para> + + <para> + + <literal>X</literal>ã®åŸºåº•ã§ã¯, + + <literal>A</literal> ãŠã‚ˆã³ <literal>B</literal>ãŒãã‚Œãžã‚Œæ¬¡ã®ã‚ˆã†ã« + + 表ã•ã‚Œã¾ã™: + + </para> + + <para> + + <literal>X'*A</literal> ãŠã‚ˆã³ <literal>X'*B</literal>. + + </para> + + <para> + + <literal>tol</literal> ã¯é–¾å€¤ã§ã™ (<literal>sqrt(%eps)</literal> ãŒãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã§ã™). + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,4); // A 㯠5 x 4, rank=3ã§ã™. +B=[A(:,2),rand(5,1)]*rand(2,2); +[X,dim]=spaninter(A,B); +X1=X(:,1:dim); //共通部分 +svd(A),svd([X1,A]) // span(A) ã® X1 +svd(B),svd([B,X1]) // span(B) ã® X1 + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spanplus">spanplus</link> + + </member> + + <member> + + <link linkend="spantwo">spantwo</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/subspaces/spanplus.xml b/modules/linear_algebra/help/ja_JP/subspaces/spanplus.xml new file mode 100755 index 000000000..b8717b88e --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/subspaces/spanplus.xml @@ -0,0 +1,184 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="spanplus"> + + <refnamediv> + + <refname>spanplus</refname> + + <refpurpose>部分空間ã®åˆè¨ˆ</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[X,dim,dima]=spanplus(A,B[,tol])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A, B</term> + + <listitem> + + <para>åŒæ•°ã®è¡Œã‚’有ã™ã‚‹å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>直交ã¾ãŸã¯ãƒ¦ãƒ‹ã‚¿ãƒªæ£æ–¹è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>dim, dima</term> + + <listitem> + + <para>æ•´æ•°, 部分空間ã®æ¬¡å…ƒ</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>éžè² ã®å®Ÿæ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 以下ã®æ§˜ãªåŸºåº•Xを計算ã—ã¾ã™: + + </para> + + <para> + + <literal>X</literal>ã®æœ€åˆã®<literal>dima</literal>列㌠+ + range(<literal>A</literal>)ã«å±•é–‹ã—, + + ã“れ以é™ã®(<literal>dim-dima</literal>)列ãŒ, + + <literal>A+B</literal> ã®<literal>A</literal>ã«é–¢ã™ã‚‹åŸºåº•ã‚’構æˆ. + + </para> + + <para> + + <literal>X</literal>ã®æœ€åˆã®<literal>dim</literal>列ã¯, + + <literal>A+B</literal>ã®åŸºåº•ã‚’構æˆã—ã¾ã™. + + </para> + + <para> + + <literal>[A,B]</literal>ã«é–¢ã™ã‚‹ä»¥ä¸‹ã®æ£æº–å½¢å¼ãŒå®šç¾©ã•ã‚Œã¾ã™: + + </para> + + <programlisting role=""><![CDATA[ + [*,*] (dima è¡Œ) +X'*[A,B]=[0,*] (dim-dima è¡Œ) + [0,0] + ]]></programlisting> + + <para> + + <literal>tol</literal> ã¯ã‚ªãƒ—ションã®å¼•æ•°ã§ã™(関数ã®ã‚³ãƒ¼ãƒ‰ã‚’å‚ç…§). + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=rand(6,2)*rand(2,5); // rank(A)=2 +B=[A(:,1),rand(6,2)]*rand(3,3); //独立ãªãƒ™ã‚¯ãƒˆãƒ«2ã¤ã‚’è¿½åŠ +[X,dim,dimA]=spanplus(A,B); +dimA +dim + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spaninter">spaninter</link> + + </member> + + <member> + + <link linkend="im_inv">im_inv</link> + + </member> + + <member> + + <link linkend="spantwo">spantwo</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/ja_JP/subspaces/spantwo.xml b/modules/linear_algebra/help/ja_JP/subspaces/spantwo.xml new file mode 100755 index 000000000..cca713c63 --- /dev/null +++ b/modules/linear_algebra/help/ja_JP/subspaces/spantwo.xml @@ -0,0 +1,202 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> + +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="spantwo"> + + <refnamediv> + + <refname>spantwo</refname> + + <refpurpose>部分空間ã®åˆè¨ˆãŠã‚ˆã³å…±é€šéƒ¨åˆ†</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[Xp,dima,dimb,dim]=spantwo(A,B, [tol])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A, B</term> + + <listitem> + + <para>åŒæ•°ã®è¡Œã‚’有ã™ã‚‹å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ•°ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Xp</term> + + <listitem> + + <para>æ£æ–¹æ£å‰‡è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>dima, dimb, dim</term> + + <listitem> + + <para>æ•´æ•°, 部分空間ã®æ¬¡å…ƒ</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>éžè² ã®å®Ÿæ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + åŒã˜è¡Œæ•°ã‚’有ã™ã‚‹è¡Œåˆ— <literal>A</literal> ãŠã‚ˆã³ <literal>B</literal> を指定ã™ã‚‹ã¨, + + 以下ã®ã‚ˆã†ãªæ£æ–¹è¡Œåˆ—<literal>Xp</literal> (æ£å‰‡ã ãŒç›´äº¤ã§ã‚ã‚‹å¿…è¦ã¯ã‚ã‚Šã¾ã›ã‚“) + + ã‚’è¿”ã—ã¾ã™: + + </para> + + <programlisting role=""><![CDATA[ + [A1, 0] (dim-dimb è¡Œ) +Xp*[A,B]=[A2,B2] (dima+dimb-dim 々) + [0, B3] (dim-dima æ¥) + [0 , 0] + ]]></programlisting> + + <para> + + <literal>inv(Xp)</literal>ã®æœ€åˆã®<literal>dima</literal>列㯠+ + range(<literal>A</literal>)ã«å±•é–‹ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>inv(Xp)</literal>ã® + + 列 <literal>dim-dimb+1</literal> ã‹ã‚‰ <literal>dima</literal> 㯠+ + range(A) 㨠range(B)ã®å…±é€šéƒ¨åˆ†ã«å±•é–‹ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>inv(Xp)</literal>ã®æœ€åˆã®<literal>dim</literal>列ã¯, + + range(<literal>A</literal>)+range(<literal>B</literal>)ã«å±•é–‹ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>inv(Xp)</literal>ã®åˆ—<literal>dim-dimb+1</literal>ã‹ã‚‰<literal>dim</literal> + + ã¯range(<literal>B</literal>)ã«å±•é–‹ã•ã‚Œã¾ã™. + + </para> + + <para> + + 行列 <literal>[A1;A2]</literal> ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯(=rank(A))ã§ã™. + + 行列<literal>[B2;B3]</literal>ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯(=rank(B))ã§ã™. + + 行列<literal>[A2,B2]</literal>ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯(=rank(A inter B))ã§ã™. + + è¡Œ<literal>[A1,0;A2,B2;0,B3]</literal> ã¯è¡Œãƒ•ãƒ«ãƒ©ãƒ³ã‚¯(=rank(A+B))ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=[1,0,0,4; + 5,6,7,8; + 0,0,11,12; + 0,0,0,16]; +B=[1,2,0,0]';C=[4,0,0,1]; +Sl=ss2ss(syslin('c',A,B,C),rand(A)); +[no,X]=contr(Sl('A'),Sl('B'));CO=X(:,1:no); //å¯åˆ¶å¾¡éƒ¨ +[uo,Y]=unobs(Sl('A'),Sl('C'));UO=Y(:,1:uo); //ä¸å¯è¦³æ¸¬éƒ¨ +[Xp,dimc,dimu,dim]=spantwo(CO,UO); //カルマン分解 +Slcan=ss2ss(Sl,inv(Xp)); + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spanplus">spanplus</link> + + </member> + + <member> + + <link linkend="spaninter">spaninter</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/linear_algebra/help/pt_BR/addchapter.sce b/modules/linear_algebra/help/pt_BR/addchapter.sce new file mode 100755 index 000000000..99f821fe3 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Linear Algebra",SCI+"/modules/linear_algebra/help/pt_BR",%T); + diff --git a/modules/linear_algebra/help/pt_BR/eigen/CHAPTER b/modules/linear_algebra/help/pt_BR/eigen/CHAPTER new file mode 100755 index 000000000..88f8bc42b --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/CHAPTER @@ -0,0 +1,2 @@ +title = Eigenvalue and Singular Value + diff --git a/modules/linear_algebra/help/pt_BR/eigen/balanc.xml b/modules/linear_algebra/help/pt_BR/eigen/balanc.xml new file mode 100755 index 000000000..670af0f56 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/balanc.xml @@ -0,0 +1,109 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="balanc" xml:lang="en"> + <refnamediv> + <refname>balanc</refname> + <refpurpose>balanceamento de uma matriz ou de um feixe de + matrizes + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Ab,X]=balanc(A) + [Eb,Ab,X,Y]=balanc(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A:</term> + <listitem> + <para>matriz quadrada de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X:</term> + <listitem> + <para>matriz quadrada de reais invertível</para> + </listitem> + </varlistentry> + <varlistentry> + <term>E:</term> + <listitem> + <para>matriz quadrada de reais (com mesma dimensão que + <literal>A</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y:</term> + <listitem> + <para>uma matriz quadrada de reais invertível</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Balanceia uma matriz quadrada para melhorar seu número de + condicionamento. + </para> + <para> + <literal>[Ab,X] = balanc(A)</literal> acha uma transformação de + similaridade <literal>X</literal> tal que + </para> + <para> + <literal>Ab = inv(X)*A*X</literal> tem aproximadamente normas iguais + de linha e de coluna. + </para> + <para>Para feixes de matrizes, o balancemento é feito para melhorar o + problema do autovalor generalizado. + </para> + <para> + <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> retorna transformações + esquerda e direita <literal>X</literal> e <literal>Y</literal> tais que + <literal>Eb=inv(X)*E*Y, Ab=inv(X)*A*Y</literal> + </para> + </refsection> + <refsection> + <title>Observação</title> + <para> + O balanceamento é feito nas funções <literal>bdiag</literal> e + <literal>spec</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=[1/2^10,1/2^10;2^10,2^10]; +[Ab,X]=balanc(A); +norm(A(1,:))/norm(A(2,:)) +norm(Ab(1,:))/norm(Ab(2,:)) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/bdiag.xml b/modules/linear_algebra/help/pt_BR/eigen/bdiag.xml new file mode 100755 index 000000000..94f586ba1 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/bdiag.xml @@ -0,0 +1,108 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bdiag" xml:lang="en"> + <refnamediv> + <refname>bdiag</refname> + <refpurpose>diagonalização em blocos, autovetores + generalizados + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rmax</term> + <listitem> + <para>número real</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ab</term> + <listitem> + <para>matriz quadrada de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz de reais ou complexos não-singular</para> + </listitem> + </varlistentry> + <varlistentry> + <term>bs</term> + <listitem> + <para>vetor de inteiros</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <programlisting role=""><![CDATA[ +[Ab [,X [,bs]]]=bdiag(A [,rmax]) + ]]></programlisting> + <para> + realiza a diagonalização em blocos da matriz <literal>A</literal>. + bs fornece a estrutura dos blocos (respectivos tamanhos dos blocos). + <literal>X</literal> é a matriz mudança de base i.e <literal>Ab = + inv(X)*A*X + </literal> + édiagonal em blocos. + </para> + <para> + <literal>rmax</literal> controla o condicionamento de + <literal>X</literal>; o valor padrão é a norma L1 de + <literal>A</literal>. + </para> + <para>Para encontrar a forma diagonal (se existir) escolha um valor + suficientemente grande para <literal>rmax</literal> + (<literal>rmax=1/%eps</literal> , por exemplo). Genericamente, (para uma + matriz A de reais aleatória) os blocos são (1x1) e (2x2) e + <literal>X</literal> é a matriz de autovetores. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//No caso de reais: blocos 1x1 e 2x2 +a=rand(5,5);[ab,x,bs]=bdiag(a);ab + +//No caso de complexos: blocos 1x1 complexos +[ab,x,bs]=bdiag(a+%i*0);ab + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="schur">schur</link> + </member> + <member> + <link linkend="sylv">sylv</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/gschur.xml b/modules/linear_algebra/help/pt_BR/eigen/gschur.xml new file mode 100755 index 000000000..2b3515dad --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/gschur.xml @@ -0,0 +1,97 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="gschur" xml:lang="en"> + <refnamediv> + <refname>gschur</refname> + <refpurpose>forma de Schur generalizada (função obsoleta) </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[As,Es]=gschur(A,E) + [As,Es,Q,Z]=gschur(A,E) + [As,Es,Z,dim] = gschur(A,E,flag) + [As,Es,Z,dim]= gschur(A,E,extern) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Descrição</title> + <para>Esta função é obsoleta e agora está inclusa na função + <literal>schur</literal> function. Na maior parte dos casos, a função + <literal>gschur</literal> irá ainda trabalhar como antes, mas será + removida em um lançamento futuro do Scilab. + </para> + <para>As três sintaxes podem ser substituídas por</para> + <programlisting role=""><![CDATA[ +[As,Es]=schur(A,E) +[As,Es,Q,Z]=schur(A,E);Q=Q' //NOTE A TRANSPOSIÇÃO AQUI +[As,Es,Z,dim] = schur(A,E,flag) + ]]></programlisting> + <para>A última sintaxe requer algumas adaptações a mais: </para> + <variablelist> + <varlistentry> + <term>if</term> + <listitem> + <para>é uma função do Scilab, a nova seqüência de chamamento deve + ser <literal>[As,Es,Z,dim]= schur(A,E,Nextern)</literal> com Nextern + definido como segue: + </para> + <programlisting role=""><![CDATA[ +function t=Nextern(R) +if R(2)==0 then + t=extern([1,R(1),R(3)])==1 +else + c=(R(1)+%i*R(2))/R(3) + t=extern([2,real(c+c'),real(c*c')])==1 +end +endfunction + ]]></programlisting> + </listitem> + </varlistentry> + <varlistentry> + <term>if</term> + <listitem> + <para>é o nome de uma função externa codificada em FORTRAN ou C, a + nova seqüência de chamamento deve ser <literal>[As,Es,Z,dim]= + schur(A,E,'nextern') + </literal> + com nextern definido como + segue: + </para> + </listitem> + </varlistentry> + </variablelist> + <programlisting role=""><![CDATA[ +logical function nextern(ar,ai,beta) +double precision ar,ai,beta +integer r,extern +if (ai.eq.0.0d0) then + r=extern(1,ar,beta,0.0d0,0.0d0) +else + r=extern(2,0.0d0,0.0d0,2.0d0*ar,ar*ar+ai*ai) +endif +nextern=r.eq.1 +end + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="external">external</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/gspec.xml b/modules/linear_algebra/help/pt_BR/eigen/gspec.xml new file mode 100755 index 000000000..ae0f5b92f --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/gspec.xml @@ -0,0 +1,45 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="gspec" xml:lang="en"> + <refnamediv> + <refname>gspec</refname> + <refpurpose>autovalores de feixe de matrizes (função + obsoleta) + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[al,be]=gspec(A,E) + [al,be,Z]=gspec(A,E) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Descrição</title> + <para> + Esta função está agora inclusa na função <literal>spec</literal> . A + seqüência de chamamento deve ser substituida por + </para> + <programlisting role=""><![CDATA[ +[al,be]=spec(A,E) +[al,be,Z]=spec(A,E) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/hess.xml b/modules/linear_algebra/help/pt_BR/eigen/hess.xml new file mode 100755 index 000000000..b9daf0150 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/hess.xml @@ -0,0 +1,91 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="hess" xml:lang="en"> + <refnamediv> + <refname>hess</refname> + <refpurpose>forma de Hessenberg</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>H = hess(A) + [U,H] = hess(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>H</term> + <listitem> + <para>matriz quadrada de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[U,H] = hess(A)</literal> produz uma matriz unitária + <literal>U</literal> e uma matriz de Hessenberg <literal>H</literal> tais + que <literal>A = U*H*U'</literal> e <literal>U'*U</literal> = Identidade. + Por si só, <literal>hess(A) </literal>retorna <literal>H</literal>. + </para> + <para>A forma de Hessenberg de uma matriz é zero abaixo da primeira + subdiagonal. Se a matriz é simetrica ou Hermitiana, a forma é + tridiagonal. + </para> + </refsection> + <refsection> + <title>Referências</title> + <para>A função hess é baseada nas rotinas Lapack DGEHRD, DORGHR para + matrizes de e ZGEHRD, ZORGHR para matrizes de complexos. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);[U,H]=hess(A); +and( abs(U*H*U'-A)<1.d-10 ) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="contr">contr</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> + <refsection> + <title/> + <para/> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/pbig.xml b/modules/linear_algebra/help/pt_BR/eigen/pbig.xml new file mode 100755 index 000000000..15b493fac --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/pbig.xml @@ -0,0 +1,125 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="pbig" xml:lang="en"> + <refnamediv> + <refname>pbig</refname> + <refpurpose>autoprojeção</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title> Parâmetros </title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>thres</term> + <listitem> + <para>número real </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string (<literal>'c'</literal> ou + <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>matrizes de reais</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Projeção sobre um auto-subespaço associado aos autovalores de parte + real>= <literal>thres</literal> (<literal>flag='c'</literal>) ou com + magnitude >= <literal>thres</literal> + (<literal>flag='d'</literal>). + </para> + <para> + A projeção é definida por <literal>Q*M</literal>, + <literal>Q</literal> tem posto-coluna cheio, <literal>M</literal> tem + posto-linha cheio e <literal>M*Q=eye</literal>. + </para> + <para> + Se <literal>flag='c'</literal>, os autovalores de + <literal>M*A*Q</literal> = autovalores de <literal>A</literal> com parte + real >= <literal>thres</literal>. + </para> + <para> + Se <literal>flag='d'</literal>, os autovalores de + <literal>M*A*Q</literal> = autovalores de <literal>A</literal> com + magnitude >= <literal>thres</literal>. + </para> + <para> + Se <literal>flag='c'</literal> e se <literal>[Q1,M1]</literal> = + fatoração em posto cheio (<literal>fullrf</literal>) de + <literal>eye()-Q*M</literal> então os autovalores de + <literal>M1*A*Q1</literal> = autovalores de <literal>A</literal> com parte + real < <literal>thres</literal>. + </para> + <para> + Se <literal>flag='d'</literal> e se <literal>[Q1,M1]</literal> + =fatoração em posto cheio (<literal>fullrf</literal>) de + <literal>eye()-Q*M</literal> então os autovalores de + <literal>M1*A*Q1</literal> = autovalores de <literal>A</literal> com + magnitude < <literal>thres</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; +[Q,M]=pbig(A,1.5,'d'); +spec(M*A*Q) +[Q1,M1]=fullrf(eye()-Q*M); +spec(M1*A*Q1) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="psmall">psmall</link> + </member> + <member> + <link linkend="projspec">projspec</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + </simplelist> + </refsection> + <refsection> + <title> Função Usada </title> + <para> + <literal>pbig</literal> é baseada na forma ordenada de Schur (função + do Scilab <literal>schur</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/projspec.xml b/modules/linear_algebra/help/pt_BR/eigen/projspec.xml new file mode 100755 index 000000000..a24fac61f --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/projspec.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="projspec" xml:lang="en"> + <refnamediv> + <refname>projspec</refname> + <refpurpose>operadores espectrais</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[S,P,D,i]=projspec(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title> Parâmetros </title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada</para> + </listitem> + </varlistentry> + <varlistentry> + <term>S, P, D</term> + <listitem> + <para>matrizes quadradas </para> + </listitem> + </varlistentry> + <varlistentry> + <term>i</term> + <listitem> + <para>inteiro (índice do autovalor zero de + <literal>A</literal>). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Características espectrais de <literal>A</literal> em 0. + </para> + <para> + <literal>S</literal> = resolvente reduzido em 0 + (<literal>S</literal> = -Inverso_de_Drazin(<literal>A</literal>)). + </para> + <para> + <literal>P</literal> = projeção espectral em 0. + </para> + <para> + <literal>D</literal> = operador nilpotente em 0. + </para> + <para> + <literal>index</literal> = índice do autovalor 0. + </para> + <para> + Tem-se <literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - + S - s*S^2 -... + </literal> + ao redor da singularidade s=0. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end') +A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7); +A=X*A*inv(X); +[S,P,D,index]=projspec(A); +index //tamanho do bloco J +trace(P) //soma das dimensões dos blocos J +A*S-(eye()-P) +norm(D^index,1) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="coff">coff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/psmall.xml b/modules/linear_algebra/help/pt_BR/eigen/psmall.xml new file mode 100755 index 000000000..e187285bc --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/psmall.xml @@ -0,0 +1,120 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="psmall" xml:lang="en"> + <refnamediv> + <refname>psmall</refname> + <refpurpose>projeção espectral</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Q,M]=psmall(A,thres,flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parameters</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>thres</term> + <listitem> + <para>número real </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string (<literal>'c'</literal> ou + <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>matrizes de reais</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para>Projeção sobre auto-subespaço associado com autovalores com parte + real < <literal>thres</literal> (<literal>flag='c'</literal>) ou com + módulo < <literal>thres</literal> (<literal>flag='d'</literal>). + </para> + <para> + A projeção é definda por <literal>Q*M</literal>, + <literal>Q</literal> é de posto-coluna cheio, <literal>M</literal> é de + posto-linha cheio e <literal>M*Q=eye</literal>. + </para> + <para> + Se <literal>flag='c'</literal>, os autovalores de + <literal>M*A*Q</literal> = autovalores de <literal>A</literal> com parte + real < <literal>thres</literal>. + </para> + <para> + Se <literal>flag='d'</literal>, os autovalores de + <literal>M*A*Q</literal> = autovalores de <literal>A</literal> com + magnitude < <literal>thres</literal>. + </para> + <para> + Se <literal>flag='c'</literal> e se <literal>[Q1,M1]</literal> = + fatoração em posto cheio (<literal>fullrf</literal>) de + <literal>eye()-Q*M</literal>então os autovalores de + <literal>M1*A*Q1</literal> = autovalores de<literal> A</literal> com parte + real >= <literal>thres</literal>. + </para> + <para> + Se <literal>flag='d'</literal> e se <literal>[Q1,M1]</literal> = + fatoração em posto cheio (<literal>fullrf</literal>) de + <literal>eye()-Q*M</literal> então os autovalores de + <literal>M1*A*Q1</literal> = autovalores de <literal>A</literal> com + magnitude >= <literal>thres</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; +[Q,M]=psmall(A,2.5,'d'); +spec(M*A*Q) +[Q1,M1]=fullrf(eye()-Q*M); +spec(M1*A*Q1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="pbig">pbig</link> + </member> + <member> + <link linkend="proj">proj</link> + </member> + <member> + <link linkend="projspec">projspec</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Used Functions</title> + <para>Esta função é baseada na forma de Schur ordenada (Função do + Scilab<literal> schur</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/schur.xml b/modules/linear_algebra/help/pt_BR/eigen/schur.xml new file mode 100755 index 000000000..f89dd7791 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/schur.xml @@ -0,0 +1,411 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="schur" xml:lang="en"> + <refnamediv> + <refname>schur</refname> + <refpurpose>decomposição (ordenada) de Schur de matrizes e + feixes + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[U,T] = schur(A) + [U,dim [,T] ]=schur(A,flag) + [U,dim [,T] ]=schur(A,extern1) + + [As,Es [,Q,Z]]=schur(A,E) + [As,Es [,Q],Z,dim] = schur(A,E,flag) + [Z,dim] = schur(A,E,flag) + [As,Es [,Q],Z,dim]= schur(A,E,extern2) + [Z,dim]= schur(A,E,extern2) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para> matriz quadrada de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>matriz quadrada de reais ou complexos com as mesmas dimensões + de<literal> A</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string (<literal>'c'</literal> + ou<literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>extern1</term> + <listitem> + <para>uma ``external'' (função externa), veja abaixo</para> + </listitem> + </varlistentry> + <varlistentry> + <term>extern2</term> + <listitem> + <para>uma ``external'', veja abaixo </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária </para> + </listitem> + </varlistentry> + <varlistentry> + <term>T</term> + <listitem> + <para>matriz quadrada triangular superior ou quasi-triangular + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>As</term> + <listitem> + <para>matriz quadrada triangular superior ou quasi-triangular + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Es</term> + <listitem> + <para>matriz quadrada triangular superior </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para>inteiro</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Formas de Schur, formas ordenadas de Schur de matrizes e feixes + </para> + <variablelist> + <varlistentry> + <term>FORMA DE SCHUR MATRICIAL</term> + <listitem> + <variablelist> + <varlistentry> + <term>Forma de Schur usual:</term> + <listitem> + <para> + <literal>[U,T] = schur(A)</literal> produz uma matriz de + Schur <literal>T</literal> e uma matriz unitária + <literal>U</literal> tais que <literal>A = U*T*U'</literal> e + <literal>U'*U = eye(U)</literal>. Por si mesmo, + schur(<literal>A</literal>) retorna <literal>T</literal>. Se + <literal>A</literal> é de complexos, a Forma de Schur Complexa + é retornada na matriz <literal>T</literal>. A Forma de Schur + Complexa é triangular superior com os autovalores de + <literal>A</literal> na diagonal. Se <literal>A</literal> é de + reais, a Forma de Schur Real é retornada. A Forma de Schur + Real tem autovalores reais na diagonal e os autovalores + complexos em blocos 2-por-2 na diagonal. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Formas de Schur ordenadas</term> + <listitem> + <para> + <literal>[U,dim]=schur(A,'c')</literal> rretorna uma + matriz unitária <literal>U</literal> que transforma + <literal>A</literal> em uma forma de Schur. Ainda, as + primeiras dim colunas de <literal>U</literal> formam uma base + para o autoespaço de <literal>A</literal> associado aos + autovalores com partes reais negativas (autoespaço de "tempo + contínuo" estável). + </para> + <para> + <literal>[U,dim]=schur(A,'d')</literal> retorna uma + matriz unitária <literal>U</literal> que transforma + <literal>A</literal> em uma forma de Schur. Ainda, as + primeiras <literal>dim</literal> colunas de + <literal>U</literal> geram uma base do autoespaço de + <literal>A</literal> associado aos autovalores de magnitude + menor que 1 (autoespaço de "tempo discreto" estável). + </para> + <para> + <literal>[U,dim]=schur(A,extern1)</literal> retorna uma + matriz unitária <literal>U</literal> que transforma + <literal>A</literal> em uma forma de Schur. Ainda, as + <literal>dim</literal> primeiras colunas de + <literal>U</literal> geram uma base para o autoespaço de + <literal>A</literal> associado aos autovalores que são + selecionados pela "external" <literal>extern1</literal> (veja + "external" para detalhes). Esta "external" pode ser descrita + por uma função do Scilab ou por um "procedure" de C ou + FORTRAN: + </para> + <variablelist> + <varlistentry> + <term>Uma Função do Scilab</term> + <listitem> + <para> + Se <literal>extern1</literal> é descrita por uma + função do Scilab, deve ter a seguinte seqüência de + chamamento: <literal>s=extern1(Ev)</literal>, onde + <literal>Ev</literal> é um autovalor e + <literal>s</literal> um booleano. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Um "Procedure" C ou FORTRAN</term> + <listitem> + <para> + Se <literal>extern1</literal> é descrita por uma + função de C ou FORTRAN, deve ter a seguinte seqüência de + chamamento: <literal>int extern1(double *EvR, double + *EvI) + </literal> + onde <literal>EvR</literal> e + <literal>EvI</literal> são partes real e complexa de + autovalor. Valor verdadeiro ou diferente de zero + retornado significa autovalor selecionado. + </para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + <varlistentry> + <term>FORMAS DE SCHUR DE FEIXES</term> + <listitem> + <variablelist> + <varlistentry> + <term>Forma de Schur de Feixe Usual</term> + <listitem> + <para> + <literal>[As,Es] = schur(A,E)</literal> produz uma + matriz <literal>As</literal> quasi-triangular e uma matriz + triangular <literal>Es</literal> que são a forma generalizada + de Schur do par <literal>A, E</literal>. + </para> + <para> + <literal>[As,Es,Q,Z] = schur(A,E)</literal> retorna, + ainda, duas matrizes unitárias <literal>Q</literal> e + <literal>Z</literal> tais que <literal>As=Q'*A*Z</literal> e + <literal>Es=Q'*E*Z</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Formas de Schur Ordenadas:</term> + <listitem> + <para> + <literal>[As,Es,Z,dim] = schur(A,E,'c')</literal> + retorna a forma real generalizada de Schur do feixe + <literal>s*E-A</literal>. Ainda, as primeiras dim colunas de + <literal>Z</literal> geram uma base para o autoespaço direito + associado aos autovalores com partes reais negativas + (autoespaço de "tempo contínuo" generalizado). + </para> + <para> + <literal>[As,Es,Z,dim] = schur(A,E,'d')</literal> + </para> + <para>retorna a forma real generalizada de Schur do feixe + <literal>s*E-A</literal>. Ainda, as dim primeiras colunas de + <literal>Z</literal> formam uma base para o autoespaço direito + associado aos autovalores de magnitude menor que 1 (autoespaço + de "tempo discreto" generalizado). + </para> + <para> + <literal>[As,Es,Z,dim] = + schur(A,E,extern2) + </literal> + </para> + <para>retorna a forma real generalizada de Schur do feixe + <literal>s*E-A</literal>. Ainda, as dim primeiras colunas de + <literal>Z</literal> formam uma base para o autoespaço direito + associado aos autovalores do feixe que são selecionados de + acordo com a regra que é dada pela "external" + <literal>extern2</literal>. (veja "external" para detalhes). + Esta external pode ser descrita por uma função do Scilab ou + por um "procedure" de C ou FORTRAN. + </para> + <variablelist> + <varlistentry> + <term>Função do Scilab</term> + <listitem> + <para> + Se <literal>extern2</literal> é descrita por uma + função do Scilab, deve ter a seqüência de chamamento: + <literal>s=extern2(Alpha,Beta)</literal>, onde + <literal>Alpha</literal> e <literal>Beta</literal> + definem um autovalor generalizado e <literal>s</literal> + um booleano. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Um "Procedure" C ou FORTRAN</term> + <listitem> + <para> + Se a "external" <literal>extern2</literal> é + descrita por um "procedure" C ou FORTRAN, deve ter a + seqüência de chamamento: + </para> + <para> + <literal>int extern2(double *AlphaR, double + *AlphaI, double *Beta) + </literal> + </para> + <para> + se <literal>A</literal> e <literal>E</literal> são + matrizes de reais e + </para> + <para> + <literal>int extern2(double *AlphaR, double + *AlphaI, double *BetaR, double *BetaI) + </literal> + </para> + <para> + se <literal>A</literal> ou <literal>E</literal> é + matriz de complexos. <literal>Alpha</literal>, e + <literal>Beta</literal> definem o autovalor + generalizado. Um valor verdadeiro ou diferente de zero + siginfica autovalor generalizado selecionado. + </para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Referências</title> + <para>As computações da forma de Schur matricial são baseadas nas rotinas + de Lapack DGEES e ZGEES. + </para> + <para>As computações da forma de Schur de feixes são baseadas nas rotinas + de Lapack DGGES e ZGGES. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//SCHUR FORM OF A MATRIX +//---------------------- +A=diag([-0.9,-2,2,0.9]);X=rand(A);A=inv(X)*A*X; +[U,T]=schur(A);T + +[U,dim,T]=schur(A,'c'); +T(1:dim,1:dim) //stable cont. eigenvalues + +function t=mytest(Ev),t=abs(Ev)<0.95,endfunction +[U,dim,T]=schur(A,mytest); +T(1:dim,1:dim) + +// The same function in C (a Compiler is required) +cd TMPDIR; +C=['int mytest(double *EvR, double *EvI) {' //the C code + 'if (*EvR * *EvR + *EvI * *EvI < 0.9025) return 1;' + 'else return 0; }';] +mputl(C,TMPDIR+'/mytest.c') + + +//build and link +lp=ilib_for_link('mytest','mytest.c',[],'c'); +link(lp,'mytest','c'); + +//run it +[U,dim,T]=schur(A,'mytest'); +//SCHUR FORM OF A PENCIL +//---------------------- +F=[-1,%s, 0, 1; + 0,-1,5-%s, 0; + 0, 0,2+%s, 0; + 1, 0, 0, -2+%s]; +A=coeff(F,0);E=coeff(F,1); +[As,Es,Q,Z]=schur(A,E); +Q'*F*Z //It is As+%s*Es + + +[As,Es,Z,dim] = schur(A,E,'c') +function t=mytest(Alpha,Beta),t=real(Alpha)<0,endfunction +[As,Es,Z,dim] = schur(A,E,mytest) + +//the same function in Fortran (a Compiler is required) +ftn=['integer function mytestf(ar,ai,b)' //the fortran code + 'double precision ar,ai,b' + 'mytestf=0' + 'if(ar.lt.0.0d0) mytestf=1' + 'end'] +mputl(' '+ftn,TMPDIR+'/mytestf.f') + +//build and link +lp=ilib_for_link('mytestf','mytestf.f',[],'F'); +link(lp,'mytestf','f'); + +//run it + +[As,Es,Z,dim] = schur(A,E,'mytestf') + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="ricc">ricc</link> + </member> + <member> + <link linkend="pbig">pbig</link> + </member> + <member> + <link linkend="psmall">psmall</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/spec.xml b/modules/linear_algebra/help/pt_BR/eigen/spec.xml new file mode 100755 index 000000000..00be379ad --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/spec.xml @@ -0,0 +1,277 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spec" xml:lang="en"> + <refnamediv> + <refname>spec</refname> + <refpurpose>autovalores de matrizes e feixes</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>evals=spec(A) + [R,diagevals]=spec(A) + + evals=spec(A,B) + [alpha,beta]=spec(A,B) + [alpha,beta,Z]=spec(A,B) + [alpha,beta,Q,Z]=spec(A,B) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>B</term> + <listitem> + <para>matriz quadrada de reais ou complexos com as mesmas dimensões + que<literal> A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>evals</term> + <listitem> + <para>vetor de reais ou complexos, os autovalores</para> + </listitem> + </varlistentry> + <varlistentry> + <term>diagevals</term> + <listitem> + <para>matriz diagonal de reais ou complexos (autovalores ao longo da + diagonal) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>alpha</term> + <listitem> + <para>vetor de reais ou complexos, al./be fornece os + autovalores + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>beta</term> + <listitem> + <para>vetor de reais, al./be fornece os autovalores</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para>matriz quadrada de reais ou complexos invertível, autovetores + direitos da matriz + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz quadrada de reais ou complexos invertível, autovetores + esquerdos do feixe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z</term> + <listitem> + <para>matriz quadrada de reais ou complexos invertível, autovetores + direitos do feixe + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <variablelist> + <varlistentry> + <term>evals=spec(A)</term> + <listitem> + <para> + retorna no vetor <literal>evals</literal> os + autovalores. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[R,diagevals] =spec(A)</term> + <listitem> + <para> + retorna na matriz diagonal <literal>evals</literal> os + autovalores e em <literal>R</literal> os autovetores + direitos. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>evals=spec(A,B)</term> + <listitem> + <para> retorna o espectro do feixe de matrizes A - s B, i.e. as + raízes da matriz de polinômios s B - A. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[alpha,beta] = spec(A,B)</term> + <listitem> + <para> + retorna o espectro do feixe de matrizes <literal>A- s + B + </literal> + ,i.e. as raízes da matriz de polinômios <literal>A - s + B + </literal> + .Auto valores generalizados alpha e beta são tais que a + matriz <literal>A - alpha./beta B</literal> é uma matriz singular. + Os autovalores são dados por <literal>al./be</literal> e se + <literal>beta(i) = 0</literal> o i-ésimo autovalor está no infinito. + (Para <literal>B = eye(A), alpha./beta</literal> é + <literal>spec(A)</literal>). É usualmente representado pelo par + (alpha,beta), já que há uma interpretação razoável para beta=0, e + até mesmo para os dois sendo zero. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[alpha,beta,R] = spec(A,B)</term> + <listitem> + <para> + retorna, ainda, a matriz <literal>R</literal> de autovetores + direitos generalizados do feixe. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[al,be,Q,Z] = spec(A,B)</term> + <listitem> + <para> + rretorna ainda a matriz <literal>Q</literal> e + <literal>Z</literal> de autovetores esquerdos e direitos + generalizados do feixe. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Referências</title> + <para>As computações de autovalores de matrizes são baseadas nas rotinas + Lapack + </para> + <itemizedlist> + <listitem> + <para>DGEEV e ZGEEV quando as matrizes não são simétricas,</para> + </listitem> + <listitem> + <para>DSYEV e ZHEEV quando as matrizes são simétricas.</para> + </listitem> + </itemizedlist> + <para>Uma matriz de complexos simétrica tem termos fora da diagonal + conjugados e termos diagonais reais. + </para> + <para>As computações de autovalores de feixes são baseadas nas rotinas + Lapack DGGEV e ZGGEV. + </para> + </refsection> + <refsection> + <title>Matrizes de reais e de complexos</title> + <para>Deve-se notar que o tipo das variáveis de saída, tais como evals ou + R por exemplo, não é necessariamente o mesmo das que das matrizes de + entrada A e B. No parágrafo seguinte, análisamos o tipo das variáveis de + saída no caso onde nos casos onde se computa os autovalores e autovetores + de uma única matriz A. + </para> + <itemizedlist> + <listitem> + <para>Matriz A de reais</para> + <itemizedlist> + <listitem> + <para>Simétrica</para> + <para>Os autovetores e autovalores são reais.</para> + </listitem> + <listitem> + <para>Não simétrica</para> + <para>Os autovetores e autovalores são complexos.</para> + </listitem> + </itemizedlist> + </listitem> + <listitem> + <para>Matriz A de complexos</para> + <itemizedlist> + <listitem> + <para>Simétrica</para> + <para>Os autovalores são reais, mas os autovetores são + complexos. + </para> + </listitem> + <listitem> + <para>Não simétrica</para> + <para>Os autovetores e autovalores são complexos.</para> + </listitem> + </itemizedlist> + </listitem> + </itemizedlist> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// AUTOVALORES DA MATRIZ +A=diag([1,2,3]); +X=rand(3,3); +A=inv(X)*A*X; +spec(A) +// +x=poly(0,'x'); +pol=det(x*eye()-A) +roots(pol) +// +[S,X]=bdiag(A); +clean(inv(X)*A*X) + +// AUTOVALORES DO FEIXE +A=rand(3,3); +[al,be,R] = spec(A,eye(A)); +al./be +clean(inv(R)*A*R) //exibindo os autovalores (matriz genérica) +A=A+%i*rand(A); +E=rand(A); +roots(det(A-%s*E)) //caso de complexos + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="schur">schur</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/sva.xml b/modules/linear_algebra/help/pt_BR/eigen/sva.xml new file mode 100755 index 000000000..0a88f269d --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/sva.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="sva" xml:lang="en"> + <refnamediv> + <refname>sva</refname> + <refpurpose>aproximação em valores singulares</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento </title> + <synopsis>[U,s,V]=sva(A,k) + [U,s,V]=sva(A,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>inteiro</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real não-negativo</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Aproximação em valores singulares.</para> + <para> + <literal>[U,S,V]=sva(A,k)</literal> com <literal>k</literal> inteiro + >=1, retorna <literal>U,S</literal> e <literal>V</literal> tais que + <literal>B=U*S*V'</literal> é a melhor aproximação L2 de + <literal>A</literal> com + posto(<literal>B</literal>)=<literal>k</literal>. + </para> + <para> + <literal>[U,S,V]=sva(A,tol)</literal> com <literal>tol</literal> + real retorna <literal>U,S</literal> e <literal>V</literal> tais que + <literal>B=U*S*V'</literal> e a norma-L2 de <literal>A-B</literal> é, no + máximo, <literal>tol</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,4)*rand(4,5); +[U,s,V]=sva(A,2); +B=U*s*V'; +svd(A) +svd(B) +clean(svd(A-B)) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/eigen/svd.xml b/modules/linear_algebra/help/pt_BR/eigen/svd.xml new file mode 100755 index 000000000..71998511e --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/eigen/svd.xml @@ -0,0 +1,132 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="svd" xml:lang="en"> + <refnamediv> + <refname>svd</refname> + <refpurpose>decomposição em valores singulares</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>s=svd(X) + [U,S,V]=svd(X) + [U,S,V]=svd(X,0) (obsolete) + [U,S,V]=svd(X,"e") + [U,S,V,rk]=svd(X [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>s</term> + <listitem> + <para>vetor de reais (valores singulares)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>S</term> + <listitem> + <para>matriz diagonal de reais (valores singulares)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U,V</term> + <listitem> + <para>matrizes quadradas ortogonais ou unitárias (vetores + singulares) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[U,S,V] = svd(X)</literal> produz uma matriz diagonal + <literal>S</literal> , com dimensão igual a de <literal>X</literal> e com + elementos da diagonal não-negativos em ordem decrescente, e matrizes + unitárias <literal>U</literal> e <literal>V</literal> tais que <literal>X + = U*S*V' + </literal> + . + </para> + <para> + <literal>[U,S,V] = svd(X,0)</literal> produz a decomposição com + "economia de tamanho". Se <literal>X</literal> é m-por-n com m > n, + então apenas as primeiras n colunas de <literal>U</literal> são computadas + e <literal>S</literal> é n-por-n. + </para> + <para> + <literal>s= svd(X)</literal> por si mesmo retorna um vetor + <literal>s</literal> contendo os valores singulares. + </para> + <para> + <literal>[U,S,V,rk]=svd(X,tol)</literal> fornece também + <literal>rk</literal>, o posto numérico de <literal>X</literal> i.e. i.e. + o número de valores singulares maiores que <literal>tol</literal>. + </para> + <para> + O valor default de <literal>tol</literal> é o mesmo que em + <literal>rank</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +X=rand(4,2)*rand(2,4) +svd(X) +sqrt(spec(X*X')) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="sva">sva</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + </simplelist> + </refsection> + <refsection> + <title> Função Usada </title> + <para>Decomposições svd são baseadas nas rotinas Lapack DGESVD para + matrizes de reais e ZGESVD no caso de matrizes de complexos. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/factorization/CHAPTER b/modules/linear_algebra/help/pt_BR/factorization/CHAPTER new file mode 100755 index 000000000..e6daeb8eb --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/factorization/CHAPTER @@ -0,0 +1,2 @@ +title = Factorization + diff --git a/modules/linear_algebra/help/pt_BR/factorization/givens.xml b/modules/linear_algebra/help/pt_BR/factorization/givens.xml new file mode 100755 index 000000000..66b9e5a73 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/factorization/givens.xml @@ -0,0 +1,91 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="givens" xml:lang="en"> + <refnamediv> + <refname>givens</refname> + <refpurpose>transformação de Givens</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>U=givens(xy) + U=givens(x,y) + [U,c]=givens(xy) + [U,c]=givens(x,y) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>x,y</term> + <listitem> + <para>dois números reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>xy</term> + <listitem> + <para>vetor coluna de reais ou complexos de tamanho 2</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz 2x2 unitária</para> + </listitem> + </varlistentry> + <varlistentry> + <term>c</term> + <listitem> + <para>vetor coluna de reais ou complexos de tamanho 2</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>U= givens(x, y)</literal> ou <literal>U = + givens(xy) + </literal> + com <literal>xy = [x;y]</literal> retorna uma matriz + unitária <literal>2</literal>x<literal>2</literal> <literal>U</literal> + tal que: + </para> + <para> + <literal>U*xy=[r;0]=c</literal>. + </para> + <para> + <note> + Note que <literal>givens(x,y)</literal> e + <literal>givens([x;y])</literal> são equivalentes. + </note> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=[3,4;5,6]; +U=givens(A(:,1)); +U*A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/factorization/householder.xml b/modules/linear_algebra/help/pt_BR/factorization/householder.xml new file mode 100755 index 000000000..8faaa7029 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/factorization/householder.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="householder" xml:lang="en"> + <refnamediv> + <refname>householder</refname> + <refpurpose>matriz de reflexão ortogonal de Householder</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>u=householder(v [,w])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>v</term> + <listitem> + <para>vetor coluna de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>w</term> + <listitem> + <para>vetor coluna de reais ou complexos com o mesmo tamanho que + <literal>v</literal>. Valor padrão é + <literal>eye(v)</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>u</term> + <listitem> + <para>vetor coluna de reais ou complexos</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Dados dois vetores coluna <literal>v</literal>, <literal> + w + </literal> + de mesmo tamanho, <literal>householder(v,w)</literal> retorna + um vetor coluna unitário <literal>u</literal>, tal que<literal> + (eye()-2*u*u')*v + </literal> + éproporcional a <literal>w</literal>. + <literal>(eye()-2*u*u')</literal> é a matriz de reflexão ortogonal de + Householder . + </para> + <para> + O valor padrão de<literal> w</literal> é<literal> eye(v)</literal>. + Neste caso, o vetor <literal> (eye()-2*u*u')*v</literal> é o + vetor<literal> eye(v)*norm(v)</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="givens">givens</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/factorization/sqroot.xml b/modules/linear_algebra/help/pt_BR/factorization/sqroot.xml new file mode 100755 index 000000000..4c5eab66e --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/factorization/sqroot.xml @@ -0,0 +1,64 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="sqroot" xml:lang="en"> + <refnamediv> + <refname>sqroot</refname> + <refpurpose>fatoração hermitiana W*W'</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>sqroot(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz simétrica, não-negativa definida de reais ou + complexos + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Retorna W tal que <literal>X=W*W'</literal> (usa SVD). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +X=rand(5,2)*rand(2,5);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) +// +X=rand(5,2)+%i*rand(5,2);X=X*X'; +W=sqroot(X) +norm(W*W'-X,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="chol">chol</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/kernel/CHAPTER b/modules/linear_algebra/help/pt_BR/kernel/CHAPTER new file mode 100755 index 000000000..be67920e1 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/CHAPTER @@ -0,0 +1,2 @@ +title = Kernel + diff --git a/modules/linear_algebra/help/pt_BR/kernel/colcomp.xml b/modules/linear_algebra/help/pt_BR/kernel/colcomp.xml new file mode 100755 index 000000000..5a281554c --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/colcomp.xml @@ -0,0 +1,112 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="colcomp" xml:lang="en"> + <refnamediv> + <refname>colcomp</refname> + <refpurpose>compressão de colunas, núcleo</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para>string</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real</para> + </listitem> + </varlistentry> + <varlistentry> + <term>W</term> + <listitem> + <para>matriz quadrada não-singular (mudança de base) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + inteiro (posto de <literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Compressão de colunas de <literal>A</literal>: <literal>Ac = + A*W + </literal> + éde colunas comprimidas ,i.e., + </para> + <para> + <literal>Ac=[0,Af]</literal> com o posto-coluna de + <literal>Af</literal> cheio, posto(<literal>Af</literal>) = + posto(<literal>A</literal>) = <literal>rk</literal>. + </para> + <para> + <literal>flag</literal> e <literal>tol</literal> são parâmetros + opcionais: <literal>flag = 'qr'</literal> ou <literal>'svd'</literal> (o + padrão é <literal>'svd'</literal>). + </para> + <para> + <literal>tol</literal> = parâmetro de tolerância (de ordem + <literal>%eps</literal> como valor padrão). + </para> + <para> + As <literal>ma-rk</literal> primeiras colunas de + <literal>W</literal> geram o núcleo de <literal>A</literal> quando + <literal>size(A)=(na,ma)</literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[X,r]=colcomp(A); +norm(A*X(:,1:$-r),1) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="kernel">kernel</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/kernel/fullrf.xml b/modules/linear_algebra/help/pt_BR/kernel/fullrf.xml new file mode 100755 index 000000000..5bf4e8220 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/fullrf.xml @@ -0,0 +1,106 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="fullrf" xml:lang="en"> + <refnamediv> + <refname>fullrf</refname> + <refpurpose>fatoração de posto completo (ou cheio)</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real (limiar para determinação do posto) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>matriz de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + inteiro(posto de <literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Fatoração de posto cheio : <literal>fullrf</literal> retorna + <literal>Q</literal> e <literal>M</literal> tais que <literal>A = + Q*M + </literal> + com Im(<literal>Q</literal>)=Im(<literal>A</literal>) e + Nuc(<literal>M</literal>)=Nuc(<literal>A</literal>), <literal>Q</literal> + de posto-coluna cheio, <literal>M</literal> de posto-linha cheio e + <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>. + </para> + <para> + <literal>tol</literal> é um parâmetro real opcional (valor real + padrão é <literal>sqrt(%eps)</literal>). O posto <literal>rk</literal> de + <literal>A</literal> é definido como o número de valores singulares + maiores que <literal>norm(A)*tol</literal>. + </para> + <para> + Se A é simétrica, <literal>fullrf</literal> retorna + <literal>M=Q'</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5); +[Q,M]=fullrf(A); +norm(Q*M-A,1) +[X,d]=rowcomp(A);Y=X'; +svd([A,Y(:,1:d),Q]) //span(Q) = span(A) = span(Y(:,1:2)) (span = "gerado") + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/kernel/fullrfk.xml b/modules/linear_algebra/help/pt_BR/kernel/fullrfk.xml new file mode 100755 index 000000000..9f7ba85f3 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/fullrfk.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="fullrfk" xml:lang="en"> + <refnamediv> + <refname>fullrfk</refname> + <refpurpose>fatoração de posto completo de A^k</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento </title> + <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou de complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>inteiro</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Bk,Ck</term> + <listitem> + <para>matrizes de reais ou de complexos</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Esta função calcula a fatoração de posto completo (ou cheio) de + <literal>A^k</literal> i.e. <literal>Bk*Ck=A^k</literal> onde + <literal>Bk</literal> é de posto-coluna cheio e <literal>Ck</literal> de + posto-linha cheio. Tem-se + Im(<literal>Bk</literal>)=Im(<literal>A^k</literal>) e + Nuc(<literal>Ck</literal>)=Nuc(<literal>A^k</literal>). + </para> + <para> + Para <literal>k=1</literal>, <literal>fullrfk</literal> é + equivalente a <literal>fullrf</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3); +norm(Bk*Ck-A^3,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="range">range</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/kernel/im_inv.xml b/modules/linear_algebra/help/pt_BR/kernel/im_inv.xml new file mode 100755 index 000000000..07f69c4b8 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/im_inv.xml @@ -0,0 +1,110 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="im_inv" xml:lang="en"> + <refnamediv> + <refname>im_inv</refname> + <refpurpose>imagem inversa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[X,dim]=im_inv(A,B [,tol]) + [X,dim,Y]=im_inv(A,B, [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A,B</term> + <listitem> + <para>duas matirzes de reais ou complexos com igual número de + colunas + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária de ordem igual ao número + de colunas de <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para>inteiro (dimensão do subespaço) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>matriz ortogonal de ordem igual ao número de linhas de + <literal>A</literal> e <literal>B</literal>. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[X,dim]=im_inv(A,B)</literal> + computa<literal>(A^-1)(B)</literal> ,i.e, vetores cujas imagens através de + <literal>A</literal> estão em Im(<literal>B</literal>) + </para> + <para> + As <literal>dim</literal> primeiras colunas de <literal>X</literal> + geram<literal> (A^-1)(B)</literal> + </para> + <para> + <literal>tol</literal> é um limiar usado para testar a inclusão de + subespaço ; o valor padrão é <literal>tol = 100*%eps</literal>. Se + <literal>Y</literal> é retornado, então <literal>[Y*A*X,Y*B]</literal> é + particionado como segue: + <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal> + </para> + <para> + onde <literal>B1</literal> tem posto-linha cheio (igual a + posto<literal>(B)</literal>) e <literal>A22</literal> tem posto-coluna + cheio e tem <literal>dim</literal> colunas. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)]; +W=rand(5,5);A=W*A;B=W*B; +[X,dim]=im_inv(A,B) +svd([A*X(:,1:dim),B]) //vetores A*X(:,1:dim) pertencem a range(B) (Imagem de B: Im(B)) +[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B] + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="spaninter">spaninter</link> + </member> + <member> + <link linkend="spanplus">spanplus</link> + </member> + <member> + <link linkend="linsolve">linsolve</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/kernel/kernel.xml b/modules/linear_algebra/help/pt_BR/kernel/kernel.xml new file mode 100755 index 000000000..93f8e850e --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/kernel.xml @@ -0,0 +1,99 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="kernel" xml:lang="en"> + <refnamediv> + <refname>kernel</refname> + <refpurpose>núcleo de uma matriz</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>W=kernel(A [,tol,[,flag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos completa ou matriz de reais + esparsa + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string <literal>'svd'</literal> (padrão) ou + <literal>'qr'</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real </para> + </listitem> + </varlistentry> + <varlistentry> + <term>W</term> + <listitem> + <para>matriz de posto-coluna completo</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>W=kernel(A)</literal> retorna o núcleo (espaço nulo) de + <literal>A</literal>. Se A tem posto-coluna completo, então uma matriz + vazia [] é retornada. + </para> + <para> + <literal>flag</literal> e <literal>tol</literal> são parâmetros + opcionais: <literal>flag = 'qr'</literal> ou<literal>'svd'</literal> (o + padrão é <literal>'svd'</literal>). + </para> + <para> + <literal>tol</literal> = parâmetro de tolerância (de ordem + <literal>%eps</literal> como valor padrão). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(3,1)*rand(1,3); +A*kernel(A) +A=sparse(A); +clean(A*kernel(A)) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="linsolve">linsolve</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/kernel/range.xml b/modules/linear_algebra/help/pt_BR/kernel/range.xml new file mode 100755 index 000000000..a82b20aa8 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/range.xml @@ -0,0 +1,95 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="range" xml:lang="en"> + <refnamediv> + <refname>range</refname> + <refpurpose>Imagem (gerado) de A^k</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[X,dim]=range(A,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos que se assume quadrada se k>1 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>inteiro</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz ortonormal </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para>inteiro (dimensão de subespaço)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Computação da imagem de <literal>A^k</literal> ; as primeiras dim + colunas de <literal>X</literal> geram a imagem de <literal>A^k</literal>. + As últimas linhas de <literal>X</literal> geram o complemento ortogonal da + imagem. <literal>X*X'</literal> é a matriz identidade. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(4,2)*rand(2,4); // 4 vetores colunas, 2 independentes. +[X,dim]=range(A,1);dim // computando a imagem + +y1=A*rand(4,1); //um vetor que está na imagem de A +y2=rand(4,1); //um vetor que não está na imagem de A +norm(X(dim+1:$,:)*y1) //as últimas entradas são zeros, y1 está na imagem de A +norm(X(dim+1:$,:)*y2) //as últimas entradas não são zeros + +I=X(1:dim,:)' //I é uma base para a imagem +coeffs=X(1:dim,:)*y1 //componentes de y1 relativos à base I + +norm(I*coeffs-y1) //verificando + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + </simplelist> + </refsection> + <refsection> + <title> Função Usada</title> + <para> + A função <literal>range</literal> é baseada na função <link linkend="rowcomp">rowcomp</link> que usa decomposição <link linkend="svd">svd</link> (decomposição em valores singulares). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/kernel/rowcomp.xml b/modules/linear_algebra/help/pt_BR/kernel/rowcomp.xml new file mode 100755 index 000000000..a01b2c735 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/kernel/rowcomp.xml @@ -0,0 +1,132 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rowcomp" xml:lang="en"> + <refnamediv> + <refname>rowcomp</refname> + <refpurpose>compressão de linhas, imagem</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[W,rk]=rowcomp(A [,flag [,tol]])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou de complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para>string opcional, com valores possíveis + <literal>'svd'</literal> ou <literal>'qr'</literal>. O valor padrão + é <literal>'svd'</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real não-negativo opcional. O valor padrão é + <literal>sqrt(%eps)*norm(A,1)</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>W</term> + <listitem> + <para>matriz quadrada não-singular (matriz mudança de base)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + inteiro (posto de <literal>A</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Compressão de linhas de <literal>A</literal>. <literal>Ac = + W*A + </literal> + éuma matriz de linhas comprimidas, i.e. + <literal>Ac=[Af;0]</literal> com <literal>Af</literal> de posto-linha + cheio. + </para> + <para> + <literal>flag</literal> e <literal>tol</literal> são parâmetros + opcionais: <literal>flag='qr'</literal> ou <literal>'svd'</literal> (o + padrão é <literal>'svd'</literal>). + </para> + <para> + <literal>tol</literal> é um parâmetro de tolerância. + </para> + <para> + As <literal>rk</literal> primeiras colunas de <literal>W'</literal> + geram a imagem de <literal>A</literal>. + </para> + <para> + As <literal>rk</literal> primeiras linhas (do topo) de + <literal>W</literal> geram a imagem de linha de + <literal>A</literal>. + </para> + <para> + Um vetor não nulo <literal>x</literal> pertence à + Im(<literal>A</literal>) se,e só se, <literal>W*x</literal> é de linhas + comprimidas de acordo com <literal>Ac</literal> i.e, a norma de seus + últimos componentes é pequena com relação a dos seus primeiros + componentes. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); // 4 vetores colunas, 2 independentes +[X,dim]=rowcomp(A);Xp=X'; +svd([Xp(:,1:dim),A]) //span(A) = span(Xp(:,1:dim) (span="gerado") +x=A*rand(4,1); //x pertence a span(A) +y=X*x +norm(y(dim+1:$))/norm(y(1:dim)) // pequeno + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + <member> + <link linkend="fullrfk">fullrfk</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Função Usada </title> + <para> + A função <literal>rowcomp</literal> é baseada nas decomposições + <link linkend="svd">svd</link> (decomposição em valores singulares) ou + <link linkend="qr">qr</link> . + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/CHAPTER b/modules/linear_algebra/help/pt_BR/linear/CHAPTER new file mode 100755 index 000000000..7d9d9cf49 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/CHAPTER @@ -0,0 +1,2 @@ +title = Linear Equations + diff --git a/modules/linear_algebra/help/pt_BR/linear/aff2ab.xml b/modules/linear_algebra/help/pt_BR/linear/aff2ab.xml new file mode 100755 index 000000000..8aa01b88e --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/aff2ab.xml @@ -0,0 +1,162 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="aff2ab" xml:lang="en"> + <refnamediv> + <refname>aff2ab</refname> + <refpurpose>Conversão de uma função linear (afim) para forma + A,b + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[A,b]=aff2ab(afunction,dimX,D [,flag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>afunction</term> + <listitem> + <para> + uma função do Scilab <literal> Y =fct(X,D) </literal> onde + <literal>X, D, Y</literal> são <literal>lists</literal> de + matrizes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dimX</term> + <listitem> + <para> + uma matriz de inteiros p x 2 (<literal>p</literal> é o número + de matrizes em X) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para> + uma <literal>list</literal> de matrizes de reais (ou qualquer + outro objeto Scilab válido). + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + parâmetro opcional (<literal>flag='f'</literal> ou + <literal>flag='sp'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>uma matriz de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>um vetor de reais tendo a mesma dimensão de linha que + <literal>A</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>aff2ab</literal> retorna a representação matricial de uma + função afim (na base canônica). + </para> + <para> + <literal>afunction</literal> é uma função com sintaxe imposta: + <literal> Y=afunction(X,D) </literal> onde <literal> X=list(X1,X2,...,Xp) + </literal> + é uma lista de p matrizes de reais, e <literal> + Y=list(Y1,...,Yq) + </literal> + éuma lista de q matrizes reais que dependem + linearmente das <literal> Xi</literal>'s. A entrada (opcional) <literal> + D + </literal> + contém parâmetros necessários para computar Y como uma função + de X (geralmente é uma lista de matrizes). + </para> + <para> + <literal> dimX</literal> é uma matriz p x 2: + <literal>dimX(i)=[nri,nci]</literal> é o número real de linhas e colunas + da matriz <literal>Xi</literal>. Estas dimensões determinam + <literal>na</literal>, a dimensão de coluna da matriz resultante + <literal>A</literal>: <literal>na=nr1*nc1 +...+ nrp*ncp</literal>. + </para> + <para> + Se o parâmetro opcional <literal>flag='sp'</literal> a matriz + resultante A é retornada como uma esparsa. + </para> + <para>Esta função é útil para resolver um sistema de equações lineares + onde as incógnitas são matrizes. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// solucionador de equação de Lyapunov (uma incógnita, uma restrição) +deff('Y=lyapunov(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q)') +A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3]; +[Aly,bly]=aff2ab(lyapunov,dimX,D); +[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); lyapunov(Xv,D) +Xm=Xv(:); A'*Xm+Xm*A-Q + +// solucionador de equação de Lyapunov com restrição redundante X=X' +// (uma variável, uma restrição) D é variável global +deff('Y=ly2(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q,Xm''-Xm)') +A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3]; +[Aly,bly]=aff2ab(ly2,dimX,D); +[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); ly2(Xv,D) + +// equações de Francis +// Achando matrizes X1 e X2 tais que: +// A1*X1 - X1*A2 + B*X2 -A3 = 0 +// D1*X1 -D2 = 0 +deff('Y=bruce(X,D)','[A1,A2,A3,B,D1,D2]=D(:),... +[X1,X2]=X(:);Y=list(A1*X1-X1*A2+B*X2-A3,D1*X1-D2)') +A1=[-4,10;-1,2];A3=[1;2];B=[0;1];A2=1;D1=[0,1];D2=1; +D=list(A1,A2,A3,B,D1,D2); +[n1,m1]=size(A1);[n2,m2]=size(A2);[n3,m3]=size(B); +dimX=[[m1,n2];[m3,m2]]; +[Af,bf]=aff2ab(bruce,dimX,D); +[Xf,KerAf]=linsolve(Af,bf);Xsol=vec2list(Xf,dimX) +bruce(Xsol,D) + +// Achando todas as X que comutam com A +deff('y=f(X,D)','y=list(D(:)*X(:)-X(:)*D(:))') +A=rand(3,3);dimX=[3,3];[Af,bf]=aff2ab(f,dimX,list(A)); +[Xf,KerAf]=linsolve(Af,bf);[p,q]=size(KerAf); +Xsol=vec2list(Xf+KerAf*rand(q,1),dimX); +C=Xsol(:); A*C-C*A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="linsolve">linsolve</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/chol.xml b/modules/linear_algebra/help/pt_BR/linear/chol.xml new file mode 100755 index 000000000..33b11e42f --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/chol.xml @@ -0,0 +1,85 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="chol" xml:lang="en"> + <refnamediv> + <refname>chol</refname> + <refpurpose>Cholesky factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[R]=chol(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>uma matriz simétrica e positiva definida de reais ou + complexos. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Se <literal>X</literal> é positiva definida, então <literal>R = + chol(X) + </literal> + produz uma matriz triangular superior + <literal>R</literal> tal que <literal>R'*R = X</literal>. + </para> + <para> + <literal>chol(X)</literal> usa apenas a diagonal e o triângulo + superior de <literal>X</literal>. O triângulo inferior é assumido como + sendo a transposta (ou complexo conjugado) da superior. + </para> + </refsection> + <refsection> + <title>Referências</title> + <para>A decomposição de Cholesky é baseada nas rotinas de Lapack DPOTRF + para matrizes de reais e ZPOTRF no caso de matrizes de complexos. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +W=rand(5,5)+%i*rand(5,5); +X=W*W'; +R=chol(X); +norm(R'*R-X) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="spchol">spchol</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/inv.xml b/modules/linear_algebra/help/pt_BR/linear/inv.xml new file mode 100755 index 000000000..6eaa5f99d --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/inv.xml @@ -0,0 +1,109 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="inv" xml:lang="en"> + <refnamediv> + <refname>inv</refname> + <refpurpose>inversa de uma matriz</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>inv(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz quadrada de reais ou complexos, matriz de polinômios, + matriz de razões de polinômios em representação de transferência ou + espaço de estados + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>inv(X)</literal> é a inversa da matriz quadrada + <literal>X</literal>. Uma aviso é impresso na tela se <literal>X</literal> + possui má escala ou é quase singular. + </para> + <para>Para matrizes de polinômios ou matrizes razões de polinômios em + representação de transferência, <literal>inv(X)</literal> é equivalente a + <literal>invr(X)</literal>. + </para> + <para>Para sistemas lineares na representação de espaço de estados (lista + <literal>syslin</literal>), <literal>invr(X)</literal> é equivalente a + <literal>invsyslin(X)</literal>. + </para> + </refsection> + <refsection> + <title>Referências</title> + <para>A função inv para matrizes de números é baseada nas rotinas de + Lapack DGETRF, DGETRI para matrizes de reais e ZGETRF, ZGETRI para o caso + de matrizes de complexos. Para matrizes de polinômios e matrizes de + funções racionais, <literal>inv</literal> é baseado na função + <literal>invr</literal> do Scilab. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);inv(A)*A + +x=poly(0,'x'); +A=[x,1,x;x^2,2,1+x;1,2,3];inv(A)*A + +A=[1/x,2;2+x,2/(1+x)] +inv(A)*A + +A=ssrand(2,2,3); +W=inv(A)*A +clean(ss2tf(W)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="slash">slash</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="coff">coff</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/linsolve.xml b/modules/linear_algebra/help/pt_BR/linear/linsolve.xml new file mode 100755 index 000000000..dffda99b7 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/linsolve.xml @@ -0,0 +1,129 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="linsolve" xml:lang="en"> + <refnamediv> + <refname>linsolve</refname> + <refpurpose>solucionador de equações lineares</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para> + uma matriz <literal>na x ma</literal> de reais (possivelmente + esparsa) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para> + um vetor <literal>na x 1</literal> (mesma dimensão de linha de + <literal>A</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x0</term> + <listitem> + <para>um vetor de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>kerA</term> + <listitem> + <para> + uma matriz <literal>ma x k</literal> de reais + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>linsolve</literal> computa todas as soluções para <literal> + A*x+b=0 + </literal> + . + </para> + <para> + <literal>x0</literal> é uma solução particular (se houver) e + <literal> kerA= </literal>núcleo de <literal>A</literal>. Qualquer + <literal>x=x0+kerA*w</literal> com <literal>w</literal> arbitrário + satisfaz <literal> A*x+b=0</literal>. + </para> + <para> + Se um compatible <literal>x0</literal> compatível é dado na entrada, + <literal>x0</literal> é retornado. Senão, um <literal>x0</literal>, + compatível é retornado, se houver. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,8); +b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b //b comatível +b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b //b incompatível +A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b //x é único + +// A benchmark of sparse linear solver + +[A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa"); + +b = zeros(size(A,1),1); + +tic(); +res = umfpack(A,'\',b); +mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc()); + +tic(); +res = linsolve(A,b); +mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc()); + +tic(); +res = A\b; +mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc()); + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="inv">inv</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="im_inv">im_inv</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="umfpack">umfpack</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/lsq.xml b/modules/linear_algebra/help/pt_BR/linear/lsq.xml new file mode 100755 index 000000000..b3f9fc62f --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/lsq.xml @@ -0,0 +1,116 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lsq" xml:lang="en"> + <refnamediv> + <refname>lsq</refname> + <refpurpose>problemas de mínimos quadrados lineares</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>X=lsq(A,B [,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou de complexos (m x n) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>B</term> + <listitem> + <para>matriz de reais ou de complexos (m x p)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>escalar positivo, usado para determinar o posto efetivo de A + (definido como sendo a ordem da maior submatriz triangular R11 + regente na fatoração QR com pivoteamento de A, cujo número de + condicionamento estimado <= 1/tol. O valor padrão de tol é + <literal>sqrt(%eps)</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz de reais ou complexos (n x p)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>X=lsq(A,B)</literal> computa a solução de mínimo quadrado + de menor norma da equação <literal>A*X=B</literal>, enquanto <literal>X=A + \ B + </literal> + computa uma solução de mínimo quadrado com no máximo + <literal>posto(A)</literal> componentes não-nulos por coluna. + </para> + </refsection> + <refsection> + <title>Referências</title> + <para> + <literal>lsq</literal> é baseado nas funções Lapack DGELSY para + matrizes de reais e ZGELSY para matrizes de complexos. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//Construindo os dados +x=(1:10)'; + +y1=3*x+4.5+3*rand(x,'normal'); +y2=1.8*x+0.5+2*rand(x,'normal'); +plot2d(x,[y1,y2],[-2,-3]) +//Achando a regressão linear +A=[x,ones(x)];B=[y1,y2]; +X=lsq(A,B); + +y1e=X(1,1)*x+X(2,1); +y2e=X(1,2)*x+X(2,2); +plot2d(x,[y1e,y2e],[2,3]) + +//Diferença entre lsq(A,b) e A\b +A=rand(4,2)*rand(2,3);//uma matriz de posto 2 +b=rand(4,1); +X1=lsq(A,b) +X2=A\b +[A*X1-b, A*X2-b] //os resíduos são os mesmos + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + <member> + <link linkend="pinv">pinv</link> + </member> + <member> + <link linkend="rank">rank</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/lu.xml b/modules/linear_algebra/help/pt_BR/linear/lu.xml new file mode 100755 index 000000000..d2418e3f7 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/lu.xml @@ -0,0 +1,124 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lu" xml:lang="en"> + <refnamediv> + <refname>lu</refname> + <refpurpose>fatores LU de eliminação Gaussiana</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[L,U]= lu(A) + [L,U,E]= lu(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos (m x n) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>L</term> + <listitem> + <para>matriz de reais ou complexos (m x min(m,n))</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz de reais ou complexos (min(m,n) x n ) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>uma matriz de permutação (n x n)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[L,U]= lu(A)</literal> produz duas matrizes + <literal>L</literal> e <literal>U</literal> tais que <literal>A = + L*U + </literal> + com <literal>U</literal> triangular superior e + <literal>E*L</literal> triangular infeiror para uma matriz de permutação + <literal>E</literal>. + </para> + <para> + Se <literal>A</literal> tem posto <literal>k</literal>, as linhas de + <literal>k+1</literal> a <literal>n</literal> de <literal>U</literal> são + zeros. + </para> + <para> + <literal>[L,U,E]= lu(A)</literal> produz três matrizes + <literal>L</literal>, <literal>U</literal> e <literal>E</literal> tais que + <literal>E*A = L*U</literal> com <literal>U</literal> triangular superior + e <literal>E*L</literal> l triangular inferior para uma matriz de + permutação <literal>E</literal>. + </para> + <para> + Se <literal>A</literal> é uma matriz de reais, usando as funções + <literal>lufact</literal> e <literal>luget</literal> é possível obter as + matrizes de permutação e, também, quando <literal>A</literal> não é de + posto cheio, a compressão de colunas da matriz + <literal>L</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +a=rand(4,4); +[l,u]=lu(a) +norm(l*u-a) + +[h,rk]=lufact(sparse(a)) // função lufact com matrizes esparsas +[P,L,U,Q]=luget(h); +ludel(h) +P=full(P);L=full(L);U=full(U);Q=full(Q); +norm(P*L*U*Q-a) // P e Q são as matrizes de permutação + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> + <refsection> + <title> Função Usada</title> + <para>As decomposições de lu são baseadas nas rotinas de Lapack DGETRF + para matrizes reais e ZGETRF para o caso de matrizes complexas. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/pinv.xml b/modules/linear_algebra/help/pt_BR/linear/pinv.xml new file mode 100755 index 000000000..9d1a5f795 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/pinv.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="pinv" xml:lang="en"> + <refnamediv> + <refname>pinv</refname> + <refpurpose>pseudo-inversa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>pinv(A,[tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>X= pinv(A)</literal> produz uma matriz + <literal>X</literal> de mesma dimensão que <literal>A'</literal> tal + que: + </para> + <para> + <literal>A*X*A = A, X*A*X = X</literal> e ambas + <literal>A*X</literal> e <literal>X*A</literal> são Hermitianas. + </para> + <para>A computação é baseada em SVD e qualquer valor singular abaixo da + tolerância é tratado como zero: esta tolerância é acessada por + <literal>X=pinv(A,tol)</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,2)*rand(2,4); +norm(A*pinv(A)*A-A,1) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Função Usada</title> + <para> + <literal>pinv</literal> é baseada na decomposição em valores + singulares (função do Scilab <literal>svd</literal>). + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/qr.xml b/modules/linear_algebra/help/pt_BR/linear/qr.xml new file mode 100755 index 000000000..bf20c82ce --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/qr.xml @@ -0,0 +1,200 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="qr" xml:lang="en"> + <refnamediv> + <refname>qr</refname> + <refpurpose>QR decomposição</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Q,R]=qr(X [,"e"]) + [Q,R,E]=qr(X [,"e"]) + [Q,R,rk,E]=qr(X [,tol]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros </title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real não-negativo</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para> + matriz com as mesmas dimensões de <literal>X</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>matriz de permutação </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + inteiro (posto QR de <literal>X</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <variablelist> + <varlistentry> + <term>[Q,R] = qr(X)</term> + <listitem> + <para> + pproduz uma matriz triangular superior <literal>R</literal> de + mesma dimensão que <literal>X</literal> e uma matriz ortogonal + (unitária no caso de matriz de complexos) <literal>Q</literal> tais + que <literal>X = Q*R</literal>. <literal>[Q,R] = qr(X,"e")</literal> + produz um "economia de tamanho": Se <literal>X</literal> é m-por-n + com m > n, então, apenas as primeiras n colunas de + <literal>Q</literal> são computadas assim como as primeiras n linhas + de <literal>R</literal>. + </para> + <para> + De <literal>Q*R = X</literal> , segue que a k-ésima coluna da + matriz <literal>X</literal>, é expressa como combinação linear das k + primeiras colunas de <literal>Q</literal> (com coeficientes + <literal> R(1,k), ..., R(k,k) </literal>). As k primeiras colunas de + <literal>Q</literal> formam uma base ortogonal para o subespaço + gerado pelas k priemiras colunas de <literal>X</literal>. Se a + coluna <literal>k</literal> de <literal>X</literal> (i.e. + <literal>X(:,k)</literal> ) é uma combinação linear das + <literal>p</literal> primeiras colunas de <literal>X</literal>, + então, as entradas de <literal>R(p+1,k), ..., R(k,k)</literal> são + zeros. Neste caso, <literal>R</literal> é trapezoidal superior. Se + <literal>X</literal> tem posto <literal>rk</literal>, as linhas + <literal>R(rk+1,:), R(rk+2,:), ...</literal> são zeros. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[Q,R,E] = qr(X)</term> + <listitem> + <para>produz uma matriz de permutação (de colunas) + <literal>E</literal>, uma matriz triangular superior + <literal>R</literal> com elementos na diagonal decrescentes e uma + matriz ortogonal (ou unitaria) <literal>Q</literal> tais que + <literal>X*E = Q*R</literal>. Se <literal>rk</literal> é o posto de + <literal>X</literal>, as <literal>rk</literal> primeiras entradas ao + longo da diagonal de <literal>R</literal>, i.e. <literal>R(1,1), + R(2,2), ..., R(rk,rk) + </literal> + são todas diferentes de zero. + <literal>[Q,R,E] = qr(X,"e")</literal> produz uma "economia de + tamanho": Se <literal>X</literal> ié m-por-n com m > n, então, + apenas as n primeiras colunas de <literal>Q</literal> são computadas + tanto quanto as n priemiras linhas de <literal>R</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[Q,R,rk,E] = qr(X ,tol)</term> + <listitem> + <para> + retorna <literal>rk</literal> = estimativa do posto de + <literal>X</literal> i.e. <literal>rk</literal> é o número elementos + da diagonal de <literal>R</literal> que são maiores que um dado + limiar <literal>tol</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>[Q,R,rk,E] = qr(X)</term> + <listitem> + <para> + retorna <literal>rk</literal> = estimativa do posto de + <literal>X</literal> i.e. <literal>rk</literal> é o número de + elementos da diagonal de <literal>R</literal> que são maiores que + <literal>tol=R(1,1)*%eps*max(size(R))</literal>. Veja + <literal>rankqr</literal> para uma fatoração QR que revela o posto + usando o número de condicionamento de <literal>R</literal>. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// fatoração QR, caso genérico +// X é alta (posto cheio) +X=rand(5,2);[Q,R]=qr(X); [Q'*X R] + +//X é gorda (posto cheio) +X=rand(2,3);[Q,R]=qr(X); [Q'*X R] + +//coluna 4 de X é uma combinação linear das colunas 1 e 2: +X=rand(8,5);X(:,4)=X(:,1)+X(:,2); [Q,R]=qr(X); R, R(:,4) + +//X tem posto 2, linhas 3 a $ de R são zero: +X=rand(8,2)*rand(2,5);[Q,R]=qr(X); R + +//Avaliando o posto rk: pivotação por colunas ==> rk primeiras +//As entradas diagonais de R são não-nulas: +A=rand(5,2)*rand(2,5); +[Q,R,rk,E] = qr(A,1.d-10); +norm(Q'*A-R) +svd([A,Q(:,1:rk)]) //span(A) =span(Q(:,1:rk)) (span="gerado") + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="rankqr">rankqr</link> + </member> + <member> + <link linkend="rank">rank</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + </simplelist> + </refsection> + <refsection> + <title> Funções Usadas</title> + <para>A decomposição qr é baseada nas rotinas de Lapack DGEQRF, DGEQPF, + DORGQR para as matrizes de reais ZGEQRF, ZGEQPF, ZORGQR para as matrizes + de complexos. + </para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/linear/rankqr.xml b/modules/linear_algebra/help/pt_BR/linear/rankqr.xml new file mode 100755 index 000000000..a09aa75b1 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/linear/rankqr.xml @@ -0,0 +1,147 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rankqr" xml:lang="en"> + <refnamediv> + <refname>rankqr</refname> + <refpurpose>fatoração QR com revelação do posto</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Q,R,JPVT,RANK,SVAL]=rankqr(A, [RCOND,JPVT])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>RCOND</term> + <listitem> + <para> número real usado para determinar o posto efetivo de + <literal>A</literal>, que é definido como sendo a ordem da maior + submatriz regente triangular <literal>R11</literal> na fatoração QR + com pivoteamento de <literal>A</literal>, cujo número de + condicionamento estimado é < <literal>1/RCOND</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>JPVT</term> + <listitem> + <para> + vetor de inteiros nas entradas, se <literal>JPVT(i)</literal> + não é 0, a <literal>i</literal>-ésimo coluna de <literal> + A + </literal> + épermtutada para a frente de <literal>AP</literal>, + senão, a coluna <literal>i</literal> é uma coluna livre. Na saída, + se <literal>JPVT(i) = k</literal>, então a + <literal>i</literal>-ésima coluna de <literal>A*P</literal> era a + <literal>k</literal>-ésima coluna de <literal>A</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>RANK</term> + <listitem> + <para> + posto efetivo de <literal>A</literal>, i.e., a ordem da + submatriz <literal>R11</literal>. É o mesmo que a ordem da submatriz + <literal>T1</literal> na fatoração ortogonal completa de + <literal>A</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>SVAL</term> + <listitem> + <para>vetor de reais com 3 componentes; as estimativas de alguns dos + valores singulares do fator triangular <literal>R</literal>. + </para> + <para> + <literal>SVAL(1)</literal> é o maior valor singular de + <literal>R(1:RANK,1:RANK)</literal>; + </para> + <para> + <literal>SVAL(2)</literal> é o menor valor singular de + <literal>R(1:RANK,1:RANK)</literal>; + </para> + <para> + <literal>SVAL(3) </literal>é o menor valor singular de + <literal>R(1:RANK+1,1:RANK+1)</literal>, se <literal>RANK</literal> + < <literal>MIN(M,N)</literal>, ou de + <literal>R(1:RANK,1:RANK)</literal>, caso contrário. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Computa (opcionalmente) uma fatoração QR com revelação do posto de + uma matriz de reais geral M-por-N, ou de complexos <literal>A</literal>, + que pode ser deficiente de posto, e estima seu posto efetivo usando + estimativa de condição incremental. + </para> + <para>A rotina usa uma fatoração QR com pivoteamento de colunas:</para> + <programlisting role=""><![CDATA[ +A * P = Q * R, onde R = [ R11 R12 ], + [ 0 R22 ] + ]]></programlisting> + <para> + com <literal>R11</literal> definida como a maior submatriz regente + cujo número de condição estimado é menor que <literal>1/RCOND</literal>. A + ordem de <literal>R11</literal>, <literal>RANK</literal>, é o posto + efetivo de<literal>A</literal>. + </para> + <para>Se a fatoração triangular revela o posto (que será o caso se as + colunas regentes forem bem condicionadas), então + <literal>SVAL(1)</literal> também será uma estimativa para o maior valor + singular de <literal>A</literal>, e <literal>SVAL(2)</literal> e + <literal>SVAL(3)</literal> serão estimativas para o + <literal>RANK</literal>-ésimo e <literal>(RANK+1)</literal>-ésimo valores + singulares de <literal>A</literal>, respectivamente. + </para> + <para>Examinando-se estes valores, pode-se confirmar que o posto é bem + definido a respeito do valor escolhido de <literal>RCOND</literal>. A + razão <literal>SVAL(1)/SVAL(2)</literal> é uma estimativa do número de + condicionamento de <literal>R(1:RANK,1:RANK)</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,7); +[Q,R,JPVT,RANK,SVAL]=rankqr(A,%eps) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rank">rank</link> + </member> + </simplelist> + </refsection> + <refsection> + <title> Funções Usadas</title> + <para>Rotinas da biblioteca Slicot MB03OD, ZB03OD.</para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/markov/CHAPTER b/modules/linear_algebra/help/pt_BR/markov/CHAPTER new file mode 100755 index 000000000..c29eb913c --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/markov/CHAPTER @@ -0,0 +1,2 @@ +title = Markov Matrices + diff --git a/modules/linear_algebra/help/pt_BR/markov/classmarkov.xml b/modules/linear_algebra/help/pt_BR/markov/classmarkov.xml new file mode 100755 index 000000000..affa1f588 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/markov/classmarkov.xml @@ -0,0 +1,102 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="classmarkov" xml:lang="en"> + <refnamediv> + <refname>classmarkov</refname> + <refpurpose>classes transientes e recorrentes da matriz de + Markov + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[perm,rec,tr,indsRec,indsT]=classmarkov(M)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>M</term> + <listitem> + <para>matriz de Markov N x N de reais. A soma das entradas em cada + linha deve ser acrescida em uma unidade + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>perm</term> + <listitem> + <para>vetor de permutação de inteiros</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rec, tr</term> + <listitem> + <para>vetor de inteiros, número (número de estados em cada classe + recorrente, número de estados transientes) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>indsRec,indsT</term> + <listitem> + <para>vetor de inteiros (índices dos estados recorrentes e + transientes) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Retorna um vetor de permutação <literal>perm</literal> tal + que + </para> + <programlisting role=""><![CDATA[ +M(perm,perm) = [M11 0 0 0 0 0] + [0 M22 0 0 0] + [0 0 M33 0] + [ ... ] + [0 0 Mrr 0] + [* * * Q] + ]]></programlisting> + <para> + Cada <literal>Mii</literal> é uma matriz de Markov de dimensão + <literal>rec(i) i=1,..,r</literal>. <literal>Q</literal> é uma submatriz + de Markov de dimensão <literal>tr</literal>. Estados de 1 a sum(rec) são + recorrentes e estados de r+1 a n são transientes. Tem-se + <literal>perm=[indsRec,indsT]</literal> onde indsRec é um vetor de tamanho + sum(rec) e indsT é um vetor de tamanho tr. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//P tem 2 classes recorrentes (com 2 e 1 estados) e 2 estados transientes +P=genmarkov([2,1],2,'perm') +[perm,rec,tr,indsRec,indsT]=classmarkov(P); +P(perm,perm) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="genmarkov">genmarkov</link> + </member> + <member> + <link linkend="eigenmarkov">eigenmarkov</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/markov/eigenmarkov.xml b/modules/linear_algebra/help/pt_BR/markov/eigenmarkov.xml new file mode 100755 index 000000000..8926b8738 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/markov/eigenmarkov.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="eigenmarkov" xml:lang="en"> + <refnamediv> + <refname>eigenmarkov</refname> + <refpurpose>Autovetores esquerdo e direito normalizados de + Markov + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[M,Q]=eigenmarkov(P)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>matriz de Markov N x N de reais. A soma das entradas de cada + linha deve ser acrescida de uma unidade + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>M</term> + <listitem> + <para>matriz de reais de N colunas</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz de reais de N linhas </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Retorna os autovetores esquerdo e direito normalizados associados ao + autovalor 1 da matriz P de transição de Markov. Se a multiplicidade deste + autovalor é m e P é N x N, M é uma matriz m x N e Q é uma matriz N x m. + M(k,:) é o vetor de distribuição de probabilidade associado ao k-ésimo + conjunto ergódico (classe recorrente). M(k,x) é zero se x não está na + k-ésima classe recorrente. Q(x,k) é a probabilidade de se terminar na + k-ésima classe recorrente começando de x. Se <literal>P^k</literal> + converge para <literal>k</literal> (sem autovalores no círculo unitário, + exceto 1), então o limite é <literal>Q*M</literal> (auto-projeção). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//P tem duas classes recorrentes (com 2 e 1 estados) e 2 estados transientes +P=genmarkov([2,1],2) +[M,Q]=eigenmarkov(P); +P*Q-Q +Q*M-P^20 + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="genmarkov">genmarkov</link> + </member> + <member> + <link linkend="classmarkov">classmarkov</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/markov/genmarkov.xml b/modules/linear_algebra/help/pt_BR/markov/genmarkov.xml new file mode 100755 index 000000000..a8da3164d --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/markov/genmarkov.xml @@ -0,0 +1,89 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="genmarkov" xml:lang="en"> + <refnamediv> + <refname>genmarkov</refname> + <refpurpose>gera uma matriz de Markov aleatória com classes recorrentes e + transientes + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>M=genmarkov(rec,tr) + M=genmarkov(rec,tr,flag) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>rec</term> + <listitem> + <para>vetor linha de inteiros (sua dimensão é o número de classes + recorrentes) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tr</term> + <listitem> + <para>inteiro (número de estados transientes)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>M</term> + <listitem> + <para>matriz de Markov de reais. A soma das entradas de cada linha + deve ser acrecsida de uma unidade + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string <literal>'perm'</literal>. Se fornecido, uma permutação + dos estados é feita. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title> Descrição </title> + <para>Retorna em M uma matriz de probabilidade de transição de Markov + aleatória com <literal>rec(1),...rec($)</literal> entradas respectivamente + e tr estados transientes. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//P tem duas classes recorrentes (com 2 e 1 states) e 2 estados transientes +P=genmarkov([2,1],2,'perm') +[perm,rec,tr,indsRec,indsT]=classmarkov(P); +P(perm,perm) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="classmarkov">classmarkov</link> + </member> + <member> + <link linkend="eigenmarkov">eigenmarkov</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/matrix/CHAPTER b/modules/linear_algebra/help/pt_BR/matrix/CHAPTER new file mode 100755 index 000000000..bb89125cd --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/CHAPTER @@ -0,0 +1,2 @@ +title = Matrix Analysis + diff --git a/modules/linear_algebra/help/pt_BR/matrix/cond.xml b/modules/linear_algebra/help/pt_BR/matrix/cond.xml new file mode 100755 index 000000000..78d153da3 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/cond.xml @@ -0,0 +1,59 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="cond" xml:lang="en"> + <refnamediv> + <refname>cond</refname> + <refpurpose>número de condicionamento de uma matriz</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>cond(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>rmatriz quadrada de reais ou complexos </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Número de condicionamento em norma-2. <literal>cond(X)</literal> é a + razão entre o maior e o menor valor singular de + <literal>X</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=testmatrix('hilb',6); +cond(A) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="rcond">rcond</link> + </member> + <member> + <link linkend="svd">svd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/matrix/det.xml b/modules/linear_algebra/help/pt_BR/matrix/det.xml new file mode 100755 index 000000000..d294693e7 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/det.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="det" xml:lang="en"> + <refnamediv> + <refname>det</refname> + <refpurpose>determinante</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>det(X) + [e,m]=det(X) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz quadrada de reais ou complexos, matriz de polinômios ou + de razões de polinômios + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>m</term> + <listitem> + <para>número real ou complexo, a mantissa de base 10 do + determinante + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>e</term> + <listitem> + <para>inteiro, o expoente de base 10 do determinante</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>det(X)</literal> ( <literal>m*10^e</literal> é o + determinante da matriz quadrada <literal>X)</literal>. + </para> + <para> + Para uma matriz de polinômios, <literal>det(X)</literal> é + equivalente a <literal>determ(X)</literal>. + </para> + <para> + Para matrizes de razões de polinômios <literal>det(X)</literal> é + equivalente a <literal>detr(X)</literal>. + </para> + </refsection> + <refsection> + <title>Referências</title> + <para>As computações da função det são baseadas nas rotinas do LAPACK + DGETRF para matrizes de reais e ZGETRF para o caso de matrizes de + complexos. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +det([x,1+x;2-x,x^2]) +w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w) //zeros do sistema linear +A=rand(3,3); +det(A), prod(spec(A)) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="determ">determ</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/matrix/orth.xml b/modules/linear_algebra/help/pt_BR/matrix/orth.xml new file mode 100755 index 000000000..d352ff212 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/orth.xml @@ -0,0 +1,76 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="orth" xml:lang="en"> + <refnamediv> + <refname>orth</refname> + <refpurpose>base ortogonal</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>Q=orth(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz de reais ou complexos</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>Q=orth(A)</literal> retorna <literal>Q</literal>, uma base + ortogonal para o gerado de <literal>A</literal>. Im(<literal>Q</literal>) + = Im(<literal>A</literal>) e <literal>Q'*Q=eye</literal>. + </para> + <para> + O número de colunas de <literal>Q</literal> é o posto de + <literal>A</literal> como determinado pelo algoritmo QR. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,4); +[X,dim]=rowcomp(A);X=X'; +svd([orth(A),X(:,1:dim)]) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="range">range</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/matrix/rank.xml b/modules/linear_algebra/help/pt_BR/matrix/rank.xml new file mode 100755 index 000000000..3cff123f5 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/rank.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rank" xml:lang="en"> + <refnamediv> + <refname>rank</refname> + <refpurpose>posto</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[i]=rank(X) + [i]=rank(X,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real não-negativo</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>rank(X)</literal> é o posto numérico de + <literal>X</literal> i.e. o número de valores singulares de X que são + maiores que <literal>norm(size(X),'inf') * norm(X) * + %eps + </literal> + . + </para> + <para> + <literal>rank(X,tol)</literal> é o número de valores singulares de + <literal>X</literal> que são maiores que <literal>tol</literal>. + </para> + <para> + Note que o valor padrão de <literal>tol</literal> é proporcional a + <literal>norm(X)</literal>. Como conseqüência, + <literal>rank([1.d-80,0;0,1.d-80])</literal> é 2 !. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +rank([1.d-80,0;0,1.d-80]) +rank([1,0;0,1.d-80]) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + <member> + <link linkend="rowcomp">rowcomp</link> + </member> + <member> + <link linkend="colcomp">colcomp</link> + </member> + <member> + <link linkend="lu">lu</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/matrix/rcond.xml b/modules/linear_algebra/help/pt_BR/matrix/rcond.xml new file mode 100755 index 000000000..0fe708628 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/rcond.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rcond" xml:lang="en"> + <refnamediv> + <refname>rcond</refname> + <refpurpose>número de condicionamento inverso</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>rcond(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz quadrada de reais ou complexos</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>rcond(X)</literal> é uma estimativa para a recíproca da + condição de <literal>X</literal> na norma-1. + </para> + <para> + Se <literal>X</literal> é bem condicionada, + <literal>rcond(X)</literal> é próximo a 1. Senão, + <literal>rcond(X)</literal> é próximo a 0. + </para> + <para> + <literal>[r,z]=rcond(X)</literal> ajusta <literal>r</literal> a + <literal>rcond(X)</literal> e retorna <literal>z</literal> tal que + <literal>norm(X*z,1) = r*norm(X,1)*norm(z,1)</literal> + </para> + <para> + Portanto, se <literal>rcond</literal> é pequeno, + <literal>z</literal> é um vetor do núcleo. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=diag([1:10]); +rcond(A) +A(1,1)=0.000001; +rcond(A) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="svd">svd</link> + </member> + <member> + <link linkend="cond">cond</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/matrix/rref.xml b/modules/linear_algebra/help/pt_BR/matrix/rref.xml new file mode 100755 index 000000000..c785ce98e --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/rref.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rref" xml:lang="en"> + <refnamediv> + <refname>rref</refname> + <refpurpose>computa a matriz-linha reduzida a forma escada por + transformações de LU + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>R=rref(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz m x n com entradas escalares </para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para>matriz m x n, forma escada de A</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>rref</literal> computa a forma escada de linhas reduzidas + da matriz dada pela decomposição esquerda LU. Se for necessária a + transformação usada, basta chamar <literal>X=rref([A,eye(m,m)])</literal> + A forma escada de linhas reduzidas <literal>R</literal> é + <literal>X(:,1:n)</literal> e a transformação esquerda + <literal>L</literal> ié dada por <literal>X(:,n+1:n+m)</literal> tal como + <literal>L*A=R</literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=[1 2;3 4;5 6]; +X=rref([A,eye(3,3)]); +R=X(:,1:2) +L=X(:,3:5);L*A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="lu">lu</link> + </member> + <member> + <link linkend="qr">qr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/matrix/trace.xml b/modules/linear_algebra/help/pt_BR/matrix/trace.xml new file mode 100755 index 000000000..4e168bcc2 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/matrix/trace.xml @@ -0,0 +1,60 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="trace" xml:lang="en"> + <refnamediv> + <refname>trace</refname> + <refpurpose>traço de uma matriz</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>trace(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz de reais ou complexos, matriz de polinômios ou de + razões de polinômios. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>trace(X)</literal> é o traço da matriz + <literal>X</literal>. + </para> + <para> + É o mesmo que <literal>sum(diag(X))</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3); +trace(A)-sum(spec(A)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/CHAPTER b/modules/linear_algebra/help/pt_BR/pencil/CHAPTER new file mode 100755 index 000000000..86d1da116 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/CHAPTER @@ -0,0 +1,2 @@ +title = Matrix Pencil + diff --git a/modules/linear_algebra/help/pt_BR/pencil/companion.xml b/modules/linear_algebra/help/pt_BR/pencil/companion.xml new file mode 100755 index 000000000..1778f00ce --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/companion.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="companion" xml:lang="en"> + <refnamediv> + <refname>companion</refname> + <refpurpose>matriz companheira</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>A=companion(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>polinômio ou vetor de polinômios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Retorna uma matriz quadrada <literal>A</literal> com o polinômio + característico igual a <literal>p</literal> se <literal>p</literal> é + mônico. Se <literal>p</literal> não é mônico, o polinômio característico + de <literal>A</literal> é igual a <literal>p/c</literal> onde + <literal>c</literal> é o coeficiente do termo de maior grau em + <literal>p</literal>. + </para> + <para> + Se <literal>p</literal> é um vetor de polinômios mônicos, + <literal>A</literal> é diagonal em blocos, e o polinômio característico do + i-ésimo bloco é <literal>p(i)</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=poly([1,2,3,4,1],'s','c') +det(s*eye()-companion(p)) +roots(p) +spec(companion(p)) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="randpencil">randpencil</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/ereduc.xml b/modules/linear_algebra/help/pt_BR/pencil/ereduc.xml new file mode 100755 index 000000000..92a68a905 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/ereduc.xml @@ -0,0 +1,123 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="ereduc" xml:lang="en"> + <refnamediv> + <refname>ereduc</refname> + <refpurpose>computa de forma escada de colunas da matriz por + transformações qz + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz m x n de entradas reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>escalar real positivo </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>matriz em forma escada de colunas </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz unitária m x m </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z</term> + <listitem> + <para>matriz unitária n x n </para> + </listitem> + </varlistentry> + <varlistentry> + <term>stair</term> + <listitem> + <para>vetor de índices,</para> + <variablelist> + <varlistentry> + <term>*</term> + <listitem> + <para> + <literal>ISTAIR(i) = + j</literal> se o elemento da + borda <literal>E(i,j)</literal> é uma quina. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>*</term> + <listitem> + <para> + <literal>ISTAIR(i) = - j</literal> se o elemento da + borda <literal>E(i,j)</literal> não é uma quina. + </para> + </listitem> + </varlistentry> + </variablelist> + <para> + <literal>(i=1,...,M)</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para>inteiro, posto estimado da matriz</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Dada uma matriz X <literal>mx n</literal> (não necessariamente + regular), a função ereduc calcula a matriz unitária transformada + <literal>E=Q*X*Z</literal> que está na forma escada de colunas (forma + trapezoidal). Ainda, o posto da matriz <literal>X</literal> é + determinado. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +X=[1 2 3;4 5 6] +[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="fstair">fstair</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Autores</title> + <para>Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT</para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/fstair.xml b/modules/linear_algebra/help/pt_BR/pencil/fstair.xml new file mode 100755 index 000000000..e78b6eae9 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/fstair.xml @@ -0,0 +1,175 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="fstair" xml:lang="en"> + <refnamediv> + <refname>fstair</refname> + <refpurpose>computa a forma escada de feixe de colunas por transformações + qz + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz m x n com entradas reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>escalar real positivo</para> + </listitem> + </varlistentry> + <varlistentry> + <term>E</term> + <listitem> + <para>matriz de forma escada de colunas </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz unitária m x m </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Z</term> + <listitem> + <para>matriz unitária n x n </para> + </listitem> + </varlistentry> + <varlistentry> + <term>stair</term> + <listitem> + <para>vetor de índices (ver ereduc)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> inteiro, posto estimado da matriz </para> + </listitem> + </varlistentry> + <varlistentry> + <term>AE</term> + <listitem> + <para>matriz m x n com entradas reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>EE</term> + <listitem> + <para>matriz de forma escada de colunas</para> + </listitem> + </varlistentry> + <varlistentry> + <term>QE</term> + <listitem> + <para>matriz unitária m x m </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ZE</term> + <listitem> + <para>matriz unitária n x n </para> + </listitem> + </varlistentry> + <varlistentry> + <term>nblcks</term> + <listitem> + <para>é o número de submatrizes com posto linha completo >= 0 + detectado na matriz <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>muk:</term> + <listitem> + <para> array (vetor ou matriz) de inteiros de dimensão (n). Contém + as dimensões de coluna mu(k) (k=1,...,nblcks) das submatrizes com + posto coluna cheio no feixe sE(eps)-A(eps) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>nuk:</term> + <listitem> + <para>array de inteiros de dimensão (m+1). Contém as dimensões de + linha nu(k) (k=1,...,nblcks) das submatrizes com posto linha cheio + no feixe sE(eps)-A(eps) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>muk0:</term> + <listitem> + <para>array de inteiros de dimensão (n). Contém as dimensões de + coluna mu(k) (k=1,...,nblcks) das submatrizes com o posto-coluna + cheio no feixe sE(eps,inf)-A(eps,inf) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>nuk:</term> + <listitem> + <para> array de inteiros de dimensão (m+1). Contém as dimensões de + linha nu(k) (k=1,...,nblcks) das submatrizes com posto-linha cheio + no feixe sE(eps,inf)-A(eps,inf) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>mnei:</term> + <listitem> + <para> array de inteiros dimensão (4). mnei(1) = dimensão de linha + de sE(eps)-A(eps) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Dado o feixe <literal>sE-A</literal> onde a matriz + <literal>E</literal> está na forma escada de colunas, a função + <literal>fstair</literal> computa, de acordo com as necessidades do + usuário, um feixe unitário transformado <literal>QE(sEE-AE)ZE</literal> + que é mais ou menos similar à forma generalizada de Schur do feixe + <literal>sE-A</literal>. A função também produz parte da estrutura de + Kronecker para um dado feixe. + </para> + <para> + <literal>Q,Z</literal> são as matrizes unitárias usadas para + computar o feixe onde E está na forma escada de colunas (ver + ereduc) + </para> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="quaskro">quaskro</link> + </member> + <member> + <link linkend="ereduc">ereduc</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/glever.xml b/modules/linear_algebra/help/pt_BR/pencil/glever.xml new file mode 100755 index 000000000..1a4b7f839 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/glever.xml @@ -0,0 +1,119 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="glever" xml:lang="en"> + <refnamediv> + <refname>glever</refname> + <refpurpose>inverso do feixe de matrizes</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>E, A</term> + <listitem> + <para>duas matrizes de reais quadradas de igual dimensão</para> + </listitem> + </varlistentry> + <varlistentry> + <term>s</term> + <listitem> + <para> + string (o valor padrão é '<literal>s</literal>') + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Bfs,Bis</term> + <listitem> + <para>duas matrizes de polinômios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>chis</term> + <listitem> + <para>polinômio</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Computação de</para> + <para> + <literal>(s*E-A)^-1</literal> + </para> + <para>pelo algoritmo generalizado de Leverrier para um feixe de + matrizes. + </para> + <programlisting role=""><![CDATA[ +(s*E-A)^-1 = (Bfs/chis) - Bis. + ]]></programlisting> + <para> + <literal>chis</literal> = polinômio característico (até uma + constante multiplicativa). + </para> + <para> + <literal>Bfs</literal> = nmatriz de polinômios como + numerador. + </para> + <para> + <literal>Bis</literal> = matriz de polinômios ( - expansão de + <literal>(s*E-A)^-1</literal> ao infinito). + </para> + <para> + Note o sinal - antes de <literal>Bis</literal>. + </para> + </refsection> + <refsection> + <title>Cuidado </title> + <para> + Esta função usa <literal>cleanp</literal> para simplificar + <literal>Bfs,Bis</literal> e <literal>chis</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1]; +[Bfs,Bis,chis]=glever(F) +inv(F)-((Bfs/chis) - Bis) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="rowshuff">rowshuff</link> + </member> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/kroneck.xml b/modules/linear_algebra/help/pt_BR/pencil/kroneck.xml new file mode 100755 index 000000000..2ca6a403d --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/kroneck.xml @@ -0,0 +1,161 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="kroneck" xml:lang="en"> + <refnamediv> + <refname>kroneck</refname> + <refpurpose>forma de Kronecker de feixe de matrizes</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F) + [Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>F</term> + <listitem> + <para> + feixe de matrizes de reais <literal>F=s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E,A</term> + <listitem> + <para>duas matrizes de reais de mesma dimensão</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,Z</term> + <listitem> + <para>duas matrizes quadradas ortogonais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Qd,Zd</term> + <listitem> + <para>dois vetores de inteiros </para> + </listitem> + </varlistentry> + <varlistentry> + <term>numbeps,numeta</term> + <listitem> + <para>dois vetores de inteiros</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Forma de Kronecker de feixe de matrizes: <literal>kroneck</literal> + computa duas matrizes ortogonais <literal>Q, Z</literal> que põem o feixe + <literal>F=s*E -A</literal> na forma triangular superior: + </para> + <programlisting role=""><![CDATA[ + | sE(eps)-A(eps) | X | X | X | + |----------------|----------------|------------|---------------| + | O | sE(inf)-A(inf) | X | X | +Q(sE-A)Z = |---------------------------------|----------------------------| + | | | | | + | 0 | 0 | sE(f)-A(f) | X | + |--------------------------------------------------------------| + | | | | | + | 0 | 0 | 0 | sE(eta)-A(eta)| + ]]></programlisting> + <para>As dimensões dos quatro blocos são dadas por:</para> + <para> + <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x + Zd(2) + </literal> + ,<literal>f = Qd(3) x Zd(3)</literal>, + <literal>eta=Qd(4)xZd(4)</literal> + </para> + <para> + O bloco <literal>inf</literal> contém modos infinitos de + feixes. + </para> + <para> + O bloco <literal>f</literal> contém modos finitos de feixes. + </para> + <para>A estrutura dos blocos epsilon e eta é dada por </para> + <para> + <literal>numbeps(1)</literal> = <literal>#</literal> de blocos eps + de tamanho 0 x 1 + </para> + <para> + <literal>numbeps(2)</literal> = <literal>#</literal> de blocos eps + de tamanho 1 x 2 + </para> + <para> + <literal>numbeps(3)</literal> = <literal>#</literal> de blocos eps + de tamanho 2 x 3 etc... + </para> + <para> + <literal>numbeta(1)</literal> = <literal>#</literal> de blocos eta + de tamanho 1 x 0 + </para> + <para> + <literal>numbeta(2)</literal> = <literal>#</literal> de blocos eta + de tamanho 2 x 1 + </para> + <para> + <literal>numbeta(3)</literal> = <literal>#</literal> de blocos eta + de tamanho 3 x 2 etc... + </para> + <para>O código foi retirado de T. Beelen (Slicot-WGS group).</para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +F=randpencil([1,1,2],[2,3],[-1,3,1],[0,3]); +Q=rand(17,17);Z=rand(18,18);F=Q*F*Z; +//feixe aleatório com eps1=1,eps2=1,eps3=1; 2 blocos J @ infty (infinito) +//com dimensões 2 e +//3 autovalores finitos em -1,3,1 e eta1=0,eta2=3 +[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F); +[Qd(1),Zd(1)] //parte eps. é sum(epsi) x (sum(epsi) + número de epsi) (sum="soma") +[Qd(2),Zd(2)] //parte infinita +[Qd(3),Zd(3)] //parte finita +[Qd(4),Zd(4)] //parte eta é (sum(etai) + number(eta1)) x sum(etai) (number=número) +numbeps +numbeta + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="gschur">gschur</link> + </member> + <member> + <link linkend="gspec">gspec</link> + </member> + <member> + <link linkend="systmat">systmat</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="randpencil">randpencil</link> + </member> + <member> + <link linkend="trzeros">trzeros</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/lyap.xml b/modules/linear_algebra/help/pt_BR/pencil/lyap.xml new file mode 100755 index 000000000..2d51a056c --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/lyap.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lyap" xml:lang="en"> + <refnamediv> + <refname>lyap</refname> + <refpurpose>equação de Lyapunov</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[X]=lyap(A,C,'c') + [X]=lyap(A,C,'d') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A, C</term> + <listitem> + <para> + matrizes quadradas de reais, <literal>C</literal> deve ser + simétrica + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>X= lyap(A,C,flag)</literal> resolve as equações matriciais + de tempo contínuo ou de tempo discreto de Lyapunov: + </para> + <programlisting role=""><![CDATA[ +A'*X + X*A = C ( flag='c' ) +A'*X*A - X = C ( flag='d' ) + ]]></programlisting> + <para>Perceba que existe uma única solução se e só se um autovalor de + <literal>A</literal> não é um autovalor de <literal>-A</literal> + (<literal>flag='c'</literal>) ou 1 sobre um autovalor de + <literal>A</literal> (<literal>flag='d'</literal>). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(4,4);C=rand(A);C=C+C'; +X=lyap(A,C,'c'); +A'*X + X*A -C +X=lyap(A,C,'d'); +A'*X*A - X -C + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sylv">sylv</link> + </member> + <member> + <link linkend="ctr_gram">ctr_gram</link> + </member> + <member> + <link linkend="obs_gram">obs_gram</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/pencan.xml b/modules/linear_algebra/help/pt_BR/pencil/pencan.xml new file mode 100755 index 000000000..fba81a530 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/pencan.xml @@ -0,0 +1,107 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="pencan" xml:lang="en"> + <refnamediv> + <refname>pencan</refname> + <refpurpose>forma canônica de feixe de matrizes</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[Q,M,i1]=pencan(Fs) + [Q,M,i1]=pencan(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para> + um feixe regular <literal>s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E,A</term> + <listitem> + <para>duas matrizes quadradas de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,M</term> + <listitem> + <para>duas matrizes não-singulares de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>i1</term> + <listitem> + <para>inteiro</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Dado o feixe regular <literal>Fs=s*E-A</literal>, + <literal>pencan</literal> retorna as matrizes <literal>Q</literal> e + <literal>M</literal> tais que <literal>M*(s*E-A)*Q</literal> está na forma + "canônica". + </para> + <para> + <literal>M*E*Q</literal> é uma matriz de blocos + </para> + <programlisting role=""><![CDATA[ +[I,0; + 0,N] + ]]></programlisting> + <para> + com <literal>N</literal> nilpotente e <literal>i1</literal> = + tamanho da matriz acima <literal>I</literal>. + </para> + <para> + <literal>M*A*Q</literal> é uma matriz de blocos: + </para> + <programlisting role=""><![CDATA[ +[Ar,0; + 0,I] + ]]></programlisting> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +F=randpencil([],[1,2],[1,2,3],[]); +F=rand(6,6)*F*rand(6,6); +[Q,M,i1]=pencan(F); +W=clean(M*F*Q) +roots(det(W(1:i1,1:i1))) +det(W($-2:$,$-2:$)) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + <member> + <link linkend="rowshuff">rowshuff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/penlaur.xml b/modules/linear_algebra/help/pt_BR/pencil/penlaur.xml new file mode 100755 index 000000000..62f4c7757 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/penlaur.xml @@ -0,0 +1,123 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="penlaur" xml:lang="en"> + <refnamediv> + <refname>penlaur</refname> + <refpurpose>Laurent coefficients of matrix pencil</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Si,Pi,Di,order]=penlaur(Fs) + [Si,Pi,Di,order]=penlaur(E,A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para> + um feixe regular <literal>s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E, A</term> + <listitem> + <para>duas matrizes quadradas de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Si,Pi,Di</term> + <listitem> + <para>três matrizes quadradas de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>order</term> + <listitem> + <para>inteiro</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>penlaur</literal> computa os primeiros coeficientes de + Laurent de <literal>(s*E-A)^-1</literal> no infinito. + </para> + <para> + <literal>(s*E-A)^-1 = ... + Si/s - Pi - s*Di + ...</literal> em + <literal>s</literal> = infinito. + </para> + <para> + <literal>order</literal> = ordem da singularidade + (ordem=índice-1). + </para> + <para> + O feixe de matrizes <literal>Fs=s*E-A</literal> deve ser + invertível. + </para> + <para> + Para um feixe de índice 0, <literal>Pi, Di,...</literal> são zero e + <literal>Si=inv(E)</literal>. + </para> + <para> + Para um feixe de índice 1 (order=0),<literal>Di</literal> =0. + </para> + <para> + Para feixes de índices maiores, os termos <literal> -s^2 Di(2), -s^3 + Di(3),... + </literal> + são dados por: + </para> + <para> + <literal> Di(2)=Di*A*Di</literal>, <literal> + Di(3)=Di*A*Di*A*Di + </literal> + (até <literal>Di(order)</literal>). + </para> + </refsection> + <refsection> + <title>Observação</title> + <para>Versão experimental: há problemas quando se tem mal-condicionamento + de<literal>so*E-A</literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +F=randpencil([],[1,2],[1,2,3],[]); +F=rand(6,6)*F*rand(6,6);[E,A]=pen2ea(F); +[Si,Pi,Di]=penlaur(F); +[Bfs,Bis,chis]=glever(F); +norm(coeff(Bis,1)-Di,1) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="rowshuff">rowshuff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/quaskro.xml b/modules/linear_algebra/help/pt_BR/pencil/quaskro.xml new file mode 100755 index 000000000..beb65fb07 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/quaskro.xml @@ -0,0 +1,134 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="quaskro" xml:lang="en"> + <refnamediv> + <refname>quaskro</refname> + <refpurpose>forma quasi-Kronecker</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F) + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A) + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F,tol) + [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>F</term> + <listitem> + <para> + feixe de matrizes de reais <literal>F=s*E-A</literal> + (<literal>s=poly(0,'s')</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>E,A</term> + <listitem> + <para>duas matrizes reais de iguais dimensões </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para> número real (tolerância, valor padrão=1.d-10) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q,Z</term> + <listitem> + <para>duas matrizes quadradas ortogonais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Qd,Zd</term> + <listitem> + <para>dois vetores de inteiros </para> + </listitem> + </varlistentry> + <varlistentry> + <term>numbeps</term> + <listitem> + <para>vetor de inteiros</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Forma quasi-Kronecker de um feixe de matrizes: + <literal>quaskro</literal> computa duas matrizes ortogonais <literal>Q, + Z + </literal> + que põem o feixe <literal>F=s*E -A</literal> na forma + triangular superior: + </para> + <programlisting role=""><![CDATA[ + | sE(eps)-A(eps) | X | X | + |----------------|----------------|------------| + | O | sE(inf)-A(inf) | X | +Q(sE-A)Z = |=================================|============| + | | | + | O | sE(r)-A(r) | + ]]></programlisting> + <para>As dimensões dos blocos são dadas por:</para> + <para> + <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x + Zd(2) + </literal> + ,<literal>r = Qd(3) x Zd(3)</literal> + </para> + <para> + O bloco <literal>inf</literal> contém os modos infinitos do + feixe. + </para> + <para> + O bloco <literal>f</literal> contém os modos finitos do feixe + </para> + <para>A estrutura dos blocos epsilon é dada por:</para> + <para> + <literal>numbeps(1)</literal> = <literal>#</literal> de blocos eps + de tamanho 0 x 1 + </para> + <para> + <literal>numbeps(2)</literal> = <literal>#</literal> de blocos eps + de tamanho 1 x 2 + </para> + <para> + <literal>numbeps(3)</literal> = <literal>#</literal> de blocos eps + de tamanho 2 x 3 etc... + </para> + <para>A forma completa (de quatro blocos) de Kronecker é dada pela função + <literal>kroneck</literal> que chama a função <literal>quaskro</literal> + sobre o feixe (pertransposto) <literal>sE(r)-A(r)</literal>. + </para> + <para>O código é retirado de T. Beelen.</para> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="kroneck">kroneck</link> + </member> + <member> + <link linkend="gschur">gschur</link> + </member> + <member> + <link linkend="gspec">gspec</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/randpencil.xml b/modules/linear_algebra/help/pt_BR/pencil/randpencil.xml new file mode 100755 index 000000000..3d0fe44e6 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/randpencil.xml @@ -0,0 +1,117 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="randpencil" xml:lang="en"> + <refnamediv> + <refname>randpencil</refname> + <refpurpose>feixe aleatório</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>F=randpencil(eps,infi,fin,eta)</synopsis> + </refsynopsisdiv> + <refsection> + <title> Parâmetros </title> + <variablelist> + <varlistentry> + <term>eps</term> + <listitem> + <para>vetor de inteiros </para> + </listitem> + </varlistentry> + <varlistentry> + <term>infi</term> + <listitem> + <para>vetor de inteiros </para> + </listitem> + </varlistentry> + <varlistentry> + <term>fin</term> + <listitem> + <para>vetor de reais, ou polinômio mônico, ou vetor de polinômios + mônicos + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>eta</term> + <listitem> + <para>vetor de inteiros </para> + </listitem> + </varlistentry> + <varlistentry> + <term>F</term> + <listitem> + <para> + feixe de matrizes de reais <literal>F=s*E-A</literal> + (<literal>s=poly(0,'s')</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Função utilitária. <literal>F=randpencil(eps,infi,fin,eta)</literal> + retorna um feixe aleatório <literal>F</literal> com dada estrutura de + Kronecker. A estrutura é dada por: <literal>eps=[eps1,...,epsk]</literal>: + estrutura de blocos epsilon (tamanho eps1x(eps1+1),....) + <literal>fin=[l1,...,ln]</literal> conjunto de autovalores finitos + (assumidos como reais) (possivelmente []) + <literal>infi=[k1,...,kp]</literal> tamanho de blocos J no infinito + <literal>ki>=1</literal> (infi=[] se não há blocos J). + <literal>eta=[eta1,...,etap]</literal>: estrutura dos blocos eta (size + eta1+1)xeta1,...) + </para> + <para> + <literal>epsi</literal>'s devem ser >=0, + <literal>etai</literal>'s devem ser >=0, <literal>infi</literal>'s + devem ser >=1. + </para> + <para> + Se <literal>fin</literal> é um polinômio (mônico), o bloco finito + admite raízes de <literal>fin</literal> como autovalores. + </para> + <para> + Se <literal>fin</literal> é um vetor de polinômios, eles são os + divisores elementares finitos de <literal>F</literal> ,i.e., as raízes de + <literal>p(i)</literal> são autovalores finitos de + <literal>F</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +F=randpencil([0,1],[2],[-1,0,1],[3]); +[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F); +Qd, Zd +s=poly(0,'s'); +F=randpencil([],[1,2],s^3-2,[]); //feixe regular +det(F) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="kroneck">kroneck</link> + </member> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/rowshuff.xml b/modules/linear_algebra/help/pt_BR/pencil/rowshuff.xml new file mode 100755 index 000000000..ff28a40ce --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/rowshuff.xml @@ -0,0 +1,111 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rowshuff" xml:lang="en"> + <refnamediv> + <refname>rowshuff</refname> + <refpurpose>algoritmo de embaralhamento</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Ws,Fs1]=rowshuff(Fs, [alfa])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para> + feixe quadrado de reais <literal>Fs = s*E-A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ws</term> + <listitem> + <para>matriz de polinômios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Fs1</term> + <listitem> + <para> + feixe quadrado de reais <literal>F1s = s*E1 -A1</literal> com + <literal>E1</literal> não-singular + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>alfa</term> + <listitem> + <para> + número real (<literal>alfa = 0</literal> é o valor + padrão) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Algoritmo de embaralhamento: dado o feixe + <literal>Fs=s*E-A</literal>, retorna Ws=W(s) (matriz quadrada de + polinômios) tal que: + </para> + <para> + <literal> Fs1 = s*E1-A1 = W(s)*(s*E-A) </literal> é um feixe com + matriz <literal>E1</literal> não-singular. + </para> + <para> + Isto é possível se, e só se, o feixe <literal>Fs = s*E-A</literal> é + regular (i.e., invertível). O grau de <literal>Ws</literal> é igual ao + índice do feixe. + </para> + <para> + Os pólos no infinito de<literal> Fs</literal> asão colocados para + <literal>alfa</literal> e os zeros de <literal>Ws</literal> estão em + <literal>alfa</literal>. + </para> + <para> + Note que <literal>(s*E-A)^-1 = (s*E1-A1)^-1 * W(s) = + (W(s)*(s*E-A))^-1 *W(s) + </literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +F=randpencil([],[2],[1,2,3],[]); +F=rand(5,5)*F*rand(5,5); // feixe regular 5 x 5 com três avaliações em 1,2,3 +[Ws,F1]=rowshuff(F,-1); +[E1,A1]=pen2ea(F1); +svd(E1) //E1 não-singular +roots(det(Ws)) +clean(inv(F)-inv(F1)*Ws,1.d-7) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="pencan">pencan</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/pencil/sylv.xml b/modules/linear_algebra/help/pt_BR/pencil/sylv.xml new file mode 100755 index 000000000..fcba9fc28 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/pencil/sylv.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="sylv" xml:lang="en"> + <refnamediv> + <refname>sylv</refname> + <refpurpose>equação de Sylvester </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>sylv(A,B,C,flag)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A,B,C</term> + <listitem> + <para>três matrizes de reais de dimensões apropriadas</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string (<literal>'c'</literal> ou + <literal>'d'</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>X= sylv(A,B,C,'c')</literal> computa <literal>X</literal>, + solução da equação de "tempo contínuo" de Sylvester. + </para> + <programlisting role=""><![CDATA[ +A*X+X*B=C + ]]></programlisting> + <para> + <literal>X=sylv(A,B,C,'d')</literal> computa <literal>X</literal>, + solução da equação de "tempo discreto" de Sylvester. + </para> + <programlisting role=""><![CDATA[ +A*X*B-X=C + ]]></programlisting> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(4,4);C=rand(4,3);B=rand(3,3); +X = sylv(A,B,C,'c'); +norm(A*X+X*B-C) +X=sylv(A,B,C,'d') +norm(A*X*B-X-C) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="lyap">lyap</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/proj.xml b/modules/linear_algebra/help/pt_BR/proj.xml new file mode 100755 index 000000000..cef345ed3 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/proj.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="proj" xml:lang="en"> + <refnamediv> + <refname>proj</refname> + <refpurpose>projeção</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>P = proj(X1,X2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X1,X2</term> + <listitem> + <para>duas matrizes reais com igual número de colunas</para> + </listitem> + </varlistentry> + <varlistentry> + <term>P</term> + <listitem> + <para> + matriz de projeção de real (<literal>P^2=P</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>P</literal> é a projeção sobre <literal>X2</literal> + paralela a <literal>X1</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <programlisting role="example"><![CDATA[ +X1=rand(5,2);X2=rand(5,3); +P=proj(X1,X2); +norm(P^2-P,1) +trace(P) // Este é dim(X2) +[Q,M]=fullrf(P); +svd([Q,X2]) // span(Q) = span(X2) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="projspec">projspec</link> + </member> + <member> + <link linkend="orth">orth</link> + </member> + <member> + <link linkend="fullrf">fullrf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/state_space/CHAPTER b/modules/linear_algebra/help/pt_BR/state_space/CHAPTER new file mode 100755 index 000000000..a0b62cdee --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/state_space/CHAPTER @@ -0,0 +1,2 @@ +title = State-Space Matrices + diff --git a/modules/linear_algebra/help/pt_BR/state_space/coff.xml b/modules/linear_algebra/help/pt_BR/state_space/coff.xml new file mode 100755 index 000000000..f75f38f77 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/state_space/coff.xml @@ -0,0 +1,99 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="coff" xml:lang="en"> + <refnamediv> + <refname>coff</refname> + <refpurpose>resolvente (método do cofator) </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[N,d]=coff(M [,var])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>M</term> + <listitem> + <para>matriz quadrada de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>var</term> + <listitem> + <para>string</para> + </listitem> + </varlistentry> + <varlistentry> + <term>N</term> + <listitem> + <para> matriz de polinômios (com o mesmo tamanho que + <literal>M</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>d</term> + <listitem> + <para>polinômio ( polinômio característico + <literal>poly(A,'s')</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>coff</literal> computa R=<literal>(s*eye()-M)^-1</literal> + para <literal>M</literal> uma matriz de reais. R é dado por + <literal>N/d</literal>. + </para> + <para> + <literal>N</literal> = matriz de polinômios como numerador. + </para> + <para> + <literal>d</literal> = denominador comum. + </para> + <para> + <literal>var</literal> string ( ('<literal>s</literal>' se + omitido) + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +M=[1,2;0,3]; +[N,d]=coff(M) +N/d +inv(%s*eye()-M) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="ss2tf">ss2tf</link> + </member> + <member> + <link linkend="nlev">nlev</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/state_space/nlev.xml b/modules/linear_algebra/help/pt_BR/state_space/nlev.xml new file mode 100755 index 000000000..90ddd6dd2 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/state_space/nlev.xml @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="nlev" xml:lang="en"> + <refnamediv> + <refname>nlev</refname> + <refpurpose>algoritmo de Leverrier</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[num,den]=nlev(A,z [,rmax])</synopsis> + </refsynopsisdiv> + <refsection> + <title> Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>z</term> + <listitem> + <para>string</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rmax</term> + <listitem> + <para> + parâmetro opcional (ver <literal>bdiag</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[num,den]=nlev(A,z [,rmax])</literal> computa + <literal>(z*eye()-A)^(-1)</literal> + </para> + <para>por diagonalização por blocos de A seguido pelo algoritmo de + Leverrier em cada bloco. + </para> + <para>Este algoritmo é melhor que o algoritmo usual de Leverrier, mas + ainda não está perfeito! + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(3,3);x=poly(0,'x'); +[NUM,den]=nlev(A,'x') +clean(den-poly(A,'x')) +clean(NUM/den-inv(x*eye()-A)) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="coff">coff</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="ss2tf">ss2tf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Autores</title> + <para>F. Delebecque., S. Steer INRIA;</para> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/subspaces/CHAPTER b/modules/linear_algebra/help/pt_BR/subspaces/CHAPTER new file mode 100755 index 000000000..d87d9ca5e --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/subspaces/CHAPTER @@ -0,0 +1,3 @@ +title = Subspaces + + diff --git a/modules/linear_algebra/help/pt_BR/subspaces/spaninter.xml b/modules/linear_algebra/help/pt_BR/subspaces/spaninter.xml new file mode 100755 index 000000000..894f73b4b --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/subspaces/spaninter.xml @@ -0,0 +1,98 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spaninter" xml:lang="en"> + <refnamediv> + <refname>spaninter</refname> + <refpurpose>interseção de subespaços</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento</title> + <synopsis>[X,dim]=spaninter(A,B [,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A, B</term> + <listitem> + <para>duas matrizes de reais ou de complexos com igual número de + linhas + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária</para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim</term> + <listitem> + <para> + inteiro, dimensão do subesbaço Im(<literal>A</literal>) inter + Im(<literal>B</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Computa a intereseção de Im(<literal>A</literal>) e + Im(<literal>B</literal>). + </para> + <para> + As primeiras <literal>dim</literal> colunas de <literal>X</literal> + geram esta interseção i.e. <literal>X(:,1:dim)</literal> é uma base + ortogonal para + </para> + <para> + Im(<literal>A</literal>) inter Im(<literal>B</literal>) + </para> + <para> + Na base <literal>X</literal>, <literal>A</literal> e + <literal>B</literal> são respectivamente representados por: + </para> + <para> + <literal>X'*A</literal> e <literal>X'*B</literal>. + </para> + <para> + <literal>tol</literal> é um limiar (<literal>sqrt(%eps)</literal> é + o valor padrão). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(5,3)*rand(3,4); // A é 5 x 4, rank=3 +B=[A(:,2),rand(5,1)]*rand(2,2); +[X,dim]=spaninter(A,B); +X1=X(:,1:dim); //A interseção +svd(A),svd([X1,A]) // X1 no gerado(A) (span(A)) +svd(B),svd([B,X1]) // X1 no gerado(B) (span(B)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="spanplus">spanplus</link> + </member> + <member> + <link linkend="spantwo">spantwo</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/subspaces/spanplus.xml b/modules/linear_algebra/help/pt_BR/subspaces/spanplus.xml new file mode 100755 index 000000000..3bed11264 --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/subspaces/spanplus.xml @@ -0,0 +1,103 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spanplus" xml:lang="en"> + <refnamediv> + <refname>spanplus</refname> + <refpurpose>soma de subespaços</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[X,dim,dima]=spanplus(A,B[,tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A, B</term> + <listitem> + <para>duas matrizes de reais ou complexos com igual número de + linhas + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz quadrada ortogonal ou unitária </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dim, dima</term> + <listitem> + <para>inteiros, dimensões de subespaços </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real não-negativo</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>Computa a base X tal que:</para> + <para> + as primeiras <literal>dima</literal> colunas de <literal>X</literal> + geram Im(<literal>A</literal>) e as (<literal>dim-dima</literal>) colunas + seguintes formam uma base de <literal>A+B</literal> em relação a + <literal>A</literal>. + </para> + <para> + As <literal>dim</literal> primeiras colunas de <literal>X</literal> + formam uma base para <literal>A+B</literal>. + </para> + <para>Tem-se a seguinte forma canônica para + <literal>[A,B]</literal>: + </para> + <programlisting role=""><![CDATA[ + [*,*] (dima rows) +X'*[A,B]=[0,*] (dim-dima rows) + [0,0] + ]]></programlisting> + <para> + <literal>tol</literal> é um argumento opcional (ver código da + função). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=rand(6,2)*rand(2,5); // rank(A)=2 (posto(A)=2) +B=[A(:,1),rand(6,2)]*rand(3,3); //dois vetores adicionais independentes +[X,dim,dimA]=spanplus(A,B); +dimA +dim + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="spaninter">spaninter</link> + </member> + <member> + <link linkend="im_inv">im_inv</link> + </member> + <member> + <link linkend="spantwo">spantwo</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/pt_BR/subspaces/spantwo.xml b/modules/linear_algebra/help/pt_BR/subspaces/spantwo.xml new file mode 100755 index 000000000..96278172b --- /dev/null +++ b/modules/linear_algebra/help/pt_BR/subspaces/spantwo.xml @@ -0,0 +1,119 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spantwo" xml:lang="en"> + <refnamediv> + <refname>spantwo</refname> + <refpurpose>soma e interseção de subespaços</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[Xp,dima,dimb,dim]=spantwo(A,B, [tol])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A, B</term> + <listitem> + <para>duas matrizes de reais ou complexos com igual número de linhas + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Xp</term> + <listitem> + <para>matriz quadrada não-singular </para> + </listitem> + </varlistentry> + <varlistentry> + <term>dima, dimb, dim</term> + <listitem> + <para>inteiros, dimensões dos subespaços </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>número real não-negativo</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Dadas duas matrizes <literal>A</literal> e <literal>B</literal> com + o mesmo número de linhas, retorna uma matriz quadrada + <literal>Xp</literal> (não-singular, mas não necessariamente ortogonal) + tal que : + </para> + <programlisting role=""><![CDATA[ + [A1, 0] (dim-dimb linhas) +Xp*[A,B]=[A2,B2] (dima+dimb-dim linhas) + [0, B3] (dim-dima linha) + [0 , 0] + ]]></programlisting> + <para> + As primeiras <literal>dima</literal> colunas de + <literal>inv(Xp)</literal> geram Im(<literal>A</literal>). + </para> + <para> + As colunas de <literal>dim-dimb+1</literal> até + <literal>dima</literal> de <literal>inv(Xp)</literal> geram a interseção + de Im(A) e Im(B). + </para> + <para> + As primeiras <literal>dim</literal> colunas de + <literal>inv(Xp)</literal> geram + Im(<literal>A</literal>)+Im(<literal>B</literal>). + </para> + <para> + As colunas de <literal>dim-dimb+1</literal> até + <literal>dim</literal> de <literal>inv(Xp)</literal> geram + Im(<literal>B</literal>). + </para> + <para> + A matrix <literal>[A1;A2]</literal> tem posto-linha cheio (= + posto(A)), a matrix <literal>[B2;B3]</literal> tem posto-linha cheio + (=posto(B)), a matriz <literal>[A2,B2]</literal> tem posto-linha (=posto(A + inter B)) e a matriz <literal>[A1,0;A2,B2;0,B3]</literal> tem posto-linha + cheio (=posto(A+B)). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=[1,0,0,4; + 5,6,7,8; + 0,0,11,12; + 0,0,0,16]; +B=[1,2,0,0]';C=[4,0,0,1]; +Sl=ss2ss(syslin('c',A,B,C),rand(A)); +[no,X]=contr(Sl('A'),Sl('B'));CO=X(:,1:no); //Parte controlável +[uo,Y]=unobs(Sl('A'),Sl('C'));UO=Y(:,1:uo); //Parte inobservável +[Xp,dimc,dimu,dim]=spantwo(CO,UO); //Decomposição de Kalman +Slcan=ss2ss(Sl,inv(Xp)); + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="spanplus">spanplus</link> + </member> + <member> + <link linkend="spaninter">spaninter</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/linear_algebra/help/ru_RU/addchapter.sce b/modules/linear_algebra/help/ru_RU/addchapter.sce new file mode 100755 index 000000000..9c126ad92 --- /dev/null +++ b/modules/linear_algebra/help/ru_RU/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Linear Algebra",SCI+"/modules/linear_algebra/help/ru_RU",%T); + |