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| author | Shashank | 2017-05-29 12:40:26 +0530 |
|---|---|---|
| committer | Shashank | 2017-05-29 12:40:26 +0530 |
| commit | 0345245e860375a32c9a437c4a9d9cae807134e9 (patch) | |
| tree | ad51ecbfa7bcd3cc5f09834f1bb8c08feaa526a4 /modules/sparse/help | |
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diff --git a/modules/sparse/help/en_US/addchapter.sce b/modules/sparse/help/en_US/addchapter.sce new file mode 100755 index 000000000..c73aab599 --- /dev/null +++ b/modules/sparse/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("Sparse Matrix",SCI+"/modules/sparse/help/en_US",%T); + diff --git a/modules/sparse/help/en_US/chfact.xml b/modules/sparse/help/en_US/chfact.xml new file mode 100755 index 000000000..d8b43a5d2 --- /dev/null +++ b/modules/sparse/help/en_US/chfact.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="en" xml:id="chfact"> + <refnamediv> + <refname>chfact</refname> + <refpurpose>sparse Cholesky factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>spcho=chfact(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>square symmetric positive sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>spcho</term> + <listitem> + <para>list containing the Cholesky factors in coded form</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>spcho=chfact(A)</literal> computes the sparse Cholesky factors of sparse + matrix <literal>A</literal>, assumed symmetric positive definite. + This function is based on the Ng-Peyton programs (ORNL). See the + Fortran programs for a complete description of the variables in + <literal>spcho</literal>. This function is to be used with <literal>chsolve</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=sprand(20,20,0.1); +A=A*A'+eye(); +chfact(A) + +sol=(1:20)'; +rhs=A*sol; +chfact(A) + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="chsolve">chsolve</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="spchol">spchol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/chsolve.xml b/modules/sparse/help/en_US/chsolve.xml new file mode 100755 index 000000000..eac01c73c --- /dev/null +++ b/modules/sparse/help/en_US/chsolve.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="chsolve"> + <refnamediv> + <refname>chsolve</refname> + <refpurpose>sparse Cholesky solver</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>sol=chsolve(spcho,rhs)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>spcho</term> + <listitem> + <para>list containing the Cholesky factors in coded form returned by chfact</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rhs, sol</term> + <listitem> + <para>full column vectors</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sol=chsolve(spcho,rhs)</literal> computes the solution of + <literal>rhs=A*sol</literal>, with <literal>A</literal> a symmetric sparse positive definite + matrix. This function is based on the Ng-Peyton programs (ORNL). See the + Fortran programs for a complete description of the variables in + <literal>spcho</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=sprand(20,20,0.1); +A=A*A'+eye(); +spcho=chfact(A); +sol=(1:20)'; +rhs=A*sol; +spcho=chfact(A); +chsolve(spcho,rhs) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="chfact">chfact</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="spchol">spchol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/decomposition/CHAPTER b/modules/sparse/help/en_US/decomposition/CHAPTER new file mode 100755 index 000000000..ccebc80d8 --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Sparse Decompositions diff --git a/modules/sparse/help/en_US/decomposition/ludel.xml b/modules/sparse/help/en_US/decomposition/ludel.xml new file mode 100755 index 000000000..2efca3fb0 --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/ludel.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) XXXX-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="ludel"> + <refnamediv> + <refname>ludel</refname> + <refpurpose>utility function used with lufact</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>ludel(hand)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>hand</term> + <listitem> + <para>handle to sparse lu factors (output of lufact)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + This function is used in conjunction with <literal>lufact</literal>. It clears + the internal memory space used to store the result of <literal>lufact</literal>. + </para> + <para> + The sequence of commands <literal>[p,r]=lufact(A);x=lusolve(p,b);ludel(p);</literal> + solves the sparse linear system <literal>A*x = b</literal> and clears <literal>p</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +non_zeros=[1,2,3,4]; +rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +[h,rk]=lufact(sp); +x=lusolve(h,[1;1;1;1]); +ludel(h) +rk,sp*x + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/decomposition/lufact.xml b/modules/sparse/help/en_US/decomposition/lufact.xml new file mode 100755 index 000000000..eba959262 --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/lufact.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) XXXX-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="lufact"> + <refnamediv> + <refname>lufact</refname> + <refpurpose>sparse lu factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[hand,rk]=lufact(A,prec)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>square sparse real matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>hand</term> + <listitem> + <para>handle to sparse lu factors</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para>integer (rank of A)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>prec</term> + <listitem> + <para> + a vector of size two <literal>prec=[eps,reps]</literal> giving the absolute and relative thresolds. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[hand,rk]=lufact(A)</literal> performs the lu factorization of sparse matrix <literal>A</literal>. + <literal>hand</literal> (no display) is used by <literal>lusolve</literal> (for solving linear + system) and <literal>luget</literal> (for retrieving the factors). + <literal>hand</literal> should be cleared by the command: <literal>ludel(hand)</literal>; + </para> + <para> + The A matrix needs not be full rank but must be square + (since A is assumed sparse one may add zeros if necessary to squaring + down A). + </para> + <variablelist> + <varlistentry> + <term>eps :</term> + <listitem> + <para> + The absolute magnitude an element must have to be considered as a pivot candidate, except as a last resort. This number should be set significantly smaller than the smallest diagonal element that is is expected to be placed in the matrix. the default value is <literal>%eps</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>reps :</term> + <listitem> + <para>This number determines what the pivot relative threshold will be. It should be between zero and one. If it is one then the pivoting method becomes complete pivoting, which is very slow and tends to fill up the matrix. If it is set close to zero the pivoting method becomes strict Markowitz with no threshold. The pivot threshold is used to eliminate pivot candidates that would cause excessive element growth if they were used. Element growth is the cause of roundoff error. Element growth occurs even in well-conditioned matrices. Setting the reps large will reduce element growth and roundoff error, but setting it too large will cause execution time to be excessive and will result in a large number of fill-ins. If this occurs, accuracy can actually be degraded because of the large number of operations required on the matrix due to the large number of fill-ins. A good value seems to be 0.001 which is the default value. The default is chosen by giving a value larger than one or less than or equal to zero. This value should be increased and the matrix resolved if growth is found to be excessive. Changing the pivot threshold does not improve performance on matrices where growth is low, as is often the case with ill-conditioned matrices. reps was chosen for use with nearly diagonally dominant matrices such as node- and modified-node admittance matrices. For these matrices it is usually best to use diagonal pivoting. For matrices without a strong diagonal, it is usually best to use a larger threshold, such as 0.01 or 0.1.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +a=rand(5,5);b=rand(5,1);A=sparse(a); +[h,rk]=lufact(A); +x=lusolve(h,b);a*x-b +ludel(h) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/decomposition/luget.xml b/modules/sparse/help/en_US/decomposition/luget.xml new file mode 100755 index 000000000..f05f01dcf --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/luget.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) XXXX-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="luget"> + <refnamediv> + <refname>luget</refname> + <refpurpose>extraction of sparse LU factors</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[P,L,U,Q]=luget(hand)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>hand</term> + <listitem> + <para> + handle, output of <literal>lufact</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P</term> + <listitem> + <para>sparse permutation matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>L</term> + <listitem> + <para> + sparse matrix, lower triangular if <literal>hand</literal> is obtained from a non singular matrix + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>square non singular upper triangular sparse matrix with ones along the main diagonal</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>sparse permutation matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[P,L,U,Q]=luget(hand)</literal> with <literal>hand</literal> obtained by + the command <literal>[hand,rk]=lufact(A)</literal> with <literal>A</literal> a sparse matrix + returns four sparse matrices such that <literal>P*L*U*Q=A</literal>. + </para> + <para> + The A matrix needs not be full rank but must be square + (since A is assumed sparse one may add zeros if necessary to squaring + down A). + </para> + <para> + If <literal>A</literal> is singular, the <literal>L</literal> matrix is column compressed (with + <literal>rk</literal> independent nonzero columns): the nonsingular sparse + matrix <literal>Q'*inv(U)</literal> column compresses <literal>A</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +a=rand(5,2)*rand(2,5);A=sparse(a); +[hand,rk]=lufact(A);[P,L,U,Q]=luget(hand); +full(L), P*L*U*Q-A +clean(P*L*U*Q-A) +ludel(hand) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/decomposition/lusolve.xml b/modules/sparse/help/en_US/decomposition/lusolve.xml new file mode 100755 index 000000000..9063c4bda --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/lusolve.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) XXXX-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="lusolve"> + <refnamediv> + <refname>lusolve</refname> + <refpurpose>sparse linear system solver</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>x=lusolve(hand,b) + x=lusolve(A,b) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>b</term> + <listitem> + <para>full real matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>real square sparse invertible matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>hand</term> + <listitem> + <para>handle to a previously computed sparse lu factors (output of lufact)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>full real matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>x=lusolve(hand,b)</literal> solves the sparse linear system + <literal>A*x = b</literal>. + </para> + <para> + <literal>[hand,rk]=lufact(A)</literal> is the output of lufact. + </para> + <para> + <literal>x=lusolve(A,b)</literal> solves the sparse linear system + <literal>A*x = b</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +non_zeros=[1,2,3,4]; +rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +[h,rk]=lufact(sp); +x=lusolve(h,[1;1;1;1]); +ludel(h) +rk,sp*x + +non_zeros=[1,2,3,4]; +rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +x=lusolve(sp,-ones(4,1)); +sp*x + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="slash">slash</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/decomposition/spchol.xml b/modules/sparse/help/en_US/decomposition/spchol.xml new file mode 100755 index 000000000..dafaf0dde --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/spchol.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) XXXX-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="spchol"> + <refnamediv> + <refname>spchol</refname> + <refpurpose>sparse cholesky factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[R,P] = spchol(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>symmetric positive definite real sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>P</term> + <listitem> + <para> permutation matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para> cholesky factor</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[R,P] = spchol(X)</literal> produces a + lower triangular matrix <literal>R</literal> such that <literal>P*R*R'*P' = X</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// Factorization: +Xfull = [ +3., 0., 0., 2., 0., 0., 2., 0., 2., 0., 0. +0., 5., 4., 0., 0., 0., 0., 0., 0., 0., 0. +0., 4., 5., 0., 0., 0., 0., 0., 0., 0., 0. +2., 0., 0., 3., 0., 0., 2., 0., 2., 0., 0. +0., 0., 0., 0. , 5., 0., 0., 0., 0., 0., 4. +0., 0., 0., 0., 0., 4., 0., 3., 0., 3., 0. +2., 0., 0., 2., 0., 0., 3., 0., 2., 0., 0. +0., 0., 0., 0., 0., 3., 0., 4., 0., 3., 0. +2., 0., 0., 2., 0., 0., 2., 0., 3., 0., 0. +0., 0., 0., 0., 0., 3., 0., 3., 0., 4., 0. +0., 0., 0., 0., 4., 0., 0., 0., 0., 0., 5.]; +X = sparse(Xfull); + +[R, P] = spchol(X); +max(P*R*R'*P'-X) + +// Factorization and solve with backslash operator: +Afull = [ +2 -1 0 0 0; +-1 2 -1 0 0; +0 -1 2 -1 0; +0 0 -1 2 -1; +0 0 0 -1 2 +]; +A = sparse(Afull); + +[L, P] = spchol(A); +max(P*L*L'*P'-A) + +n = size(A, "r"); e = (1:n)'; b = A * e; +x = P*(L'\(L\(P'*b))); +A*x-b + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="chol">chol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/iterativesolvers/CHAPTER b/modules/sparse/help/en_US/iterativesolvers/CHAPTER new file mode 100755 index 000000000..c59edd550 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/CHAPTER @@ -0,0 +1 @@ +title = Linear Equations (Iterative Solvers) diff --git a/modules/sparse/help/en_US/iterativesolvers/conjgrad.xml b/modules/sparse/help/en_US/iterativesolvers/conjgrad.xml new file mode 100755 index 000000000..e011282e4 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/conjgrad.xml @@ -0,0 +1,406 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2013 - Scilab Enterprises - Paul Bignier + * + * 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="conjgrad" xml:lang="en"> + <refnamediv> + <refname>conjgrad</refname> + <refpurpose>conjugate gradient solvers</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + [x, flag, err, iter, res] = conjgrad(A, b [, method [, tol [, maxIter [, M [, M2 [, x0 [, verbose]]]]]]]) + [x, flag, err, iter, res] = conjgrad(A, b [, method [, key=value,...]]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <term/> + <listitem> + <para>a matrix, or a function, or a list computing + <literal>A*x</literal> for each given <literal>x</literal>. The + following is a description of the computation of A*x depending on + the type of A. + </para> + <itemizedlist> + <listitem> + <para> + <literal>matrix.</literal>If A is a matrix, it can be + dense or sparse + </para> + </listitem> + <listitem> + <para> + <literal>function.</literal>If A is a function, it must + have the following header : + </para> + <programlisting role=""><![CDATA[ +function y = A ( x ) + ]]></programlisting> + </listitem> + <listitem> + <para> + <literal>list.</literal>If A is a list, the first element + of the list is expected to be a function and the other elements + in the list are the arguments of the function, from index 2 to + the end. When the function is called, the current value of x is + passed to the function as the first argument. The other + arguments passed are the one given in the list. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>right hand side vector (size: nx1)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>mehtod</term> + <listitem> + <para>scalar string, "pcg", "cgs", "bicg" or "bicgstab" (default "bicgstab")</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>error relative tolerance (default: 1e-8). + The termination criteria is based on the 2-norm of the + residual r=b-Ax, divided by the 2-norm of the right hand side b. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>maxIter</term> + <listitem> + <para>maximum number of iterations (default: n)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>M</term> + <listitem> + <para>preconditioner: full or sparse matrix or function returning + <literal>M\x</literal> (default: none) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>M2</term> + <listitem> + <para>preconditioner: full or sparse matrix or function returning + <literal>M2\x</literal> for each <literal>x</literal> (default: + none) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x0</term> + <listitem> + <para>initial guess vector (default: zeros(n,1))</para> + </listitem> + </varlistentry> + <varlistentry> + <term>verbose</term> + <listitem> + <para>set to 1 to enable verbose logging (default 0)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>solution vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + 0 if <literal>conjgrad</literal> converged to the desired tolerance + within <literal>maxi</literal> iterations, 1 else + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>err</term> + <listitem> + <para>final relative norm of the residual (the 2-norm of the right-hand side b is used)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>iter</term> + <listitem> + <para>number of iterations performed</para> + </listitem> + </varlistentry> + <varlistentry> + <term>res</term> + <listitem> + <para>vector of the residual relative norms</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Solves the linear system <literal>Ax=b</literal> using the conjugate + gradient method with or without preconditioning. The preconditionning + should be defined by a symmetric positive definite matrix + <literal>M</literal>, or two matrices <literal>M1</literal> and + <literal>M2</literal> such that <literal>M=M1*M2</literal>. in the case + the function solves <literal>inv(M)*A*x = inv(M)*b</literal> for + <literal>x</literal>. <literal>M</literal>, <literal>M1</literal> and + <literal>M2</literal> can be Scilab functions with calling sequence + <literal>y=Milx(x)</literal> which computes the corresponding left + division <literal>y=Mi\x</literal>. + </para> + <para> + The <literal>method</literal> input argument selects the solver to be used: + <simplelist type="inline"> + <member> + "pcg" Preconditioned Conjugate Gradient + </member> + <member> + "cgs" preconditioned Conjugate Gradient Squared + </member> + <member> + "bicg" preconditioned BiConjugate Gradient + </member> + <member> + "bicgstab" preconditioned BiConjugate Gradient Stabilized (default) + </member> + </simplelist> + </para> + <para> + If <literal>method="pcg"</literal>, then the <literal>A</literal> matrix + must be a symmetric positive definite matrix (full or sparse) + or a function with calling sequence <literal>y=Ax(x)</literal> which computes + <literal>y=A*x</literal>. + Otherwise (<literal>method="cgs", "bicg" or "bicgstab"</literal>), + <literal>A</literal> just needs to be square. + </para> + </refsection> + <refsection> + <title>Example with well-conditionned and ill-conditionned + problems + </title> + <para>In the following example, two linear systems are solved. The first + maxtrix has a condition number equals to ~0.02, which makes the algorithm + converge in exactly 10 iterations. Since this is the size of the matrix, + it is an expected behaviour for a gradient conjugate method. The second + one has a low condition number equals to 1.d-6, which makes the algorithm + converge in a larger 22 iterations. This is why the parameter maxIter is + set to 30. See below for other examples of the "key=value" syntax. + </para> + <programlisting role="example"><![CDATA[ +// Well-conditionned problem +A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + +b = ones(10, 1); +[x, fail, err, iter, res] = conjgrad(A, b, "bicg", 1d-12, 15); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) + +// Ill-contionned one +A = [ 894 0 0 0 0 28 0 0 1000 70000 + 0 5 13 5 0 0 0 0 0 0 + 0 13 72 34 0 0 0 0 0 6500 + 0 5 34 1 0 0 0 0 0 55 + 0 0 0 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 0 0 0 32 0 39 46 8 0 + 1000 0 0 0 12 33 0 8 82 11 + 70000 0 6500 55 0 0 0 0 11 100]; + +[x, fail, err, iter, res] = conjgrad(A, b, method="pcg", maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) + ]]></programlisting> + </refsection> + <refsection> + <title>Examples with A given as a sparse matrix, or function, or + list + </title> + <para>The following example shows that the method can handle sparse + matrices as well. It also shows the case where a function, computing the + right-hand side, is given to the "conjgrad" primitive. The final case shown by + this example, is when a list is passed to the primitive. + </para> + <programlisting role="example"><![CDATA[ +// Well-conditionned problem +A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b = ones(10, 1); + +// Convert A into a sparse matrix +Asparse=sparse(A); +[x, fail, err, iter, res] = conjgrad(Asparse, b, "cgs", maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) + +// Define a function which computes the right-hand side. +function y = Atimesx(x) + A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A*x +endfunction + +// Pass the script Atimesx to the primitive +[x, fail, err, iter, res] = conjgrad(Atimesx, b, maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) + +// Define a function which computes the right-hand side. +function y = Atimesxbis(x, A) + y = A*x +endfunction + +// Pass a list to the primitive +Alist = list(Atimesxbis, Asparse); +[x, fail, err, iter, res] = conjgrad(Alist, b, maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) + ]]></programlisting> + </refsection> + <refsection> + <title>Examples with key=value syntax</title> + <para>The following example shows how to pass arguments with the + "key=value" syntax. This allows to set non-positionnal arguments, that is, + to set arguments which are not depending on their order in the list of + arguments. The available keys are the names of the optional arguments, + that is : tol, maxIter, %M, %M2, x0, verbose. Notice that, in the + following example, the verbose option is given before the maxIter option. + Without the "key=value" syntax, the positionnal arguments would require + that maxIter come first and verbose after. + </para> + <programlisting role="example"><![CDATA[ +// Example of an argument passed with key=value syntax +A = [100 1; 1 10]; +b = [101; 11]; +[xcomputed, flag, err, iter, res] = conjgrad(A, b, verbose=1); + +// With key=value syntax, the order does not matter +[xcomputed, flag, err, iter, res] = conjgrad(A, b, verbose=1, maxIter=0); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="qmr">qmr</link> + </member> + <member> + <link linkend="gmres">gmres</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>References</title> + <para> + <emphasis role="bold">PCG</emphasis> + </para> + <para>"Templates for the Solution of Linear Systems: Building Blocks for + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993, ftp + netlib2.cs.utk.edu/linalg/templates.ps + </para> + <para>"Iterative Methods for Sparse Linear Systems, Second Edition", Saad, + SIAM Publications, 2003, ftp + ftp.cs.umn.edu/dept/users/saad/PS/all_ps.zip + </para> + <para> + <emphasis role="bold">CGS</emphasis> + </para> + <para> + "CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems" by Peter Sonneveld. + </para> + <para> + <ulink url="http://epubs.siam.org/doi/abs/10.1137/0910004">Original article</ulink> + </para> + <para> + <ulink url="http://dl.acm.org/citation.cfm?id=64888&preflayout=flat">Article on ACM</ulink> + </para> + <para> + <ulink url="http://mathworld.wolfram.com/ConjugateGradientSquaredMethod.html">Some theory around CGS</ulink> + </para> + <para> + <emphasis role="bold">BICG</emphasis> + </para> + <para> + "Numerical Recipes: The Art of Scientific Computing." (third ed.) by William Press, Saul Teukolsky, William Vetterling, Brian Flannery. + </para> + <para> + <ulink url="http://apps.nrbook.com/empanel/index.html?pg=87">http://apps.nrbook.com/empanel/index.html?pg=87</ulink> + </para> + <para> + <ulink url="http://dl.acm.org/citation.cfm?doid=1874391.187410">Article on ACM</ulink> + </para> + <para> + <ulink url="http://mathworld.wolfram.com/BiconjugateGradientMethod.html">Some theory around BICG</ulink> + </para> + <para> + <emphasis role="bold">BICGSTAB</emphasis> + </para> + <para> + "Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems" by Henk van der Vorst. 339 + </para> + <para> + <ulink url="http://epubs.siam.org/doi/abs/10.1137/0913035">Original article</ulink> + </para> + <para> + <ulink url="http://dl.acm.org/citation.cfm?id=131916.131930&coll=DL&dl=GUIDE&CFID=372773884&CFTOKEN=56630250">Article on ACM</ulink> + </para> + <para> + <ulink url="http://mathworld.wolfram.com/BiconjugateGradientStabilizedMethod.html">Some theory around BICG</ulink> + </para> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revdescription> + Introduction + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/iterativesolvers/gmres.xml b/modules/sparse/help/en_US/iterativesolvers/gmres.xml new file mode 100755 index 000000000..f54361ef0 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/gmres.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) XXXX-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="gmres"> + <refnamediv> + <refname>gmres</refname> + <refpurpose>Generalized Minimum RESidual method</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[x,flag,err,iter,res] = gmres(A,b,[rstr,[tol,[maxi,[M,[x0]]]]])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para> + n-by-n matrix or function returning <literal>A*x</literal>. If <literal>A</literal> is a function, it must have the following header : + </para> + <programlisting role=""><![CDATA[ +function y = A ( x ) + ]]></programlisting> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>right hand side vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x0</term> + <listitem> + <para>initial guess vector (default: zeros(n,1))</para> + </listitem> + </varlistentry> + <varlistentry> + <term>M</term> + <listitem> + <para> + preconditioner: matrix of size n-by-n or function returning <literal>M*x</literal> (In the first case, default: eye(n,n)). If M is a function, it must have the following header : + </para> + <programlisting role=""><![CDATA[ +function y = M ( x ) + ]]></programlisting> + </listitem> + </varlistentry> + <varlistentry> + <term>rstr</term> + <listitem> + <para>number of iterations between restarts (default: 10)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>maxi</term> + <listitem> + <para>maximum number of iterations (default: n)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>error tolerance (default: 1e-6)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>solution vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>err</term> + <listitem> + <para>final residual norm</para> + </listitem> + </varlistentry> + <varlistentry> + <term>iter</term> + <listitem> + <para>number of iterations performed</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <variablelist> + <varlistentry> + <term>0 =</term> + <listitem> + <para> + <literal>gmres</literal> converged to the desired tolerance within <literal>maxi</literal> iterations + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>1 =</term> + <listitem> + <para> + no convergence given <literal>maxi</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + <varlistentry> + <term>res</term> + <listitem> + <para>residual vector</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term>GMRES </term> + <listitem> + <para> + solves the linear system <literal>Ax=b</literal> using the Generalized Minimal residual method with restarts. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Details </term> + <listitem> + <para>of this algorithm are described in :</para> + <para>"Templates for the Solution of Linear Systems: Building Blocks for + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993 (ftp + netlib2.cs.utk.edu; cd linalg; get templates.ps). + </para> + <para>"Iterative Methods for Sparse Linear Systems, Second Edition" Saad, + SIAM Publications, 2003 (ftp ftp.cs.umn.edu; cd dept/users/saad/PS; get + all_ps.zip). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ + // If A and M are matrices +A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b=ones(10,1); +[x,flag,err,iter,res] = gmres(A, b) + +M = eye(10, 10); + +[x,flag,err,iter,res] = gmres(A, b, 10, 1d-12, 20, M, zeros(10, 1)) + + // If A is a matrix and M is a function + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b=ones(10,1); + +function y = Mtimesx(x) +M = eye(10,10); +y = M*x; +endfunction + +[x,flag,err,iter,res] = gmres(A, b, 10, 1d-12, 20, Mtimesx, zeros(10, 1)) + + // If A is a function and M is a matrix + function y = Atimesx(x) + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A * x; + endfunction + + b = ones(10,1); + M = eye(10, 10); + + [x,flag,err,iter,res] = gmres(Atimesx, b) + + [x,flag,err,iter,res] = gmres(Atimesx, b, 10, 1d-12, 20, M, zeros(10,1)) + + // If A and M are functions + function y = Atimesx(x) + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A * x; + endfunction + + function y = Mtimesx(x) +M = eye(10,10); +y = M*x; +endfunction + + [x,flag,err,iter,res] = gmres(Atimesx, b, 10, 1d-12, 20, Mtimesx, zeros(10,1)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="conjgrad">conjgrad</link> + </member> + <member> + <link linkend="qmr">qmr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/iterativesolvers/qmr.xml b/modules/sparse/help/en_US/iterativesolvers/qmr.xml new file mode 100755 index 000000000..71b37cc11 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/qmr.xml @@ -0,0 +1,374 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="qmr"> + <refnamediv> + <refname>qmr</refname> + <refpurpose>quasi minimal residual method with preconditioning </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[x,flag,err,iter,res] = qmr(A,Ap,b,x0,M1,M1p,M2,M2p,maxi,tol) + [x,flag,err,iter,res] = qmr(A,b,x0,M1,M2,maxi,tol) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para> + matrix of size n-by-n or function. + </para> + <itemizedlist> + <listitem> + <para> + <literal>matrix.</literal>If A is a matrix, it can be + dense or sparse + </para> + </listitem> + <listitem> + <para> + <literal>function.</literal>If A is a function which returns <literal>A*x</literal>, it must + have the following header : + </para> + <programlisting role=""><![CDATA[ +function y = A ( x ) + ]]></programlisting> + <para> + If A is a function which returns <literal>A*x</literal> or <literal>A'*x</literal> depending t. + If <literal>t = "notransp"</literal>, the function returns <literal>A*x</literal>. + If <literal>t = "transp"</literal>, the function returns <literal>A'*x</literal>. It must + have the following header : + </para> + <programlisting role=""><![CDATA[ +function y = A ( x, t ) + ]]></programlisting> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + <varlistentry> + <term>Ap</term> + <listitem> + <para> + function returning <literal>A'*x</literal>. It must have the following header : + </para> + <programlisting role=""><![CDATA[ +function y = Ap ( x ) + ]]></programlisting> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>right hand side vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x0</term> + <listitem> + <para>initial guess vector (default: zeros(n,1))</para> + </listitem> + </varlistentry> + <varlistentry> + <term>M1</term> + <listitem> + <para> + left preconditioner : matrix or function (In the first case, default: eye(n,n)). If <literal>M1</literal> is a function, she returns either, + </para> + <itemizedlist> + <listitem> + <para> + only <literal>M1*x</literal> + </para> + </listitem> + <para> or + </para> + <listitem> + <para> + <literal>M1*x</literal> or <literal>M1'*x</literal> depending <literal>t</literal>. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + <varlistentry> + <term>M1p</term> + <listitem> + <para> + must only be provided when <literal>M1</literal> is a function returning <literal>M1*x</literal>. + In this case <literal>M1p</literal> is the function which returns <literal>M1'*x</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>M2</term> + <listitem> + <para> + right preconditioner : matrix or function (In the first case, default: eye(n,n)). If <literal>M2</literal> is a function, she returns either + </para> + <itemizedlist> + <listitem> + <para> + only <literal>M2*x</literal> + </para> + </listitem> + <para> or + </para> + <listitem> + <para> + <literal>M2*x</literal> or <literal>M2'*x</literal> depending <literal>t</literal>. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + <varlistentry> + <term>M2p</term> + <listitem> + <para> + must only be provided when <literal>M2</literal> is a function returning <literal>M2*x</literal>. + In this case <literal>M2p</literal> is the function which returns <literal>M2'*x</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>maxi</term> + <listitem> + <para>maximum number of iterations (default: n) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>error tolerance (default: 1000*%eps)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>solution vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <itemizedlist> + <listitem> + <para> + <varname>flag</varname>=0: <code>qmr</code> converged to the desired tolerance within <varname>maxi</varname> + iterations, + </para> + </listitem> + <listitem> + <para> + <varname>flag</varname>=1: no convergence given <varname>maxi</varname>, + </para> + </listitem> + <listitem> + <para> + <literal>-7 < flag < 0</literal>: A breakdown occurred because one of the scalar quantities calculated during + <code>qmr</code> was equal to zero. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + <varlistentry> + <term>res</term> + <listitem> + <para>residual vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>err</term> + <listitem> + <para>final residual norm</para> + </listitem> + </varlistentry> + <varlistentry> + <term>iter</term> + <listitem> + <para>number of iterations performed</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Solves the linear system <literal>Ax=b</literal> using the Quasi Minimal Residual Method with preconditioning. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ + // If A is a matrix +A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b=ones(10,1); +[x,flag,err,iter,res] = qmr(A, b) + +[x,flag,err,iter,res] = qmr(A, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) + + // If A is a function + function y = Atimesx(x,t) + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + if (t == 'notransp') then + y = A*x; + elseif (t == 'transp') then + y = A'*x; + end + endfunction + + [x,flag,err,iter,res] = qmr(Atimesx, b) + + [x,flag,err,iter,res] = qmr(Atimesx, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) + + // OR + + function y = funA(x) + A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A*x + endfunction + + function y = funAp(x) + A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A'*x + endfunction + + [x,flag,err,iter,res] = qmr(funA, funAp, b) + + [x,flag,err,iter,res] = qmr(funA, funAp, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) + + // If A is a matrix, M1 and M2 are functions + function y = M1timesx(x,t) + M1 = eye(10,10); + if(t=="notransp") then + y = M1*x; + elseif (t=="transp") then + y = M1'*x; + end + endfunction + + function y = M2timesx(x,t) + M2 = eye(10,10); + if(t=="notransp") then + y = M2*x; + elseif (t=="transp") then + y = M2'*x; + end + endfunction + + [x,flag,err,iter,res] = qmr(A, b, zeros(10,1), M1timesx, M2timesx, 10, 1d-12) + + // OR + + function y = funM1(x) + M1 = eye(10,10); + y = M1*x; + endfunction + + function y = funM1p(x) + M1 = eye(10,10); + y = M1'*x; + endfunction + + function y = funM2(x) + M2 = eye(10,10); + y = M2*x; + endfunction + + function y = funM2p(x) + M2 = eye(10,10); + y = M2'*x; + endfunction + + [x,flag,err,iter,res] = qmr(A, b, zeros(10,1), funM1, funM1p, funM2, funM2p, 10, 1d-12) + + // If A, M1, M2 are functions + [x,flag,err,iter,res] = qmr(funA, funAp, b, zeros(10,1), funM1, funM1p, funM2, funM2p, 10, 1d-12) + [x,flag,err,iter,res] = qmr(Atimesx, b, zeros(10,1), M1timesx, M2timesx, 10, 1d-12) + + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gmres">gmres</link> + </member> + <member> + <link linkend="conjgrad">conjgrad</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revdescription> + Calling qmr(A, Ap) is deprecated. qmr(A) should be used instead. The following function is an example : + <programlisting role=""><![CDATA[ +function y = A ( x, t ) +Amat = eye(2,2); +if ( t== "notransp") then +y = Amat*x; +elseif (t == "transp") then +y = Amat'*x; +end +endfunction + ]]></programlisting> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/matrixmanip/CHAPTER b/modules/sparse/help/en_US/matrixmanip/CHAPTER new file mode 100755 index 000000000..a797a77e1 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Manipulation diff --git a/modules/sparse/help/en_US/matrixmanip/issparse.xml b/modules/sparse/help/en_US/matrixmanip/issparse.xml new file mode 100755 index 000000000..6bac33ba4 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/issparse.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) 2011 - DIGITEO - Allan CORNET + * + * 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="issparse" xml:lang="en"> + <refnamediv> + <refname>issparse</refname> + <refpurpose>determine whether input is sparse</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>res = issparse(S)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>S</term> + <listitem> + <para>a scilab object</para> + </listitem> + </varlistentry> + <varlistentry> + <term>res</term> + <listitem> + <para>1 is the matrix is a sparse and 0 otherwise/</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>res = issparse(S)</literal> returns 1 if S is a sparse + matrix and 0 otherwise. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example">sp = sparse([1,2;4,5;3,10],[1,2,3]); + if issparse(sp) == 1 then + disp("It is a sparse"); + end + + A = 1; + if issparse(A) == 0 then + disp("It is not a sparse"); + end + </programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="type">type</link> + </member> + <member> + <link linkend="typeof">typeof</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/matrixmanip/nnz.xml b/modules/sparse/help/en_US/matrixmanip/nnz.xml new file mode 100755 index 000000000..9bb90e77f --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/nnz.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) XXXX-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="nnz"> + <refnamediv> + <refname>nnz</refname> + <refpurpose>number of non zero entries in a matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>n=nnz(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex sparse (or full) matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>n</term> + <listitem> + <para>integer, the number of non zero elements in X</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>nnz</literal> counts the number of non zero entries in a sparse or full matrix + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]); +nnz(sp) +a=[1 0 0 0 2]; +nnz(a) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/matrixmanip/speye.xml b/modules/sparse/help/en_US/matrixmanip/speye.xml new file mode 100755 index 000000000..a79e4d3ae --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/speye.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: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="speye" xml:lang="en"> + <refnamediv> + <refname>speye</refname> + <refpurpose>sparse identity matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>Isp=speye(nrows,ncols) + Isp=speye(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>integer (number of rows)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>integer (number os columns)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>sparse identity matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>Isp=speye(nrows,ncols)</literal> returns a sparse identity + matrix <literal>Isp</literal> with <literal>nrows</literal> rows, + <literal>ncols</literal> columns. (Non square identity matrix have a + maximal number of ones along the main diagonal). + </para> + <para> + <literal>Isp=speye(A)</literal> returns a sparse identity matrix + with same dimensions as <literal>A</literal>. If + <literal>[m,n]=size(A)</literal>, <literal>speye(m,n)</literal> and + <literal>speye(A)</literal> are equivalent. In particular + <literal>speye(3)</literal> is not equivalent to + <literal>speye(3,3)</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +eye(3,3)-full(speye(3,3)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="spzeros">spzeros</link> + </member> + <member> + <link linkend="spones">spones</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/matrixmanip/spones.xml b/modules/sparse/help/en_US/matrixmanip/spones.xml new file mode 100755 index 000000000..76e2aec02 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/spones.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: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="spones" xml:lang="en"> + <refnamediv> + <refname>spones</refname> + <refpurpose>sparse matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>sp=spones(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>sparse matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sp=spones(A)</literal> generates a matrix with the same + sparsity structure as <literal>A</literal>, but with ones in the nonzero + positions. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=sprand(10,12,0.1); +sp=spones(A) +B = A~=0 +bool2s(B) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="spzeros">spzeros</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/matrixmanip/sprand.xml b/modules/sparse/help/en_US/matrixmanip/sprand.xml new file mode 100755 index 000000000..69ee87075 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/sprand.xml @@ -0,0 +1,190 @@ +<?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: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="sprand" xml:lang="en"> + <refnamediv> + <refname>sprand</refname> + <refpurpose>sparse random matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>sp=sprand(nrows,ncols,density [,typ])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>integer (number of rows)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>integer (number of columns)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>density</term> + <listitem> + <para>filling coefficient (density)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>typ</term> + <listitem> + <para> + character string, <literal>"uniform"</literal> (default) or + <literal>"normal"</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>sparse matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sp=sprand(nrows,ncols,density)</literal> returns a sparse + matrix <literal>sp</literal> with <literal>nrows</literal> rows, + <literal>ncols</literal> columns and approximately + <literal>density*nrows*ncols</literal> non-zero entries. + </para> + <para> + The <literal>density</literal> parameter is expected to be in the + <literal>[0,1]</literal> interval. If not, it is automatically + projected into this interval. Therefore, using a density which is + lower than 0 or greater than 1 will generate neither an error, + nor a warning: the formula <literal>density=max(min(density,1),0)</literal> + is used. + </para> + <para> + If <literal>typ="uniform"</literal> uniformly distributed values on + [0,1] are generated. If <literal>typ="normal"</literal> normally + distributed values are generated (mean=0 and standard deviation=1). + </para> + <para> + The entries of the output matrix are computed from the given + distribution function <literal>typ</literal>. + The indices of the non-zeros entries are computed + randomly, so that the average number of nonzeros is equal to + <literal>density</literal>. + The actual indices values are computed from the exponential distribution + function, where the parameter of the distribution function is + computed accordingly. + </para> + </refsection> + <refsection> + <title>Examples</title> + <para> + In the following example, we generate a 100x1000 sparse matrix with + approximate density 0.001, i.e. with approximately + 100*1000*0.001=100 nonzero entries. + </para> + <programlisting role="example"><![CDATA[ +// The entries of the matrix are uniform. +W=sprand(100,1000,0.001); +// The entries of the matrix are normal. +W=sprand(100,1000,0.001,"normal"); + ]]></programlisting> + <para> + In the following script, we check that the entries of the matrix + have the expected distribution. + We use the spget function in order to get the nonzero entries. + Then we compute the min, mean and max of the entries and compare + them with the limit values. + </para> + <programlisting role="example"><![CDATA[ +typ = "normal"; +// typ = "uniform"; +nrows = 1000; +ncols = 2000; +density = 1/100; +s=sprand(nrows,ncols,density,typ); +nnzs=nnz(s); +[ij,v]=spget(s); +[%inf -%inf 0 %inf 1] // Limit values for "normal" +[nnzs min(v) mean(v) max(v) variance(v)] +[%inf 0 0.5 1 1/12] // Limit values for "uniform" + ]]></programlisting> + <para> + In the following script, we check that the entry indices, which + are also chosen at random, have the correct distribution. + We generate <literal>kmax</literal> sparse random matrices with + uniform distribution. + For each matrix, we consider the indices of the nonzero + entries which were generated, i.e. we see if the event + <literal>Aij = {the entry (i,j) is nonzero}</literal> occurred for + each <literal>i</literal> and <literal>j</literal>, for <literal>i=1,2,...,nrows</literal> + and <literal>j=1,2,...,ncols</literal>. + The matrix <literal>C(i,j)</literal> stores the number of times that the event <literal>Aij</literal> + occurred. + The matrix <literal>R(k)</literal> stores the actual density of the try number <literal>k</literal>, + where <literal>k=1,2,...,kmax</literal>. + </para> + <programlisting role="example"><![CDATA[ + kmax = 1000; + ncols=10; + nrows=15; + density=0.01; + typ="uniform"; + C=zeros(nrows,ncols); + R=[]; + for k=1:kmax + M=sprand(nrows,ncols,density,typ); + NZ=find(M<>0); + NZratio = size(NZ,"*")/(nrows*ncols); + R=[R NZratio]; + C(NZ)=C(NZ)+1; + end + ]]></programlisting> + <para> + Now that this algorithm has been performed (which may require some time), + we can compute elementary statistics to check that the algorithm performed + well. + </para> + <programlisting role="no-scilab-exec"><![CDATA[ + // The expectation of A_ij is + density * kmax + // Compare this with the actual events : + C + // The average number should be close to the expectation. + [density*kmax mean(C)] + // The density should be close to expected density + [density mean(R)] + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="rand">rand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/matrixmanip/spzeros.xml b/modules/sparse/help/en_US/matrixmanip/spzeros.xml new file mode 100755 index 000000000..32d23952f --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/spzeros.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: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="spzeros" xml:lang="en"> + <refnamediv> + <refname>spzeros</refname> + <refpurpose>sparse zero matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>sp=spzeros(nrows,ncols) + sp=spzeros(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>integer (number of rows)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>integer (number os columns)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>sparse zero matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sp=spzeros(nrows,ncols)</literal> returns a sparse zero + matrix <literal>sp</literal> with <literal>nrows</literal> rows, + <literal>ncols</literal> columns. (Equivalent to + <literal>sparse([],[],[nrow,ncols])</literal>) + </para> + <para> + <literal>sp=spzeros(A)</literal> returns a sparse zero matrix with + same dimensions as <literal>A</literal>. If + <literal>[m,n]=size(A)</literal>, <literal>spzeros(m,n)</literal> and + <literal>spzeros(A)</literal> are equivalent. In particular + <literal>spzeros(3)</literal> is not equivalent to + <literal>spzeros(3,3)</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +m=spzeros(2,2) +a=rand(10,12); +m=spzeros(a) +sum(spzeros(1000,1000)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="spones">spones</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/ordmmd.xml b/modules/sparse/help/en_US/ordmmd.xml new file mode 100755 index 000000000..f9d61c1a2 --- /dev/null +++ b/modules/sparse/help/en_US/ordmmd.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) 2011 - 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: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="ordmmd" xml:lang="en"> + <refnamediv> + <refname>ordmmd</refname> + <refpurpose> + Compute multiple minimum degree ordering + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + [perm,invp,nofsub]=ordmmd(xadj,iadj,n) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>n</term> + <listitem> + <para>a 1-by-1 matrix of doubles, integer value, the number of equations</para> + </listitem> + </varlistentry> + <varlistentry> + <term>xadj</term> + <listitem> + <para>(n+1)-by-1 matrix of doubles, integer value, pointer to the rows of A</para> + </listitem> + </varlistentry> + <varlistentry> + <term>iadj</term> + <listitem> + <para>nnz-by-1 matrix of doubles, integer value, the row indices of A</para> + </listitem> + </varlistentry> + <varlistentry> + <term>perm</term> + <listitem> + <para>n-by-1 matrix of doubles, integer value, the minimum degree ordering</para> + </listitem> + </varlistentry> + <varlistentry> + <term>invp</term> + <listitem> + <para>n-by-1 matrix of doubles, integer value, the inverse of perm</para> + </listitem> + </varlistentry> + <varlistentry> + <term>nofsub</term> + <listitem> + <para> + 1-by-1 matrix of doubles, integer value, + an upper bound on the number of nonzero subscripts for the compressed storage scheme + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + The minimum degree algorithm is used to permute the rows and + columns of a symmetric sparse matrix before applying the Cholesky decomposition. + This algorithm reduces the number of non-zeros in the Cholesky factor. + </para> + <para> + Given a n-by-n real symmetric sparse square matrix <literal>A</literal>, + the Cholesky factor <literal>U</literal> will typically suffer "fill in", that is have more + non-zeros than the upper triangle of <literal>A</literal>. + We seek a permutation matrix <literal>P</literal>, so that the matrix <literal>P'*A*P</literal>, + which is also symmetric, has the least possible fill in its Cholesky factor. + </para> + </refsection> + <refsection> + <title>Examples</title> + <para> + In the following example, we compute an ordering for a symmetric + sparse matrix. + We use the <literal>sp2adj</literal> function to compute the adjacency structure. + </para> + <programlisting role="example"><![CDATA[ +A = [ +4. 1. 2. 0.5 2. +1. 0.5 0. 0. 0. +2. 0. 3. 0. 0. +0.5 0. 0. 5./8. 0. +2. 0. 0. 0. 16. +]; +A = sparse(A); +[xadj,iadj,val]=sp2adj(A); +n = size(A,"r"); +[perm,invp,nofsub]=ordmmd(xadj,iadj,n) + ]]></programlisting> + <para> + In the following example, we compute an ordering for a symmetric + sparse matrix. + We check that <literal>invp</literal> is the inverse of <literal>perm</literal>. + </para> + <programlisting role="example"><![CDATA[ + A = [ + 0., 0., 0., 2., 0., 0., 2., 0., 2., 0., 0. ; + 0., 0., 4., 0., 0., 0., 0., 0., 0., 0., 0. ; + 0., 4., 0., 0., 0., 0., 0., 0., 0., 0., 0. ; + 2., 0., 0., 0., 0., 0., 2., 0., 2., 0., 0. ; + 0., 0., 0., 0. , 0., 0., 0., 0., 0., 0., 4. ; + 0., 0., 0., 0., 0., 0., 0., 3., 0., 3., 0. ; + 2., 0., 0., 2., 0., 0., 0., 0., 2., 0., 0. ; + 0., 0., 0., 0., 0., 3., 0., 0., 0., 3., 0. ; + 2., 0., 0., 2., 0., 0., 2., 0., 0., 0., 0. ; + 0., 0., 0., 0., 0., 3., 0., 3., 0., 0., 0. ; + 0., 0., 0., 0., 4., 0., 0., 0., 0., 0., 0.]; + n=size(A,1); + A=sparse(A); + [xadj,adjncy,anz]=sp2adj(A); + [perm,invp,nofsub]=ordmmd(xadj,adjncy,n); + perm(invp) + ]]></programlisting> + <para> + In the following example, we compare the sparsity pattern of the Cholesky + factor of a matrix <literal>A</literal> and the matrix <literal>P'*A*P</literal>. + See p. 3, "Chapter 1: Introduction" in + "Computer Solution of Large Sparse Positive Definite Systems". + We see that the number of nonzeros in the Cholesky decomposition is + 15, while the matrix <literal>P'*A*P</literal> has a Cholesky decomposition with + 9 nonzeros. + </para> + <programlisting role="example"><![CDATA[ +A = [ +4. 1. 2. 0.5 2. +1. 0.5 0. 0. 0. +2. 0. 3. 0. 0. +0.5 0. 0. 5./8. 0. +2. 0. 0. 0. 16. +]; +A = sparse(A); +// See the sparsity pattern of the Cholesky factors of A +U = sparse(chol(full(A))); +scf(); +subplot(2,1,1); +PlotSparse(U,"x"); +xtitle("Sparsity pattern of U, such that A=U''*U"); +// Get the adjacency structure +[xadj,iadj,val]=sp2adj(A); +// Compute multiple minimum degree ordering +n = size(A,"r"); +[perm,invp,nofsub]=ordmmd(xadj,iadj,n); +// Convert the permutation vector into matrix. +P=spzeros(n,n); +for i=1:n + P(perm(i),i)=1; +end +// See the sparsity pattern of the Cholesky factors +// of P'*A*P +U = sparse(chol(full(P'*A*P))); +subplot(2,1,2); +PlotSparse(U,"x"); +xtitle("Sparsity pattern of U, such that P''*A*P=U''*U"); + ]]></programlisting> + <scilab:image localized="true"> + A = [ + 4. 1. 2. 0.5 2. + 1. 0.5 0. 0. 0. + 2. 0. 3. 0. 0. + 0.5 0. 0. 0.625 0. + 2. 0. 0. 0. 16. + ]; + A = sparse(A); + U = sparse(chol(full(A))); + scf(); + subplot(2,1,1); + PlotSparse(U,"x"); + xtitle("Sparsity pattern of U, such that A=U''*U"); + [xadj,iadj,val]=sp2adj(A); + n = size(A,"r"); + [perm,invp,nofsub]=ordmmd(xadj,iadj,n); + P=spzeros(n,n); + for i=1:n + P(perm(i),i)=1; + end + U = sparse(chol(full(P'*A*P))); + subplot(2,1,2); + PlotSparse(U,"x"); + xtitle("Sparsity pattern of U, such that P''*A*P=U''*U"); + </scilab:image> + </refsection> + <refsection> + <title>Implementation notes</title> + <para> + This function is based on "ordmmd.f" a source code (1994) by Esmond G. Ng and Barry W. Peyton + from Mathematical Sciences Section, Oak Ridge National Laboratory. + The algorithm is based on the genmmd routine by Joseph W.H. Liu from the + SPARSPAK library. + </para> + </refsection> + <refsection> + <title>Bibliography</title> + <para> + "Minimum degree algorithm", Wikipedia contributors, Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Minimum_degree_algorithm + </para> + <para> + "A new release of SPARSPAK: the Waterloo sparse matrix package", Alan George and Esmond Ng. 1984. SIGNUM Newsl. 19, 4 (October 1984), 9-13. + </para> + <para> + "Computer Solution of Large Sparse Positive Definite Systems" by Alan George and Joseph Liu, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981 + </para> + <para> + "Implementation of Lipsol in Scilab", Rubio Scola, 1997, INRIA, No 0215 + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sp2adj">sp2adj</link> + </member> + <member> + <link linkend="spchol">spchol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/sparseconvert/CHAPTER b/modules/sparse/help/en_US/sparseconvert/CHAPTER new file mode 100755 index 000000000..42d5e0bf2 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Conversion diff --git a/modules/sparse/help/en_US/sparseconvert/adj2sp.xml b/modules/sparse/help/en_US/sparseconvert/adj2sp.xml new file mode 100755 index 000000000..1b90969ce --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/adj2sp.xml @@ -0,0 +1,230 @@ +<?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: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="adj2sp" xml:lang="en"> + <refnamediv> + <refname>adj2sp</refname> + <refpurpose>converts adjacency form into sparse matrix.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + A=adj2sp(xadj,iadj,v) + A=adj2sp(xadj,iadj,v,mn) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>xadj</term> + <listitem> + <para> + a (n+1)-by-1 matrix of floating point integers. + For <literal>j=1:n</literal>, the floating point integer + <literal>xadj(j+1)-xadj(j)</literal> is the number of non zero entries in + column j. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>iadj</term> + <listitem> + <para> + a nz-by-1 matrix of floating point integers, the row indices for the + nonzeros. + For <literal>j=1:n</literal>, for <literal>k = xadj(j):xadj(j+1)-1</literal>, the floating point integer + <literal>i = iadj(k)</literal> is the row index of the nonzero entry #k. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para> + a nz-by-1 matrix of floating point integers, the non-zero entries of A. + For <literal>j=1:n</literal>, for <literal>k = xadj(j):xadj(j+1)-1</literal>, the floating point integer + <literal>Aij = v(k)</literal> is the value of the nonzero entry #k. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>mn</term> + <listitem> + <para> + a 1-by-2 or 2-by-1 matrix of floating point integers, optional, + <literal>mn(1)</literal> is the number of rows in A, + <literal>mn(2)</literal> is the number of columns in A. + If <literal>mn</literal> is not provided, then <literal>mn=[m,n]</literal> is the default with + <literal>m=max(iadj)</literal> and <literal>n=size(xadj,"*")-1</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>m-by-n real or complex sparse matrix (with nz non-zero entries)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + adj2sp converts a sparse matrix into its adjacency form format. + The values in the adjacency format are stored colum-by-column. + This is why this format is sometimes called "Compressed sparse column" or CSC. + </para> + </refsection> + <refsection> + <title>Examples</title> + <para> + In the following example, we create a sparse matrix from its adjacency format. + Then we check that it matches the expected sparse matrix. + </para> + <programlisting role="example"><![CDATA[ +xadj = [1 3 4 7 9 11]'; +iadj = [3 5 3 1 2 4 3 5 1 4]'; +v = [1 2 3 4 5 6 7 8 9 10]'; +B=adj2sp(xadj,iadj,v) +A = [ +0 0 4 0 9 +0 0 5 0 0 +1 3 0 7 0 +0 0 6 0 10 +2 0 0 8 0 +]; +C=sparse(A) +and(B==C) + ]]></programlisting> + <para> + In the following example, we create a sparse matrix from its adjacency format. + Then we check that it matches the expected sparse matrix. + </para> + <programlisting role="example"><![CDATA[ +xadj = [1 2 3 4 5 5 6 6 7 8 9]'; +iadj = [2 5 2 3 1 2 7 6]'; +v = [3 7 5 3 6 5 2 3]'; +C=adj2sp(xadj,iadj,v) +A = [ +0 0 0 0 0 6 0 0 0 0 +3 0 5 0 0 0 0 5 0 0 +0 0 0 3 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 +0 7 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 3 +0 0 0 0 0 0 0 0 2 0 +]; +B=sparse(A) +and(B==C) + ]]></programlisting> + <para> + In the following example, we check the use of the mn parameter. + The consistency between the mn parameter and the actual content of + xadj and iadj is checked by adj2sp. + </para> + <programlisting role="example"><![CDATA[ +xadj = [1 2 3 4 5 5 6 6 7 8 9]'; +iadj = [2 5 2 3 1 2 7 6]'; +v = [3 7 5 3 6 5 2 3]'; +mn=[7 10]; +C=adj2sp(xadj,iadj,v,mn) + ]]></programlisting> + <para> + In the following example, create a 3-by-3 sparse matrix. + This example is adapted from the documentation of SciPy. + </para> + <programlisting role="example"><![CDATA[ +xadj = [1,3,4,7] +iadj = [1,3,3,1,2,3] +v = [1,2,3,4,5,6] +full(adj2sp(xadj,iadj,v)) + ]]></programlisting> + <para> + The previous script produces the following output. + </para> + <programlisting role="no-scilab-exec"><![CDATA[ +-->full(adj2sp(xadj,iadj,v)) + ans = + 1. 0. 4. + 0. 0. 5. + 2. 3. 6. + ]]></programlisting> + <para> + In the following example, we check that the sp2adj and adj2sp functions + are inverse. + </para> + <programlisting role="example"><![CDATA[ +// Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide +// Edited by Zhaojun Bai, James Demmel, Jack Dongarra, Axel Ruhe, and Henk van der Vorst +// "Sparse Matrix Storage Formats", J. Dongarra +// http://web.eecs.utk.edu/~dongarra/etemplates/book.html + +A = [ +10 0 0 0 -2 0 +3 9 0 0 0 3 +0 7 8 7 0 0 +3 0 8 7 5 0 +0 8 0 9 9 13 +0 4 0 0 2 -1 +]; +A = sparse(A) + +// To get the Compressed Sparse Column (CSC) : +[col_ptr,row_ind,val]=sp2adj(A) +// To convert back to sparse: +AAsp=adj2sp(col_ptr,row_ind,val) +// Check the conversion +AAsp - A + +// To get the Compressed Sparse Row (CSR) : +[row_ptr,col_ind,val]=sp2adj(A') +// To convert back to sparse: +AAsp=adj2sp(row_ptr,col_ind,val)' +// Check the conversion +AAsp - A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sp2adj">sp2adj</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="spcompack">spcompack</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>References</title> + <para> + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + </para> + <para> + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + </para> + <para> + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + </para> + <para> + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + </para> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/sparseconvert/full.xml b/modules/sparse/help/en_US/sparseconvert/full.xml new file mode 100755 index 000000000..8253f7991 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/full.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) XXXX-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="full"> + <refnamediv> + <refname>full</refname> + <refpurpose>sparse to full matrix conversion</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>X=full(sp)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>sp</term> + <listitem> + <para>real or complex sparse (or full) matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>full matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>X=full(sp)</literal> converts the sparse matrix <literal>sp</literal> into its + full representation. (If <literal>sp</literal> is already full then <literal>X</literal> equals + <literal>sp</literal>). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;5,4;3,1],[1,2,3]); +A=full(sp) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="sprand">sprand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/sparseconvert/mtlb_sparse.xml b/modules/sparse/help/en_US/sparseconvert/mtlb_sparse.xml new file mode 100755 index 000000000..cc8d8fdf6 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/mtlb_sparse.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) XXXX-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="mtlb_sparse"> + <refnamediv> + <refname>mtlb_sparse</refname> + <refpurpose>convert sparse matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>Y=mtlb_sparse(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>sparse matrix in Matlab format</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>Y=mtlb_sparse(X)</literal> is used to convert <literal>X</literal>, a Scilab sparse matrix, to + Matlab format. <literal>Y</literal> is the a variable with type 7, + i.e. <literal>type(Y)</literal> is equal to 7. + This function should be used in mexfiles (a Matlab mexfile containing sparse + matrices can be used only if the Scilab sparse matrices are converted + to that format). The functions <literal>full</literal> and <literal>spget</literal> work + with this format. + </para> + <para> + Other operations and functions using this format + can be overloaded with Scilab functions using the prefix "%msp". + For instance the function + <literal>%msp_p(x)</literal> (see SCI/modules/overloading/macros directory) is used to + display such "type 7" objects. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +X=sparse(rand(2,2)); Y=mtlb_sparse(X); +Y, full(Y), [ij,v,mn]=spget(Y) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/sparseconvert/sp2adj.xml b/modules/sparse/help/en_US/sparseconvert/sp2adj.xml new file mode 100755 index 000000000..90fd92c18 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/sp2adj.xml @@ -0,0 +1,229 @@ +<?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: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="sp2adj" xml:lang="en"> + <refnamediv> + <refname>sp2adj</refname> + <refpurpose>converts sparse matrix into adjacency form</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + [xadj,iadj,v]=sp2adj(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>m-by-n real or complex sparse matrix (with nz non-zero entries)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>xadj</term> + <listitem> + <para> + a (n+1)-by-1 matrix of floating point integers, pointers to the starting + index in iadj and v for each column. + For <literal>j=1:n</literal>, the floating point integer + <literal>xadj(j+1)-xadj(j)</literal> is the number of non zero entries in + column j. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>iadj</term> + <listitem> + <para> + a nz-by-1 matrix of floating point integers, the row indices for the + nonzeros. + For <literal>j=1:n</literal>, for <literal>k = xadj(j):xadj(j+1)-1</literal>, the floating point integer + <literal>i = iadj(k)</literal> is the row index of the nonzero entry #k. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para> + a nz-by-1 matrix of floating point integers, the non-zero entries of A. + For <literal>j=1:n</literal>, for <literal>k = xadj(j):xadj(j+1)-1</literal>, the floating point integer + <literal>Aij = v(k)</literal> is the value of the nonzero entry #k. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + sp2adj converts a sparse matrix into its adjacency format. + The values in the adjacency format are stored colum-by-column. + This is why this format is sometimes called "Compressed sparse column" or CSC. + </para> + </refsection> + <refsection> + <title>Examples</title> + <para> + In the following example, we create a full matrix, which entries + goes from 1 to 10. + Then we convert it into a sparse matrix, which removes the zeros. + Finally, we compute the adjacency represention of this matrix. + The matrix v contains only the nonzero entries of A. + </para> + <programlisting role="example"><![CDATA[ +A = [ +0 0 4 0 9 +0 0 5 0 0 +1 3 0 7 0 +0 0 6 0 10 +2 0 0 8 0 +]; +B=sparse(A); +[xadj,iadj,v]=sp2adj(B) +expected_xadj = [1 3 4 7 9 11]'; +expected_adjncy = [3 5 3 1 2 4 3 5 1 4]'; +expected_anz = [1 2 3 4 5 6 7 8 9 10]'; +and(expected_xadj == xadj) // Should be %t +and(expected_adjncy == iadj) // Should be %t +and(expected_anz == v) // Should be %t +// j is the column index +for j = 1 : size(xadj,"*")-1 + irows = iadj(xadj(j):xadj(j+1)-1); + vcolj = v(xadj(j):xadj(j+1)-1); + mprintf("Column #%d:\n",j) + mprintf(" Rows = %s:\n",sci2exp(irows)) + mprintf(" Values= %s:\n",sci2exp(vcolj)) +end + ]]></programlisting> + <para> + The previous script produces the following output. + </para> + <programlisting role="no-scilab-exec"><![CDATA[ +Column #1: + Rows = [3;5]: + Values= [1;2]: +Column #2: + Rows = 3: + Values= 3: +Column #3: + Rows = [1;2;4]: + Values= [4;5;6]: +Column #4: + Rows = [3;5]: + Values= [7;8]: +Column #5: + Rows = [1;4]: + Values= [9;10]: + ]]></programlisting> + <para> + Let us consider the column #1. + The equality xadj(2)-xadj(1)=2 indicates that there are two + nonzeros in the column #1. + The row indices are stored in iadj, which tells us that the + nonzero entries in column #1 are at rows #3 and #5. + The v matrix tells us the actual entries are equal to 1 and 2. + </para> + <para> + In the following example, we browse the nonzero entries of + a sparse matrix by looping on the adjacency structure. + </para> + <programlisting role="example"><![CDATA[ +A = [ +0 0 0 0 0 6 0 0 0 0 +3 0 5 0 0 0 0 5 0 0 +0 0 0 3 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 +0 7 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 3 +0 0 0 0 0 0 0 0 2 0 +]; +B=sparse(A); +[xadj,iadj,v]=sp2adj(B) +expected_xadj = [1 2 3 4 5 5 6 6 7 8 9]'; +expected_adjncy = [2 5 2 3 1 2 7 6]'; +expected_anz = [3 7 5 3 6 5 2 3]'; +and(expected_xadj == xadj) // Should be %t +and(expected_adjncy == iadj) // Should be %t +and(expected_anz == v) // Should be %t + ]]></programlisting> + <para> + In the following example, we check that the sp2adj and adj2sp functions + are inverse. + </para> + <programlisting role="example"><![CDATA[ +// Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide +// Edited by Zhaojun Bai, James Demmel, Jack Dongarra, Axel Ruhe, and Henk van der Vorst +// "Sparse Matrix Storage Formats", J. Dongarra +// http://web.eecs.utk.edu/~dongarra/etemplates/book.html + +A = [ +10 0 0 0 -2 0 +3 9 0 0 0 3 +0 7 8 7 0 0 +3 0 8 7 5 0 +0 8 0 9 9 13 +0 4 0 0 2 -1 +]; +A = sparse(A) + +// To get the Compressed Sparse Column (CSC) : +[col_ptr,row_ind,val]=sp2adj(A) +// To convert back to sparse: +AAsp=adj2sp(col_ptr,row_ind,val) +// Check the conversion +AAsp - A + +// To get the Compressed Sparse Row (CSR) : +[row_ptr,col_ind,val]=sp2adj(A') +// To convert back to sparse: +AAsp=adj2sp(row_ptr,col_ind,val)' +// Check the conversion +AAsp - A + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="adj2sp">adj2sp</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="spcompack">spcompack</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>References</title> + <para> + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + </para> + <para> + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + </para> + <para> + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + </para> + <para> + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + </para> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/sparseconvert/sparse.xml b/modules/sparse/help/en_US/sparseconvert/sparse.xml new file mode 100755 index 000000000..6f9aec111 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/sparse.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) XXXX-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="sparse"> + <refnamediv> + <refname>sparse</refname> + <refpurpose>sparse matrix definition</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>sp=sparse(X) + sp=sparse(ij,v [,mn]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>real or complex or boolean full (or sparse) matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ij</term> + <listitem> + <para>two columns integer matrix (indices of non-zeros entries)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>mn</term> + <listitem> + <para>integer vector with two entries (row-dimension, column-dimension)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>sparse matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sparse</literal> is used to build a sparse matrix. Only non-zero entries + are stored. + </para> + <para> + <literal>sp = sparse(X)</literal> converts a full matrix to sparse form by + squeezing out any zero elements. (If <literal>X</literal> is already sparse + <literal>sp</literal> is <literal>X</literal>). + </para> + <para> + <literal>sp=sparse(ij,v [,mn])</literal> builds an <literal>mn(1)</literal>-by-<literal>mn(2)</literal> + sparse matrix with <literal>sp(ij(k,1),ij(k,2))=v(k)</literal>. + <literal>ij</literal> and <literal>v</literal> must have the same column dimension. + If optional <literal>mn</literal> parameter is not given the <literal>sp</literal> + matrix dimensions are the max value of <literal>ij(:,1)</literal> and <literal>ij(:,2)</literal> + respectively. + </para> + <para> + Operations (concatenation, addition, etc,) with sparse matrices are + made using the same syntax as for full matrices. + </para> + <para> + Elementary functions are also available (<literal>abs,maxi,sum,diag,...</literal>) + for sparse matrices. + </para> + <para> + Mixed operations (full-sparse) are allowed. Results are full or sparse + depending on the operations. + </para> + <para> + Note : Any operation involing dense matrices of the same size, either as argument (e.g. <literal>sp=sparse(d)</literal>) + or as result (e.g. <literal>d= sp + 1.</literal>) is provided for convenience purposes but should of course be avoided. + Furthermore, random access to elements (<literal>sp(r,c)</literal>), especially for insertions, is not efficient, so + any performance-constrained access should be done in batches with <link linkend="spget">spget</link> for read access + and the three arguments constructor <literal>sp=sparse(ij, v, mn)</literal> for write access. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]) +size(sp) +x=rand(2,2);abs(x)-full(abs(sparse(x))) +// sparse constructor taking a single dense matrix +// removes the zeros. +dense=[0., 1., 0., 0., 0., +1., 0., 2., 0., 0. +0., 0., 0., 0., 0. +0., 0., 0., 0., -0.5]; +sp=sparse(dense) +// complex matrices are also supported +sp=sparse(dense*(1+2*%i)) +// for boolean matrices, the boolean sparse matrix +// only stores true values (and removes false values). +dense=[%F, %F, %T, %F, %F +%T, %F, %F, %F, %F +%F, %F, %F, %F, %F +%F, %F, %F, %F, %T]; +sp=sparse(dense) + + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + <member> + <link linkend="sprand">sprand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/sparseconvert/spcompack.xml b/modules/sparse/help/en_US/sparseconvert/spcompack.xml new file mode 100755 index 000000000..13deb634c --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/spcompack.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) XXXX-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="spcompack"> + <refnamediv> + <refname>spcompack</refname> + <refpurpose>converts a compressed adjacency representation</refpurpose> + </refnamediv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>xadj</term> + <listitem> + <para> integer vector of length (n+1).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>xlindx</term> + <listitem> + <para> integer vector of length n+1 (pointers).</para> + </listitem> + </varlistentry> + <varlistentry> + <term>lindx</term> + <listitem> + <para> integer vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>adjncy</term> + <listitem> + <para> integer vector</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <programlisting role=""><![CDATA[ +Utility fonction spcompak is used to convert a compressed adjacency +representation into standard adjacency representation. + ]]></programlisting> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// A is the sparse matrix: +A=[1,0,0,0,0,0,0; + 0,1,0,0,0,0,0; + 0,0,1,0,0,0,0; + 0,0,1,1,0,0,0; + 0,0,1,1,1,0,0; + 0,0,1,1,0,1,0; + 0,0,1,1,0,1,1]; +A=sparse(A); +//For this matrix, the standard adjacency representation is given by: +xadj=[1,2,3,8,12,13,15,16]; +adjncy=[1, 2, 3,4,5,6,7, 4,5,6,7, 5, 6,7, 7]; +//(see sp2adj). +// increments in vector xadj give the number of non zero entries in each column +// ie there is 2-1=1 entry in the column 1 +// there is 3-2=1 entry in the column 2 +// there are 8-3=5 entries in the column 3 +// 12-8=4 4 +//etc +//The row index of these entries is given by the adjncy vector +// for instance, +// adjncy (3:7)=adjncy(xadj(3):xadj(4)-1)=[3,4,5,6,7] +// says that the 5=xadj(4)-xadj(3) entries in column 3 have row +// indices 3,4,5,6,7. +//In the compact representation, the repeated sequences in adjncy +//are eliminated. +//Here in adjncy the sequences 4,5,6,7 and 7 are eliminated. +//The standard structure (xadj,adjncy) takes the compressed form (lindx,xlindx) +lindx=[1, 2, 3,4,5,6,7, 5, 6,7]; +xlindx=[1,2,3,8,9,11]; +//(Columns 4 and 7 of A are eliminated). +//A can be reconstructed from (xadj,xlindx,lindx). +[xadj,adjncy,anz]= sp2adj(A); +adjncy-spcompack(xadj,xlindx,lindx) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sp2adj">sp2adj</link> + </member> + <member> + <link linkend="adj2sp">adj2sp</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/en_US/sparseconvert/spget.xml b/modules/sparse/help/en_US/sparseconvert/spget.xml new file mode 100755 index 000000000..20cb9db9d --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/spget.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) XXXX-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="spget"> + <refnamediv> + <refname>spget</refname> + <refpurpose>retrieves entries of sparse matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[ij,v,mn]=spget(sp)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>sp</term> + <listitem> + <para>real, complex or boolean sparse matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ij</term> + <listitem> + <para>two columns integer matrix (indices of non-zeros or true entries)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>mn</term> + <listitem> + <para>integer vector with two entries (row-dimension, column-dimension)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>column vector</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>spget</literal> is used to convert the internal representation of sparse + matrices into the standard <literal>ij, v</literal> representation. + </para> + <para> + Non zero entries (or entries set to true for a boolean sparse matrix) of <literal>sp</literal> are located in rows and columns + with indices in <literal>ij</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]) +[ij,v,mn]=spget(sp); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="sprand">sprand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/addchapter.sce b/modules/sparse/help/fr_FR/addchapter.sce new file mode 100755 index 000000000..5744e12ad --- /dev/null +++ b/modules/sparse/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("Matrices creuses",SCI+"/modules/sparse/help/fr_FR",%T); + diff --git a/modules/sparse/help/fr_FR/chfact.xml b/modules/sparse/help/fr_FR/chfact.xml new file mode 100755 index 000000000..67b1eb75d --- /dev/null +++ b/modules/sparse/help/fr_FR/chfact.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="fr" xml:id="chfact"> + <refnamediv> + <refname>chfact</refname> + <refpurpose>Factorisation de Cholesky creuse </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>spcho=chfact(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice creuse réelle ou complexe + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>spcho </term> + <listitem> + <para>liste contenant les facteurs de Cholesky + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Si <literal>A</literal> est creuse et hermitienne (symétrique dans le cas réel) définie positive, <literal>spcho=chfact(A)</literal> calcule les facteurs de sa factorisation de Cholesky. + Cette fonction est basée sur le programme Ng-Peyton (ORNL). Voir le programme Fortran pour une description complète des variables de la liste <literal>spcho</literal>. Cette fonction est à utiliser conjointement avec <literal>chsolve</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="chsolve">chsolve</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="spchol">spchol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/chsolve.xml b/modules/sparse/help/fr_FR/chsolve.xml new file mode 100755 index 000000000..6b054fcde --- /dev/null +++ b/modules/sparse/help/fr_FR/chsolve.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="chsolve"> + <refnamediv> + <refname>chsolve</refname> + <refpurpose>solveur de Cholesky creux </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>sol=chsolve(spcho,rhs)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>spcho </term> + <listitem> + <para>liste contenant les facteurs de Cholesky renvoyés par chfact + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rhs, sol </term> + <listitem> + <para>vecteurs + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sol=chsolve(spcho,rhs)</literal> calcule la solution de + <literal>rhs=A*sol</literal>, où <literal>A</literal> est une matrice symétrique + définie positive. Cette fonction est basée sur le programme Ng-Peyton + (ORNL). Voir le programme Fortran pour une description complète des + variables de la liste <literal>spcho</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=sprand(20,20,0.1); +A=A*A'+eye(); +spcho=chfact(A); +sol=(1:20)';rhs=A*sol; +spcho=chfact(A); +chsolve(spcho,rhs) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="chfact">chfact</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="spchol">spchol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/decomposition/CHAPTER b/modules/sparse/help/fr_FR/decomposition/CHAPTER new file mode 100755 index 000000000..41ee03202 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Décompositions Creuses diff --git a/modules/sparse/help/fr_FR/decomposition/ludel.xml b/modules/sparse/help/fr_FR/decomposition/ludel.xml new file mode 100755 index 000000000..8ed809f20 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/ludel.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) XXXX-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="ludel"> + <refnamediv> + <refname>ludel</refname> + <refpurpose>libération de la mémoire allouée à des facteurs LU creux </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>ludel(hand)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>hand </term> + <listitem> + <para>pointeur vers des facteurs L,U creux déjà calculés (sortie de lufact) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Cette fonction est à utiliser conjointement avec <literal>lufact</literal>. Elle libère la mémoire allouée pour le stockage des facteurs L,U creux renvoyés par <literal>lufact</literal>. + </para> + <para> + La suite de commandes <literal>[p,r]=lufact(A);x=lusolve(p,b);ludel(p);</literal> + résout le système linéaire creux <literal>A*x = b</literal> et libère les facteurs creux dont <literal>p</literal> est le pointeur. + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/decomposition/lufact.xml b/modules/sparse/help/fr_FR/decomposition/lufact.xml new file mode 100755 index 000000000..21a82f726 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/lufact.xml @@ -0,0 +1,109 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="lufact"> + <refnamediv> + <refname>lufact</refname> + <refpurpose>factorisation LU d'une matrice creuse </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[hand,rk]=lufact(A,prec)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice réelle carrée creuse + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>hand </term> + <listitem> + <para>pointeur vers des facteurs L,U creux + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para>entier (rang de A) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>prec </term> + <listitem> + <para> + vecteur à 2 composantes <literal>prec=[eps,reps]</literal> (tolérances absolue et relative). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[hand,rk]=lufact(A)</literal> calcule la factorisation LU d'une matrice creuse <literal>A</literal>. + <literal>hand</literal> (variable non affichable) est utilisé par <literal>lusolve</literal> (pour la résolution d'un système linéaire Ax=B) et <literal>luget</literal> (pour récupérer L et U à partir du pointeur <literal>hand</literal>). + <literal>hand</literal> doit être détruit après utilisation (par luget ou lusolve) : <literal>ludel(hand)</literal>; + </para> + <para> + La matrice A n'est pas obligatoirement de rang plein mais doit être carrée + (puisque A est supposée creuse on peut lui ajouter des lignes ou des colonnes nulles pour la rendre carrée). + </para> + <variablelist> + <varlistentry> + <term>eps :</term> + <listitem> + <para> + La valeur absolue qu'un élément de A doit avoir pour être utilisé comme pivot, sauf éventuellement en dernier recours. Ce nombre doit être significativement plus petit que le plus petit élément diagonal attendu dans la matrice. La valeur par défaut est <literal>%eps</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>reps :</term> + <listitem> + <para> + Ce nombre donne le seuil relatif pour les pivots. Il doit être compris entre zéro et un. S'il vaut un, la méthode se comporte comme un pivot total, qui est très lent et qui a tendance à remplir la matrice. S'il est proche de zéro, la méthode de pivotage est de type Markowitz stricte sans utilisation de seuil. Ce seuil est utilisé pour éliminer les pivots qui causeraient une croissance excessive des termes de la matrice. La croissance des éléments est source d'erreurs d'arrondi, et peut avoir lieu même si la matrice est bien conditionnée. Prendre reps grand réduit cette croissance excessive, et donc les erreurs d'arrondi, mais le prendre trop grand risque d'augmenter le temps d'exécution, ainsi que le remplissage de la matrice. La précision peut donc ainsi être dégradée à cause du nombre élevé d'opérations à effectuer à cause du remplissage. Une valeur correcte semble être 0.001 qui est la valeur par défaut (cette valeur par défaut est aussi utilisée si reps>1 ou reps<0). Cette valeur doit être augmentée et la factorisation doit être recommencée si la croissance s'avère trop importante. Changer le seuil sur les pivots n'améliore pas les performances pour les matrices où la croissance est faible, comme c'est souvent le cas pour les matrices mal conditionnées. La valeur par défaut de reps a été choisie pour un usage de lufact avec des matrices à diagonale à peu près dominante (matrices provenant de problèmes de type éléments finis). Pour ces matrices un pivotage diagonal donne les meilleurs résultats. Pour les matrices à diagonale non dominante, on obtient de meilleurs résultats en prenant un seuil plus élevé, comme 0.01 ou 0.1. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +a=rand(5,5);b=rand(5,1);A=sparse(a); +[h,rk]=lufact(A); +x=lusolve(h,b);a*x-b +ludel(h) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/decomposition/luget.xml b/modules/sparse/help/fr_FR/decomposition/luget.xml new file mode 100755 index 000000000..68076a9cb --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/luget.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) XXXX-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="luget"> + <refnamediv> + <refname>luget</refname> + <refpurpose>extraction de facteurs LU creux </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[P,L,U,Q]=luget(hand)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>hand </term> + <listitem> + <para>pointeur vers des facteurs L,U creux déjà calculés (sortie de lufact) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P </term> + <listitem> + <para>matrice de permutation (creuse) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>L </term> + <listitem> + <para> + matrice creuse, triangulaire inférieure si <literal>hand</literal> provient de la factorisation d'une matrice régulière. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U </term> + <listitem> + <para>matrice carrée creuse, régulière, triangulaire supérieure à diagonale unité. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q </term> + <listitem> + <para>matrice de permutation (creuse) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[P,L,U,Q]=luget(hand)</literal> avec <literal>hand</literal> obtenue avec la commande <literal>[hand,rk]=lufact(A)</literal> avec <literal>A</literal> une matrice creuse, renvoie quatre matrices P,L,U,Q telles que <literal>P*L*U*Q=A</literal>. + </para> + <para> + La matrice A n'est pas obligatoirement de rang plein mais doit être carrée + (puisque A est supposée creuse on peut lui ajouter des lignes ou des colonnes nulles pour la rendre carrée). + </para> + <para> + Si <literal>A</literal> est singulière, la matrice <literal>L</literal> est à colonnes compressées (avec + <literal>rk</literal> colonnes indépendantes non nulles) : la matrice creuse régulière + <literal>Q'*inv(U)</literal> compresse les colonnes de <literal>A</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +a=rand(5,2)*rand(2,5);A=sparse(a); +[hand,rk]=lufact(A);[P,L,U,Q]=luget(hand); +full(L), P*L*U*Q-A +clean(P*L*U*Q-A) +ludel(hand) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/decomposition/lusolve.xml b/modules/sparse/help/fr_FR/decomposition/lusolve.xml new file mode 100755 index 000000000..e9fc2fe80 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/lusolve.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) XXXX-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="lusolve"> + <refnamediv> + <refname>lusolve</refname> + <refpurpose>solveur de système linéaire creux </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>x=lusolve(hand,b) + x=lusolve(A,b) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>b</term> + <listitem> + <para>matrice réelle pleine + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matrice réelle carrée creuse inversible + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>hand</term> + <listitem> + <para>pointeur vers des facteurs L,U creux déjà calculés (sortie de lufact) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>matrice réelle pleine</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>x=lusolve(hand,b)</literal> résout le système linéaire + <literal>A*x = b</literal>, où <literal>hand</literal> est obtenu par un appel + préliminaire à <literal>lufact</literal> :<literal>[hand,rk]=lufact(A)</literal>. + </para> + <para> + <literal>x=lusolve(A,b)</literal> résout le système linéaire creux + <literal>A*x = b</literal> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +non_zeros=[1,2,3,4];rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +[h,rk]=lufact(sp);x=lusolve(h,[1;1;1;1]);ludel(h) +rk,sp*x + +non_zeros=[1,2,3,4];rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +x=lusolve(sp,-ones(4,1)); +sp*x + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="slash">slash</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/decomposition/spchol.xml b/modules/sparse/help/fr_FR/decomposition/spchol.xml new file mode 100755 index 000000000..6a74c4fc7 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/spchol.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) XXXX-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="spchol"> + <refnamediv> + <refname>spchol</refname> + <refpurpose>Factorisation de Cholesky creuse</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[R,P] = spchol(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matrice creuse réelle symétrique et définie positive. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P</term> + <listitem> + <para> matrice de permutation + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para> facteur de Cholesky + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[R,P] = spchol(X)</literal> produit une matrice triangulaire inférieure <literal>R</literal> telle que <literal>P*R*R'*P' = X</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +// Factorisation: +Xfull = [ +3., 0., 0., 2., 0., 0., 2., 0., 2., 0., 0. +0., 5., 4., 0., 0., 0., 0., 0., 0., 0., 0. +0., 4., 5., 0., 0., 0., 0., 0., 0., 0., 0. +2., 0., 0., 3., 0., 0., 2., 0., 2., 0., 0. +0., 0., 0., 0. , 5., 0., 0., 0., 0., 0., 4. +0., 0., 0., 0., 0., 4., 0., 3., 0., 3., 0. +2., 0., 0., 2., 0., 0., 3., 0., 2., 0., 0. +0., 0., 0., 0., 0., 3., 0., 4., 0., 3., 0. +2., 0., 0., 2., 0., 0., 2., 0., 3., 0., 0. +0., 0., 0., 0., 0., 3., 0., 3., 0., 4., 0. +0., 0., 0., 0., 4., 0., 0., 0., 0., 0., 5.]; +X = sparse(Xfull); + +[R, P] = spchol(X); +max(P*R*R'*P'-X) + +// Factorisation puis résolution avec l'opérateur '\': +Afull = [ +2 -1 0 0 0; +-1 2 -1 0 0; +0 -1 2 -1 0; +0 0 -1 2 -1; +0 0 0 -1 2 +]; +A = sparse(Afull); + +[L, P] = spchol(A); +max(P*L*L'*P'-A) + +n = size(A, "r"); e = (1:n)'; b = A * e; +x = P*(L'\(L\(P'*b))); +A*x-b + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="chol">chol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/matrixmanip/CHAPTER b/modules/sparse/help/fr_FR/matrixmanip/CHAPTER new file mode 100755 index 000000000..7a8eeab21 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Manipulation des Matrices Creuses diff --git a/modules/sparse/help/fr_FR/matrixmanip/nnz.xml b/modules/sparse/help/fr_FR/matrixmanip/nnz.xml new file mode 100755 index 000000000..89d92c41f --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/nnz.xml @@ -0,0 +1,64 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="nnz"> + <refnamediv> + <refname>nnz</refname> + <refpurpose>nombre de termes non nuls dans une matrice </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>n=nnz(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>X </term> + <listitem> + <para>matrice réelle ou complexe (pleine ou creuse) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>n </term> + <listitem> + <para>entier, le nombre de termes non nuls + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>nnz</literal> compte le nombre de termes non nuls dans une matrice pleine ou creuse. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]); +nnz(sp) +a=[1 0 0 0 2]; +nnz(a) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/matrixmanip/speye.xml b/modules/sparse/help/fr_FR/matrixmanip/speye.xml new file mode 100755 index 000000000..191953450 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/speye.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="UTF-8"?> +<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="speye" xml:lang="fr"> + <refnamediv> + <refname>speye</refname> + <refpurpose>matrice identité creuse</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>Isp=speye(nrows,ncols) + Isp=speye(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>entier (nombre de lignes)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>entier (nombre de colonnes)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matrice creuse</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matrice identité creuse</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>Isp=speye(nrows,ncols)</literal> renvoie une matrice + identité creuse <literal>Isp</literal> avec <literal>nrows</literal> + lignes et <literal>ncols</literal> colonnes. + </para> + <para> + <literal>Isp=speye(A)</literal> renvoie une matrice identité creuse + de même taille que <literal>A</literal>. Si + <literal>[m,n]=size(A)</literal>, les commandes + <literal>speye(m,n)</literal> et <literal>speye(A)</literal> sont + équivalentes. En particulier <literal>speye(3)</literal> n'est pas + équivalent à <literal>speye(3,3)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +eye(3,3)-full(speye(3,3)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="spzeros">spzeros</link> + </member> + <member> + <link linkend="spones">spones</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/matrixmanip/spones.xml b/modules/sparse/help/fr_FR/matrixmanip/spones.xml new file mode 100755 index 000000000..31f894370 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/spones.xml @@ -0,0 +1,65 @@ +<?xml version="1.0" encoding="UTF-8"?> +<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="spones" xml:lang="fr"> + <refnamediv> + <refname>spones</refname> + <refpurpose>matrice creuse dont les termes valent 1</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>sp = spones(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matrice creuse</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matrice creuse</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sp=spones(A)</literal> génère une matrice creuse de même + structure que <literal>A</literal>, mais où les termes non-nuls ont été + remplacés par la valeur 1. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=sprand(10,12,0.1); +sp=spones(A) +B = A~=0 +bool2s(B) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="spzeros">spzeros</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/matrixmanip/sprand.xml b/modules/sparse/help/fr_FR/matrixmanip/sprand.xml new file mode 100755 index 000000000..9ac2048f7 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/sprand.xml @@ -0,0 +1,86 @@ +<?xml version="1.0" encoding="UTF-8"?> +<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="sprand" xml:lang="fr"> + <refnamediv> + <refname>sprand</refname> + <refpurpose>matrice creuse aléatoire</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>sp=sprand(nrows,ncols,fill [,typ])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>entier (nombre de lignes)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>entier (nombre de colonnes)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>fill</term> + <listitem> + <para>coefficient de remplissage (densité)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>typ</term> + <listitem> + <para> + chaîne de caractères (<literal>'uniform'</literal> (par + défaut) ou <literal>'normal'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matrice creuse</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sp=sprand(nrows,ncols,fill)</literal> renvoie une matrice + creuse <literal>sp</literal> avec <literal>nrows</literal> lignes, + <literal>ncols</literal> colonnes et approximativement + <literal>fill*nrows*ncols</literal> termes non-nuls. + </para> + <para> + Si <literal>typ='uniform'</literal> les termes non nuls suivent une + loi uniforme sur [0,1]. Si <literal>typ='normal'</literal> les termes non + nuls suivent une loi normale centrée réduite. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +W=sprand(100,1000,0.001); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="rand">rand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/fr_FR/matrixmanip/spzeros.xml b/modules/sparse/help/fr_FR/matrixmanip/spzeros.xml new file mode 100755 index 000000000..cc4398e84 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/spzeros.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<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="spzeros" xml:lang="fr"> + <refnamediv> + <refname>spzeros</refname> + <refpurpose>matrice creuse nulle</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>sp = spzeros(nrows, ncols) + sp = spzeros(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>entier (nombre de lignes)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>entier (nombre de colonnes)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matrice creuse</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matrice creuse nulle</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sp=spzeros(nrows,ncols)</literal> renvoie une matrice + creuse nulle <literal>sp</literal> avec <literal>nrows</literal> lignes et + <literal>ncols</literal> colonnes (Équivalent à + <literal>sparse([],[],[nrow,ncols])</literal>). + </para> + <para> + <literal>sp=spzeros(A)</literal> renvoie une matrice creuse nulle de + mêmes dimensions que <literal>A</literal>. Si + <literal>[m,n]=size(A)</literal>, les commandes + <literal>spzeros(m,n)</literal> et <literal>spzeros(A)</literal> sont + équivalentes. En particulier <literal>spzeros(3)</literal> n'est pas + équivalent à <literal>spzeros(3,3)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +m=spzeros(2,2) +a=rand(10,12); +m=spzeros(a) +sum(spzeros(1000,1000)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="spones">spones</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/ja_JP/addchapter.sce b/modules/sparse/help/ja_JP/addchapter.sce new file mode 100755 index 000000000..f63ec568a --- /dev/null +++ b/modules/sparse/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("Sparses Matrix",SCI+"/modules/sparse/help/ja_JP",%T); + diff --git a/modules/sparse/help/ja_JP/chfact.xml b/modules/sparse/help/ja_JP/chfact.xml new file mode 100755 index 000000000..867ce4744 --- /dev/null +++ b/modules/sparse/help/ja_JP/chfact.xml @@ -0,0 +1,148 @@ +<?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="chfact"> + + <refnamediv> + + <refname>chfact</refname> + + <refpurpose>疎行列ã®ã‚³ãƒ¬ã‚¹ã‚ー分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>spcho=chfact(A)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>æ£æ–¹æ£å®šå¯¾ç§°ç–Žè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>spcho</term> + + <listitem> + + <para>コード形å¼ã®ã‚³ãƒ¬ã‚¹ã‚ー分解をå«ã‚€ãƒªã‚¹ãƒˆ</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>spcho=chfact(A)</literal> ã¯, + + æ£å®šå¯¾ç§°è¡Œåˆ—ã¨ä»®å®šã—ã¦ç–Žè¡Œåˆ—<literal>A</literal>ã® + + コレスã‚ー分解を計算ã—ã¾ã™. + + ã“ã®é–¢æ•°ã¯,Ng-Peyton プãƒã‚°ãƒ©ãƒ (ORNL)ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + <literal>spcho</literal>ã®å¤‰æ•°ã®è©³ç´°ãªèª¬æ˜Žã«ã¤ã„ã¦ã¯, + + Fortran プãƒã‚°ãƒ©ãƒ ã‚’å‚ç…§ãã ã•ã„. + + ã“ã®é–¢æ•°ã¯ <literal>chsolve</literal>ã¨å…±ã«ä½¿ç”¨ã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=sprand(20,20,0.1); +A=A*A'+eye(); +chfact(A) + +sol=(1:20)'; +rhs=A*sol; +chfact(A) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="chsolve">chsolve</link> + + </member> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="lufact">lufact</link> + + </member> + + <member> + + <link linkend="luget">luget</link> + + </member> + + <member> + + <link linkend="spchol">spchol</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/chsolve.xml b/modules/sparse/help/ja_JP/chsolve.xml new file mode 100755 index 000000000..8a95951ba --- /dev/null +++ b/modules/sparse/help/ja_JP/chsolve.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="chsolve"> + + <refnamediv> + + <refname>chsolve</refname> + + <refpurpose>疎行列ã®ã‚³ãƒ¬ã‚¹ã‚ーソルãƒ</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>sol=chsolve(spcho,rhs)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>spcho</term> + + <listitem> + + <para>chfact ã‹ã‚‰è¿”ã•ã‚ŒãŸã‚³ãƒ¼ãƒ‰å½¢å¼ã®ã‚³ãƒ¬ã‚¹ã‚ー分解をå«ã‚€ãƒªã‚¹ãƒˆ</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rhs, sol</term> + + <listitem> + + <para>フル列ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>sol=chsolve(spcho,rhs)</literal> ã¯, + + <literal>A</literal>を疎行列ã®æ£å®šå¯¾ç§°è¡Œåˆ—ã¨ã—㦠+ + <literal>rhs=A*sol</literal>ã®è§£ã‚’計算ã—ã¾ã™. + + ã“ã®é–¢æ•°ã¯,Ng-Peyton プãƒã‚°ãƒ©ãƒ (ORNL)ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + <literal>spcho</literal>ã®å¤‰æ•°ã®è©³ç´°ãªèª¬æ˜Žã«ã¤ã„ã¦ã¯, + + Fortran プãƒã‚°ãƒ©ãƒ ã‚’å‚ç…§ãã ã•ã„. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=sprand(20,20,0.1); +A=A*A'+eye(); +spcho=chfact(A); +sol=(1:20)';rhs=A*sol; +spcho=chfact(A); +chsolve(spcho,rhs) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="chfact">chfact</link> + + </member> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="lufact">lufact</link> + + </member> + + <member> + + <link linkend="luget">luget</link> + + </member> + + <member> + + <link linkend="spchol">spchol</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/decomposition/CHAPTER b/modules/sparse/help/ja_JP/decomposition/CHAPTER new file mode 100755 index 000000000..ccebc80d8 --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Sparse Decompositions diff --git a/modules/sparse/help/ja_JP/decomposition/ludel.xml b/modules/sparse/help/ja_JP/decomposition/ludel.xml new file mode 100755 index 000000000..30ccb122d --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/ludel.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) XXXX-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="ludel"> + + <refnamediv> + + <refname>ludel</refname> + + <refpurpose>lufactã§ä½¿ç”¨ã•ã‚Œã‚‹ãƒ¦ãƒ¼ãƒ†ã‚£ãƒªãƒ†ã‚£é–¢æ•°</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>ludel(hand)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>hand</term> + + <listitem> + + <para>疎行列LU分解ã®ãƒãƒ³ãƒ‰ãƒ« (lufactã®å‡ºåŠ›)</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + ã“ã®é–¢æ•°ã¯,<literal>lufact</literal>ã¨çµ„ã¿åˆã‚ã›ã¦ä½¿ç”¨ã•ã‚Œã¾ã™. + + ã“ã®é–¢æ•°ã¯,<literal>lufact</literal>ã®çµæžœã‚’ä¿å˜ã™ã‚‹ãŸã‚ã«ä½¿ç”¨ã•ã‚Œã‚‹ + + 内部メモリ空間を消去ã—ã¾ã™. + + </para> + + <para> + + 一連ã®ã‚³ãƒžãƒ³ãƒ‰,<literal>[p,r]=lufact(A);x=lusolve(p,b);ludel(p);</literal> + + ã«ã‚ˆã‚Šç·šå½¢ç–Žè¡Œåˆ—システム<literal>A*x = b</literal>を解ã, + + <literal>p</literal>を消去ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +non_zeros=[1,2,3,4]; +rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +[h,rk]=lufact(sp); +x=lusolve(h,[1;1;1;1]); +ludel(h) +rk,sp*x + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="lufact">lufact</link> + + </member> + + <member> + + <link linkend="luget">luget</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/decomposition/lufact.xml b/modules/sparse/help/ja_JP/decomposition/lufact.xml new file mode 100755 index 000000000..49e6e99c4 --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/lufact.xml @@ -0,0 +1,271 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="lufact"> + + <refnamediv> + + <refname>lufact</refname> + + <refpurpose>疎行列LU分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[hand,rk]=lufact(A,prec)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>æ£æ–¹ç–Žè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>hand</term> + + <listitem> + + <para>疎行列LU分解ã¸ã®ãƒãƒ³ãƒ‰ãƒ«</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rk</term> + + <listitem> + + <para>æ•´æ•° (Aã®ãƒ©ãƒ³ã‚¯)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>prec</term> + + <listitem> + + <para> + + 大ãã•2ã®ãƒ™ã‚¯ãƒˆãƒ«<literal>prec=[eps,reps]</literal>ã§, + + 絶対ãŠã‚ˆã³ç›¸å¯¾é–¾å€¤ã‚’指定ã—ã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>[hand,rk]=lufact(A)</literal>ã¯, + + 疎行列<literal>A</literal>ã®LU分解を行ãªã„ã¾ã™. + + <literal>hand</literal> (表示ã•ã‚Œã¾ã›ã‚“) ãŒ, + + (線形システムを解ã)<literal>lusolve</literal>ãŠã‚ˆã³ + + (LU分解をå–å¾—ã™ã‚‹)<literal>luget</literal>㧠+ + 使用ã•ã‚Œã¾ã™. + + <literal>hand</literal> ã¯ä»¥ä¸‹ã®ã‚³ãƒžãƒ³ãƒ‰ã«ã‚ˆã‚Šæ¶ˆåŽ»ã—ã¾ã™: <literal>ludel(hand)</literal>; + + </para> + + <para> + + 行列Aã¯,フルランクã§ã‚ã‚‹å¿…è¦ã¯ã‚ã‚Šã¾ã›ã‚“ãŒ,æ£æ–¹ã§ã‚ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™ + + (Aã¯ç–Žè¡Œåˆ—ã§ã‚ã‚‹ã¨ä»®å®šã•ã‚Œã‚‹ãŸã‚,å¿…è¦ã«å¿œã˜ã¦Aã®ä¸‹ã«æ£æ–¹ã«ã™ã‚‹ãŸã‚ã® + + ゼãƒã‚’è¿½åŠ ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™). + + </para> + + <variablelist> + + <varlistentry> + + <term>eps :</term> + + <listitem> + + <para> + + 最終的ã«è¦ç´ ãŒãƒ”ボットã®å€™è£œã¨ã¿ãªã•ã‚Œã‚‹å¤§ãã•. + + ã“ã®æ•°ã¯è¡Œåˆ—ã®ä¸ã§å˜åœ¨ã™ã‚‹ã¨æ€ã‚れる最もå°ã•ã„å¯¾è§’é …ã‚ˆã‚Šã‚‚ + + è‘—ã—ãå°ã•ãªå€¤ã«è¨å®šã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + デフォルトã¯<literal>%eps</literal>ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>reps :</term> + + <listitem> + + <para>ã“ã®æ•°ã¯,ピãƒãƒƒãƒˆç›¸å¯¾é–¾å€¤ã‚’定義ã—ã¾ã™. + + ã“ã®å€¤ã¯,0ã¨1ã®é–“ã¨ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + 1ã®å ´åˆ,ピボットé¸æŠžã¯å®Œå…¨ãƒ”ボットé¸æŠžã¨ãªã‚Š, + + éžå¸¸ã«é…ã,通常ã®è¡Œåˆ—ã«è¿‘ããªã‚‹ã¾ã§è¦ç´ ãŒåŸ‹ã‚られる + + 傾å‘ãŒã‚ã‚Šã¾ã™. 0 ã«è¿‘ã„値をè¨å®šã—ãŸå ´åˆ, + + ピボットé¸æŠžã¯é–¾å€¤ãªã—ã®åŽ³å¯†ãªMarkowitz法ã¨ãªã‚Šã¾ã™. + + ピボットã®é–¾å€¤ã¯ã“れらãŒä½¿ç”¨ã•ã‚ŒãŸå ´åˆã«ã¯ + + è¦ç´ ãŒå¢—åŠ ã—ã™ãŽã‚‹ã‚ˆã†ãªãƒ”ボット候補を消去ã™ã‚‹éš›ã«ä½¿ç”¨ã•ã‚Œã¾ã™. + + è¦ç´ ã®å¢—åŠ ãŒä¸¸ã‚誤差ã®åŽŸå› ã§ã™. + + è¦ç´ ã®å¢—åŠ ã¯æ¡ä»¶ã®è‰¯ã„行列ã«ãŠã„ã¦ã‚‚発生ã—ã¾ã™. + + reps ã«å¤§ããªå€¤ã‚’è¨å®šã™ã‚‹ã“ã¨ã§, + + è¦ç´ ã®å¢—åŠ ã¨ä¸¸ã‚誤差ãŒæ¸›å°‘ã—ã¾ã™ãŒ, + + 大ãã™ãŽã‚‹å€¤ã‚’è¨å®šã™ã‚‹ã¨å®Ÿè¡Œæ™‚é–“ãŒéŽå¤§ã¨ãªã‚Š, + + 代入ã®æ•°ãŒéŽå¤§ã¨ãªã‚Šã¾ã™. + + ã“ã®ã‚ˆã†ãªå ´åˆ, + + 多ãã®ä»£å…¥ã«å¿…è¦ãªè¡Œåˆ—ã®æ“作ã®å›žæ•°ãŒå¤šããªã‚‹ãŸã‚,実際㮠+ + 精度ã¯ä½Žä¸‹ã—ã¾ã™. + + 良ã„値㯠0.001 ã¨æ€ã‚ã‚Œ,ã“ã‚ŒãŒãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã§ã™. + + ã“ã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤ã¯,1より大ãã„ã‹,0以下ã®å€¤ã‚’指定ã™ã‚‹ã“ã¨ã«ã‚ˆã‚Š + + é¸æŠžã•ã‚Œã¾ã™. + + ã“ã®å€¤ã¯,éŽåº¦ãªè¦ç´ æ•°ã®å¢—åŠ ãŒèªã‚られãŸå ´åˆã«ã¯, + + å¢—åŠ ã•ã›,行列を決定ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + ピボット閾値ã®å¤‰æ›´ã¯,è¦ç´ æ•°ã®å¢—åŠ ãŒå°ã•ã„行列ã«ãŠã„ã¦ã¯, + + æ¡ä»¶ãŒæ‚ªã„行列ã«ãŠã„ã¦æœŸå¾…ã•ã‚Œã‚‹ã‚ˆã†ãªæ€§èƒ½ã®æ”¹å–„効果を, + + å¾—ã‚‹ã“ã¨ã¯ã§ãã¾ã›ã‚“. + + reps ã¯, ノードãŠã‚ˆã³ä¿®æ£ãƒŽãƒ¼ãƒ‰ã‚¢ãƒ‰ãƒŸã‚¿ãƒ³ã‚¹è¡Œåˆ—ã®ã‚ˆã†ãª + + 近似的ã«å¯¾è§’優ä½ã®è¡Œåˆ—ã§ä½¿ç”¨ã™ã‚‹ã‚ˆã†ã«é¸æŠžã•ã‚Œã¦ã„ã¾ã™. + + ã“れらã®è¡Œåˆ—ã§ã¯,通常ã¯å¯¾è§’ピボットé¸æŠžã‚’使用ã™ã‚‹ã®ãŒæœ€è‰¯ã§ã™. + + 大ããªå¯¾è§’é …ãŒãªã„行列ã®å ´åˆã¯, + + 通常ã¯0.01ã¾ãŸã¯0.1ã®ã‚ˆã†ãªã‚ˆã‚Šå¤§ããªé–¾å€¤ã‚’使用ã™ã‚‹ã®ãŒæœ€å–„ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +a=rand(5,5);b=rand(5,1);A=sparse(a); +[h,rk]=lufact(A); +x=lusolve(h,b);a*x-b +ludel(h) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="lusolve">lusolve</link> + + </member> + + <member> + + <link linkend="luget">luget</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/decomposition/luget.xml b/modules/sparse/help/ja_JP/decomposition/luget.xml new file mode 100755 index 000000000..c5a2b3943 --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/luget.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) XXXX-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="luget"> + + <refnamediv> + + <refname>luget</refname> + + <refpurpose>疎行列LU分解ã®å±•é–‹</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[P,L,U,Q]=luget(hand)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>hand</term> + + <listitem> + + <para> + + ãƒãƒ³ãƒ‰ãƒ«, <literal>lufact</literal>ã®å‡ºåŠ› + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>P</term> + + <listitem> + + <para>疎交æ›è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>L</term> + + <listitem> + + <para> + + 疎行列, lower triangular if <literal>hand</literal>㌠+ + æ£å‰‡è¡Œåˆ—ã‹ã‚‰å¾—られãŸå ´åˆã¯ä¸Šä¸‰è§’ + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>U</term> + + <listitem> + + <para>æ£æ–¹æ£å‰‡ä¸Šä¸‰è§’疎行列(ä¸»å¯¾è§’é …ã¯1)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Q</term> + + <listitem> + + <para>疎交æ›è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + 疎行列 <literal>A</literal>ã«é–¢ã—㦠+ + コマンド<literal>[hand,rk]=lufact(A)</literal>ã«ã‚ˆã‚Šå¾—られ㟠+ + <literal>hand</literal>を指定ã™ã‚‹ã¨,<literal>[P,L,U,Q]=luget(hand)</literal> + + ã¯,<literal>P*L*U*Q=A</literal>ã¨ãªã‚‹ã‚ˆã†ãª4ã¤ã®ç–Žè¡Œåˆ—ã‚’è¿”ã—ã¾ã™. + + </para> + + <para> + + 行列Aã¯ãƒ•ãƒ«ãƒ©ãƒ³ã‚¯ã§ã‚ã‚‹å¿…è¦ã¯ã‚ã‚Šã¾ã›ã‚“ãŒæ£æ–¹è¡Œåˆ—ã§ã‚ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™ + + (Aã¯ç–Žè¡Œåˆ—ã¨ä»®å®šã•ã‚Œã‚‹ãŸã‚,æ£æ–¹åŒ–ã™ã‚‹ãŸã‚ã«å¿…è¦ã«å¿œã˜ã¦0ã‚’è¿½åŠ ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™). + + </para> + + <para> + + <literal>A</literal>ãŒæ£å‰‡ã§ãªã„å ´åˆ, + + 行列<literal>L</literal>ã¯(<literal>rk</literal>個㮠+ + 独立ã—ãŸéžã‚¼ãƒåˆ—ã«ã¤ã„ã¦)列圧縮ã•ã‚Œã¾ã™ + + æ£å‰‡ãªç–Žè¡Œåˆ— <literal>Q'*inv(U)</literal> 㯠+ + <literal>A</literal>を列圧縮ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +a=rand(5,2)*rand(2,5);A=sparse(a); +[hand,rk]=lufact(A);[P,L,U,Q]=luget(hand); +full(L), P*L*U*Q-A +clean(P*L*U*Q-A) +ludel(hand) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="lusolve">lusolve</link> + + </member> + + <member> + + <link linkend="luget">luget</link> + + </member> + + <member> + + <link linkend="clean">clean</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/decomposition/lusolve.xml b/modules/sparse/help/ja_JP/decomposition/lusolve.xml new file mode 100755 index 000000000..a0befa06e --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/lusolve.xml @@ -0,0 +1,175 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="lusolve"> + + <refnamediv> + + <refname>lusolve</refname> + + <refpurpose>ç–Žãªç·šå½¢ã‚·ã‚¹ãƒ†ãƒ ã®è§£ã‚’å¾—ã‚‹</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>x=lusolve(hand,b) + + x=lusolve(A,b) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>b</term> + + <listitem> + + <para>通常ã®å®Ÿæ•°è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>å¯é€†ãªå®Ÿæ•°æ£æ–¹ç–Žè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>hand</term> + + <listitem> + + <para>疎行列LU分解を計算ã—ãŸéš›ã®ãƒãƒ³ãƒ‰ãƒ«(lufactã®å‡ºåŠ›)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>x</term> + + <listitem> + + <para>通常ã®å®Ÿæ•°è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>x=lusolve(hand,b)</literal> ã¯ç–Žãªç·šå½¢ã‚·ã‚¹ãƒ†ãƒ + + <literal>A*x = b</literal>を解ãã¾ã™. + + </para> + + <para> + + <literal>[hand,rk]=lufact(A)</literal> 㯠lufact ã®å‡ºåŠ›ã§ã™. + + </para> + + <para> + + <literal>x=lusolve(A,b)</literal>ã¯,ç–Žãªç·šå½¢ã‚·ã‚¹ãƒ†ãƒ + + <literal>A*x = b</literal>を解ãã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +non_zeros=[1,2,3,4];rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +[h,rk]=lufact(sp);x=lusolve(h,[1;1;1;1]);ludel(h) +rk,sp*x +non_zeros=[1,2,3,4];rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +x=lusolve(sp,-ones(4,1)); +sp*x + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="lufact">lufact</link> + + </member> + + <member> + + <link linkend="slash">slash</link> + + </member> + + <member> + + <link linkend="backslash">backslash</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/decomposition/spchol.xml b/modules/sparse/help/ja_JP/decomposition/spchol.xml new file mode 100755 index 000000000..f9369d81b --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/spchol.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) XXXX-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="spchol"> + + <refnamediv> + + <refname>spchol</refname> + + <refpurpose>疎行列コレスã‚ー分解</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[R,P] = spchol(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>対称æ£å®šå®Ÿç–Žè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>P</term> + + <listitem> + + <para>é †åˆ—è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>R</term> + + <listitem> + + <para>コレスã‚ー分解</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>[R,P] = spchol(X)</literal> ã¯, + + <literal>P*R*R'*P' = X</literal>ã¨ãªã‚‹ã‚ˆã†ãª + + 上三角行列<literal>R</literal> を出力ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +// Factorization: +Xfull = [ +3., 0., 0., 2., 0., 0., 2., 0., 2., 0., 0. +0., 5., 4., 0., 0., 0., 0., 0., 0., 0., 0. +0., 4., 5., 0., 0., 0., 0., 0., 0., 0., 0. +2., 0., 0., 3., 0., 0., 2., 0., 2., 0., 0. +0., 0., 0., 0. , 5., 0., 0., 0., 0., 0., 4. +0., 0., 0., 0., 0., 4., 0., 3., 0., 3., 0. +2., 0., 0., 2., 0., 0., 3., 0., 2., 0., 0. +0., 0., 0., 0., 0., 3., 0., 4., 0., 3., 0. +2., 0., 0., 2., 0., 0., 2., 0., 3., 0., 0. +0., 0., 0., 0., 0., 3., 0., 3., 0., 4., 0. +0., 0., 0., 0., 4., 0., 0., 0., 0., 0., 5.]; +X = sparse(Xfull); + +[R, P] = spchol(X); +max(P*R*R'*P'-X) + +// Factorization and solve with backslash operator: +Afull = [ +2 -1 0 0 0; +-1 2 -1 0 0; +0 -1 2 -1 0; +0 0 -1 2 -1; +0 0 0 -1 2 +]; +A = sparse(Afull); + +[L, P] = spchol(A); +max(P*L*L'*P'-A) + +n = size(A, "r"); e = (1:n)'; b = A * e; +x = P*(L'\(L\(P'*b))); +A*x-b + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="lusolve">lusolve</link> + + </member> + + <member> + + <link linkend="luget">luget</link> + + </member> + + <member> + + <link linkend="chol">chol</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/iterativesolvers/CHAPTER b/modules/sparse/help/ja_JP/iterativesolvers/CHAPTER new file mode 100755 index 000000000..c59edd550 --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/CHAPTER @@ -0,0 +1 @@ +title = Linear Equations (Iterative Solvers) diff --git a/modules/sparse/help/ja_JP/iterativesolvers/conjgrad.xml b/modules/sparse/help/ja_JP/iterativesolvers/conjgrad.xml new file mode 100755 index 000000000..a8c61a1bb --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/conjgrad.xml @@ -0,0 +1,402 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2013 - Scilab Enterprises - Paul Bignier + * + * 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="conjgrad" xml:lang="ja"> + <refnamediv> + <refname>conjgrad</refname> + <refpurpose>共役勾é…ソルãƒ</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼ã³å‡ºã—æ‰‹é †</title> + <synopsis> + [x, flag, err, iter, res] = conjgrad(A, b [, method [, tol [, maxIter [, M [, M2 [, x0 [, verbose]]]]]]]) + [x, flag, err, iter, res] = conjgrad(A, b [, method [, key=value,...]]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>A</term> + <term/> + <listitem> + <para> + 指令ã—ãŸå„<literal>x</literal>ã«ã¤ã„ã¦<literal>A*x</literal>を計算ã™ã‚‹ + 行列ã¾ãŸã¯é–¢æ•°ã¾ãŸã¯ãƒªã‚¹ãƒˆ. + Aã®ãã‚Œãžã‚Œã®åž‹ã«é–¢ã™ã‚‹ A*x ã®è¨ˆç®—ã«é–¢ã—ã¦ä»¥ä¸‹ã«ç¤ºã—ã¾ã™. + </para> + <itemizedlist> + <listitem> + <para> + <literal>行列.</literal>AãŒè¡Œåˆ—ã®å ´åˆ, 通常ã¾ãŸã¯ç–Žè¡Œåˆ—ãŒä½¿ç”¨å¯èƒ½ + </para> + </listitem> + <listitem> + <para> + <literal>関数.</literal>AãŒé–¢æ•°ã®å ´åˆ, 以下ã®ãƒ˜ãƒƒãƒ€ã‚’有ã™ã‚‹ + å¿…è¦ãŒã‚ã‚Šã¾ã™ : + </para> + <programlisting role=""><![CDATA[ +function y = A ( x ) + ]]></programlisting> + </listitem> + <listitem> + <para> + <literal>リスト.</literal>AãŒãƒªã‚¹ãƒˆã®å ´åˆ, + リストã®æœ€åˆã®è¦ç´ ã«ã¯é–¢æ•°ã‚’指定ã—, + æ·»å—2ã‹ã‚‰æœ€å¾Œã¾ã§ã®ãƒªã‚¹ãƒˆã®ä»–ã®è¦ç´ ã«ã¯é–¢æ•°ã®å¼•æ•°ã‚’指定ã—ã¾ã™. + ã“ã®é–¢æ•°ãŒã‚³ãƒ¼ãƒ«ã•ã‚ŒãŸéš›, + xã®ã‚«ãƒ¬ãƒ³ãƒˆã®å€¤ãŒé–¢æ•°ã®æœ€åˆã®å¼•æ•°ã«æŒ‡å®šã•ã‚Œ, + ãã®ä»–ã®å¼•æ•°ã«ã¯ãƒªã‚¹ãƒˆã§æŒ‡å®šã•ã‚ŒãŸã‚‚ã®ãŒæŒ‡å®šã•ã‚Œã¾ã™. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>å³è¾ºãƒ™ã‚¯ãƒˆãƒ« (大ãã•: nx1)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>mehtod</term> + <listitem> + <para>スカラー文å—列, "pcg", "cgs", "bicg" ã¾ãŸã¯ "bicgstab" (デフォルト "bicgstab")</para> + </listitem> + </varlistentry> + <varlistentry> + <term>tol</term> + <listitem> + <para>相対許容誤差 (デフォルト: 1e-8). + 終了基準ã¯æ®‹å·® r=b-Ax ã®äºŒä¹—ノルムをå³è¾º b ã®äºŒä¹—ノルムã§å‰²ã£ãŸã‚‚ã®ã« + 基ã¥ãã¾ã™. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>maxIter</term> + <listitem> + <para>最大å復回数 (デフォルト: n)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>M</term> + <listitem> + <para>プリコンディショナ: 通常ã¾ãŸã¯ç–Žè¡Œåˆ—ã¾ãŸã¯ + <literal>M\x</literal> ã‚’è¿”ã™é–¢æ•° (デフォルト: none) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>M2</term> + <listitem> + <para> + プリコンディショナ: 通常ã¾ãŸã¯ç–Žè¡Œåˆ—ã¾ãŸã¯å„<literal>x</literal>ã® + <literal>M2\x</literal> ã‚’è¿”ã™é–¢æ•° (デフォルト: none) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x0</term> + <listitem> + <para>åˆæœŸæŽ¨å®šãƒ™ã‚¯ãƒˆãƒ« (デフォルト: zeros(n,1))</para> + </listitem> + </varlistentry> + <varlistentry> + <term>verbose</term> + <listitem> + <para>冗長ãªãƒã‚°ã‚’有効ã«ã™ã‚‹å ´åˆã¯1を指定 (デフォルト 0)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>解ベクトル</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + <literal>conjgrad</literal> ãŒå復回数<literal>maxi</literal>以内㫠+ 許容誤差以内ã«åŽæŸã—ãŸå ´åˆã¯ 0, + ãれ以外㯠1 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>err</term> + <listitem> + <para>残差ノルムã®æœ€çµ‚値 (å³è¾º b ã®äºŒä¹—ノルムを使用)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>iter</term> + <listitem> + <para>実行ã—ãŸå復回数</para> + </listitem> + </varlistentry> + <varlistentry> + <term>res</term> + <listitem> + <para>相対ノルム残差ã®ãƒ™ã‚¯ãƒˆãƒ«</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + プリコンディショニング有りã¾ãŸã¯ç„¡ã—ã® + 共役勾é…法ã«ã‚ˆã‚Šç·šå½¢ã‚·ã‚¹ãƒ†ãƒ <literal>Ax=b</literal> を解ãã¾ã™. + プリコンディショナã¯å¯¾ç§°æ£å®šè¡Œåˆ—<literal>M</literal>,ã¾ãŸã¯ + <literal>M=M1*M2</literal>ã¨ãªã‚‹2ã¤ã®è¡Œåˆ— + <literal>M1</literal>ã¨<literal>M2</literal> + ã«ã‚ˆã‚Šå®šç¾©ã•ã‚Œã¾ã™. + ã“ã®å ´åˆ,ã“ã®é–¢æ•°ã¯<literal>inv(M)*A*x = inv(M)*b</literal>ã‚’ + <literal>x</literal>ã«ã¤ã„ã¦è§£ãã¾ã™. + <literal>M</literal>, <literal>M1</literal> ãŠã‚ˆã³ + <literal>M2</literal> ã¯, 呼ã³å‡ºã—æ‰‹é †<literal>y=Milx(x)</literal> + ã§å¯¾å¿œã™ã‚‹å·¦é™¤ç®—<literal>y=Mi\x</literal>を計算ã™ã‚‹Scilab関数㨠+ ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™. + </para> + <para> + 入力引数 <literal>method</literal> ã¯,使用ã™ã‚‹ã‚½ãƒ«ãƒã‚’指定ã—ã¾ã™: + <simplelist type="inline"> + <member> + "pcg" プリコンディショナ付ã共役勾é…法 + </member> + <member> + "cgs" プリコンディショナ付ã二乗共役勾é…法 + </member> + <member> + "bicg" プリコンディショナ付ãåŒå…±å½¹å‹¾é…法 + </member> + <member> + "bicgstab" プリコンディショナ付ã安定化åŒå…±å½¹å‹¾é…法 (デフォルト) + </member> + </simplelist> + </para> + <para> + <literal>method="pcg"</literal>ã®å ´åˆ, <literal>A</literal> 行列㯠+ 対称æ£å®šè¡Œåˆ—(通常ã¾ãŸã¯ç–Žè¡Œåˆ—)ã¾ãŸã¯å‘¼ã³å‡ºã—æ‰‹é †<literal>y=Ax(x)</literal>㧠+ <literal>y=A*x</literal>を計算ã™ã‚‹é–¢æ•°ã¨ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + ãã®ä»–ã®å ´åˆ (<literal>method="cgs", "bicg" or "bicgstab"</literal>), + <literal>A</literal> ã¯æ£æ–¹è¡Œåˆ—ã§ã‚ã‚‹ã“ã¨ã®ã¿å¿…è¦ã§ã™. + </para> + </refsection> + <refsection> + <title>良æ¡ä»¶ãŠã‚ˆã³æ‚ªæ¡ä»¶ã®å•é¡Œã®ä¾‹ + </title> + <para> + 以下ã®ä¾‹ã§ã¯, 2ã¤ã®ç·šå½¢ã‚·ã‚¹ãƒ†ãƒ を解ãã¾ã™. + 最åˆã®è¡Œåˆ—ã¯æ¡ä»¶æ•°ãŒ ~0.02ã§,アルゴリズムã¯10回ã§åŽæŸã—ã¾ã™. + ã“ã‚Œã¯è¡Œåˆ—ã®å¤§ãã•ã¨åŒã˜ã§,共役勾é…法ã§æœŸå¾…ã•ã‚Œã‚‹å‹•ä½œã§ã™. + 2番目ã®è¡Œåˆ—ã¯æ¡ä»¶æ•°ãŒ1.d-6ã¨å°ã•ã,アルゴリズムã¯åŽæŸã¾ã§ã«22回㨠+ より多ãã®å復をè¦ã—ã¾ã™.ã“ã‚ŒãŒãƒ‘ラメータ maxIter ㌠30 ã«è¨å®šã•ã‚Œã¦ã„ã‚‹ + ç†ç”±ã§ã™. + "key=value" 構文ã®ä»–ã®ä¾‹ã«ã¤ã„ã¦ã¯ä»¥ä¸‹ã‚’å‚ç…§ãã ã•ã„. + </para> + <programlisting role="example"><![CDATA[ +// 良æ¡ä»¶å•é¡Œ +A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b = ones(10, 1); +[x, fail, err, iter, res] = conjgrad(A, b, "bicg", 1d-12, 15); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) +// 悪æ¡ä»¶å•é¡Œ +A = [ 894 0 0 0 0 28 0 0 1000 70000 + 0 5 13 5 0 0 0 0 0 0 + 0 13 72 34 0 0 0 0 0 6500 + 0 5 34 1 0 0 0 0 0 55 + 0 0 0 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 0 0 0 32 0 39 46 8 0 + 1000 0 0 0 12 33 0 8 82 11 + 70000 0 6500 55 0 0 0 0 11 100]; +[x, fail, err, iter, res] = conjgrad(A, b, method="pcg", maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) + ]]></programlisting> + </refsection> + <refsection> + <title>Aã«ç–Žè¡Œåˆ—ã¾ãŸã¯é–¢æ•°ã¾ãŸã¯ãƒªã‚¹ãƒˆã‚’指定ã™ã‚‹ä¾‹ + </title> + <para> + 以下ã®ä¾‹ã¯,ã“ã®æ‰‹æ³•ãŒç–Žè¡Œåˆ—ã‚’åŒæ§˜ã«å‡¦ç†ã§ãã‚‹ã“ã¨ã‚’示ã™ã‚‚ã®ã§ã™. + ã¾ãŸ,ã“ã®ä¾‹ã¯å³è¾ºã‚’計算ã™ã‚‹é–¢æ•°ã‚’"conjgrad"ã®ãƒ—リミティブã«æŒ‡å®šã™ã‚‹ + ケースも示ã—ã¾ã™. + ã“ã®ä¾‹ã®æœ€å¾Œã®ã‚±ãƒ¼ã‚¹ã¯, + リストをプリミティブã«æŒ‡å®šã™ãŸå ´åˆã§ã™. + </para> + <programlisting role="example"><![CDATA[ +// 良æ¡ä»¶å•é¡Œ +A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b = ones(10, 1); +// Aを疎行列ã«å¤‰æ› +Asparse=sparse(A); +[x, fail, err, iter, res] = conjgrad(Asparse, b, "cgs", maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) +// å³è¾ºã‚’計算ã™ã‚‹é–¢æ•°ã‚’定義 +function y = Atimesx(x) + A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A*x +endfunction +// スクリプトAtimesx をプリミティブã«æŒ‡å®š +[x, fail, err, iter, res] = conjgrad(Atimesx, b, maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) +// å³è¾ºã‚’計算ã™ã‚‹é–¢æ•°ã‚’定義 +function y = Atimesxbis(x, A) + y = A*x +endfunction +// プリミティブã¸ã®ãƒªã‚¹ãƒˆã‚’指定 +Alist = list(Atimesxbis, Asparse); +[x, fail, err, iter, res] = conjgrad(Alist, b, maxIter=30, tol=1d-12); +mprintf(" fail=%d, iter=%d, errrel=%e\n",fail,iter,err) + ]]></programlisting> + </refsection> + <refsection> + <title>key=value 構文ã®ä¾‹</title> + <para> + 以下ã®ä¾‹ã¯"key=value"構文ã§å¼•æ•°ã‚’指定ã™ã‚‹æ–¹æ³•ã‚’示ã™ã‚‚ã®ã§ã™. + ã“ã‚Œã«ã‚ˆã‚Š,ä½ç½®ã‚’固定ã›ãšã«å¼•æ•°ã‚’指定ã§ã, + ã¤ã¾ã‚Š, 引数リストã«ãŠã‘ã‚‹é †åºã«ä¾å˜ã›ãšã«, + 引数をè¨å®šã§ãã¾ã™. + 有効ãªã‚ーã¯ã‚ªãƒ—ション引数ã®åå‰,ã¤ã¾ã‚Š, + tol, maxIter, %M, %M2, x0, verbose ã§ã™. + 以下ã®ä¾‹ã§ã¯, verbose オプション㌠maxIterオプション㮠+ å‰ã«æŒ‡å®šã•ã‚Œã¦ã„ã‚‹ã“ã¨ã«æ³¨æ„ã—ã¦ãã ã•ã„. + "key=value"構文ã§ã¯ãªã„å ´åˆã¯å¼•æ•°ã®ä½ç½®ãŒå›ºå®šã•ã‚Œã‚‹ãŸã‚, + maxIter ã¯å…ˆ, verbose ã¯å¾Œã§ä½¿ç”¨ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + </para> + <programlisting role="example"><![CDATA[ +// key=value 構文ã§æŒ‡å®šã•ã‚Œã‚‹å¼•æ•°ã®ä¾‹ +A = [100 1; 1 10]; +b = [101; 11]; +[xcomputed, flag, err, iter, res] = conjgrad(A, b, verbose=1); +// key=value 構文ã®å ´åˆ, é †åºã¯é–¢ä¿‚ã‚ã‚Šã¾ã›ã‚“ +[xcomputed, flag, err, iter, res] = conjgrad(A, b, verbose=1, maxIter=0); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>å‚ç…§</title> + <simplelist type="inline"> + <member> + <link linkend="backslash">backslash</link> + </member> + <member> + <link linkend="qmr">qmr</link> + </member> + <member> + <link linkend="gmres">gmres</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>å‚考文献</title> + <para> + <emphasis role="bold">PCG</emphasis> + </para> + <para>"Templates for the Solution of Linear Systems: Building Blocks for + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993, ftp + netlib2.cs.utk.edu/linalg/templates.ps + </para> + <para>"Iterative Methods for Sparse Linear Systems, Second Edition", Saad, + SIAM Publications, 2003, ftp + ftp.cs.umn.edu/dept/users/saad/PS/all_ps.zip + </para> + <para> + <emphasis role="bold">CGS</emphasis> + </para> + <para> + "CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems" by Peter Sonneveld. + </para> + <para> + <ulink url="http://epubs.siam.org/doi/abs/10.1137/0910004">Original article</ulink> + </para> + <para> + <ulink url="http://dl.acm.org/citation.cfm?id=64888&preflayout=flat">Article on ACM</ulink> + </para> + <para> + <ulink url="http://mathworld.wolfram.com/ConjugateGradientSquaredMethod.html">Some theory around CGS</ulink> + </para> + <para> + <emphasis role="bold">BICG</emphasis> + </para> + <para> + "Numerical Recipes: The Art of Scientific Computing." (third ed.) by William Press, Saul Teukolsky, William Vetterling, Brian Flannery. + </para> + <para> + <ulink url="http://apps.nrbook.com/empanel/index.html?pg=87">http://apps.nrbook.com/empanel/index.html?pg=87</ulink> + </para> + <para> + <ulink url="http://dl.acm.org/citation.cfm?doid=1874391.187410">Article on ACM</ulink> + </para> + <para> + <ulink url="http://mathworld.wolfram.com/BiconjugateGradientMethod.html">Some theory around BICG</ulink> + </para> + <para> + <emphasis role="bold">BICGSTAB</emphasis> + </para> + <para> + "Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems" by Henk van der Vorst. 339 + </para> + <para> + <ulink url="http://epubs.siam.org/doi/abs/10.1137/0913035">Original article</ulink> + </para> + <para> + <ulink url="http://dl.acm.org/citation.cfm?id=131916.131930&coll=DL&dl=GUIDE&CFID=372773884&CFTOKEN=56630250">Article on ACM</ulink> + </para> + <para> + <ulink url="http://mathworld.wolfram.com/BiconjugateGradientStabilizedMethod.html">Some theory around BICG</ulink> + </para> + </refsection> + <refsection> + <title>å±¥æ´</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revdescription> + å°Žå…¥ + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/sparse/help/ja_JP/iterativesolvers/gmres.xml b/modules/sparse/help/ja_JP/iterativesolvers/gmres.xml new file mode 100755 index 000000000..46bff29f2 --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/gmres.xml @@ -0,0 +1,406 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="gmres"> + + <refnamediv> + + <refname>gmres</refname> + + <refpurpose>Generalized Minimum RESidual 法</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[x,flag,err,iter,res] = gmres(A,b,[rstr,[tol,[maxi,[M,[x0]]]]])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para> + + nè¡Œn列行列ã¾ãŸã¯<literal>A*x</literal>ã‚’è¿”ã™é–¢æ•°. + + <literal>A</literal>ãŒé–¢æ•°ã®å ´åˆ,以下ã®ã‚ˆã†ãªãƒ˜ãƒƒãƒ€ã‚’有ã™ã‚‹ã“ã¨: + + </para> + + <programlisting role=""><![CDATA[ +function y = A ( x ) +]]></programlisting> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>b</term> + + <listitem> + + <para>å³è¾ºãƒ™ã‚¯ãƒˆãƒ«</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>x0</term> + + <listitem> + + <para>åˆæœŸæŽ¨å®šå€¤ãƒ™ã‚¯ãƒˆãƒ«(デフォルト: zeros(n,1))</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>M</term> + + <listitem> + + <para> + + プリコンディショナ: nè¡Œn列行列（デフォルト: eye(n,n)）ã¾ãŸã¯ + + <literal>M*x</literal>ã‚’è¿”ã™é–¢æ•°. + + M ãŒé–¢æ•°ã®å ´åˆ,以下ã®ã‚ˆã†ãªãƒ˜ãƒƒãƒ€ã‚’有ã™ã‚‹ã“ã¨: + + </para> + + <programlisting role=""><![CDATA[ +function y = M ( x ) + ]]></programlisting> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>rstr</term> + + <listitem> + + <para>リスタートã¾ã§ã®å復回数 (デフォルト: 10)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>maxi</term> + + <listitem> + + <para>最大å復回数 (デフォルト: n)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>許容誤差 (デフォルト: 1e-6)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>x</term> + + <listitem> + + <para>解ã®ãƒ™ã‚¯ãƒˆãƒ«</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>err</term> + + <listitem> + + <para>最終残差ノルム</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>iter</term> + + <listitem> + + <para>実行ã—ãŸå復回数</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <variablelist> + + <varlistentry> + + <term>0 =</term> + + <listitem> + + <para> + + <literal>gmres</literal>ã¯, + + <literal>maxi</literal>回ã®å復内㫠+ + 指定ã—ãŸè¨±å®¹èª¤å·®ã«åŽæŸã—ã¾ã—㟠+ + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>1 =</term> + + <listitem> + + <para> + + 指定ã—㟠<literal>maxi</literal>回ã§ã¯åŽæŸã—ã¾ã›ã‚“ã§ã—㟠+ + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>res</term> + + <listitem> + + <para>残差ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <variablelist> + + <varlistentry> + + <term>GMRES </term> + + <listitem> + + <para> + + 線形システム<literal>Ax=b</literal>をリスタート付ãã® + + Generalized Minimal residual法ã«ã‚ˆã‚Šè§£ãã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>詳細</term> + + <listitem> + + <para>ã“ã®ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã®è©³ç´°ã¯ä»¥ä¸‹ã®æ–‡çŒ®ã«è¨˜è¿°ã•ã‚Œã¦ã„ã¾ã™ :</para> + + <para>"Templates for the Solution of Linear Systems: Building Blocks for + + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993 (ftp + + netlib2.cs.utk.edu; cd linalg; get templates.ps). + + </para> + + <para>"Iterative Methods for Sparse Linear Systems, Second Edition" Saad, + + SIAM Publications, 2003 (ftp ftp.cs.umn.edu; cd dept/users/saad/PS; get + + all_ps.zip). + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ + // A ãŠã‚ˆã³ M ãŒè¡Œåˆ—ã®å ´åˆ +A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b=ones(10,1); +[x,flag,err,iter,res] = gmres(A, b) +M = eye(10, 10); +[x,flag,err,iter,res] = gmres(A, b, 10, 1d-12, 20, M, zeros(10, 1)) + // AãŒè¡Œåˆ—, MãŒé–¢æ•°ã®å ´åˆ + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b=ones(10,1); +function y = Mtimesx(x) +M = eye(10,10); +y = M*x; +endfunction +[x,flag,err,iter,res] = gmres(A, b, 10, 1d-12, 20, Mtimesx, zeros(10, 1)) + // A ãŒé–¢æ•°, M ãŒè¡Œåˆ—ã®å ´åˆ + function y = Atimesx(x) + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A * x; + endfunction + b = ones(10,1); + M = eye(10, 10); + [x,flag,err,iter,res] = gmres(Atimesx, b) + [x,flag,err,iter,res] = gmres(Atimesx, b, 10, 1d-12, 20, M, zeros(10,1)) + // A ãŠã‚ˆã³ M ãŒé–¢æ•° + function y = Atimesx(x) + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A * x; + endfunction + function y = Mtimesx(x) +M = eye(10,10); +y = M*x; +endfunction + [x,flag,err,iter,res] = gmres(Atimesx, b, 10, 1d-12, 20, Mtimesx, zeros(10,1)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="conjgrad">conjgrad</link> + + </member> + + <member> + + <link linkend="qmr">qmr</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/iterativesolvers/qmr.xml b/modules/sparse/help/ja_JP/iterativesolvers/qmr.xml new file mode 100755 index 000000000..5d5b392b4 --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/qmr.xml @@ -0,0 +1,490 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="qmr"> + + <refnamediv> + + <refname>qmr</refname> + + <refpurpose>プリコンディショナ付ãã®Quasi Minimal Residual法</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>[x,flag,err,iter,res] = qmr(A,b,x0,M1,M1p,M2,M2p,maxi,tol)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>Parameters</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para> + + 大ãã•nè¡Œn列ã®è¡Œåˆ—ã¾ãŸã¯<literal>A*x</literal>ã‚’è¿”ã™é–¢æ•° + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>b</term> + + <listitem> + + <para>å³è¾ºãƒ™ã‚¯ãƒˆãƒ«</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>x0</term> + + <listitem> + + <para>åˆæœŸæŽ¨å®šãƒ™ã‚¯ãƒˆãƒ« (デフォルト: zeros(n,1))</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>M1</term> + + <listitem> + + <para> + + 左プリコンディショナ: 行列ã¾ãŸã¯<literal>M1*x</literal>ã‚’è¿”ã™é–¢æ•° + + (å‰è€…ã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤: eye(n,n)) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>M1p</term> + + <listitem> + + <para> + + <literal>M1</literal>ãŒé–¢æ•°ã®å ´åˆã®ã¿æŒ‡å®šã™ã‚‹ + + å¿…è¦ãŒã‚ã‚Šã¾ã™. ã“ã®å ´åˆ, <literal>M1p</literal> 㯠+ + <literal>M1'*x</literal>ã‚’è¿”ã™é–¢æ•°ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>M2</term> + + <listitem> + + <para> + + å³ãƒ—リコンディショナ: 行列ã¾ãŸã¯<literal>M2*x</literal>ã‚’ + + è¿”ã™é–¢æ•° (å‰è€…ã®ãƒ‡ãƒ•ã‚©ãƒ«ãƒˆå€¤: eye(n,n)) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>M2p</term> + + <listitem> + + <para> + + <literal>M2</literal>ãŒé–¢æ•°ã®å ´åˆã®ã¿æŒ‡å®šã™ã‚‹ + + å¿…è¦ãŒã‚ã‚Šã¾ã™. ã“ã®å ´åˆ, + + <literal>M2p</literal>ã¯<literal>M2'*x</literal>ã‚’è¿”ã™é–¢æ•°ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>maxi</term> + + <listitem> + + <para>最大å復回数 (デフォルト: n) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>tol</term> + + <listitem> + + <para>許容誤差 (デフォルト: 1000*%eps)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>x</term> + + <listitem> + + <para>解ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>flag</term> + + <listitem> + + <variablelist> + + <varlistentry> + + <term>0 =</term> + + <listitem> + + <para> + + <literal>gmres</literal> 㯠+ + <literal>maxi</literal>回ã®å復ã®é–“ã« + + 許容誤差内ã«åŽæŸã—ã¾ã—㟠+ + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>1 =</term> + + <listitem> + + <para> + + 指定ã—ãŸ<literal>maxi</literal>回ã®å復ã®é–“ã« + + åŽæŸã—ã¾ã›ã‚“ã§ã—㟠+ + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>res</term> + + <listitem> + + <para>残差ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>err</term> + + <listitem> + + <para>最終残差ノルム</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>iter</term> + + <listitem> + + <para>実行ã—ãŸå復回数</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + プリコンディショナ付ãã®Quasi Minimal Residual法ã«ã‚ˆã‚Š, + + 線形システム<literal>Ax=b</literal>を解ãã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ + // If A is a matrix +A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; +b=ones(10,1); +[x,flag,err,iter,res] = qmr(A, b) + +[x,flag,err,iter,res] = qmr(A, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) + + // If A is a function + function y = Atimesx(x,t) + A=[ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + if (t == 'notransp') then + y = A*x; + elseif (t == 'transp') then + y = A'*x; + end + endfunction + + [x,flag,err,iter,res] = qmr(Atimesx, b) + + [x,flag,err,iter,res] = qmr(Atimesx, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) + + // OR + + function y = funA(x) + A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A*x + endfunction + + function y = funAp(x) + A = [ 94 0 0 0 0 28 0 0 32 0 + 0 59 13 5 0 0 0 10 0 0 + 0 13 72 34 2 0 0 0 0 65 + 0 5 34 114 0 0 0 0 0 55 + 0 0 2 0 70 0 28 32 12 0 + 28 0 0 0 0 87 20 0 33 0 + 0 0 0 0 28 20 71 39 0 0 + 0 10 0 0 32 0 39 46 8 0 + 32 0 0 0 12 33 0 8 82 11 + 0 0 65 55 0 0 0 0 11 100]; + y = A'*x + endfunction + + [x,flag,err,iter,res] = qmr(funA, funAp, b) + + [x,flag,err,iter,res] = qmr(funA, funAp, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) + + // If A is a matrix, M1 and M2 are functions + function y = M1timesx(x,t) + M1 = eye(10,10); + if(t=="notransp") then + y = M1*x; + elseif (t=="transp") then + y = M1'*x; + end + endfunction + + function y = M2timesx(x,t) + M2 = eye(10,10); + if(t=="notransp") then + y = M2*x; + elseif (t=="transp") then + y = M2'*x; + end + endfunction + + [x,flag,err,iter,res] = qmr(A, b, zeros(10,1), M1timesx, M2timesx, 10, 1d-12) + + // OR + + function y = funM1(x) + M1 = eye(10,10); + y = M1*x; + endfunction + + function y = funM1p(x) + M1 = eye(10,10); + y = M1'*x; + endfunction + + function y = funM2(x) + M2 = eye(10,10); + y = M2*x; + endfunction + + function y = funM2p(x) + M2 = eye(10,10); + y = M2'*x; + endfunction + + [x,flag,err,iter,res] = qmr(A, b, zeros(10,1), funM1, funM1p, funM2, funM2p, 10, 1d-12) + + // If A, M1, M2 are functions + [x,flag,err,iter,res] = qmr(funA, funAp, b, zeros(10,1), funM1, funM1p, funM2, funM2p, 10, 1d-12) + [x,flag,err,iter,res] = qmr(Atimesx, b, zeros(10,1), M1timesx, M2timesx, 10, 1d-12) + + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="gmres">gmres</link> + + </member> + + <member> + + <link linkend="conjgrad">conjgrad</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>å±¥æ´</title> + + <revhistory> + + <revision> + + <revnumber>5.4.0</revnumber> + + <revdescription> + + qmr(A, Ap) ã®ã‚³ãƒ¼ãƒ«ã¯å»ƒæ¢ã•ã‚Œã¾ã—ãŸ. + + qmr(A) を代ã‚ã‚Šã«ä½¿ç”¨ã—ã¦ãã ã•ã„. + + 以下ã®é–¢æ•°ãŒä¾‹ã¨ãªã‚Šã¾ã™ : + + <programlisting role=""><![CDATA[ +function y = A ( x, t ) +Amat = eye(2,2); +if ( t== "notransp") then +y = Amat*x; +elseif (t == "transp") then +y = Amat'*x; +end +endfunction + ]]></programlisting> + + </revdescription> + + </revision> + + </revhistory> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/matrixmanip/CHAPTER b/modules/sparse/help/ja_JP/matrixmanip/CHAPTER new file mode 100755 index 000000000..a797a77e1 --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Manipulation diff --git a/modules/sparse/help/ja_JP/matrixmanip/issparse.xml b/modules/sparse/help/ja_JP/matrixmanip/issparse.xml new file mode 100755 index 000000000..19ce3bf8d --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/issparse.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) 2011 - DIGITEO - Allan CORNET + * + * 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="issparse" xml:lang="ja"> + <refnamediv> + <refname>issparse</refname> + <refpurpose>入力値ãŒç–Žè¡Œåˆ—ã‹ã©ã†ã‹ã‚’調ã¹ã‚‹</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼ã³å‡ºã—æ‰‹é †</title> + <synopsis>res = issparse(S)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>S</term> + <listitem> + <para>scilabオブジェクト</para> + </listitem> + </varlistentry> + <varlistentry> + <term>res</term> + <listitem> + <para>1: 行列ã¯ç–Žè¡Œåˆ—, 0: ãã®ä»–</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>res = issparse(S)</literal> ã¯ã€S ãŒç–Žè¡Œåˆ—ã®æ™‚ã«1, + ãれ以外ã®æ™‚ã«0ã‚’è¿”ã—ã¾ã™. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example">sp = sparse([1,2;4,5;3,10],[1,2,3]); + if issparse(sp) == 1 then + disp("It is a sparse"); + end + A = 1; + if issparse(A) == 0 then + disp("It is not a sparse"); + end + </programlisting> + </refsection> + <refsection role="see also"> + <title>å‚ç…§</title> + <simplelist type="inline"> + <member> + <link linkend="type">type</link> + </member> + <member> + <link linkend="typeof">typeof</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/ja_JP/matrixmanip/nnz.xml b/modules/sparse/help/ja_JP/matrixmanip/nnz.xml new file mode 100755 index 000000000..c0826a9ea --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/nnz.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) XXXX-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="nnz"> + + <refnamediv> + + <refname>nnz</refname> + + <refpurpose>行列ã«ãŠã‘ã‚‹éžã‚¼ãƒè¦ç´ ã®æ•°</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>n=nnz(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ ç–Ž(ã¾ãŸã¯é€šå¸¸)行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>n</term> + + <listitem> + + <para>æ•´æ•°, Xã®éžã‚¼ãƒè¦ç´ ã®æ•°</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>nnz</literal> ã¯ç–Žè¡Œåˆ—ã¾ãŸã¯é€šå¸¸ã®è¡Œåˆ—ã«ãŠã‘ã‚‹ + + éžã‚¼ãƒè¦ç´ ã®æ•°ã‚’æ•°ãˆã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]); +nnz(sp) +a=[1 0 0 0 2]; +nnz(a) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="spget">spget</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/matrixmanip/speye.xml b/modules/sparse/help/ja_JP/matrixmanip/speye.xml new file mode 100755 index 000000000..b224401de --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/speye.xml @@ -0,0 +1,182 @@ +<?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="speye" xml:lang="ja"> + + <refnamediv> + + <refname>speye</refname> + + <refpurpose>ç–Žå˜ä½è¡Œåˆ—</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>Isp=speye(nrows,ncols) + + Isp=speye(A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>nrows</term> + + <listitem> + + <para>æ•´æ•° (行数)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ncols</term> + + <listitem> + + <para>æ•´æ•° (列数)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>疎行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>sp</term> + + <listitem> + + <para>ç–Žå˜ä½è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>Isp=speye(nrows,ncols)</literal> ã¯, + + <literal>nrows</literal> è¡Œ, + + <literal>ncols</literal> 列㮠+ + ç–Žå˜ä½è¡Œåˆ—<literal>Isp</literal>ã‚’è¿”ã—ã¾ã™. + + (éžæ£æ–¹è¡Œåˆ—ã¯ä¸»å¯¾è§’é …ã«1を有ã—ã¾ã™). + + </para> + + <para> + + <literal>Isp=speye(A)</literal>ã¯<literal>A</literal>㨠+ + åŒã˜æ¬¡å…ƒã®ç–Žå˜ä½è¡Œåˆ—ã‚’è¿”ã—ã¾ã™. + + <literal>[m,n]=size(A)</literal>ã®å ´åˆ, <literal>speye(m,n)</literal> ãŠã‚ˆã³ + + <literal>speye(A)</literal>ã¯ç‰ä¾¡ã§ã™. ãªãŠ, + + <literal>speye(3)</literal> 㯠+ + <literal>speye(3,3)</literal>ã¨ç‰ä¾¡ã§ã¯ã‚ã‚Šã¾ã›ã‚“. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +eye(3,3)-full(speye(3,3)) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="full">full</link> + + </member> + + <member> + + <link linkend="eye">eye</link> + + </member> + + <member> + + <link linkend="spzeros">spzeros</link> + + </member> + + <member> + + <link linkend="spones">spones</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/matrixmanip/spones.xml b/modules/sparse/help/ja_JP/matrixmanip/spones.xml new file mode 100755 index 000000000..64971b973 --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/spones.xml @@ -0,0 +1,137 @@ +<?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="spones" xml:lang="ja"> + + <refnamediv> + + <refname>spones</refname> + + <refpurpose>疎行列</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>sp=spones(A)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>疎行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>sp</term> + + <listitem> + + <para>疎行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>sp=spones(A)</literal> 㯠+ + <literal>A</literal>ã¨åŒã˜ç–Žæ§‹é€ を有㗠+ + ãã®éžã‚¼ãƒè¦ç´ ã®ä½ç½®ã«1を有ã™ã‚‹,行列を生æˆã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +A=sprand(10,12,0.1); +sp=spones(A) +B = A~=0 +bool2s(B) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="full">full</link> + + </member> + + <member> + + <link linkend="eye">eye</link> + + </member> + + <member> + + <link linkend="speye">speye</link> + + </member> + + <member> + + <link linkend="spzeros">spzeros</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/matrixmanip/sprand.xml b/modules/sparse/help/ja_JP/matrixmanip/sprand.xml new file mode 100755 index 000000000..6aacb19fa --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/sprand.xml @@ -0,0 +1,332 @@ +<?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: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="sprand" xml:lang="ja"> + + <refnamediv> + + <refname>sprand</refname> + + <refpurpose>ランダム疎行列</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>sp=sprand(nrows,ncols,density [,typ])</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>nrows</term> + + <listitem> + + <para>æ•´æ•° (行数)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ncols</term> + + <listitem> + + <para>æ•´æ•° (列数)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>density</term> + + <listitem> + + <para>å 有率 (密度)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>typ</term> + + <listitem> + + <para> + + æ–‡å—列, <literal>"uniform"</literal> (デフォルト) ã¾ãŸã¯ + + <literal>"normal"</literal> + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>sp</term> + + <listitem> + + <para>疎行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>sp=sprand(nrows,ncols,density)</literal> ã¯, + + <literal>nrows</literal> è¡Œ<literal>ncols</literal>列, + + 近似的ã«<literal>density*nrows*ncols</literal>個ã®éžã‚¼ãƒ + + エントリを有ã™ã‚‹ç–Žè¡Œåˆ—<literal>sp</literal>ã‚’è¿”ã—ã¾ã™. + + </para> + + <para> + + <literal>density</literal>パラメータ㯠+ + <literal>[0,1]</literal> ã®ç¯„囲ã§æŒ‡å®šã•ã‚Œã¾ã™. + + ãã†ã§ãªã„å ´åˆ, + + 自動的ã«ã“ã®ç¯„囲ã«å¤‰æ›ã•ã‚Œã¾ã™. + + ã“ã®ãŸã‚, 0 よりå°ã•ã„ã‹ 1より大ãã„ density を使用ã—ã¦ã‚‚, + + エラーもè¦å‘Šã‚‚発生ã—ã¾ã›ã‚“: + + å¼<literal>density=max(min(density,1),0)</literal>ãŒä½¿ç”¨ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>typ="uniform"</literal>ã®å ´åˆ, 一様分布㮠+ + 値 [0,1]ãŒç”Ÿæˆã•ã‚Œã¾ã™. + + <literal>typ="normal"</literal> ã®å ´åˆ,æ£è¦åˆ†å¸ƒã® + + 値ãŒç”Ÿæˆã•ã‚Œã¾ã™ (å¹³å‡=0 ãŠã‚ˆã³æ¨™æº–åå·®=1). + + </para> + + <para> + + 出力行列ã®ã‚¨ãƒ³ãƒˆãƒªã¯æŒ‡å®šã•ã‚ŒãŸåˆ†å¸ƒé–¢æ•°<literal>typ</literal>ã« + + 基ã¥ã計算ã•ã‚Œã¾ã™. + + éžã‚¼ãƒè¦ç´ ã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã¯ãƒ©ãƒ³ãƒ€ãƒ ã«è¨ˆç®—ã•ã‚Œ, + + éžã‚¼ãƒã®å¹³å‡çš„ãªæ•°ã¯<literal>density</literal>ã¨ãªã‚Šã¾ã™. + + 実際ã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã®å€¤ã¯,指数分布関数ã«ã‚ˆã‚Šè¨ˆç®—ã•ã‚Œã¾ã™. + + ãŸã ã—,分布関数ã®ãƒ‘ラメータã¯åŒæ™‚ã«è¨ˆç®—ã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <para> + + 以下ã®ä¾‹ã§ã¯,近似的ã«å¯†åº¦0.001ã® + + 100x1000疎行列を生æˆã—ã¾ã™. + + ã™ãªã‚ã¡,ãŠã‚ˆã 100*1000*0.001=100個ã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã¨ãªã‚Šã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +// 行列ã®ã‚¨ãƒ³ãƒˆãƒªã¯ä¸€æ§˜åˆ†å¸ƒã¨ãªã‚Šã¾ã™. +W=sprand(100,1000,0.001); +// 行列ã®ã‚¨ãƒ³ãƒˆãƒªã¯æ£è¦åˆ†å¸ƒã¨ãªã‚Šã¾ã™. +W=sprand(100,1000,0.001,"normal"); + ]]></programlisting> + + <para> + + 以下ã®ã‚¹ã‚¯ãƒªãƒ—トã¯, + + 行列ã®ã‚¨ãƒ³ãƒˆãƒªãŒæŒ‡å®šã—ãŸåˆ†å¸ƒã‚’有ã™ã‚‹ã“ã¨ã‚’確èªã—ã¾ã™. + + éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã‚’å–å¾—ã™ã‚‹ãŸã‚ã«spget関数を用ã„ã¾ã™. + + 次ã«,エントリã®æœ€å°å€¤,最大値,å¹³å‡ã‚’計算ã—, + + limit値ã¨æ¯”較ã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +typ = "normal"; +// typ = "uniform"; +nrows = 1000; +ncols = 2000; +density = 1/100; +s=sprand(nrows,ncols,density,typ); +nnzs=nnz(s); +[ij,v]=spget(s); +[%inf -%inf 0 %inf 1] // Limit values for "normal" +[nnzs min(v) mean(v) max(v) variance(v)] +[%inf 0 0.5 1 1/12] // Limit values for "uniform" + ]]></programlisting> + + <para> + + 以下ã®ã‚¹ã‚¯ãƒªãƒ—トã§ã¯,ランダムã«é¸æŠžã—ãŸã‚¨ãƒ³ãƒˆãƒªã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã‚’調ã¹, + + æ£ã—ã„分布を有ã™ã‚‹ã“ã¨ã‚’確èªã—ã¾ã™. + + 一様分布ã®<literal>kmax</literal>ランダム疎行列を生æˆã—ã¾ã™. + + ã“ã“ã§,å„行列ã«ã¤ã„ã¦,生æˆã™ã‚‹éžã‚¼ãƒã®ã‚¨ãƒ³ãƒˆãƒªã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã«ã¤ã„㦠+ + 考ãˆã¾ã™. + + ã™ãªã‚ã¡, + + <literal>i=1,2,...,nrows</literal> + + ãŠã‚ˆã³ <literal>j=1,2,...,ncols</literal>ï½’ã¨ãªã‚‹ + + å„<literal>i</literal> ãŠã‚ˆã³ <literal>j</literal>ã«ã¤ã„㦠+ + イベント <literal>Aij = {エントリ (i,j) ãŒéžã‚¼ãƒ}</literal> + + ãŒç™ºç”Ÿã™ã‚‹ã‹ã©ã†ã‹ã‚’調ã¹ã¾ã™. + + 行列<literal>C(i,j)</literal>ã¯ã‚¤ãƒ™ãƒ³ãƒˆ<literal>Aij</literal> + + ãŒç™ºç”Ÿã™ã‚‹å›žæ•°ã‚’ä¿å˜ã—ã¾ã™. + + 行列 <literal>R(k)</literal> ã¯,<literal>k=1,2,...,kmax</literal> + + ã«ã¤ã„ã¦è©¦è¡Œå›žæ•°<literal>k</literal>ã®å®Ÿéš›ã®å¯†åº¦ã‚’ä¿å˜ã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ + kmax = 1000; + ncols=10; + nrows=15; + density=0.01; + typ="uniform"; + C=zeros(nrows,ncols); + R=[]; + for k=1:kmax + M=sprand(nrows,ncols,density,typ); + NZ=find(M<>0); + NZratio = size(NZ,"*")/(nrows*ncols); + R=[R NZratio]; + C(NZ)=C(NZ)+1; + end + ]]></programlisting> + + <para> + + ã“ã®ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ãŒå®Ÿè¡Œã•ã‚Œã‚‹å ´åˆ(時々必è¦ã¨ãªã‚‹å¯èƒ½æ€§ãŒã‚ã‚Šã¾ã™), + + アルゴリズムãŒæ£ã—ã実行ã•ã‚Œã¦ã„ã‚‹ã“ã¨ã‚’確èªã™ã‚‹ãŸã‚ã« + + è¦ç´ ã®çµ±è¨ˆå€¤ã‚’計算ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™. + + </para> + + <programlisting role="no-scilab-exec"><![CDATA[ + // A_ijã®æœŸå¾…値㯠+ density * kmax + // ã“ã®å€¤ã‚’実際ã®ã‚¤ãƒ™ãƒ³ãƒˆã¨æ¯”較 : + C + // å¹³å‡å€¤ã¯æœŸå¾…値ã«è¿‘ããªã‚Šã¾ã™. + [density*kmax mean(C)] + // 密度ã¯å¯†åº¦ã®æœŸå¾…値ã«è¿‘ããªã‚Šã¾ã™ + [density mean(R)] + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="full">full</link> + + </member> + + <member> + + <link linkend="rand">rand</link> + + </member> + + <member> + + <link linkend="speye">speye</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/matrixmanip/spzeros.xml b/modules/sparse/help/ja_JP/matrixmanip/spzeros.xml new file mode 100755 index 000000000..f4128e96f --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/spzeros.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: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="spzeros" xml:lang="ja"> + <refnamediv> + <refname>spzeros</refname> + <refpurpose>疎ゼãƒè¡Œåˆ—</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼ã³å‡ºã—æ‰‹é †</title> + <synopsis>sp=spzeros(nrows,ncols) + sp=spzeros(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>æ•´æ•° (行数)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>æ•´æ•° (列数)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>疎行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>疎ゼãƒè¡Œåˆ—</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>sp=spzeros(nrows,ncols)</literal>ã¯, + <literal>nrows</literal> è¡Œ, + <literal>ncols</literal> 列㮠+ 疎ゼãƒè¡Œåˆ—ã‚’è¿”ã—ã¾ã™. + (<literal>sparse([],[],[nrow,ncols])</literal>ã¨ç‰ä¾¡ã§ã™) + </para> + <para> + <literal>sp=spzeros(A)</literal> ã¯, + <literal>A</literal>ã¨åŒã˜æ¬¡å…ƒã‚’有ã™ã‚‹ç–Žã‚¼ãƒè¡Œåˆ—ã‚’è¿”ã—ã¾ã™. + <literal>[m,n]=size(A)</literal>ã®å ´åˆ, <literal>spzeros(m,n)</literal> ãŠã‚ˆã³ + <literal>spzeros(A)</literal> ã¯ç‰ä¾¡ã§ã™. ãªãŠ, + <literal>spzeros(3)</literal> 㯠+ <literal>spzeros(3,3)</literal>ã¨ç‰ã—ããªã‚Šã¾ã›ã‚“. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +m=spzeros(2,2) +a=rand(10,12); +m=spzeros(a) +sum(spzeros(1000,1000)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>å‚ç…§</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="spones">spones</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/ja_JP/ordmmd.xml b/modules/sparse/help/ja_JP/ordmmd.xml new file mode 100755 index 000000000..6095241eb --- /dev/null +++ b/modules/sparse/help/ja_JP/ordmmd.xml @@ -0,0 +1,388 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2011 - 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: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="ordmmd" xml:lang="ja"> + + <refnamediv> + + <refname>ordmmd</refname> + + <refpurpose> + + 複数ã®æœ€å°æ¬¡å…ƒé †åºä»˜ã‘を計算ã™ã‚‹ + + </refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis> + + [perm,invp,nofsub]=ordmmd(xadj,iadj,n) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>n</term> + + <listitem> + + <para>doubleã€æ•´æ•°å€¤ã®1è¡Œ1列ã®è¡Œåˆ—,方程å¼ã®æ•°</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>xadj</term> + + <listitem> + + <para>doubleã€æ•´æ•°å€¤ã®(n+1)è¡Œ1列ã®è¡Œåˆ—,Aã®è¡Œã¸ã®ãƒã‚¤ãƒ³ã‚¿</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>iadj</term> + + <listitem> + + <para>doubleã€æ•´æ•°å€¤ã®nnzè¡Œ1列ã®è¡Œåˆ—,Aã®è¡Œæ·»å—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>perm</term> + + <listitem> + + <para>doubleã€æ•´æ•°å€¤ã®nè¡Œ1列ã®è¡Œåˆ—,最å°æ¬¡å…ƒè¦å‰‡é…列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>invp</term> + + <listitem> + + <para>doubleã€æ•´æ•°å€¤ã®nè¡Œ1列ã®è¡Œåˆ—,permã®é€†è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>nofsub</term> + + <listitem> + + <para> + + doubleã€æ•´æ•°å€¤ã®1è¡Œ1列ã®è¡Œåˆ—,圧縮記憶方å¼ã«ãŠã‘ã‚‹éžã‚¼ãƒè¦ç´ ã®æ•°ã®ä¸Šé™ + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + コレスã‚ー分解をé©ç”¨ã™ã‚‹å‰ã«å¯¾ç§°ç–Žè¡Œåˆ—ã®è¡ŒãŠã‚ˆã³åˆ—を交æ›ã™ã‚‹éš›ã« + + 最å°æ¬¡å…ƒã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ãŒä½¿ç”¨ã•ã‚Œã¾ã™. + + ã“ã®ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã¯ã‚³ãƒ¬ã‚¹ã‚ー分解ã®éžã‚¼ãƒè¦ç´ ã®æ•°ã‚’減らã—ã¾ã™. + + </para> + + <para> + + nè¡Œn列ã®å®Ÿå¯¾ç§°ç–Žè¡Œåˆ—<literal>A</literal>を指定ã™ã‚‹ã¨, + + ã“ã®ã‚³ãƒ¬ã‚¹ã‚ー分解 <literal>U</literal> ã¯,通常, + + <literal>A</literal>ã®ä¸Šä¸‰è§’è¦ç´ よりもéžã‚¼ãƒè¦ç´ ãŒå¤šããªã‚‹ + + "å¡—ã‚Šã¤ã¶ã—(fill in)"ã«è‹¦ã—ã‚られã¾ã™. + + 行列<literal>P'*A*P</literal>ãŒåŒã˜ã対称ã§, + + ãã®ã‚³ãƒ¬ã‚¹ã‚ー分解ã®éžã‚¼ãƒè¦ç´ ã®æ•°ãŒæœ€å°ã¨ãªã‚‹ + + 交æ›è¡Œåˆ— <literal>P</literal>を探ã—ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <para> + + 以下ã®ä¾‹ã§ã¯,対称疎行列ã®é †åºä»˜ã‘を計算ã—ã¾ã™. + + éš£æŽ¥æ§‹é€ ä½“ã‚’è¨ˆç®—ã™ã‚‹éš›ã«<literal>sp2adj</literal> を使用ã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +A = [ +4. 1. 2. 0.5 2. +1. 0.5 0. 0. 0. +2. 0. 3. 0. 0. +0.5 0. 0. 5./8. 0. +2. 0. 0. 0. 16. +]; +A = sparse(A); +[xadj,iadj,val]=sp2adj(A); +n = size(A,"r"); +[perm,invp,nofsub]=ordmmd(xadj,iadj,n) + ]]></programlisting> + + <para> + + 以下ã®ä¾‹ã§ã¯,対称疎行列ã®é †åºä»˜ã‘を計算ã—ã¾ã™. + + <literal>invp</literal>ãŒ<literal>perm</literal>ã® + + 逆行列ã§ã‚ã‚‹ã“ã¨ã‚’確èªã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ + A = [ + 0., 0., 0., 2., 0., 0., 2., 0., 2., 0., 0. ; + 0., 0., 4., 0., 0., 0., 0., 0., 0., 0., 0. ; + 0., 4., 0., 0., 0., 0., 0., 0., 0., 0., 0. ; + 2., 0., 0., 0., 0., 0., 2., 0., 2., 0., 0. ; + 0., 0., 0., 0. , 0., 0., 0., 0., 0., 0., 4. ; + 0., 0., 0., 0., 0., 0., 0., 3., 0., 3., 0. ; + 2., 0., 0., 2., 0., 0., 0., 0., 2., 0., 0. ; + 0., 0., 0., 0., 0., 3., 0., 0., 0., 3., 0. ; + 2., 0., 0., 2., 0., 0., 2., 0., 0., 0., 0. ; + 0., 0., 0., 0., 0., 3., 0., 3., 0., 0., 0. ; + 0., 0., 0., 0., 4., 0., 0., 0., 0., 0., 0.]; + n=size(A,1); + A=sparse(A); + [xadj,adjncy,anz]=sp2adj(A); + [perm,invp,nofsub]=ordmmd(xadj,adjncy,n); + perm(invp) + ]]></programlisting> + + <para> + + 以下ã®ä¾‹ã§ã¯, 行列<literal>A</literal>ã¨è¡Œåˆ—<literal>P'*A*P</literal> + + ã®ã‚³ãƒ¬ã‚¹ã‚ー分解ã®ç–Žãƒ‘ターンを計算ã—ã¾ã™. + + "Computer Solution of Large Sparse Positive Definite Systems"ã®p.3 "Chapter 1: Introduction"ã‚’å‚ç…§. + + コレスã‚ー分解ã®éžã‚¼ãƒè¦ç´ ã®æ•°ã¯15,一方,行列<literal>P'*A*P</literal>ã®ã‚³ãƒ¬ã‚¹ã‚ー分解㯠+ + 9個ã®éžã‚¼ãƒè¦ç´ を有ã™ã‚‹ã“ã¨ãŒã‚ã‹ã‚Šã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +A = [ +4. 1. 2. 0.5 2. +1. 0.5 0. 0. 0. +2. 0. 3. 0. 0. +0.5 0. 0. 5./8. 0. +2. 0. 0. 0. 16. +]; +A = sparse(A); +// Aã®ã‚³ãƒ¬ã‚¹ã‚ー分解ã®ç–Žãƒ‘ターンを調ã¹ã‚‹ +U = sparse(chol(full(A))); +scf(); +subplot(2,1,1); +PlotSparse(U,"x"); +xtitle("Sparsity pattern of U, such that A=U''*U"); +// éš£æŽ¥æ§‹é€ ä½“ã‚’å–å¾— +[xadj,iadj,val]=sp2adj(A); +// 複数ã®æœ€å°æ¬¡å…ƒè¦å‰‡é…列を計算 +n = size(A,"r"); +[perm,invp,nofsub]=ordmmd(xadj,iadj,n); +// 交æ›ãƒ™ã‚¯ãƒˆãƒ«ã‚’行列ã«å¤‰æ› +P=spzeros(n,n); +for i=1:n + P(perm(i),i)=1; +end +// P'*A*Pã®ã‚³ãƒ¬ã‚¹ã‚ー分解ã®ç–Žãƒ‘ターンを調ã¹ã‚‹ +U = sparse(chol(full(P'*A*P))); +subplot(2,1,2); +PlotSparse(U,"x"); +xtitle("Sparsity pattern of U, such that P''*A*P=U''*U"); + ]]></programlisting> + + <scilab:image localized="true"> + + A = [ + + 4. 1. 2. 0.5 2. + + 1. 0.5 0. 0. 0. + + 2. 0. 3. 0. 0. + + 0.5 0. 0. 0.625 0. + + 2. 0. 0. 0. 16. + + ]; + + A = sparse(A); + + U = sparse(chol(full(A))); + + scf(); + + subplot(2,1,1); + + PlotSparse(U,"x"); + + xtitle("Sparsity pattern of U, such that A=U''*U"); + + [xadj,iadj,val]=sp2adj(A); + + n = size(A,"r"); + + [perm,invp,nofsub]=ordmmd(xadj,iadj,n); + + P=spzeros(n,n); + + for i=1:n + + P(perm(i),i)=1; + + end + + U = sparse(chol(full(P'*A*P))); + + subplot(2,1,2); + + PlotSparse(U,"x"); + + xtitle("Sparsity pattern of U, such that P''*A*P=U''*U"); + + </scilab:image> + + </refsection> + + <refsection> + + <title>実装ã«é–¢ã™ã‚‹æ³¨è¨˜</title> + + <para> + + ã“ã®é–¢æ•°ã¯Mathematical Sciences Section, Oak Ridge National Laboratoryã® + + Esmond G. Ng ãŠã‚ˆã³ Barry W. Peytonã«ã‚ˆã‚‹ + + ソースコード "ordmmd.f",ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + アルゴリズムã¯SPARSPAKライブラリã®Joseph W.H. Liuã«ã‚ˆã‚‹ genmmdルーãƒãƒ³ã«åŸºã¥ã„ã¦ã„ã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>å‚考文献</title> + + <para> + + "Minimum degree algorithm", Wikipedia contributors, Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Minimum_degree_algorithm + + </para> + + <para> + + "A new release of SPARSPAK: the Waterloo sparse matrix package", Alan George and Esmond Ng. 1984. SIGNUM Newsl. 19, 4 (October 1984), 9-13. + + </para> + + <para> + + "Computer Solution of Large Sparse Positive Definite Systems" by Alan George and Joseph Liu, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981 + + </para> + + <para> + + "Implementation of Lipsol in Scilab", Rubio Scola, 1997, INRIA, No 0215 + + </para> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sp2adj">sp2adj</link> + + </member> + + <member> + + <link linkend="spchol">spchol</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/sparseconvert/CHAPTER b/modules/sparse/help/ja_JP/sparseconvert/CHAPTER new file mode 100755 index 000000000..42d5e0bf2 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Conversion diff --git a/modules/sparse/help/ja_JP/sparseconvert/adj2sp.xml b/modules/sparse/help/ja_JP/sparseconvert/adj2sp.xml new file mode 100755 index 000000000..816ab53b8 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/adj2sp.xml @@ -0,0 +1,384 @@ +<?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="adj2sp" xml:lang="ja"> + + <refnamediv> + + <refname>adj2sp</refname> + + <refpurpose>隣接形å¼ã‚’疎行列ã«å¤‰æ›.</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis> + + A=adj2sp(xadj,iadj,v) + + A=adj2sp(xadj,iadj,v,mn) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>xadj</term> + + <listitem> + + <para> + + é•·ã• (n+1)ã®æ•´æ•°ãƒ™ã‚¯ãƒˆãƒ«. + + <literal>j=1:n</literal>ã®å ´åˆ, + + 浮動å°æ•°ç‚¹æ•´æ•° + + <literal>xadj(j+1)-xadj(j)</literal> 㯠+ + j列ã«ãŠã‘ã‚‹éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã®æ•°ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>iadj</term> + + <listitem> + + <para> + + nzè¡Œ1列ã®æµ®å‹•å°æ•°ç‚¹æ•´æ•°ã®è¡Œåˆ—, éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã®è¡Œæ·»å—. + + <literal>j=1:n</literal>ãŠã‚ˆã³, + + <literal>k = xadj(j):xadj(j+1)-1</literal>ã«é–¢ã—ã¦, + + 浮動å°æ•°ç‚¹æ•´æ•° <literal>i = iadj(k)</literal> 㯠+ + éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª #k ã®è¡Œæ·»å—ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>v</term> + + <listitem> + + <para> + + nzè¡Œ1列ã®æµ®å‹•å°æ•°ç‚¹æ•´æ•°ã®è¡Œåˆ—, Aã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª. + + <literal>j=1:n</literal>ãŠã‚ˆã³, + + <literal>k = xadj(j):xadj(j+1)-1</literal>ã«é–¢ã—ã¦, + + 浮動å°æ•°ç‚¹æ•´æ•°<literal>Aij = v(k)</literal>㯠+ + éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª #k ã®å€¤ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>mn</term> + + <listitem> + + <para> + + 1è¡Œ2列ã¾ãŸã¯2è¡Œ1列ã®æµ®å‹•å°æ•°ç‚¹æ•´æ•°ã®è¡Œåˆ—(オプション), + + <literal>mn(1)</literal> ã¯Aã®è¡Œæ•°, + + <literal>mn(2)</literal> ã¯Aã®åˆ—æ•°ã§ã™. + + <literal>mn</literal> ãŒæŒ‡å®šã•ã‚Œãªã„å ´åˆ, + + <literal>mn=[m,n]</literal> ã¯, + + <literal>m=max(iadj)</literal> ãŠã‚ˆã³ + + <literal>n=size(xadj,"*")-1</literal>ãŒãƒ‡ãƒ•ã‚©ãƒ«ãƒˆã¨ãªã‚Šã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para>mè¡Œn列実数ã¾ãŸã¯è¤‡ç´ æ•°ã®ç–Žè¡Œåˆ— (nz 個ã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª)</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + adj2sp ã¯,隣接形å¼ã‚’疎行列ã«å¤‰æ›ã—ã¾ã™. + + 隣接形å¼ã®å€¤ã¯åˆ—毎ã«ä¿å˜ã•ã‚Œã¦ã„ã¾ã™. + + ã“ã‚Œã¯,ã“ã®å½¢å¼ãŒã—ã°ã—ã° + + "Compressed sparse column" ã¾ãŸã¯ CSCã¨å‘¼ã°ã‚Œã‚‹ç†ç”±ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <para> + + 以下ã®ä¾‹ã§ã¯,隣接形å¼ã‹ã‚‰ç–Žè¡Œåˆ—を作æˆã—ã¾ã™. + + ãã®å¾Œ,期待ã—ãŸç–Žè¡Œåˆ—ã¨ä¸€è‡´ã™ã‚‹ã‹ã©ã†ã‹ã‚’確èªã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +xadj = [1 3 4 7 9 11]'; +iadj = [3 5 3 1 2 4 3 5 1 4]'; +v = [1 2 3 4 5 6 7 8 9 10]'; +B=adj2sp(xadj,iadj,v) +A = [ +0 0 4 0 9 +0 0 5 0 0 +1 3 0 7 0 +0 0 6 0 10 +2 0 0 8 0 +]; +C=sparse(A) +and(B==C) + ]]></programlisting> + + <para> + + 以下ã®ä¾‹ã§ã¯,隣接形å¼ã‹ã‚‰ç–Žè¡Œåˆ—を作æˆã—ã¾ã™. + + ãã®å¾Œ,期待ã—ãŸç–Žè¡Œåˆ—ã¨ä¸€è‡´ã™ã‚‹ã‹ã©ã†ã‹ã‚’確èªã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +xadj = [1 2 3 4 5 5 6 6 7 8 9]'; +iadj = [2 5 2 3 1 2 7 6]'; +v = [3 7 5 3 6 5 2 3]'; +C=adj2sp(xadj,iadj,v) +A = [ +0 0 0 0 0 6 0 0 0 0 +3 0 5 0 0 0 0 5 0 0 +0 0 0 3 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 +0 7 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 3 +0 0 0 0 0 0 0 0 2 0 +]; +B=sparse(A) +and(B==C) + ]]></programlisting> + + <para> + + 以下ã®ä¾‹ã§ã¯,mnパラメータã®ä½¿ç”¨æ³•ã‚’確èªã—ã¾ã™. + + mnパラメータã¨xadjãŠã‚ˆã³iadjã®å®Ÿéš›ã®å†…容ã®æ•´åˆæ€§ã‚’adj2spã§ç¢ºèªã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +xadj = [1 2 3 4 5 5 6 6 7 8 9]'; +iadj = [2 5 2 3 1 2 7 6]'; +v = [3 7 5 3 6 5 2 3]'; +mn=[7 10]; +C=adj2sp(xadj,iadj,v,mn) + ]]></programlisting> + + <para> + + 以下ã®ä¾‹ã§ã¯,3è¡Œ3列ã®ç–Žè¡Œåˆ—を作æˆã—ã¾ã™. + + ã“ã®ä¾‹ã¯, SciPyã®æ–‡æ›¸ã‹ã‚‰ã®å¼•ç”¨ã§ã™. + + </para> + + <programlisting role="example"><![CDATA[ +xadj = [1,3,4,7] +iadj = [1,3,3,1,2,3] +v = [1,2,3,4,5,6] +full(adj2sp(xadj,iadj,v)) + ]]></programlisting> + + <para> + + å‰ã®ã‚¹ã‚¯ãƒªãƒ—トã¯ä»¥ä¸‹ã®å‡ºåŠ›ã‚’生æˆã—ã¾ã™. + + </para> + + <programlisting role="no-scilab-exec"><![CDATA[ +-->full(adj2sp(xadj,iadj,v)) + ans = + 1. 0. 4. + 0. 0. 5. + 2. 3. 6. + ]]></programlisting> + + <para> + + 以下ã®ä¾‹ã§ã¯,sp2adjãŠã‚ˆã³adj2sp関数ãŒé€†é–¢æ•°ã§ã‚ã‚‹ã“ã¨ã‚’ + + 確èªã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +// Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide +// Edited by Zhaojun Bai, James Demmel, Jack Dongarra, Axel Ruhe, and Henk van der Vorst +// "Sparse Matrix Storage Formats", J. Dongarra +// http://web.eecs.utk.edu/~dongarra/etemplates/book.html + +A = [ +10 0 0 0 -2 0 +3 9 0 0 0 3 +0 7 8 7 0 0 +3 0 8 7 5 0 +0 8 0 9 9 13 +0 4 0 0 2 -1 +]; +A = sparse(A) + +// To get the Compressed Sparse Column (CSC) : +[col_ptr,row_ind,val]=sp2adj(A) +// To convert back to sparse: +AAsp=adj2sp(col_ptr,row_ind,val) +// Check the conversion +AAsp - A + +// To get the Compressed Sparse Row (CSR) : +[row_ptr,col_ind,val]=sp2adj(A') +// To convert back to sparse: +AAsp=adj2sp(row_ptr,col_ind,val)' +// Check the conversion +AAsp - A + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sp2adj">sp2adj</link> + + </member> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="spcompack">spcompack</link> + + </member> + + <member> + + <link linkend="spget">spget</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>å‚考文献</title> + + <para> + + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + + </para> + + <para> + + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + + </para> + + <para> + + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + + </para> + + <para> + + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/sparseconvert/full.xml b/modules/sparse/help/ja_JP/sparseconvert/full.xml new file mode 100755 index 000000000..753d84dbb --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/full.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) XXXX-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="full"> + + <refnamediv> + + <refname>full</refname> + + <refpurpose>疎行列を通常ã®è¡Œåˆ—ã«å¤‰æ›ã™ã‚‹</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>X=full(sp)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>sp</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®ç–Ž(ã¾ãŸã¯é€šå¸¸ã®)行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>通常ã®è¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>X=full(sp)</literal> ã¯ç–Žè¡Œåˆ— <literal>sp</literal> ã‚’ + + 通常ã®è¡Œåˆ—表ç¾ã«å¤‰æ›ã—ã¾ã™. + + (<literal>sp</literal> ãŒæ—¢ã«é€šå¸¸ã®è¡Œåˆ—ã®å ´åˆ,<literal>X</literal> 㯠+ + <literal>sp</literal>ã«ç‰ã—ããªã‚Šã¾ã™). + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;5,4;3,1],[1,2,3]); +A=full(sp) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="sprand">sprand</link> + + </member> + + <member> + + <link linkend="speye">speye</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/sparseconvert/mtlb_sparse.xml b/modules/sparse/help/ja_JP/sparseconvert/mtlb_sparse.xml new file mode 100755 index 000000000..a1a26114c --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/mtlb_sparse.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) XXXX-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="mtlb_sparse"> + + <refnamediv> + + <refname>mtlb_sparse</refname> + + <refpurpose>疎行列ã«å¤‰æ›</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>Y=mtlb_sparse(X)</synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>疎行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>Y</term> + + <listitem> + + <para>Matlabå½¢å¼ã®ç–Žè¡Œåˆ—</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>ã›ã¤</title> + + <para> + + <literal>Y=mtlb_sparse(X)</literal> 㯠+ + Scilab疎行列<literal>X</literal>ã‚’Matlabå½¢å¼ã«å¤‰æ›ã™ã‚‹éš›ã« + + 使用ã•ã‚Œã¾ã™. + + <literal>Y</literal> ã¯7åž‹ã®å¤‰æ•°,ã™ãªã‚ã¡, + + <literal>type(Y)</literal>ã¯7ã¨ãªã‚Šã¾ã™. + + ã“ã®é–¢æ•°ã¯, mexfilesã§ä½¿ç”¨ã•ã‚Œã¾ã™ (疎行列をå«ã‚€Matlab mexileã¯Scilab疎行列を + + ã“ã®å½¢å¼ã«å¤‰æ›ã—ãŸå ´åˆã®ã¿ä½¿ç”¨ã§ãã¾ã™). + + 関数<literal>full</literal> ãŠã‚ˆã³ <literal>spget</literal>ã¯ã“ã®å½¢å¼ã§ã‚‚ + + 動作ã—ã¾ã™. + + </para> + + <para> + + ã“ã®å½¢å¼ã‚’用ã„ã‚‹ãã®ä»–ã®å‡¦ç†ãŠã‚ˆã³é–¢æ•°ã¯, + + 接é 辞 "%msp" を用ã„㦠+ + Scilab関数ã«ã‚ˆã‚Šã‚ªãƒ¼ãƒãƒ¼ãƒãƒ¼ãƒ‰ã™ã‚‹ã“ã¨ãŒã§ãã¾ã™. + + 例ãˆã°,関数 + + <literal>%msp_p(x)</literal> (SCIDIR/macros/percent ディレクトリå‚ç…§)㯠+ + ã“ã®ã‚ˆã†ãª"7åž‹"オブジェクトを表示ã™ã‚‹éš›ã«ä½¿ç”¨ã•ã‚Œã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +X=sparse(rand(2,2)); Y=mtlb_sparse(X); +Y, full(Y), [ij,v,mn]=spget(Y) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="full">full</link> + + </member> + + <member> + + <link linkend="spget">spget</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/sparseconvert/sp2adj.xml b/modules/sparse/help/ja_JP/sparseconvert/sp2adj.xml new file mode 100755 index 000000000..0f0e77986 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/sp2adj.xml @@ -0,0 +1,369 @@ +<?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="sp2adj" xml:lang="ja"> + + <refnamediv> + + <refname>sp2adj</refname> + + <refpurpose>疎行列を隣接形å¼ã«å¤‰æ›ã™ã‚‹</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis> + + [xadj,iadj,v]=sp2adj(A) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>A</term> + + <listitem> + + <para> + + mè¡Œn列ã®å®Ÿæ•°ã¾ãŸã¯è¤‡ç´ æ•°ã®ç–Žè¡Œåˆ— (nz 個ã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª) + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>xadj</term> + + <listitem> + + <para> + + (n+1)è¡Œ1列ã®æµ®å‹•å°æ•°ç‚¹æ•´æ•°ã®è¡Œåˆ—ã§, + + å„列ã®iadjã¨vã®å…ˆé ã®æ·»å—を指ã—ã¾ã™. + + <literal>j=1:n</literal>ã®å ´åˆ, + + 浮動å°æ•°ç‚¹æ•´æ•° + + <literal>xadj(j+1)-xadj(j)</literal> 㯠+ + j列ã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã®æ•°ã«ãªã‚Šã¾ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>iadj</term> + + <listitem> + + <para> + + nzè¡Œ1列ã®æµ®å‹•å°æ•°ç‚¹æ•´æ•°ã®è¡Œåˆ—, éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã®è¡Œæ·»å—. + + <literal>j=1:n</literal>ãŠã‚ˆã³, + + <literal>k = xadj(j):xadj(j+1)-1</literal>ã«é–¢ã—ã¦, + + 浮動å°æ•°ç‚¹æ•´æ•° <literal>i = iadj(k)</literal> 㯠+ + éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª #k ã®è¡Œæ·»å—ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>v</term> + + <listitem> + + <para> + + nzè¡Œ1列ã®æµ®å‹•å°æ•°ç‚¹æ•´æ•°ã®è¡Œåˆ—, Aã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª. + + <literal>j=1:n</literal>ãŠã‚ˆã³, + + <literal>k = xadj(j):xadj(j+1)-1</literal>ã«é–¢ã—ã¦, + + 浮動å°æ•°ç‚¹æ•´æ•°<literal>Aij = v(k)</literal>㯠+ + éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒª #k ã®å€¤ã§ã™. + + </para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + sp2adjã¯,疎行列を隣接形å¼ã«å¤‰æ›ã—ã¾ã™. + + 隣接形å¼ã®å€¤ã¯åˆ—毎ã«ä¿å˜ã•ã‚Œã¦ã„ã¾ã™. + + ã“ã‚Œã¯,ã“ã®å½¢å¼ãŒã—ã°ã—ã° + + "Compressed sparse column" ã¾ãŸã¯ CSCã¨å‘¼ã°ã‚Œã‚‹ç†ç”±ã§ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <para> + + 以下ã®ä¾‹ã§ã¯,1ã‹ã‚‰10ã®ã‚¨ãƒ³ãƒˆãƒªã‚’有ã™ã‚‹é€šå¸¸ã®è¡Œåˆ—を作æˆã—ã¾ã™. + + 次ã«,ã“れを疎行列ã«å¤‰æ›ã—,ゼãƒã‚’除ãã¾ã™. + + 最後ã«,ã“ã®è¡Œåˆ—ã®éš£æŽ¥å½¢å¼ã‚’計算ã—ã¾ã™. + + 行列bã¯Aã®éžã‚¼ãƒè¦ç´ ã®ã¿ã‚’有ã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +A = [ +0 0 4 0 9 +0 0 5 0 0 +1 3 0 7 0 +0 0 6 0 10 +2 0 0 8 0 +]; +B=sparse(A); +[xadj,iadj,v]=sp2adj(B) +expected_xadj = [1 3 4 7 9 11]'; +expected_adjncy = [3 5 3 1 2 4 3 5 1 4]'; +expected_anz = [1 2 3 4 5 6 7 8 9 10]'; +and(expected_xadj == xadj) // Should be %t +and(expected_adjncy == iadj) // Should be %t +and(expected_anz == v) // Should be %t +// j is the column index +for j = 1 : size(xadj,"*")-1 + irows = iadj(xadj(j):xadj(j+1)-1); + vcolj = v(xadj(j):xadj(j+1)-1); + mprintf("Column #%d:\n",j) + mprintf(" Rows = %s:\n",sci2exp(irows)) + mprintf(" Values= %s:\n",sci2exp(vcolj)) +end + ]]></programlisting> + + <para> + + å‰ã®ã‚¹ã‚¯ãƒªãƒ—トã¯ä»¥ä¸‹ã®å‡ºåŠ›ã‚’生æˆã—ã¾ã™. + + </para> + + <programlisting role="no-scilab-exec"><![CDATA[ +Column #1: + Rows = [3;5]: + Values= [1;2]: +Column #2: + Rows = 3: + Values= 3: +Column #3: + Rows = [1;2;4]: + Values= [4;5;6]: +Column #4: + Rows = [3;5]: + Values= [7;8]: +Column #5: + Rows = [1;4]: + Values= [9;10]: + ]]></programlisting> + + <para> + + 列 #1ã«ã¤ã„ã¦è€ƒãˆã¦ã¿ã¾ã—ょã†. + + ç‰å¼ xadj(2)-xadj(1)=2 ã¯åˆ— #1ã«éžã‚¼ãƒè¦ç´ ãŒ2個ã‚ã‚‹ã“ã¨ã‚’示ã—ã¾ã™. + + 行添å—㯠iadjã«ä¿å˜ã•ã‚Œ, 列 #1 ã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã¯ + + è¡Œ #3 ãŠã‚ˆã³ #5ã§ã‚ã‚‹ã“ã¨ã‚’示ã—ã¾ã™. + + 行列 v ã¯å®Ÿéš›ã®ã‚¨ãƒ³ãƒˆãƒªãŒ 1ãŠã‚ˆã³2ã§ã‚ã‚‹ã“ã¨ã‚’示ã—ã¾ã™. + + </para> + + <para> + + 以下ã®ä¾‹ã§ã¯,疎行列ã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã‚’éš£æŽ¥æ§‹é€ ã§ãƒ«ãƒ¼ãƒ—処ç†ã‚’ + + ã™ã‚‹ã“ã¨ã«ã‚ˆã‚Š,調ã¹ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +A = [ +0 0 0 0 0 6 0 0 0 0 +3 0 5 0 0 0 0 5 0 0 +0 0 0 3 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 +0 7 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 3 +0 0 0 0 0 0 0 0 2 0 +]; +B=sparse(A); +[xadj,iadj,v]=sp2adj(B) +expected_xadj = [1 2 3 4 5 5 6 6 7 8 9]'; +expected_adjncy = [2 5 2 3 1 2 7 6]'; +expected_anz = [3 7 5 3 6 5 2 3]'; +and(expected_xadj == xadj) // Should be %t +and(expected_adjncy == iadj) // Should be %t +and(expected_anz == v) // Should be %t + ]]></programlisting> + + <para> + + 以下ã®ä¾‹ã§ã¯,sp2adjãŠã‚ˆã³adj2sp関数ãŒé€†é–¢æ•°ã§ã‚ã‚‹ã“ã¨ã‚’ + + 確èªã—ã¾ã™. + + </para> + + <programlisting role="example"><![CDATA[ +// Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide +// Edited by Zhaojun Bai, James Demmel, Jack Dongarra, Axel Ruhe, and Henk van der Vorst +// "Sparse Matrix Storage Formats", J. Dongarra +// http://web.eecs.utk.edu/~dongarra/etemplates/book.html + +A = [ +10 0 0 0 -2 0 +3 9 0 0 0 3 +0 7 8 7 0 0 +3 0 8 7 5 0 +0 8 0 9 9 13 +0 4 0 0 2 -1 +]; +A = sparse(A) + +// To get the Compressed Sparse Column (CSC) : +[col_ptr,row_ind,val]=sp2adj(A) +// To convert back to sparse: +AAsp=adj2sp(col_ptr,row_ind,val) +// Check the conversion +AAsp - A + +// To get the Compressed Sparse Row (CSR) : +[row_ptr,col_ind,val]=sp2adj(A') +// To convert back to sparse: +AAsp=adj2sp(row_ptr,col_ind,val)' +// Check the conversion +AAsp - A + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="adj2sp">adj2sp</link> + + </member> + + <member> + + <link linkend="sparse">sparse</link> + + </member> + + <member> + + <link linkend="spcompack">spcompack</link> + + </member> + + <member> + + <link linkend="spget">spget</link> + + </member> + + </simplelist> + + </refsection> + + <refsection> + + <title>å‚考文献</title> + + <para> + + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + + </para> + + <para> + + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + + </para> + + <para> + + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + + </para> + + <para> + + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + + </para> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/sparseconvert/sparse.xml b/modules/sparse/help/ja_JP/sparseconvert/sparse.xml new file mode 100755 index 000000000..7b6095c57 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/sparse.xml @@ -0,0 +1,277 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="sparse"> + + <refnamediv> + + <refname>sparse</refname> + + <refpurpose>疎行列を定義</refpurpose> + + </refnamediv> + + <refsynopsisdiv> + + <title>呼ã³å‡ºã—æ‰‹é †</title> + + <synopsis>sp=sparse(X) + + sp=sparse(ij,v [,mn]) + + </synopsis> + + </refsynopsisdiv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>X</term> + + <listitem> + + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®é€šå¸¸ã®(ã¾ãŸã¯ç–Ž)行列</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>ij</term> + + <listitem> + + <para>2列ã®æ•´æ•°è¡Œåˆ— (éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹)</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>v</term> + + <listitem> + + <para>ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>mn</term> + + <listitem> + + <para>2ã¤ã®ã‚¨ãƒ³ãƒˆãƒª(è¡Œã®æ¬¡å…ƒ, 列ã®æ¬¡å…ƒc)を有ã™ã‚‹æ•´æ•°ãƒ™ã‚¯ãƒˆãƒ«</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>sp</term> + + <listitem> + + <para>疎行列</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <para> + + <literal>sparse</literal>ã¯ç–Žè¡Œåˆ—を作æˆã™ã‚‹ãŸã‚ã«ä½¿ç”¨ã•ã‚Œã¾ã™. + + ゼãƒã§ãªã„エントリã®ã¿ãŒä¿å˜ã•ã‚Œã¾ã™. + + </para> + + <para> + + <literal>sp = sparse(X)</literal> ã¯, + + 0è¦ç´ を除外ã™ã‚‹ã“ã¨ã«ã‚ˆã‚Š,通常ã®è¡Œåˆ—を疎行列ã«å¤‰æ›ã—ã¾ã™. + + (<literal>X</literal>ãŒæ—¢ã«ç–Žè¡Œåˆ—ã®å ´åˆ, + + <literal>sp</literal>ã¯<literal>X</literal>ã¨ãªã‚Šã¾ã™). + + </para> + + <para> + + <literal>sp=sparse(ij,v [,mn])</literal>ã¯, + + <literal>sp(ij(k,1),ij(k,2))=v(k)</literal>ã¨ãªã‚‹ + + <literal>mn(1)</literal>è¡Œ<literal>mn(2)</literal>列ã®ç–Žè¡Œåˆ— + + を作æˆã—ã¾ã™. + + <literal>ij</literal> ãŠã‚ˆã³ <literal>v</literal>ã¯åˆ—ã®æ¬¡å…ƒãŒ + + åŒã˜ã§ã‚ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™. + + オプションã®<literal>mn</literal>パラメータãŒæŒ‡å®šã•ã‚Œãªã„å ´åˆ, + + 行列<literal>sp</literal>ã®æ¬¡å…ƒã¯,ãã‚Œãžã‚Œ + + <literal>ij(:,1)</literal> ãŠã‚ˆã³ <literal>ij(:,2)</literal>ã® + + 最大値ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + 疎行列ã«é–¢ã™ã‚‹æ“作(çµåˆ,åŠ ç®—,ç‰,)ã¯é€šå¸¸ã®è¡Œåˆ—ã¨åŒã˜æ§‹æ–‡ã«ã‚ˆã‚Š + + è¡Œãªã„ã¾ã™. + + </para> + + <para> + + 基本的ãªé–¢æ•°(<literal>abs,maxi,sum,diag,...</literal>)ã¯ç–Žè¡Œåˆ—ã§ã‚‚ + + 利用å¯èƒ½ã§ã™. + + </para> + + <para> + + (通常ã®è¡Œåˆ—ã¨ç–Žè¡Œåˆ—ã®)混用もå¯èƒ½ã§ã™. + + çµæžœã¯å‡¦ç†ã«å¿œã˜ã¦é€šå¸¸ã¾ãŸã¯ç–Žè¡Œåˆ—ã¨ãªã‚Šã¾ã™. + + </para> + + <para> + + æ³¨æ„ : + + åŒã˜å¤§ãã•ã®é€šå¸¸ã®è¡Œåˆ—ã‚’å«ã‚€ä»»æ„ã®æ¼”ç®—ã¯, + + 引数(例: <literal>sp=sparse(d)</literal>), + + ã¾ãŸã¯,çµæžœ(例 <literal>d= sp + 1.</literal>) ã®ã©ã¡ã‚‰ + + ã«ã¤ã„ã¦ã‚‚利便性ã®ãŸã‚ã«æä¾›ã•ã‚Œã¦ã„ã¾ã™ãŒ,当然é¿ã‘ã‚‹ã¹ãã§ã™. + + æ›´ã«,è¦ç´ (<literal>sp(r,c)</literal>)ã¸ã®ãƒ©ãƒ³ãƒ€ãƒ アクセス, + + 特ã«æŒ¿å…¥,ã¯åŠ¹çŽ‡çš„ã§ã¯ã‚ã‚Šã¾ã›ã‚“. + + ã“ã®ãŸã‚,性能é¢ã®åˆ¶ç´„ãŒã‚るアクセスã§ã¯, + + èªè¾¼ã¿ã‚¢ã‚¯ã‚»ã‚¹ã¯<link linkend="spget">spget</link>, + + 書込ã¿ã‚¢ã‚¯ã‚»ã‚¹ã¯<literal>sp=sparse(ij, v, mn)</literal>ã«ã‚ˆã‚‹ + + ãƒãƒƒãƒå‡¦ç†ã«ã‚ˆã‚Šè¡Œã†å¿…è¦ãŒã‚ã‚Šã¾ã™. + + </para> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]) +size(sp) +x=rand(2,2);abs(x)-full(abs(sparse(x))) +// sparse constructor taking a single dense matrix +// removes the zeros. +dense=[0., 1., 0., 0., 0., +1., 0., 2., 0., 0. +0., 0., 0., 0., 0. +0., 0., 0., 0., -0.5]; +sp=sparse(dense) +// complex matrices are also supported +sp=sparse(dense*(1+2*%i)) +// for boolean matrices, the boolean sparse matrix +// only stores true values (and removes false values). +dense=[%F, %F, %T, %F, %F +%T, %F, %F, %F, %F +%F, %F, %F, %F, %F +%F, %F, %F, %F, %T]; +sp=sparse(dense) + + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="full">full</link> + + </member> + + <member> + + <link linkend="spget">spget</link> + + </member> + + <member> + + <link linkend="sprand">sprand</link> + + </member> + + <member> + + <link linkend="speye">speye</link> + + </member> + + <member> + + <link linkend="lufact">lufact</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/sparseconvert/spcompack.xml b/modules/sparse/help/ja_JP/sparseconvert/spcompack.xml new file mode 100755 index 000000000..12a02f148 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/spcompack.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) XXXX-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="spcompack"> + + <refnamediv> + + <refname>spcompack</refname> + + <refpurpose>圧縮隣接表ç¾ã«å¤‰æ›ã™ã‚‹</refpurpose> + + </refnamediv> + + <refsection> + + <title>引数</title> + + <variablelist> + + <varlistentry> + + <term>xadj</term> + + <listitem> + + <para>é•·ã• (n+1)ã®æ•´æ•°ãƒ™ã‚¯ãƒˆãƒ«.</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>xlindx</term> + + <listitem> + + <para>é•·ã• n+1ã®æ•´æ•°ãƒ™ã‚¯ãƒˆãƒ«(ãƒã‚¤ãƒ³ã‚¿).</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>lindx</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + <varlistentry> + + <term>adjncy</term> + + <listitem> + + <para>整数ベクトル</para> + + </listitem> + + </varlistentry> + + </variablelist> + + </refsection> + + <refsection> + + <title>説明</title> + + <programlisting role=""><![CDATA[ +ユーティリティ関数spcompakã¯åœ§ç¸®éš£æŽ¥å½¢å¼ã‚’ +標準隣接形å¼ã«å¤‰æ›ã™ã‚‹éš›ã«ä½¿ç”¨ã•ã‚Œã¾ã™. + ]]></programlisting> + + </refsection> + + <refsection> + + <title>例</title> + + <programlisting role="example"><![CDATA[ +// A is the sparse matrix: +A=[1,0,0,0,0,0,0; + 0,1,0,0,0,0,0; + 0,0,1,0,0,0,0; + 0,0,1,1,0,0,0; + 0,0,1,1,1,0,0; + 0,0,1,1,0,1,0; + 0,0,1,1,0,1,1]; +A=sparse(A); +//ã“ã®è¡Œåˆ—ã®å ´åˆ,標準隣接形å¼ã¯ä»¥ä¸‹ã®ã‚ˆã†ã«å®šç¾©ã•ã‚Œã¾ã™: +xadj=[1,2,3,8,12,13,15,16]; +adjncy=[1, 2, 3,4,5,6,7, 4,5,6,7, 5, 6,7, 7]; +//(sp2adjå‚ç…§). +// ベクトル xadjã®å¢—分ã¯,å„列ã®éžã‚¼ãƒè¦ç´ ã®æ•°ã‚’指定ã—ã¾ã™. +// ã™ãªã‚ã¡,列1ã«ã¯ 2-1=1個ã®ã‚¨ãƒ³ãƒˆãƒªãŒå˜åœ¨ +// 列2ã«ã¯ 3-2=1個ã®ã‚¨ãƒ³ãƒˆãƒªãŒå˜åœ¨ +// 列3ã«ã¯ 8-3=5個ã®ã‚¨ãƒ³ãƒˆãƒªãŒå˜åœ¨ +// 列3ã«ã¯ 12-8=4個ã®ã‚¨ãƒ³ãƒˆãƒªãŒå˜åœ¨ +// ãªã© +// ã“れらã®ã‚¨ãƒ³ãƒˆãƒªã®è¡Œã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã¯éš£æŽ¥ãƒ™ã‚¯ãƒˆãƒ«ã«ã‚ˆã‚Šä¾‹ãˆã° +// 以下ã®ã‚ˆã†ã«æŒ‡å®šã§ã¾ã™ +// adjncy (3:7)=adjncy(xadj(3):xadj(4)-1)=[3,4,5,6,7] +// ã“ã‚Œã¯, 列3ã®5=xadj(4)-xadj(3)個ã®ã‚¨ãƒ³ãƒˆãƒªã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã‚’ +// 3,4,5,6,7 ã¨ã—ãŸã“ã¨ã‚’æ„味ã—ã¾ã™. +// 圧縮表ç¾ã§ã¯,隣接ã™ã‚‹é‡è¤‡ã™ã‚‹ã‚·ãƒ¼ã‚±ãƒ³ã‚¹ã¯æ¶ˆåŽ»ã•ã‚Œã¾ã™. +// ã“ã“ã§,隣接表ç¾ã§ã¯ä¸¦ã³ 4,5,6,7ãŠã‚ˆã³7ãŒæ¶ˆåŽ»ã•ã‚Œã¾ã™. +// æ¨™æº–æ§‹é€ (xadj,adjncy)ã¯åœ§ç¸®å½¢å¼(lindx,xlindx)ã‚’å—ã‘付ã‘ã¾ã™ +lindx=[1, 2, 3,4,5,6,7, 5, 6,7]; +xlindx=[1,2,3,8,9,11]; +//(Aã®åˆ— 4 ãŠã‚ˆã³ 7ã¯æ¶ˆåŽ»ã•ã‚Œã¾ã™). +//Aã¯(xadj,xlindx,lindx)ã«ã‚ˆã‚Šå†æ§‹ç¯‰ã§ãã¾ã™. +[xadj,adjncy,anz]= sp2adj(A); +adjncy-spcompack(xadj,xlindx,lindx) + ]]></programlisting> + + </refsection> + + <refsection role="see also"> + + <title>å‚ç…§</title> + + <simplelist type="inline"> + + <member> + + <link linkend="sp2adj">sp2adj</link> + + </member> + + <member> + + <link linkend="adj2sp">adj2sp</link> + + </member> + + <member> + + <link linkend="spget">spget</link> + + </member> + + </simplelist> + + </refsection> + +</refentry> + diff --git a/modules/sparse/help/ja_JP/sparseconvert/spget.xml b/modules/sparse/help/ja_JP/sparseconvert/spget.xml new file mode 100755 index 000000000..4d20506b5 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/spget.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) XXXX-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="spget"> + <refnamediv> + <refname>spget</refname> + <refpurpose>疎行列ã®ã‚¨ãƒ³ãƒˆãƒªã‚’å–å¾—</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼ã³å‡ºã—æ‰‹é †</title> + <synopsis>[ij,v,mn]=spget(sp)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>sp</term> + <listitem> + <para>実数ã¾ãŸã¯è¤‡ç´ æ•°ã®ç–Žè¡Œåˆ—</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ij</term> + <listitem> + <para>2列ã®æ•´æ•°è¡Œåˆ—t (éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>mn</term> + <listitem> + <para>2ã¤ã®ã‚¨ãƒ³ãƒˆãƒª(è¡Œã®æ¬¡å…ƒ, 列ã®æ¬¡å…ƒ)を有ã™ã‚‹æ•´æ•°ãƒ™ã‚¯ãƒˆãƒ«</para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>列ベクトル</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>spget</literal> ã¯ç–Žè¡Œåˆ—ã®å†…部形å¼ã‚’ + 標準的ãª<literal>ij, v</literal> å½¢å¼ã«å¤‰æ›ã™ã‚‹éš›ã«ä½¿ç”¨ã•ã‚Œã¾ã™. + </para> + <para> + <literal>sp</literal>ã®éžã‚¼ãƒã‚¨ãƒ³ãƒˆãƒªã¯, + <literal>ij</literal>ã®ã‚¤ãƒ³ãƒ‡ãƒƒã‚¯ã‚¹ã«ã‚ˆã‚Šè¡ŒãŠã‚ˆã³åˆ—ã® + ä½ç½®ãŒæ±ºå®šã•ã‚Œã¾ã™. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]) +[ij,v,mn]=spget(sp); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>å‚ç…§</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="sprand">sprand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/addchapter.sce b/modules/sparse/help/pt_BR/addchapter.sce new file mode 100755 index 000000000..848ab0920 --- /dev/null +++ b/modules/sparse/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("Matrizes Esparsas",SCI+"/modules/sparse/help/pt_BR",%T); + diff --git a/modules/sparse/help/pt_BR/chfact.xml b/modules/sparse/help/pt_BR/chfact.xml new file mode 100755 index 000000000..12f52dbca --- /dev/null +++ b/modules/sparse/help/pt_BR/chfact.xml @@ -0,0 +1,72 @@ +<?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="chfact" xml:lang="en"> + <refnamediv> + <refname>chfact</refname> + <refpurpose>fatoração esparsa de Cholesky</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>spcho=chfact(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title> Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>uma matriz simétrica, positiva e esparsa</para> + </listitem> + </varlistentry> + <varlistentry> + <term>spcho</term> + <listitem> + <para>lista contendo os fatores de Cholesky em forma + codificada + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>spcho=chfact(A)</literal> computa os fatores esparsos de + Cholesky da matriz esparsa <literal>A</literal>, assumida simétrica e + positiva definida. A função é baseada nos programas Ng-Peyton (ORNL). Ver + os programas FORTRAN para uma completa descrição das variáveis em + <literal>spcho</literal>. Esta função deve ser usada com a função + <literal>chsolve</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="chsolve">chsolve</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="spchol">spchol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/chsolve.xml b/modules/sparse/help/pt_BR/chsolve.xml new file mode 100755 index 000000000..a72657022 --- /dev/null +++ b/modules/sparse/help/pt_BR/chsolve.xml @@ -0,0 +1,82 @@ +<?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="chsolve" xml:lang="en"> + <refnamediv> + <refname>chsolve</refname> + <refpurpose>solucionador esparso de Cholesky</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>sol=chsolve(spcho,rhs)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>spcho</term> + <listitem> + <para>lista contendo os fatores de Cholesky na forma codificada + retornados por chfact + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rhs, sol</term> + <listitem> + <para>vetores colunas cheios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>sol=chsolve(spcho,rhs)</literal> computa a solução de + <literal>rhs=A*sol</literal>, com <literal>A</literal> uma matriz + simétrica e positiva definida. Esta função é baseada nos programas + Ng-Peyton (ORNL). Veja os programas FORTRAN para uma descrição completa + das variáveis em <literal>spcho</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=sprand(20,20,0.1); +A=A*A'+eye(); +spcho=chfact(A); +sol=(1:20)';rhs=A*sol; +spcho=chfact(A); +chsolve(spcho,rhs) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="chfact">chfact</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="spchol">spchol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/decomposition/CHAPTER b/modules/sparse/help/pt_BR/decomposition/CHAPTER new file mode 100755 index 000000000..ccebc80d8 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Sparse Decompositions diff --git a/modules/sparse/help/pt_BR/decomposition/ludel.xml b/modules/sparse/help/pt_BR/decomposition/ludel.xml new file mode 100755 index 000000000..427bc9743 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/ludel.xml @@ -0,0 +1,60 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="ludel" xml:lang="en"> + <refnamediv> + <refname>ludel</refname> + <refpurpose>função utilitária usada com lufact</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>ludel(hand)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>hand</term> + <listitem> + <para>manipulador para fatores lu esparsos (saÃda de lufact)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + Esta função é usada de modo conjunto com <literal>lufact</literal>. + Ela limpa o espaço de memória interna usado para guardar o resultado de + <literal>lufact</literal>. + </para> + <para>A seqüência de comandos + <literal>[p,r]=lufact(A);x=lusolve(p,b);ludel(p);</literal> resolve o + sistema linear esparso <literal>A*x = b</literal> e limpa + <literal>p</literal>. + </para> + </refsection> + <refsection> + <title>Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/decomposition/lufact.xml b/modules/sparse/help/pt_BR/decomposition/lufact.xml new file mode 100755 index 000000000..b90c5d284 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/lufact.xml @@ -0,0 +1,136 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="lufact" xml:lang="en"> + <refnamediv> + <refname>lufact</refname> + <refpurpose>fatoração LU esparsa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[hand,rk]=lufact(A,prec)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada esparsa </para> + </listitem> + </varlistentry> + <varlistentry> + <term>hand</term> + <listitem> + <para>manipulador para fatores LU esparsos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para>inteiro (posto de A) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>prec</term> + <listitem> + <para> + vetor de tamanho 2 <literal>prec=[eps,reps]</literal> + fornecendo os limiares absoluto e relativo. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[hand,rk]=lufact(A)</literal> realiza a fatoração LU da + matriz esparsa <literal>A</literal>. <literal>hand</literal> (sem + exibição) é usado por <literal>lusolve</literal> (para resolver sistemas + lineares) e <literal>luget</literal> (para retirar os fatores). + <literal>hand</literal> deve ser limpo pelo comando: + <literal>ludel(hand)</literal>; + </para> + <para>A matriz A não precisa ser de posto cheio, mas deve ser quadrada + (desde que A é assumida como sendo esparsa, pode-se adicionar 0, se + necessário, para quadrá-la). + </para> + <variablelist> + <varlistentry> + <term>eps :</term> + <listitem> + <para>a magnitude absoluta que um elemento deve ter para ser + considerado um candidato a pivô, exceto como último recurso. Este + número deve ser posto de modo a ser significantemente menor que o + menor elemento da diagonal que se espera estar localizado na matriz. + O valor padrão é <literal>%eps</literal>. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>reps :</term> + <listitem> + <para>Este número determina qual será o limiar relativo do pivô. + Deve estar entre 0 e 1. Se for 1, então o método de pivoteamento + torna-se pivotação completa, que é muito lento e tende a completar a + matriz. Se o número acertado é próximo de 0, o método de + pivoteamento torna-se estritamente de Markowitz, sem limiar. O + limiar de pivô é usado para eliminar candidatos a pivô que poderiam + causar crescimento excessivo de elementos se fossem usados. + Crescimento de elementos é a causa dos erros de arredondamento. + Crescimento de elementos ocorre mesmo em matrizes bem condicionadas. + Definir o reps como um número grande reduzirá o crescimento de + elementos e os erros de arredondamento, mas colocá-lo muito grande + aumentará muito o tempo de execução e resultará num grande número de + preenchimentos. Se isto ocorrer, a precisão pode ficar prejudicada + por causa do grande número de operações requeridas na matriz devido + ao grande número de preenchimentos. 0.001 parece um bom valor, e é o + valor default. O default é escolhido fornecendo-se um valor maior + que 1 ou menor que ou igual a 0. Este valor deve ser aumentado e a + matriz resolvida se o crescimento for excessivo. Mudar o limiar do + pivô não melhora o desempenho em matrizes onde o crescimento é + baixo, como é geralmente o caso de matrizes mal-condicionadas. reps + foi escolhido para uso com matrizes quase diagonalmente dominantes + como uma matriz de admissão de nó e nó modificado. Para estas + matrizes, geralmente o melhor é usar pivotação diagonal. Para + matrizes sem uma diagonal forte, geralmente é melhor usar um limiar + maior, como 0.01 ou 0.1. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +a=rand(5,5);b=rand(5,1);A=sparse(a); +[h,rk]=lufact(A); +x=lusolve(h,b);a*x-b +ludel(h) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/decomposition/luget.xml b/modules/sparse/help/pt_BR/decomposition/luget.xml new file mode 100755 index 000000000..2025bac26 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/luget.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) XXXX-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="luget" xml:lang="en"> + <refnamediv> + <refname>luget</refname> + <refpurpose>extração dos fatores LU esparsos</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[P,L,U,Q]=luget(hand)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>hand</term> + <listitem> + <para> + manipulador, saÃda de <literal>lufact</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P</term> + <listitem> + <para>matriz de permutação esparsa</para> + </listitem> + </varlistentry> + <varlistentry> + <term>L</term> + <listitem> + <para> + matriz esparsa, triangular infeiror se <literal>hand</literal> + é obtida de uma matriz não-singular + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz quadrada triangular superior esparsa não-snigular + preenchida com 1 ao longo da diagonal principal + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Q</term> + <listitem> + <para>matriz de permutação esparsa</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[P,L,U,Q]=luget(hand)</literal> com <literal>hand</literal> + obtida pelo comando <literal>[hand,rk]=lufact(A)</literal> com + <literal>A</literal> uma matriz esparsa retorna quatro matrizes esparsas + tais que <literal>P*L*U*Q=A</literal>. + </para> + <para>A matriz A não precisa ser de posto cheio, mas deve ser quadrada + (desde que A é assumida esparsa, pode-se adicionar 0, se necessário, para + quadrar A). + </para> + <para> + Se <literal>A</literal> é singular, a matriz <literal>L</literal> é + de colunas comprimidas (com <literal>rk</literal> colunas independentes + não-nulas): a matriz não-singular esparsa <literal>Q'*inv(U)</literal> + comprime em colunas <literal>A</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +a=rand(5,2)*rand(2,5);A=sparse(a); +[hand,rk]=lufact(A);[P,L,U,Q]=luget(hand); +full(L), P*L*U*Q-A +clean(P*L*U*Q-A) +ludel(hand) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/decomposition/lusolve.xml b/modules/sparse/help/pt_BR/decomposition/lusolve.xml new file mode 100755 index 000000000..3011c9513 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/lusolve.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) XXXX-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="lusolve" xml:lang="en"> + <refnamediv> + <refname>lusolve</refname> + <refpurpose>solucionador de sistemas lineares esparsos</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>x=lusolve(hand,b) + x=lusolve(A,b) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>b</term> + <listitem> + <para>matriz de reais completa </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada de reais esparsa e invertÃvel </para> + </listitem> + </varlistentry> + <varlistentry> + <term>hand</term> + <listitem> + <para>manipulador para fatores de lu esparsos previamente computados + (saÃda de lufact) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>matriz de reais completa </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>x=lusolve(hand,b)</literal> resolve o sistema linear + esparso <literal>A*x = b</literal>. + </para> + <para> + <literal>[hand,rk]=lufact(A)</literal> é a saÃda de lufact. + </para> + <para> + <literal>x=lusolve(A,b)</literal> resolve o sistema linear esparso + <literal>A*x = b</literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +non_zeros=[1,2,3,4];rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +[h,rk]=lufact(sp);x=lusolve(h,[1;1;1;1]);ludel(h) +rk,sp*x + +non_zeros=[1,2,3,4];rows_cols=[1,1;2,2;3,3;4,4]; +sp=sparse(rows_cols,non_zeros); +x=lusolve(sp,-ones(4,1)); +sp*x + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + <member> + <link linkend="slash">slash</link> + </member> + <member> + <link linkend="backslash">backslash</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/decomposition/spchol.xml b/modules/sparse/help/pt_BR/decomposition/spchol.xml new file mode 100755 index 000000000..7388acd2e --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/spchol.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) XXXX-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="spchol" xml:lang="en"> + <refnamediv> + <refname>spchol</refname> + <refpurpose>fatoração esparsa de Cholesky</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[R,P] = spchol(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz simétrica, esparsa e positiva definida de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P</term> + <listitem> + <para>matriz de permutação </para> + </listitem> + </varlistentry> + <varlistentry> + <term>R</term> + <listitem> + <para>fator de Cholesky</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>[R,P] = spchol(X)</literal> produz uma matriz triângular + inferior <literal>R</literal> tal que <literal>P*R*R'*P' = + X + </literal> + . + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +X=[ +3., 0., 0., 2., 0., 0., 2., 0., 2., 0., 0. ; +0., 5., 4., 0., 0., 0., 0., 0., 0., 0., 0. ; +0., 4., 5., 0., 0., 0., 0., 0., 0., 0., 0. ; +2., 0., 0., 3., 0., 0., 2., 0., 2., 0., 0. ; +0., 0., 0., 0. , 5., 0., 0., 0., 0., 0., 4. ; +0., 0., 0., 0., 0., 4., 0., 3., 0., 3., 0. ; +2., 0., 0., 2., 0., 0., 3., 0., 2., 0., 0. ; +0., 0., 0., 0., 0., 3., 0., 4., 0., 3., 0. ; +2., 0., 0., 2., 0., 0., 2., 0., 3., 0., 0. ; +0., 0., 0., 0., 0., 3., 0., 3., 0., 4., 0. ; +0., 0., 0., 0., 4., 0., 0., 0., 0., 0., 5.]; +X=sparse(X);[R,P] = spchol(X); +max(P*R*R'*P'-X) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="lusolve">lusolve</link> + </member> + <member> + <link linkend="luget">luget</link> + </member> + <member> + <link linkend="chol">chol</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/matrixmanip/CHAPTER b/modules/sparse/help/pt_BR/matrixmanip/CHAPTER new file mode 100755 index 000000000..a797a77e1 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Manipulation diff --git a/modules/sparse/help/pt_BR/matrixmanip/nnz.xml b/modules/sparse/help/pt_BR/matrixmanip/nnz.xml new file mode 100755 index 000000000..eb9971745 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/nnz.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) XXXX-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="nnz" xml:lang="en"> + <refnamediv> + <refname>nnz</refname> + <refpurpose>número de entradas não-nulas de uma matriz</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>n=nnz(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz de reais ou complexos esparsa (ou cheia) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>n</term> + <listitem> + <para>inteiro, número de elementos não-nulos de X. </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>nnz</literal> conta o número de entradas não-nulas de uma + matriz esparsa ou cheia. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]); +nnz(sp) +a=[1 0 0 0 2]; +nnz(a) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/matrixmanip/speye.xml b/modules/sparse/help/pt_BR/matrixmanip/speye.xml new file mode 100755 index 000000000..fe21e17d6 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/speye.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: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="speye" xml:lang="en"> + <refnamediv> + <refname>speye</refname> + <refpurpose>matriz identidade esparsa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>Isp=speye(nrows,ncols) + Isp=speye(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>inteiro (número de linhas) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>inteiro (número de colunas) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz esparsa </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matriz identidade esparsa </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>Isp=speye(nrows,ncols)</literal> retorna uma matriz + identidade esparsa <literal>Isp</literal> com <literal>nrows</literal> + linhas e , <literal>ncols</literal> colunas (matrizes identidades + não-quadradas têm um número máximo de algarismos 1 na diagonal + principal). + </para> + <para> + <literal>Isp=speye(A)</literal> retorna uma matriz identidade + esparsa com as mesmas dimensões de <literal>A</literal>. + Se<literal>[m,n]=size(A)</literal>, <literal>speye(m,n)</literal> e + <literal>speye(A)</literal> são equivalentes. Em particular + <literal>speye(3)</literal> não é equivalente a + <literal>speye(3,3)</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +eye(3,3)-full(speye(3,3)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="spzeros">spzeros</link> + </member> + <member> + <link linkend="spones">spones</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/matrixmanip/spones.xml b/modules/sparse/help/pt_BR/matrixmanip/spones.xml new file mode 100755 index 000000000..f9f099ae6 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/spones.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: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="spones" xml:lang="en"> + <refnamediv> + <refname>spones</refname> + <refpurpose>matriz esparsa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>sp=spones(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz esparsa </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matriz esparsa </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>sp=spones(A)</literal> gera uma matriz com a mesma + estrutura de espargimento de <literal>A</literal>, mas com 1 em posições + não-nulas; + </para> + </refsection> + <refsection> + <title>Exemplos </title> + <programlisting role="example"><![CDATA[ +A=sprand(10,12,0.1); +sp=spones(A) +B = A~=0 +bool2s(B) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="spzeros">spzeros</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/matrixmanip/sprand.xml b/modules/sparse/help/pt_BR/matrixmanip/sprand.xml new file mode 100755 index 000000000..00d9e12bd --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/sprand.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: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="sprand" xml:lang="en"> + <refnamediv> + <refname>sprand</refname> + <refpurpose>matriz esparsa randômica</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>sp=sprand(nrows,ncols,fill [,typ])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>inteiro (número de linhas) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>inteiro (número de colunas)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>fill</term> + <listitem> + <para>coeficiente de preenchimento (densidade) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>typ</term> + <listitem> + <para> + string (<literal>'uniform'</literal> (padrão) ou + <literal>'normal'</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matriz esparsa</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>sp=sprand(nrows,ncols,fill)</literal> retorna uma matriz + esparsa <literal>sp</literal> com <literal>nrows</literal> linhas e + <literal>ncols</literal> colunas e aproximadamente + <literal>fill*nrows*ncols</literal> entradas não-nulas. + </para> + <para> + Se <literal>typ='uniform'</literal> valores uniformemente + distribuídos em [0,1] são gerados. Se <literal>typ='normal'</literal> + valores normalmente distribuídos são gerados (média=0 e desvio + padrão=1). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +W=sprand(100,1000,0.001); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="rand">rand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/matrixmanip/spzeros.xml b/modules/sparse/help/pt_BR/matrixmanip/spzeros.xml new file mode 100755 index 000000000..ade8f85a8 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/spzeros.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: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="spzeros" xml:lang="en"> + <refnamediv> + <refname>spzeros</refname> + <refpurpose>matriz nula esparsa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>sp=spzeros(nrows,ncols) + sp=spzeros(A) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>nrows</term> + <listitem> + <para>inteiro (número de linhas) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ncols</term> + <listitem> + <para>inteiro (número de colunas) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz esparsa </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matriz nula esparsa </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>sp=spzeros(nrows,ncols)</literal> retorna uma matriz nula + esparsa <literal>sp</literal> com <literal>nrows</literal> linhas e, + <literal>ncols</literal> colunas. (Equivalente a + <literal>sparse([],[],[nrow,ncols])</literal>) + </para> + <para> + <literal>sp=spzeros(A)</literal> retorna uma matriz nula esparsa com + as mesmas dimensões que <literal>A</literal>. Se + <literal>[m,n]=size(A)</literal>, <literal>spzeros(m,n)</literal> e + <literal>spzeros(A)</literal> são equivalentes. Em particular + <literal>spzeros(3)</literal> não é equivalente a + <literal>spzeros(3,3)</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +m=spzeros(2,2) +a=rand(10,12); +m=spzeros(a) +sum(spzeros(1000,1000)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="eye">eye</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="spones">spones</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/sparseconvert/CHAPTER b/modules/sparse/help/pt_BR/sparseconvert/CHAPTER new file mode 100755 index 000000000..42d5e0bf2 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Conversion diff --git a/modules/sparse/help/pt_BR/sparseconvert/adj2sp.xml b/modules/sparse/help/pt_BR/sparseconvert/adj2sp.xml new file mode 100755 index 000000000..b792725d7 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/adj2sp.xml @@ -0,0 +1,101 @@ +<?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="adj2sp" xml:lang="en"> + <refnamediv> + <refname>adj2sp</refname> + <refpurpose>converte forma de adjacência para matriz esparsa </refpurpose> + </refnamediv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>xadj</term> + <listitem> + <para>vetor de inteiros de comprimento (n+1). </para> + </listitem> + </varlistentry> + <varlistentry> + <term>adjncy</term> + <listitem> + <para>vetor de inteiros de comprimento nz contendo os índices de + linha para os elementos correspondentes em anz + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>anz</term> + <listitem> + <para>vetor coluna de comprimento nz contendo os elementos não-nulos + de A + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>mn</term> + <listitem> + <para> + vetor linha com duas entradas, <literal>mn=size(A)</literal> + (opcional). + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz quadrada esparsa de reais ou complexos (nz entradas + não-nulas) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <programlisting role=""><![CDATA[ +adj2sp converte uma representação em forma de adjacência de uma matriz +em sua representação padrão do Scilab (função utilitária). +xadj, adjncy, anz = representação de adjacência de A i.e: + ]]></programlisting> + <para> + <literal>xadj(j+1)-xadj(j)</literal> = número de entradas não-nulas + na linha j. <literal>adjncy</literal> = índice de coluna das entradas + não-nulas nas linha 1, linha 2..., linha n.<literal> anz</literal> = + valores das entradas não-nulas nas linha 1, linha 2,..., linha n. + <literal>xadj</literal> é um vetor (coluna) de tamanho n+1 e + <literal>adjncy</literal> é um vetor (coluna) de inteiros de tamanho + <literal>nz=nnz(A)</literal>. <literal>anz</literal> é um vetor de reais + de tamanho <literal>nz=nnz(A)</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A = sprand(100,50,.05); +[xadj,adjncy,anz]= sp2adj(A); +[n,m]=size(A); +p = adj2sp(xadj,adjncy,anz,[n,m]); +A-p, + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sp2adj">sp2adj</link> + </member> + <member> + <link linkend="spcompack">spcompack</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/sparseconvert/full.xml b/modules/sparse/help/pt_BR/sparseconvert/full.xml new file mode 100755 index 000000000..b362e23aa --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/full.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) XXXX-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="full" xml:lang="en"> + <refnamediv> + <refname>full</refname> + <refpurpose>conversão de matriz esparsa para cheia (completa)</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>X=full(sp)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>sp</term> + <listitem> + <para>matriz esparsa (ou cheia) de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz cheia (completa)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>X=full(sp)</literal> converte a matriz esparsa + <literal>sp</literal> em sua representação cheia (completa). (Se + <literal>sp</literal> já é cheia, então <literal>X</literal> é igual a + <literal>sp</literal>). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;5,4;3,1],[1,2,3]); +A=full(sp) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="sprand">sprand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/sparseconvert/mtlb_sparse.xml b/modules/sparse/help/pt_BR/sparseconvert/mtlb_sparse.xml new file mode 100755 index 000000000..7d6072515 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/mtlb_sparse.xml @@ -0,0 +1,75 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="mtlb_sparse" xml:lang="en"> + <refnamediv> + <refname>mtlb_sparse</refname> + <refpurpose>converte matriz esparsa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>Y=mtlb_sparse(X)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz esparsa </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>matriz esparsa em formato Matlab </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>Y=mtlb_sparse(X)</literal> é usado para converter + <literal>X</literal>, uma matriz esparsa Scilab, para formato Matlab. + <literal>Y</literal> é uma variável de tipo 7, i.e., + <literal>type(Y)</literal> é igual a 7. Esta função deve ser usada em + mexfiles (um mexfile Matlab contendo matrizes esparsas pode ser usado + apenas se as matrizes esparsas do Scilab forem convertidas para este + formato). As funções <literal>full</literal> e <literal>spget</literal> + funcionam com este formato. + </para> + <para>Outras operações e funções usando este formato podem ficar + sobrecarregadas com funções do Scilab usando o prefixo "%msp". Por + exemplo, a função <literal>%msp_p(x)</literal> (ver diretório + SCI/modules/overloading/macros) é usada para exibir tais objetos "tipo 7". + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +X=sparse(rand(2,2)); Y=mtlb_sparse(X); +Y, full(Y), [ij,v,mn]=spget(Y) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/sparseconvert/sp2adj.xml b/modules/sparse/help/pt_BR/sparseconvert/sp2adj.xml new file mode 100755 index 000000000..f4b6d1009 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/sp2adj.xml @@ -0,0 +1,100 @@ +<?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="sp2adj" xml:lang="en"> + <refnamediv> + <refname>sp2adj</refname> + <refpurpose>converte uma matriz esparsa para forma de + adjacência + </refpurpose> + </refnamediv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz esparsa de reais ou complexos (nz entradas não-nulas) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>xadj</term> + <listitem> + <para>vetor de inteiros de comprimento (n+1). </para> + </listitem> + </varlistentry> + <varlistentry> + <term>adjncy</term> + <listitem> + <para>vetor de inteiros de comprimento nz contendo os índices de + linha para os elementos correspondentes em anz + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>anz</term> + <listitem> + <para>vetor coluna de comprimento nz contendo os elementos não-nulos + de A + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <programlisting role=""><![CDATA[ +sp2adj converte uma matriz esparsa para usa forma de adjacência +(função utilitária). +A = matriz esparsa n x m . xadj, adjncy, anz = representação +em adjacência de A, i.e.: + ]]></programlisting> + <para> + <literal>xadj(j+1)-xadj(j)</literal> = número de entradas não-nulas + na linha j. <literal>adjncy</literal> = índice de coluna das entradas + não-nulas nas linha 1, linha 2,..., linha n. <literal>anz</literal> = + valores de entradas não-nulas nas linha 1, linha 2,..., linha n. + <literal>xadj</literal> é um vetor (coluna) de tamanho n+1 e + <literal>adjncy</literal> é um vetor (coluna) de inteiros de tamanho + <literal>nz=nnz(A)</literal>. <literal>anz</literal> é um vetor de reais + de tamanho <literal>nz=nnz(A)</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos </title> + <programlisting role="example"><![CDATA[ +A = sprand(100,50,.05); +[xadj,adjncy,anz]= sp2adj(A); +[n,m]=size(A); +p = adj2sp(xadj,adjncy,anz,[n,m]); +A-p, + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="adj2sp">adj2sp</link> + </member> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="spcompack">spcompack</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/sparseconvert/sparse.xml b/modules/sparse/help/pt_BR/sparseconvert/sparse.xml new file mode 100755 index 000000000..7950c5676 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/sparse.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) XXXX-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="sparse" xml:lang="en"> + <refnamediv> + <refname>sparse</refname> + <refpurpose>definição de matriz esparsa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>sp=sparse(X) + sp=sparse(ij,v [,mn]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>X</term> + <listitem> + <para>matriz completa (ou esparsa) de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ij</term> + <listitem> + <para>matriz de inteiros de duas colunas (Ãndices das entradas não + nulas) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>vetor</para> + </listitem> + </varlistentry> + <varlistentry> + <term>mn</term> + <listitem> + <para>vetor de inteiros com duas entradas (dimensão de linha, + dimensão de coluna) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sp</term> + <listitem> + <para>matriz esparsa </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>sparse</literal> é usado para construir uma matriz esparsa. + Apenas entradas não-nulas são armazenadas. + </para> + <para> + <literal>sp = sparse(X)</literal> converte uma matriz completa para + sua forma esparsa retirando qualquer elemento nulo. (Se + <literal>X</literal> já é esparsa <literal>sp</literal> é + <literal>X</literal>). + </para> + <para> + <literal>sp=sparse(ij,v [,mn])</literal> constrói uma matriz esparsa + <literal>mn(1)</literal>-por-<literal>mn(2)</literal> sparse matrix com + <literal>sp(ij(k,1),ij(k,2))=v(k)</literal>. <literal>ij</literal> e + <literal>v</literal> devem ter a mesma dimensão de coluna. Se o parâmetro + opcional <literal>mn</literal> não for dado, as dimensões da matriz + <literal>sp</literal> são os valores máximos de <literal>ij(:,1)</literal> + e <literal>ij(:,2)</literal> respectivamente. + </para> + <para>Operações (concatenação, adição, etc,) com matrizes esparsas são + feitas usando a mesma sintaxe para matrizes completas. + </para> + <para>Funções elementares também estão disponÃveis + (<literal>abs,maxi,sum,diag,...</literal>) para matrizes esparsas. + </para> + <para>Operações mistas (completas-esparsas) são permitidas. Os resultados + são completos ou esparsos dependendo das operações. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]) +size(sp) +x=rand(2,2);abs(x)-full(abs(sparse(x))) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="full">full</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + <member> + <link linkend="sprand">sprand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/sparseconvert/spcompack.xml b/modules/sparse/help/pt_BR/sparseconvert/spcompack.xml new file mode 100755 index 000000000..a9de7f93d --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/spcompack.xml @@ -0,0 +1,109 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) XXXX-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="spcompack" xml:lang="en"> + <refnamediv> + <refname>spcompack</refname> + <refpurpose>converte uma representação de adjacência comprimida em + representação de adjacência padrão + </refpurpose> + </refnamediv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>xadj</term> + <listitem> + <para>vetor de inteiros de comprimento (n+1). </para> + </listitem> + </varlistentry> + <varlistentry> + <term>xlindx</term> + <listitem> + <para>vetor de inteiros de comprimento n+1 (ponteiros). </para> + </listitem> + </varlistentry> + <varlistentry> + <term>lindx</term> + <listitem> + <para>vetor de inteiros </para> + </listitem> + </varlistentry> + <varlistentry> + <term>adjncy</term> + <listitem> + <para>vetor de inteiros </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <programlisting role=""><![CDATA[ +A função utilitária spcompak é usada para converter uma representação de adjacência +comprimida em uma representação de adjacência padrão. + ]]></programlisting> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// A é a matriz esparsa: +A=[1,0,0,0,0,0,0; + 0,1,0,0,0,0,0; + 0,0,1,0,0,0,0; + 0,0,1,1,0,0,0; + 0,0,1,1,1,0,0; + 0,0,1,1,0,1,0; + 0,0,1,1,0,1,1]; +A=sparse(A); +//Para esta matriz a representação padrão de adjacência é dada por: +xadj=[1,2,3,8,12,13,15,16]; +adjncy=[1, 2, 3,4,5,6,7, 4,5,6,7, 5, 6,7, 7]; +//(ver sp2adj). +// Incrementos no vetor xadj dão o número de entradas não nulas em cada coluna +// i.e., há 2-1=1 entrada na coluna 1 +// há 3-2=1 entrada na coluna 2 +// há 8-3=5 entradas na coluna 3 +// 12-8=4 4 +//etc. +//O Ãndice de linha dessas entradas é dado pelo vetor adjncy +// por exemplo, +// adjncy (3:7)=adjncy(xadj(3):xadj(4)-1)=[3,4,5,6,7] +// diz que as 5=xadj(4)-xadj(3) entradas na coluna 3 têm Ãndices de linha +// 3,4,5,6,7. +//Na representação compacta, as seqüências repetidas em adjncy +//são eliminadas. +//Aqui em adjncy, as seqüências 4,5,6,7 e 7 são eliminadas. +//A estrutura padrão (xadj,adjncy) toma a forma comprimida (lindx,xlindx) +lindx=[1, 2, 3,4,5,6,7, 5, 6,7]; +xlindx=[1,2,3,8,9,11]; +//(colunas 4 e 7 de A são eliminadas). +//A pode ser reconstruÃda de (xadj,xlindx,lindx). +[xadj,adjncy,anz]= sp2adj(A); +adjncy-spcompack(xadj,xlindx,lindx) + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sp2adj">sp2adj</link> + </member> + <member> + <link linkend="adj2sp">adj2sp</link> + </member> + <member> + <link linkend="spget">spget</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/pt_BR/sparseconvert/spget.xml b/modules/sparse/help/pt_BR/sparseconvert/spget.xml new file mode 100755 index 000000000..725d52944 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/spget.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) XXXX-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="spget" xml:lang="en"> + <refnamediv> + <refname>spget</refname> + <refpurpose>recupera entradas de matriz esparsa</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[ij,v,mn]=spget(sp)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>sp</term> + <listitem> + <para>matriz esparsa de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ij</term> + <listitem> + <para>matriz de inteiros de duas colunas (Ãndices das entradas + não-nulas) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>mn</term> + <listitem> + <para>vetor de inteiros com duas entradas (dimensão de linha, + dimensão de coluna) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>vetor coluna </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>spget</literal> é usado para converter a representação + interna de matrizes esparsas na representação padrão <literal>ij, + v + </literal> + . + </para> + <para> + Entradas não-nulas de <literal>sp</literal> estão localizadas em + linhas e colunas com Ãndices em <literal>ij</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +sp=sparse([1,2;4,5;3,10],[1,2,3]) +[ij,v,mn]=spget(sp); + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="sparse">sparse</link> + </member> + <member> + <link linkend="sprand">sprand</link> + </member> + <member> + <link linkend="speye">speye</link> + </member> + <member> + <link linkend="lufact">lufact</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/sparse/help/ru_RU/addchapter.sce b/modules/sparse/help/ru_RU/addchapter.sce new file mode 100755 index 000000000..22a8a387a --- /dev/null +++ b/modules/sparse/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("Sparse Matrix",SCI+"/modules/sparse/help/ru_RU",%T); + |