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Diffstat (limited to 'modules/special_functions/help')
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diff --git a/modules/special_functions/help/en_US/addchapter.sce b/modules/special_functions/help/en_US/addchapter.sce new file mode 100755 index 000000000..2a73e65de --- /dev/null +++ b/modules/special_functions/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("Special Functions",SCI+"/modules/special_functions/help/en_US",%T); + diff --git a/modules/special_functions/help/en_US/amell.xml b/modules/special_functions/help/en_US/amell.xml new file mode 100755 index 000000000..ad77edbdb --- /dev/null +++ b/modules/special_functions/help/en_US/amell.xml @@ -0,0 +1,65 @@ +<?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="amell"> + <refnamediv> + <refname>amell</refname> + <refpurpose>Jacobi's am function</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[sn]=amell(u,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>u</term> + <listitem> + <para>real scalar or vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>scalar</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sn</term> + <listitem> + <para>real scalar or vector</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Computes Jacobi's elliptic function <literal>am(u,k)</literal> + where <literal>k</literal> is the parameter and <literal>u</literal> is the argument. If <literal>u</literal> + is a vector <literal>sn</literal> is the vector of the (element wise) computed values. + Used in function <literal>%sn</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/bessel.xml b/modules/special_functions/help/en_US/bessel.xml new file mode 100755 index 000000000..f90086fdc --- /dev/null +++ b/modules/special_functions/help/en_US/bessel.xml @@ -0,0 +1,346 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2012 - Scilab Enterprises - Adeline CARNIS + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="bessel" xml:lang="en"> + <refnamediv xml:id="besseli"> + <refname>besseli</refname> + <refpurpose>Modified Bessel functions of the first kind (I sub + alpha). + </refpurpose> + </refnamediv> + <refnamediv xml:id="besselj"> + <refname>besselj</refname> + <refpurpose>Bessel functions of the first kind (J sub alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="besselk"> + <refname>besselk</refname> + <refpurpose>Modified Bessel functions of the second kind (K sub + alpha). + </refpurpose> + </refnamediv> + <refnamediv xml:id="bessely"> + <refname>bessely</refname> + <refpurpose>Bessel functions of the second kind (Y sub + alpha). + </refpurpose> + </refnamediv> + <refnamediv xml:id="besselh"> + <refname>besselh</refname> + <refpurpose>Bessel functions of the third kind (aka Hankel + functions) + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = besseli(alpha,x [,ice]) + y = besselj(alpha,x [,ice]) + y = besselk(alpha,x [,ice]) + y = bessely(alpha,x [,ice]) + y = besselh(alpha,x) + y = besselh(alpha,K,x [,ice]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real or complex vector.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>alpha</term> + <listitem> + <para>real vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ice</term> + <listitem> + <para>integer flag, with default value 0</para> + </listitem> + </varlistentry> + <varlistentry> + <term>K</term> + <listitem> + <para>integer, with possible values 1 or 2, the Hankel function + type. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <itemizedlist> + <listitem> + <para> + <literal>besseli(alpha,x)</literal> computes modified Bessel + functions of the first kind (I sub alpha), for real order + <literal>alpha</literal> and argument <literal>x</literal>. + <literal>besseli(alpha,x,1)</literal> computes + <literal>besseli(alpha,x).*exp(-abs(real(x)))</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>besselj(alpha,x)</literal> computes Bessel functions of + the first kind (J sub alpha), for real order <literal>alpha</literal> + and argument <literal>x</literal>. + <literal>besselj(alpha,x,1)</literal> computes + <literal>besselj(alpha,x).*exp(-abs(imag(x)))</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>besselk(alpha,x)</literal> computes modified Bessel + functions of the second kind (K sub alpha), for real order + <literal>alpha</literal> and argument <literal>x</literal>. + <literal>besselk(alpha,x,1)</literal> computes + <literal>besselk(alpha,x).*exp(x)</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>bessely(alpha,x)</literal> computes Bessel functions of + the second kind (Y sub alpha), for real order <literal>alpha</literal> + and argument <literal>x</literal>. + <literal>bessely(alpha,x,1)</literal> computes + <literal>bessely(alpha,x).*exp(-abs(imag(x)))</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>besselh(alpha [,K] ,x)</literal> computes Bessel + functions of the third kind (Hankel function H1 or H2 depending on + <literal>K</literal>), for real order <literal>alpha</literal> and + argument <literal>x</literal>. If omitted <literal>K</literal> is + supposed to be equal to 1. <literal>besselh(alpha,1,x,1)</literal> + computes <literal>besselh(alpha,1,x).*exp(-%i*x)</literal> and + <literal>besselh(alpha,2,x,1)</literal> computes + <literal>besselh(alpha,2,x).*exp(%i*x)</literal> + </para> + </listitem> + </itemizedlist> + </refsection> + <refsection> + <title>Remarks</title> + <para> + If <literal>alpha</literal> and <literal>x</literal> are arrays of + the same size, the result <literal>y</literal> is also that size. If + either input is a scalar, it is expanded to the other input's size. If one + input is a row vector and the other is a column vector, the + result<literal>y</literal> is a two-dimensional table of function + values. + </para> + <para>Y_alpha and J_alpha Bessel functions are 2 independent solutions of + the Bessel 's differential equation : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>K_alpha and I_alpha modified Bessel functions are 2 independant + solutions of the modified Bessel 's differential equation : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation2.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>H^1_alpha and H^2_alpha, the Hankel functions of first and second + kind, are linear linear combinations of Bessel functions of the first and + second kinds: + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation3.mml"/> + </imageobject> + </mediaobject> + </informalequation> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// besselI functions +// ================== + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besseli(0:4,x), style=2:6) + legend('I'+string(0:4),2); + xtitle("Some modified Bessel functions of the first kind") + subplot(2,1,2) + plot2d(x,besseli(0:4,x,1), style=2:6) + legend('I'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the first kind") + ]]></programlisting> + + <scilab:image> + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besseli(0:4,x), style=2:6) + legend('I'+string(0:4),2); + xtitle("Some modified Bessel functions of the first kind") + subplot(2,1,2) + plot2d(x,besseli(0:4,x,1), style=2:6) + legend('I'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the first kind") + + </scilab:image> + + + <programlisting role="example"><![CDATA[ +// besselJ functions +// ================= + clf() + x = linspace(0,40,5000)'; + plot2d(x,besselj(0:4,x), style=2:6, leg="J0@J1@J2@J3@J4") + legend('I'+string(0:4),1); + xtitle("Some Bessel functions of the first kind") + ]]></programlisting> + + <scilab:image> + x = linspace(0,40,5000)'; + plot2d(x,besselj(0:4,x), style=2:6, leg="J0@J1@J2@J3@J4") + legend('I'+string(0:4),1); + xtitle("Some Bessel functions of the first kind") + </scilab:image> + + <programlisting role="example"><![CDATA[ +// use the fact that J_(1/2)(x) = sqrt(2/(x pi)) sin(x) +// to compare the algorithm of besselj(0.5,x) with a more direct formula + x = linspace(0.1,40,5000)'; + y1 = besselj(0.5, x); + y2 = sqrt(2 ./(%pi*x)).*sin(x); + er = abs((y1-y2)./y2); + ind = find(er > 0 & y2 ~= 0); + clf() + subplot(2,1,1) + plot2d(x,y1,style=2) + xtitle("besselj(0.5,x)") + subplot(2,1,2) + plot2d(x(ind), er(ind), style=2, logflag="nl") + xtitle("relative error between 2 formulae for besselj(0.5,x)") + ]]></programlisting> + + <scilab:image><![CDATA[ + x = linspace(0.1,40,5000)'; + y1 = besselj(0.5, x); + y2 = sqrt(2 ./(%pi*x)).*sin(x); + er = abs((y1-y2)./y2); + ind = find(er > 0 & y2 ~= 0); + clf() + subplot(2,1,1) + plot2d(x,y1,style=2) + xtitle("besselj(0.5,x)") + subplot(2,1,2) + plot2d(x(ind), er(ind), style=2, logflag="nl") + xtitle("relative error between 2 formulae for besselj(0.5,x)") + ]]></scilab:image> + + <programlisting role="example"><![CDATA[ +// besselK functions +// ================= + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besselk(0:4,x), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified Bessel functions of the second kind") + subplot(2,1,2) + plot2d(x,besselk(0:4,x,1), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the second kind") + ]]></programlisting> + + <scilab:image> + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besselk(0:4,x), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified Bessel functions of the second kind") + subplot(2,1,2) + plot2d(x,besselk(0:4,x,1), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the second kind") + </scilab:image> + + <programlisting role="example"><![CDATA[ +// besselY functions +// ================= + x = linspace(0.1,40,5000)'; // Y Bessel functions are unbounded for x -> 0+ + clf() + plot2d(x,bessely(0:4,x), style=0:4, rect=[0,-1.5,40,0.6]) + legend('Y'+string(0:4),4); + xtitle("Some Bessel functions of the second kind") + ]]></programlisting> + + <scilab:image> + x = linspace(0.1,40,5000)'; // Y Bessel functions are unbounded for x -> 0+ + clf() + plot2d(x,bessely(0:4,x), style=0:4, rect=[0,-1.5,40,0.6]) + legend('Y'+string(0:4),4); + xtitle("Some Bessel functions of the second kind") + </scilab:image> + + <programlisting role="example"><![CDATA[ +// besselH functions +// ================= + x=-4:0.025:2; y=-1.5:0.025:1.5; + [X,Y] = ndgrid(x,y); + H = besselh(0,1,X+%i*Y); + clf();f=gcf(); + xset("fpf"," ") + f.color_map=jetcolormap(16); + contour2d(x,y,abs(H),0.2:0.2:3.2,strf="034",rect=[-4,-1.5,3,1.5]) + legends(string(0.2:0.2:3.2),1:16,"ur") + xtitle("Level curves of |H1(0,z)|") + ]]></programlisting> + + <scilab:image> + x=-4:0.025:2; y=-1.5:0.025:1.5; + [X,Y] = ndgrid(x,y); + H = besselh(0,1,X+%i*Y); + clf();f=gcf(); + xset("fpf"," ") + f.color_map=jetcolormap(16); + contour2d(x,y,abs(H),0.2:0.2:3.2,strf="034",rect=[-4,-1.5,3,1.5]) + legends(string(0.2:0.2:3.2),1:16,"ur") + xtitle("Level curves of |H1(0,z)|") + </scilab:image> + + </refsection> + <refsection> + <title>Used Functions</title> + <para>The source codes can be found in SCI/modules/special_functions/src/fortran/slatec and + SCI/modules/special_functions/src/fortran + </para> + <para>Slatec : dbesi.f, zbesi.f, dbesj.f, zbesj.f, dbesk.f, zbesk.f, + dbesy.f, zbesy.f, zbesh.f + </para> + <para>Drivers to extend definition area (Serge Steer INRIA): dbesig.f, + zbesig.f, dbesjg.f, zbesjg.f, dbeskg.f, zbeskg.f, dbesyg.f, zbesyg.f, + zbeshg.f + </para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/beta.xml b/modules/special_functions/help/en_US/beta.xml new file mode 100755 index 000000000..2a94b8a80 --- /dev/null +++ b/modules/special_functions/help/en_US/beta.xml @@ -0,0 +1,124 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="beta" xml:lang="en"> + <refnamediv> + <refname>beta</refname> + <refpurpose>beta function (Euler integral of the first kind)</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>z = beta(x,y)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x, y</term> + <listitem> + <para> + 2 positive real scalars, vectors or matricesof equal sizes. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>z</term> + <listitem> + <para> + a real or a matrix of the same size than <literal>x</literal> + with <literal>z(i,j) = beta(x(i,j),y(i,j))</literal>. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para>Computes the complete beta function :</para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/beta_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para> + For small <literal>x</literal> and <literal>y</literal> (<literal>x+y≤2</literal> elementwise), + the algorithm uses the expression in function of the gamma function, else it + applies the exponential function onto the result of the + <literal>betaln</literal> function provided with the DCDFLIB: Library of + Fortran Routines for Cumulative Distribution Functions, Inverses, and + Other Parameter (see <link linkend="cdfbet">cdfbet</link> for more + information about DCDFLIB). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// example 1 : +beta(5,2) - beta(2,5) // symmetry (must be exactly 0) +beta(0.5,0.5) // exact value is pi + ]]></programlisting> + <programlisting role="example"><![CDATA[ +// example 2 : an error study based on the relation B(1,x) = 1/x +// (computing 1/x must lead to only a relative error of eps_m, so +// it may be used near as a reference to evaluate the error in B(1,x)) +x = logspace(-8,8,20000)'; +e = beta(ones(x),x) - (1)./x; +er = abs(e) .* x; +ind = find(er ~= 0); +eps = ones(x(ind))*number_properties("eps"); +clf() +plot2d(x(ind),[er(ind) eps 2*eps],style=[1 2 3],logflag="ll",leg="er@eps_m@2 eps_m") +xtitle("approximate relative error in computing beta(1,x)") +show_window() + ]]></programlisting> + <scilab:image> + x = logspace(-8,8,20000)'; + e = beta(ones(x),x) - (1)./x; + er = abs(e) .* x; + ind = find(er ~= 0); + eps = ones(x(ind))*number_properties("eps"); + plot2d(x(ind),[er(ind) eps 2*eps],style=[1 2 3],logflag="ll",leg="er@eps_m@2 eps_m") + xtitle("approximate relative error in computing beta(1,x)") + </scilab:image> + <programlisting role="example"><![CDATA[ +// example 3 : plotting the beta function +t = linspace(0.2,10,60); +X = t'*ones(t); Y = ones(t')*t; +Z = beta(X,Y); +clf() +plot3d(t, t, Z, flag=[2 4 4], leg="x@y@z", alpha=75, theta=30) +xtitle("The beta function on [0.2,10]x[0.2,10]") +show_window() + ]]></programlisting> + <scilab:image> + t = linspace(0.2,10,60); + X = t'*ones(t); Y = ones(t')*t; + Z = beta(X,Y); + clf() + plot3d(t, t, Z, flag=[2 4 4], leg="x@y@z", alpha=75, theta=30) + xtitle("The beta function on [0.2,10]x[0.2,10]") + </scilab:image> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="cdfbet">cdfbet</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/calerf.xml b/modules/special_functions/help/en_US/calerf.xml new file mode 100755 index 000000000..1ba1dd21f --- /dev/null +++ b/modules/special_functions/help/en_US/calerf.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="calerf" xml:lang="en"> + <refnamediv> + <refname>calerf</refname> + <refpurpose>computes error functions.</refpurpose> + </refnamediv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para>integer indicator</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>real vector or matrix (of same size than x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>calerf(x,0)</literal> computes the error function + <literal>erf(x)</literal> + </para> + <para> + <literal>calerf(x,1)</literal> computes the complementary error + function <literal>erfc(x)</literal> + </para> + <para> + <literal>calerf(x,2)</literal> computes the scaled complementary + error function <literal>erfcx(x)</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +calerf(1,0) +2/sqrt(%pi)*intg(0,1,f) + ]]></programlisting> + </refsection> + <refsection> + <title>Algorithms</title> + <para> + This function is based on the <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva package</ulink> library. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>The calerf function is based on the fadddeeva package</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/dawson.xml b/modules/special_functions/help/en_US/dawson.xml new file mode 100755 index 000000000..4ed3285fd --- /dev/null +++ b/modules/special_functions/help/en_US/dawson.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="dawson" xml:lang="en"> + <refnamediv> + <refname>dawson</refname> + <refpurpose>Compute the Dawson (scaled imaginary error) function.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = dawson(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vector or matrix (of same size than x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>dawson</literal> computes scaled imaginary error function + function: + </para> + <para> + <latex> + \mathrm{Dawson}(z) = \frac{\sqrt{\pi}}{2} e^{-z^2} \mathrm{erfi}(z) + </latex> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x = [0.1, 1, 1+2*%i,-1+2*%i,1e-4+2e-4*%i,0+2*%i]; +dawson(x) +dawson(-x) + ]]></programlisting> + </refsection> + <refsection> + <title>Algorithms</title> + <para> + This function is based on the <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva package</ulink> library. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>Function dawson introduced</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/delip.xml b/modules/special_functions/help/en_US/delip.xml new file mode 100755 index 000000000..193e2f39a --- /dev/null +++ b/modules/special_functions/help/en_US/delip.xml @@ -0,0 +1,146 @@ +<?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: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="delip" xml:lang="en"> + <refnamediv> + <refname>delip</refname> + <refpurpose>complete and incomplete elliptic integral of first + kind + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[r]=delip(x,ck)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real vector/matrix with nonnegative elements</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ck</term> + <listitem> + <para>real number between -1 and 1</para> + </listitem> + </varlistentry> + <varlistentry> + <term>r</term> + <listitem> + <para>real or complex number (or vector/matrix) with the same size as + <literal>x</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para>The elliptic integral of the first kind with parameter + <literal>ck</literal> is defined as follow: + </para> + <para> + <inlinemediaobject> + <imageobject> + <imagedata align="center"> + <mml:math> + <mml:semantics> + <mml:mrow> + <mml:munderover> + <mml:mo mml:stretchy="false">∫</mml:mo> + <mml:mn>0</mml:mn> + <mml:mi>x</mml:mi> + </mml:munderover> + <mml:mfrac> + <mml:mi mml:fontstyle="italic">dt</mml:mi> + <mml:msqrt> + <mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msubsup> + <mml:mi>c</mml:mi> + <mml:mi>k</mml:mi> + <mml:mn>2</mml:mn> + </mml:msubsup> + </mml:mrow> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + </mml:mrow> + </mml:msqrt> + </mml:mfrac> + </mml:mrow> + <mml:annotation mml:encoding="StarMath 5.0">int from{0} to{x} {{dt} over sqrt{ + (1-t^2)(1-c_k^2 t^2)}} + </mml:annotation> + </mml:semantics> + </mml:math> + </imagedata> + </imageobject> + </inlinemediaobject> + </para> + <para> + Where <literal>x</literal> is real and positive, + <literal>ck</literal> is in <literal>[-1 1]</literal>. + </para> + <para> + If <literal>x</literal> is less than 1 the result is real. + </para> + <para> + When called with <literal>x</literal> a vector/matrix <literal>r</literal> + is evaluated for each entry of <literal>x</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +ck=0.5; +delip([1,2],ck) +deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))') +intg(0,1,f) //OK since real solution! + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="amell">amell</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/dlgamma.xml b/modules/special_functions/help/en_US/dlgamma.xml new file mode 100755 index 000000000..bfade6dd1 --- /dev/null +++ b/modules/special_functions/help/en_US/dlgamma.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="dlgamma" xml:lang="en"> + <refnamediv> + <refname>dlgamma</refname> + <refpurpose>derivative of gammaln function, psi function</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = dlgamma(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>real vector with same size.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>dlgamma(x)</literal> evaluates, at all the elements of + <literal>x</literal> the logarithmic derivative of the gamma function + which corresponds also to the derivative of the gammaln function : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/dlgamma_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para> + <literal>x</literal> must be real. Also known as the psi + function. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +dlgamma(0.5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="gammaln">gammaln</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark>Overloading allowed for list, mlist, tlist and hypermatrix types.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/erf.xml b/modules/special_functions/help/en_US/erf.xml new file mode 100755 index 000000000..e456a62bb --- /dev/null +++ b/modules/special_functions/help/en_US/erf.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: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="erf" xml:lang="en"> + <refnamediv> + <refname>erf</refname> + <refpurpose>The error function.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = erf(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vector or matrix (of same size than x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>erf</literal> computes the error function: + <latex> + \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt + </latex> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +erf(0.5)-2/sqrt(%pi)*intg(0,0.5,f) + +x = [1+2*%i, -1+2*%i, 1e-6+2e-6*%i,0+2*%i]; +a=erf(x) + +// Equivalent to +1-erfc(x) +]]></programlisting> + </refsection> + <refsection> + <title>Algorithms</title> + <para> + This function is based on the <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva package</ulink> library. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="calerf">calerf</link> + </member> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="erfinv">erfinv</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>Function erf supports complex arguments</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/erfc.xml b/modules/special_functions/help/en_US/erfc.xml new file mode 100755 index 000000000..41666de5f --- /dev/null +++ b/modules/special_functions/help/en_US/erfc.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="erfc" xml:lang="en"> + <refnamediv> + <refname>erfc</refname> + <refpurpose>The complementary error function.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = erfc(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vector or matrix (of same size than x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Compute the complementary error function of x, defined by: <latex>1- \operatorname{erf}(x)</latex> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +erf([0.5,0.2])+erfc([0.5,0.2]) + +x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfc(x) + + ]]></programlisting> + </refsection> + <refsection> + <title>Algorithms</title> + <para> + This function is based on the <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva package</ulink> library. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>Function erfc supports complex arguments</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/erfcx.xml b/modules/special_functions/help/en_US/erfcx.xml new file mode 100755 index 000000000..0a85ce2f2 --- /dev/null +++ b/modules/special_functions/help/en_US/erfcx.xml @@ -0,0 +1,85 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="erfcx" xml:lang="en"> + <refnamediv> + <refname>erfcx</refname> + <refpurpose>scaled complementary error function.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = erfcx(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vector or matrix (of same size than x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Compute the scaled complementary error function of x, defined by <latex>e^{x^2} \operatorname{erfc}(x)</latex>. Note also that <latex>\operatorname{erfcx}(-ix)</latex> computes the Faddeeva function w(x). + + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfcx(x) +// Equivalent to +exp (x.^2) .* erfc(x) + ]]></programlisting> + </refsection> + <refsection> + <title>Algorithms</title> + <para> + This function is based on the <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva package</ulink> library. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>Improve the behavior of erfcx on big values.</revremark> + </revision> + </revhistory> + </refsection> + +</refentry> diff --git a/modules/special_functions/help/en_US/erfi.xml b/modules/special_functions/help/en_US/erfi.xml new file mode 100755 index 000000000..93ba46c11 --- /dev/null +++ b/modules/special_functions/help/en_US/erfi.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="erfi" xml:lang="en"> + <refnamediv> + <refname>erfi</refname> + <refpurpose>The imaginary error function.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = erfi(z)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>z</term> + <listitem> + <para>vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vector or matrix (of same size than x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>erfi</literal> computes the imaginary error function of x, defined by <latex>-i \operatorname{erf}(ix)</latex> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +erfi(1.234) + +x = [-0.1, 0.1, 1, 1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfi(x) +// equivalent to +-%i * erf(%i*x) + ]]></programlisting> + </refsection> + <refsection> + <title>Algorithms</title> + <para> + This function is based on the <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva package</ulink> library. + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>Function erfi supports complex arguments</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/erfinv.xml b/modules/special_functions/help/en_US/erfinv.xml new file mode 100755 index 000000000..f511219b6 --- /dev/null +++ b/modules/special_functions/help/en_US/erfinv.xml @@ -0,0 +1,89 @@ +<?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 - Vincent LIARD + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<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="erfinv"> + <refnamediv> + <refname>erfinv</refname> + <refpurpose>inverse error function</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = erfinv(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vector or matrix (same size as x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + The <literal>erfinv</literal> function computes the inverse of + the <literal>erf</literal> error function. Thus, erf(erfinv(x)) + = x for all <literal>x</literal> such that <literal>-1 ≤ x ≤ + 1 + </literal> + . + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x = linspace(-0.99, 0.99, 100); +y = erfinv(x); +plot2d(x, y) +]]></programlisting> + <scilab:image> + x = linspace(-0.99, 0.99, 100); + y = erfinv(x); + plot2d(x, y); + </scilab:image> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>References</title> + <para> + Milton Abramowitz and Irene A. Stegun, eds. Handbook of + Mathematical Functions with Formulas, Graphs, and Mathematical + Tables. New York: Dover, 1972. + </para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/findm.xml b/modules/special_functions/help/en_US/findm.xml new file mode 100755 index 000000000..af1f5f526 --- /dev/null +++ b/modules/special_functions/help/en_US/findm.xml @@ -0,0 +1,26 @@ +<?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: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="findm"> + <refnamediv> + <refname>findm</refname> + <refpurpose>for elliptic filter design</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[m]=findm(chi)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Description</title> + <para> + Search for <literal>m</literal> such that <literal>chi = %k(1-m)/%k(m)</literal> + (For use with <literal>find_freq</literal>). + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="percentk">%k</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/gamma.xml b/modules/special_functions/help/en_US/gamma.xml new file mode 100755 index 000000000..464c05a2d --- /dev/null +++ b/modules/special_functions/help/en_US/gamma.xml @@ -0,0 +1,105 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="gamma" xml:lang="en"> + <refnamediv> + <refname>gamma</refname> + <refpurpose>The gamma function.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = gamma(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>real vector or matrix with same size than x.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>gamma(x)</literal> evaluates the gamma function at all the + elements of <literal>x</literal>. The gamma function is defined by + : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/gamma_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>and generalizes the factorial function for real numbers + (<literal>gamma(n+1) = n!</literal>). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// simple examples +gamma(0.5) +gamma(6)-prod(1:5) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +// the graph of the Gamma function on [a,b] +a = -3; b = 5; +x = linspace(a,b,40000)'; +y = gamma(x); +clf() +c=xget("color") +xset("color",2) +plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10]) +xset("color",c) +xtitle("The gamma function on ["+string(a)+","+string(b)+"]") +show_window() + ]]></programlisting> + <scilab:image> + a = -3; b = 5; + x = linspace(a,b,40000)'; + y = gamma(x); + plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10]) + xtitle("The gamma function on ["+string(a)+","+string(b)+"]") + </scilab:image> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gammaln">gammaln</link> + </member> + <member> + <link linkend="dlgamma">dlgamma</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark>Overloading allowed for list, mlist, tlist and hypermatrix types.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/gammaln.xml b/modules/special_functions/help/en_US/gammaln.xml new file mode 100755 index 000000000..b66942ae8 --- /dev/null +++ b/modules/special_functions/help/en_US/gammaln.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="gammaln" xml:lang="en"> + <refnamediv> + <refname>gammaln</refname> + <refpurpose>The logarithm of gamma function.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = gammaln(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real vector</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>real vector with same size.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>gammaln(x)</literal> evaluates the logarithm of gamma + function at all the elements of <literal>x</literal>, avoiding underflow + and overflow. <literal>x</literal> must be real. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +gammaln(0.5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="dlgamma">dlgamma</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark>Overloading allowed for list, mlist, tlist and hypermatrix types.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/legendre.xml b/modules/special_functions/help/en_US/legendre.xml new file mode 100755 index 000000000..db287e60c --- /dev/null +++ b/modules/special_functions/help/en_US/legendre.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 + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<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="legendre" xml:lang="en"> + <refnamediv> + <refname>legendre</refname> + <refpurpose>associated Legendre functions</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>y = legendre(n,m,x [,normflag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>n</term> + <listitem> + <para>non negative integer or vector of non negative integers + regularly spaced with increment equal to 1 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>m</term> + <listitem> + <para>non negative integer or vector of non negative integers + regularly spaced with increment equal to 1 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para> + real matrix(elements of <literal>x</literal> must be in + the <literal>[-1,1]</literal> interval) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>normflag</term> + <listitem> + <para>(optional) scalar string</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + When <literal>n</literal> and <literal>m</literal> are scalars, + <literal>legendre(n,m,x)</literal> evaluates the associated Legendre + function Pnm(x) at all the elements of <literal>x</literal>. The + definition used is : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/legendre_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para> + where <literal>Pn</literal> is the Legendre polynomial of degree + <literal>n</literal>. So <literal>legendre(n,0,x)</literal> evaluates the + Legendre polynomial Pn(x) at all the elements of + <literal>x</literal>. + </para> + <para>When the normflag is equal to "norm" you get a normalized version + (without the <literal>(-1)^m</literal> factor), precisely : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/legendre_equation2.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>which is useful to compute spherical harmonic functions (see Example + 3): + </para> + <para>For efficiency, one of the two first arguments may be a vector, for + instance <literal>legendre(n1:n2,0,x)</literal> evaluates all the Legendre + polynomials of degree <emphasis>n1, n1+1, ..., n2</emphasis> at the + elements of <literal>x</literal> and + <literal>legendre(n,m1:m2,x)</literal> evaluates all the Legendre + associated functions Pnm for <emphasis>m=m1, m1+1, ..., m2</emphasis> at + <literal>x</literal>. + </para> + </refsection> + <refsection> + <title>Output format</title> + <para> + In any case, the format of <literal>y</literal> is : + </para> + <programlisting role="no-scilab-exec"><![CDATA[ +max(length(n),length(m)) x length(x) + ]]></programlisting> + <para>and :</para> + <programlisting role="no-scilab-exec"><![CDATA[ +y(i,j) = P(n(i),m;x(j)) if n is a vector +y(i,j) = P(n,m(i);x(j)) if m is a vector +y(1,j) = P(n,m;x(j)) if both n and m are scalars + ]]></programlisting> + <para> + so that <literal>x</literal> is preferably a row vector but any + <literal>mx x nx</literal> matrix is expected and considered as an + <literal>1 x (mx * nx)</literal> matrix, reshaped following the column + order. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// example 1 : plot of the 6 first Legendre polynomials on (-1,1) +l = nearfloat("pred",1); +x = linspace(-l,l,200)'; +y = legendre(0:5, 0, x); +clf() +plot2d(x,y', leg="p0@p1@p2@p3@p4@p5@p6") +xtitle("the 6 th first Legendre polynomials") + ]]></programlisting> + <scilab:image> + l = nearfloat("pred",1); + x = linspace(-l,l,200)'; + y = legendre(0:5, 0, x); + plot2d(x,y', leg="p0@p1@p2@p3@p4@p5@p6") + xtitle("the 6 th first Legendre polynomials") + </scilab:image> + <programlisting role="example"><![CDATA[ +// example 2 : plot of the associated Legendre functions of degree 5 +l = nearfloat("pred",1); +x = linspace(-l,l,200)'; +y = legendre(5, 0:5, x, "norm"); +clf() +plot2d(x,y', leg="p5,0@p5,1@p5,2@p5,3@p5,4@p5,5") +xtitle("the (normalized) associated Legendre functions of degree 5") + ]]></programlisting> + <scilab:image> + l = nearfloat("pred",1); + x = linspace(-l,l,200)'; + y = legendre(5, 0:5, x, "norm"); + plot2d(x,y', leg="p5,0@p5,1@p5,2@p5,3@p5,4@p5,5") + xtitle("the (normalized) associated Legendre functions of degree 5") + </scilab:image> + <programlisting role="example"><![CDATA[ +// example 3 : define then plot a spherical harmonic +// 3-1 : define the function Ylm +function [y] = Y(l,m,theta,phi) + // theta may be a scalar or a row vector + // phi may be a scalar or a column vector + if m >= 0 then + y = (-1)^m/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, m, cos(theta), "norm") + else + y = 1/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, -m, cos(theta), "norm") + end +endfunction + +// 3.2 : define another useful function +function [x,y,z] = sph2cart(theta,phi,r) + // theta row vector 1 x nt + // phi column vector np x 1 + // r scalar or np x nt matrix (r(i,j) the length at phi(i) theta(j)) + x = r.*(cos(phi)*sin(theta)); + y = r.*(sin(phi)*sin(theta)); + z = r.*(ones(phi)*cos(theta)); +endfunction + +// 3-3 plot Y31(theta,phi) +l = 3; m = 1; +theta = linspace(0.1,%pi-0.1,60); +phi = linspace(0,2*%pi,120)'; +f = Y(l,m,theta,phi); +[x1,y1,z1] = sph2cart(theta,phi,abs(f)); [xf1,yf1,zf1] = nf3d(x1,y1,z1); +[x2,y2,z2] = sph2cart(theta,phi,abs(real(f))); [xf2,yf2,zf2] = nf3d(x2,y2,z2); +[x3,y3,z3] = sph2cart(theta,phi,abs(imag(f))); [xf3,yf3,zf3] = nf3d(x3,y3,z3); + +clf() +subplot(1,3,1) +plot3d(xf1,yf1,zf1,flag=[2 4 4]); xtitle("|Y31(theta,phi)|") +subplot(1,3,2) +plot3d(xf2,yf2,zf2,flag=[2 4 4]); xtitle("|Real(Y31(theta,phi))|") +subplot(1,3,3) +plot3d(xf3,yf3,zf3,flag=[2 4 4]); xtitle("|Imag(Y31(theta,phi))|") + ]]></programlisting> + <!-- Commented. Too slow + <scilab:image> +function [y] = Y(l,m,theta,phi) + if m >= 0 then + y = (-1)^m/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, m, cos(theta), "norm") + else + y = 1/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, -m, cos(theta), "norm") + end +endfunction + +function [x,y,z] = sph2cart(theta,phi,r) + x = r.*(cos(phi)*sin(theta)); + y = r.*(sin(phi)*sin(theta)); + z = r.*(ones(phi)*cos(theta)); +endfunction + +l = 3; m = 1; +theta = linspace(0.1,%pi-0.1,60); +phi = linspace(0,2*%pi,120)'; +f = Y(l,m,theta,phi); +[x1,y1,z1] = sph2cart(theta,phi,abs(f)); [xf1,yf1,zf1] = nf3d(x1,y1,z1); +[x2,y2,z2] = sph2cart(theta,phi,abs(real(f))); [xf2,yf2,zf2] = nf3d(x2,y2,z2); +[x3,y3,z3] = sph2cart(theta,phi,abs(imag(f))); [xf3,yf3,zf3] = nf3d(x3,y3,z3); + +clf() +subplot(1,3,1) +plot3d(xf1,yf1,zf1,flag=[2 4 4]); xtitle("|Y31(theta,phi)|") +subplot(1,3,2) +plot3d(xf2,yf2,zf2,flag=[2 4 4]); xtitle("|Real(Y31(theta,phi))|") +subplot(1,3,3) +plot3d(xf3,yf3,zf3,flag=[2 4 4]); xtitle("|Imag(Y31(theta,phi))|") + </scilab:image> +--> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/percentk.xml b/modules/special_functions/help/en_US/percentk.xml new file mode 100755 index 000000000..a57a3d821 --- /dev/null +++ b/modules/special_functions/help/en_US/percentk.xml @@ -0,0 +1,59 @@ +<?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: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="percentk"> + <refnamediv> + <refname>%k</refname> + <refpurpose>Jacobi's complete elliptic integral</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[K]=%k(m)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>m</term> + <listitem> + <para> + parameter of the elliptic integral <literal>0<m<1</literal> (<literal>m</literal> can be a vector) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>K</term> + <listitem> + <para>value of the elliptic integral from 0 to 1 on the real axis</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Calculates Jacobi's complete elliptic integral + of the first kind : + </para> + </refsection> + <refsection> + <title>References</title> + <para> + Abramowitz and Stegun page 598 + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +m=0.4; +delip(1,sqrt(m)) +%k(m) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/en_US/percentsn.xml b/modules/special_functions/help/en_US/percentsn.xml new file mode 100755 index 000000000..6e5fc66f9 --- /dev/null +++ b/modules/special_functions/help/en_US/percentsn.xml @@ -0,0 +1,100 @@ +<?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: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="percentsn"> + <refnamediv> + <refname>%sn</refname> + <refpurpose>Jacobi's elliptic function</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[y]=%sn(x,m)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para> + a point inside the fundamental rectangle defined by the elliptic integral; <literal>x</literal> is a vector of complex numbers + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>m</term> + <listitem> + <para> + parameter of the elliptic integral (<literal>0<m<1</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>result</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Jacobi 's sn elliptic function with parameter <literal>m</literal>: the inverse + of the elliptic integral for the parameter <literal>m</literal>. + </para> + <para> + The amplitude am is computed in fortran and + the addition formulas for elliptic functions are applied + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +m=0.36; +K=%k(m); +P=4*K; //Real period +real_val=0:(P/50):P; +plot(real_val,real(%sn(real_val,m))) + ]]></programlisting> + <scilab:image> + m=0.36; + K=%k(m); + P=4*K; + real_val=0:(P/50):P; + plot(real_val,real(%sn(real_val,m))) + </scilab:image> + <programlisting role="example"><![CDATA[ +clf(); +m=0.36; +KK=%k(1-m); +Ip=2*KK; +ima_val1=0:(Ip/50):KK-0.001; +ima_val2=(KK+0.05):(Ip/25):(Ip+KK); +z1=%sn(%i*ima_val1,m); +z2=%sn(%i*ima_val2,m); +plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']); +xgrid(3) + ]]></programlisting> + <scilab:image> + m=0.36; + KK=%k(1-m); + Ip=2*KK; + ima_val1=0:(Ip/50):KK-0.001; + ima_val2=(KK+0.05):(Ip/25):(Ip+KK); + z1=%sn(%i*ima_val1,m); + z2=%sn(%i*ima_val2,m); + plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']); + xgrid(3) + </scilab:image> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentk">%k</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/addchapter.sce b/modules/special_functions/help/fr_FR/addchapter.sce new file mode 100755 index 000000000..51491de7d --- /dev/null +++ b/modules/special_functions/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("Fonctions spéciales",SCI+"/modules/special_functions/help/fr_FR",%T); + diff --git a/modules/special_functions/help/fr_FR/amell.xml b/modules/special_functions/help/fr_FR/amell.xml new file mode 100755 index 000000000..5dda0c197 --- /dev/null +++ b/modules/special_functions/help/fr_FR/amell.xml @@ -0,0 +1,57 @@ +<?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: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="amell"> + <refnamediv> + <refname>amell</refname> + <refpurpose>Fonction am de Jacobi </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[sn]=amell(u,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>u </term> + <listitem> + <para>scalaire ou vecteur réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k </term> + <listitem> + <para>scalaire + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sn </term> + <listitem> + <para>scalaire ou vecteur réel + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Calcule la fonction elliptique de Jacobi <literal>am(u,k)</literal> + où <literal>k</literal> est le paramètre et <literal>u</literal> l'argument. Si <literal>u</literal> + est un vecteur <literal>sn</literal> est le vecteur des valeurs calculées (élément par élément). + Utilisé dans la fonction <literal>%sn</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/calerf.xml b/modules/special_functions/help/fr_FR/calerf.xml new file mode 100755 index 000000000..80c729be0 --- /dev/null +++ b/modules/special_functions/help/fr_FR/calerf.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="calerf"> + <refnamediv> + <refname>calerf</refname> + <refpurpose>calcule différentes fonctions d'erreur. </refpurpose> + </refnamediv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x </term> + <listitem> + <para>vecteur réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para>un entier + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y </term> + <listitem> + <para>vecteur réel (de même taille que x) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>calerf(x,0)</literal> calcule la fonction erreur :<literal>erf(x)</literal> + </para> + <para> + <literal>calerf(x,1)</literal> calcule la fonction erreur complémentaire :<literal>erfc(x)</literal> + </para> + <para> + <literal>calerf(x,2)</literal> calcule la fonction erreur complémentaire normalisée :<literal>erfcx(x)</literal> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +calerf(1,0) +2/sqrt(%pi)*intg(0,1,f) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/delip.xml b/modules/special_functions/help/fr_FR/delip.xml new file mode 100755 index 000000000..d573d8c2b --- /dev/null +++ b/modules/special_functions/help/fr_FR/delip.xml @@ -0,0 +1,134 @@ +<?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: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="delip" xml:lang="fr"> + <refnamediv> + <refname>delip</refname> + <refpurpose>intégrale elliptique complete ou incomplete du premier + type + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[r]=delip(x,ck)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vecteur réel à éléments non négatifs</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ck</term> + <listitem> + <para>scalaire entre -1 et 1</para> + </listitem> + </varlistentry> + <varlistentry> + <term>r</term> + <listitem> + <para>réel ou complexe (ou vecteur)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para>L'integrale élliptique du premier type pour le paramètre + <literal>ck</literal> est définie par: + </para> + <para> + <inlinemediaobject> + <imageobject> + <imagedata> + <mml:math> + <mml:semantics> + <mml:mrow> + <mml:munderover> + <mml:mo mml:stretchy="false">∫</mml:mo> + <mml:mn>0</mml:mn> + <mml:mi>x</mml:mi> + </mml:munderover> + <mml:mfrac> + <mml:mi mml:fontstyle="italic">dt</mml:mi> + <mml:msqrt> + <mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msubsup> + <mml:mi>c</mml:mi> + <mml:mi>k</mml:mi> + <mml:mn>2</mml:mn> + </mml:msubsup> + </mml:mrow> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + </mml:mrow> + </mml:msqrt> + </mml:mfrac> + </mml:mrow> + <mml:annotation mml:encoding="StarMath 5.0">int from{0} to{x} {{dt} over sqrt{ + (1-t^2)(1-c_k^2 t^2)}} + </mml:annotation> + </mml:semantics> + </mml:math> + </imagedata> + </imageobject> + </inlinemediaobject> + </para> + <para> + Où <literal>x</literal> est réel et positif,<literal>ck</literal> + est dans l'intervalle <literal>[-1 1]</literal>. + </para> + <para> + Si <literal>x</literal> est plus petit ou égal a 1 le resultat est + réel + </para> + <para> + Quand <literal>x</literal> est un vecteur <literal>r</literal> est + évalué pour chaque composante de <literal>x</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +ck=0.5; +delip([1,2],ck) +deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))') +intg(0,1,f) // OK puisque la solution est réelle ! + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="amell">amell</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/dlgamma.xml b/modules/special_functions/help/fr_FR/dlgamma.xml new file mode 100755 index 000000000..5e1ba47ff --- /dev/null +++ b/modules/special_functions/help/fr_FR/dlgamma.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="dlgamma" xml:lang="fr"> + <refnamediv> + <refname>dlgamma</refname> + <refpurpose>dérivée de la fonction gammaln ou fonction psi.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>y = dlgamma(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vecteur réel.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vecteur réel de même taille.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>dlgamma(x)</literal> calcule la dérivée de la fonction + gammaln pour chaque composante de <literal>x</literal>. + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/dlgamma_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para> + <literal>x</literal> doit être réel. Cette fonction est aussi connue + sous le nom de fonction psi + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +dlgamma(0.5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="gammaln">gammaln</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark>Surcharge autorisée pour les types list, mlist, tlist et hypermatrices.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/erf.xml b/modules/special_functions/help/fr_FR/erf.xml new file mode 100755 index 000000000..7b9326660 --- /dev/null +++ b/modules/special_functions/help/fr_FR/erf.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: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="erf" xml:lang="fr"> + <refnamediv> + <refname>erf</refname> + <refpurpose>fonction erreur</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>y = erf(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vecteur</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vecteur (de même taille que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>erf</literal>calcule la fonction erreur : + <latex> + \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt + </latex> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +erf(0.5)-2/sqrt(%pi)*intg(0,0.5,f) + +x = [1+2*%i, -1+2*%i, 1e-6+2e-6*%i,0+2*%i]; +a=erf(x) + +// Equivalent à +1-erfc(x) +]]></programlisting> + </refsection> + + <refsection> + <title>Algorithmes</title> + <para> + Cette fonction est basée sur la bibliothèque <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva</ulink>. + </para> + </refsection> + + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="calerf">calerf</link> + </member> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="erfinv">erfinv</link> + </member> + </simplelist> + </refsection> + + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>La fonction erf supporte les arguments complexes.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/erfc.xml b/modules/special_functions/help/fr_FR/erfc.xml new file mode 100755 index 000000000..ac1927892 --- /dev/null +++ b/modules/special_functions/help/fr_FR/erfc.xml @@ -0,0 +1,74 @@ +<?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: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="erfc" xml:lang="fr"> + <refnamediv> + <refname>erfc</refname> + <refpurpose>fonction erreur complémentaire.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>y = erfc(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vecteur</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vecteur (de même taille que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>erfc</literal> calcule la fonction erreur + complémentaire définie par : <latex>1- \operatorname{erf}(x)</latex> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +erf([0.5,0.2])+erfc([0.5,0.2]) + +x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfc(x) + ]]></programlisting> + </refsection> + + <refsection> + <title>Algorithmes</title> + <para> + Cette fonction est basée sur la bibliothèque <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva</ulink>. + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>La fonction erfc supporte les arguments complexes.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/erfcx.xml b/modules/special_functions/help/fr_FR/erfcx.xml new file mode 100755 index 000000000..f138774a0 --- /dev/null +++ b/modules/special_functions/help/fr_FR/erfcx.xml @@ -0,0 +1,75 @@ +<?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: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="erfcx" xml:lang="fr"> + <refnamediv> + <refname>erfcx</refname> + <refpurpose>fonction erreur complémentaire normalisée.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>y = erfcx(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vecteur</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vecteur (de même taille que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>erfcx</literal> calcule la fonction erreur complémentaire + normalisée définie par <latex>e^{x^2} \operatorname{erfc}(x)</latex>. <latex>\operatorname{erfcx}(-ix)</latex> calcul aussi la fonction Faddeeva w(x). + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfcx(x) +// Equivalent à +exp (x.^2) .* erfc(x) + ]]></programlisting> + </refsection> + + <refsection> + <title>Algorithmes</title> + <para> + Cette fonction est basée sur la bibliothèque <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeeva</ulink>. + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>La fonction erfc supporte les arguments complexes.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/erfinv.xml b/modules/special_functions/help/fr_FR/erfinv.xml new file mode 100755 index 000000000..17e4c86b8 --- /dev/null +++ b/modules/special_functions/help/fr_FR/erfinv.xml @@ -0,0 +1,80 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2010 - Digiteo - Vincent LIARD + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<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="erfinv"> + <refnamediv> + <refname>erfinv</refname> + <refpurpose>fonction erreur inverse</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>y = erfinv(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vecteur réel</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vecteur réel (de même taille que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + La fonction <literal>erfinv</literal> calcule l'inverse de la + fonction d'erreur <literal>erf</literal>. Donc, erf(erfinv(x)) = + x pour tout <literal>x</literal> tel que <literal>-1 ≤ x ≤ + 1 + </literal> + . + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +x=linspace(-0.99,0.99,100); +y=erfinv(x); +plot2d(x,y) +]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Références</title> + <para>Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.</para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/fr_FR/gammaln.xml b/modules/special_functions/help/fr_FR/gammaln.xml new file mode 100755 index 000000000..713cc3745 --- /dev/null +++ b/modules/special_functions/help/fr_FR/gammaln.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: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="gammaln" xml:lang="fr"> + <refnamediv> + <refname>gammaln</refname> + <refpurpose>Le logarithme de la fonction gamma.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>y = gammaln(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vecteur ou matrice de nombres réels.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vecteur ou matrice de nombres réels de même taille que + x. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>gammaln(x)</literal> évalue le logarithme de la fonction + gamma pour les composantes de <literal>x</literal>., en évitant les + valeurs conduisant à un underflow ou un overflow. <literal>x</literal> + doit être à composantes réelles. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +gammaln(0.5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="dlgamma">dlgamma</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark>Surcharge autorisée pour les types list, mlist, tlist et hypermatrices.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/addchapter.sce b/modules/special_functions/help/ja_JP/addchapter.sce new file mode 100755 index 000000000..99079eca7 --- /dev/null +++ b/modules/special_functions/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("Special Functions",SCI+"/modules/special_functions/help/ja_JP",%T); + diff --git a/modules/special_functions/help/ja_JP/amell.xml b/modules/special_functions/help/ja_JP/amell.xml new file mode 100755 index 000000000..a04d96250 --- /dev/null +++ b/modules/special_functions/help/ja_JP/amell.xml @@ -0,0 +1,66 @@ +<?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="amell"> + <refnamediv> + <refname>amell</refname> + <refpurpose>ヤコビのam関数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[sn]=amell(u,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>u</term> + <listitem> + <para>実数スカラーまたはベクトル</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>スカラー</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sn</term> + <listitem> + <para>実数スカラーまたはベクトル</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + ヤコビの楕円関数 <literal>am(u,k)</literal>を計算します. + ただし, + <literal>k</literal> はパラメータ, <literal>u</literal> は引数です. <literal>u</literal> + はベクトル, <literal>sn</literal> は(要素毎の)計算値のベクトルです. + 関数<literal>%sn</literal>で使用されます. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/bessel.xml b/modules/special_functions/help/ja_JP/bessel.xml new file mode 100755 index 000000000..10598930e --- /dev/null +++ b/modules/special_functions/help/ja_JP/bessel.xml @@ -0,0 +1,322 @@ +<?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: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="bessel" xml:lang="ja"> + <refnamediv xml:id="besseli"> + <refname>besseli</refname> + <refpurpose>第1種修正ベッセル関数 (I_alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="besselj"> + <refname>besselj</refname> + <refpurpose>第1種ベッセル関数 (J_alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="besselk"> + <refname>besselk</refname> + <refpurpose>第2種修正ベッセル関数 (K_alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="bessely"> + <refname>bessely</refname> + <refpurpose>第2種ベッセル関数 (Y_alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="besselh"> + <refname>besselh</refname> + <refpurpose>第3種ベッセル関数 (ハンケル関数と同じ)</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = besseli(alpha,x [,ice]) + y = besselj(alpha,x [,ice]) + y = besselk(alpha,x [,ice]) + y = bessely(alpha,x [,ice]) + y = besselh(alpha,x) + y = besselh(alpha,K,x [,ice]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>実数または複素数のベクトル.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>alpha</term> + <listitem> + <para>r実数ベクトル</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ice</term> + <listitem> + <para>整数フラグ, デフォルト値: 0</para> + </listitem> + </varlistentry> + <varlistentry> + <term>K</term> + <listitem> + <para>整数, 指定可能な値は 1 または 2, ハンケル関数の型.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <itemizedlist> + <listitem> + <para> + <literal>besseli(alpha,x)</literal> は, + 実数の次数<literal>alpha</literal> および引数 <literal>x</literal>に関する + 第1種修正ベッセル関数(I_alpha)を計算します, + <literal>besseli(alpha,x,1)</literal> は + <literal>besseli(alpha,x).*exp(-abs(real(x)))</literal>を計算します. + </para> + </listitem> + <listitem> + <para> + <literal>besselj(alpha,x)</literal> は第1種のベッセル関数(J_alpha)を + 実数の次数<literal>alpha</literal> および引数 <literal>x</literal>に関して + 計算します. + <literal>besselj(alpha,x,1)</literal> は + <literal>besselj(alpha,x).*exp(-abs(imag(x)))</literal>を計算します. + </para> + </listitem> + <listitem> + <para> + <literal>besselk(alpha,x)</literal> は第2種修正ベッセル関数 + (K_alpha)を + 実数の次数<literal>alpha</literal> および引数 <literal>x</literal>に関して + 計算します. + <literal>besselk(alpha,x,1)</literal> は + <literal>besselk(alpha,x).*exp(x)</literal>を計算します. + </para> + </listitem> + <listitem> + <para> + <literal>bessely(alpha,x)</literal>は第2種のベッセル関数(Y_alpha)を + 実数の次数<literal>alpha</literal> および引数 <literal>x</literal>に関して + 計算します. + <literal>bessely(alpha,x,1)</literal> は + <literal>bessely(alpha,x).*exp(-abs(imag(x)))</literal>を計算します. + </para> + </listitem> + <listitem> + <para> + <literal>besselh(alpha [,K] ,x)</literal> は第3種のベッセル関数 + (<literal>K</literal>に依存してハンケル関数 H1 または H2)を + 実数の次数<literal>alpha</literal> および引数 <literal>x</literal>に関して + 計算します.<literal>K</literal>が省略された場合, + 1に等しいと仮定されます. + <literal>besselh(alpha,1,x,1)</literal>は + <literal>besselh(alpha,1,x).*exp(-%i*x)</literal>を計算し, + <literal>besselh(alpha,2,x,1)</literal> は + <literal>besselh(alpha,2,x).*exp(%i*x)</literal>を計算します. + </para> + </listitem> + </itemizedlist> + </refsection> + <refsection> + <title>注意</title> + <para> + <literal>alpha</literal>および <literal>x</literal>が同じ大きさの + 配列の場合,結果<literal>y</literal>も同じ大きさとなります. + 入力のどちらかがスカラーの場合, + もう片方の大きさにまで拡張されます. + 片方の入力が行ベクトルでもう片方が列ベクトルの場合, + 結果<literal>y</literal>は関数値の二次元テーブルとなります. + </para> + <para>Y_alpha および J_alpha ベッセル関数はベッセルの微分方程式の + 2つの独立解です: + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>修正ベッセル関数K_alpha および I_alphaは + 修正ベッセル微分方程式の2つの独立解です: + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation2.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>H^1_alpha および H^2_alphaは第1種および第2種のハンケル関数 + で,第1種および第2種のベッセル関数の線形結合です: + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation3.mml"/> + </imageobject> + </mediaobject> + </informalequation> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +// besselI 関数 +// ================== + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besseli(0:4,x), style=2:6) + legend('I'+string(0:4),2); + xtitle("Some modified Bessel functions of the first kind") + subplot(2,1,2) + plot2d(x,besseli(0:4,x,1), style=2:6) + legend('I'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the first kind") + ]]></programlisting> + <scilab:image> + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besseli(0:4,x), style=2:6) + legend('I'+string(0:4),2); + xtitle("Some modified Bessel functions of the first kind") + subplot(2,1,2) + plot2d(x,besseli(0:4,x,1), style=2:6) + legend('I'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the first kind") + </scilab:image> + <programlisting role="example"><![CDATA[ +// besselJ 関数 +// ================= + x = linspace(0,40,5000)'; + clf() + plot2d(x,besselj(0:4,x), style=2:6, leg="J0@J1@J2@J3@J4") + legend('I'+string(0:4),1); + xtitle("Some Bessel functions of the first kind") + ]]></programlisting> + <scilab:image> + x = linspace(0,40,5000)'; + plot2d(x,besselj(0:4,x), style=2:6, leg="J0@J1@J2@J3@J4") + legend('I'+string(0:4),1); + xtitle("Some Bessel functions of the first kind") + </scilab:image> + <programlisting role="example"><![CDATA[ +// J_(1/2)(x) = sqrt(2/(x pi)) sin(x) の関係を用いて +// besselj(0.5,x) のアルゴリズムをより直接的な式と比較します + x = linspace(0.1,40,5000)'; + y1 = besselj(0.5, x); + y2 = sqrt(2 ./(%pi*x)).*sin(x); + er = abs((y1-y2)./y2); + ind = find(er > 0 & y2 ~= 0); + clf() + subplot(2,1,1) + plot2d(x,y1,style=2) + xtitle("besselj(0.5,x)") + subplot(2,1,2) + plot2d(x(ind), er(ind), style=2, logflag="nl") + xtitle("relative error between 2 formulae for besselj(0.5,x)") + ]]></programlisting> + <scilab:image><![CDATA[ + x = linspace(0.1,40,5000)'; + y1 = besselj(0.5, x); + y2 = sqrt(2 ./(%pi*x)).*sin(x); + er = abs((y1-y2)./y2); + ind = find(er > 0 & y2 ~= 0); + clf() + subplot(2,1,1) + plot2d(x,y1,style=2) + xtitle("besselj(0.5,x)") + subplot(2,1,2) + plot2d(x(ind), er(ind), style=2, logflag="nl") + xtitle("relative error between 2 formulae for besselj(0.5,x)") + ]]></scilab:image> + <programlisting role="example"><![CDATA[ +// besselK 関数 +// ================= + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besselk(0:4,x), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified Bessel functions of the second kind") + subplot(2,1,2) + plot2d(x,besselk(0:4,x,1), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the second kind") + ]]></programlisting> + <scilab:image> + x = linspace(0.01,10,5000)'; + clf() + subplot(2,1,1) + plot2d(x,besselk(0:4,x), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified Bessel functions of the second kind") + subplot(2,1,2) + plot2d(x,besselk(0:4,x,1), style=0:4, rect=[0,0,6,10]) + legend('K'+string(0:4),1); + xtitle("Some modified scaled Bessel functions of the second kind") + </scilab:image> + <programlisting role="example"><![CDATA[ +// besselY 関数 +// ================= + x = linspace(0.1,40,5000)'; // Y ベッセル関数は x -> 0+ については制限されません + clf() + plot2d(x,bessely(0:4,x), style=0:4, rect=[0,-1.5,40,0.6]) + legend('Y'+string(0:4),4); + xtitle("Some Bessel functions of the second kind") + ]]></programlisting> + <scilab:image> + x = linspace(0.1,40,5000)'; // Y Bessel functions are unbounded for x -> 0+ + clf() + plot2d(x,bessely(0:4,x), style=0:4, rect=[0,-1.5,40,0.6]) + legend('Y'+string(0:4),4); + xtitle("Some Bessel functions of the second kind") + </scilab:image> + <programlisting role="example"><![CDATA[ +// besselH 関数 +// ================= + x=-4:0.025:2; y=-1.5:0.025:1.5; + [X,Y] = ndgrid(x,y); + H = besselh(0,1,X+%i*Y); + clf();f=gcf(); + xset("fpf"," ") + f.color_map=jetcolormap(16); + contour2d(x,y,abs(H),0.2:0.2:3.2,strf="034",rect=[-4,-1.5,3,1.5]) + legends(string(0.2:0.2:3.2),1:16,"ur") + xtitle("Level curves of |H1(0,z)|") + ]]></programlisting> + <scilab:image> + x=-4:0.025:2; y=-1.5:0.025:1.5; + [X,Y] = ndgrid(x,y); + H = besselh(0,1,X+%i*Y); + clf();f=gcf(); + xset("fpf"," ") + f.color_map=jetcolormap(16); + contour2d(x,y,abs(H),0.2:0.2:3.2,strf="034",rect=[-4,-1.5,3,1.5]) + legends(string(0.2:0.2:3.2),1:16,"ur") + xtitle("Level curves of |H1(0,z)|") + </scilab:image> + </refsection> + <refsection> + <title>使用される関数</title> + <para>ソースコードは SCI/modules/special_functions/src/fortran/slatec および + SCI/modules/special_functions/src/fortran にあります + </para> + <para>Slatec : dbesi.f, zbesi.f, dbesj.f, zbesj.f, dbesk.f, zbesk.f, + dbesy.f, zbesy.f, zbesh.f + </para> + <para>拡張定義領域(Serge Steer INRIA)のドライバ (Serge Steer INRIA): dbesig.f, + zbesig.f, dbesjg.f, zbesjg.f, dbeskg.f, zbeskg.f, dbesyg.f, zbesyg.f, + zbeshg.f + </para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/beta.xml b/modules/special_functions/help/ja_JP/beta.xml new file mode 100755 index 000000000..5453c2a36 --- /dev/null +++ b/modules/special_functions/help/ja_JP/beta.xml @@ -0,0 +1,126 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="beta" xml:lang="ja"> + <refnamediv> + <refname>beta</refname> + <refpurpose>ベータ関数 (第１種オイラー積分) </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>z = beta(x,y)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>x, y</term> + <listitem> + <para> + 正の実数または同じ大きさの正の実数の行列(ベクトル). + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>z</term> + <listitem> + <para> + 実数または + <literal>z(i,j) = beta(x(i,j),y(i,j))</literal>となる + <literal>x</literal>と同じ大きさの行列. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para>完全ベータ関数を計算します :</para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/beta_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para> + <literal>x</literal> および<literal>y</literal>が小さい場合, + このアルゴリズムは,関数内でガンマ関数の式を使用します. + そうでない場合はDCDFLIBにより提供される + <literal>betaln</literal>関数の結果に指数関数を適用します: + DCDFLIBは累積密度関数,逆,およびその他のパラメータに関する + Fortranルーチンのライブラリです + (DCDFLIBに関する詳細については <link linkend="cdfbet">cdfbet</link> を参照 + ). + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +// 例 1 : +beta(5,2) - beta(2,5) // 対称性 (0になります) +beta(0.5,0.5) // 値はpiになります + ]]></programlisting> + <programlisting role="example"><![CDATA[ +// 例 2 : 関係 B(1,x) = 1/xに基づく誤差解析 +// (1/x の計算は eps_mの相対誤差のみを発生するため, +// B(1,x)の誤差を評価する際の基準として使用できます) +x = logspace(-8,8,20000)'; +e = beta(ones(x),x) - (1)./x; +er = abs(e) .* x; +ind = find(er ~= 0); +eps = ones(x(ind))*number_properties("eps"); +clf() +plot2d(x(ind),[er(ind) eps 2*eps],style=[1 2 3],logflag="ll",leg="er@eps_m@2 eps_m") +xtitle("approximate relative error in computing beta(1,x)") +show_window() + ]]></programlisting> + <scilab:image> + x = logspace(-8,8,20000)'; + e = beta(ones(x),x) - (1)./x; + er = abs(e) .* x; + ind = find(er ~= 0); + eps = ones(x(ind))*number_properties("eps"); + plot2d(x(ind),[er(ind) eps 2*eps],style=[1 2 3],logflag="ll",leg="er@eps_m@2 eps_m") + xtitle("approximate relative error in computing beta(1,x)") + </scilab:image> + <programlisting role="example"><![CDATA[ +// 例 3 : ベータ関数をプロット +t = linspace(0.2,10,60); +X = t'*ones(t); Y = ones(t')*t; +Z = beta(X,Y); +clf() +plot3d(t, t, Z, flag=[2 4 4], leg="x@y@z", alpha=75, theta=30) +xtitle("The beta function on [0.2,10]x[0.2,10]") +show_window() + ]]></programlisting> + <scilab:image> + t = linspace(0.2,10,60); + X = t'*ones(t); Y = ones(t')*t; + Z = beta(X,Y); + clf() + plot3d(t, t, Z, flag=[2 4 4], leg="x@y@z", alpha=75, theta=30) + xtitle("The beta function on [0.2,10]x[0.2,10]") + </scilab:image> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="cdfbet">cdfbet</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/calerf.xml b/modules/special_functions/help/ja_JP/calerf.xml new file mode 100755 index 000000000..c0a9f8e1b --- /dev/null +++ b/modules/special_functions/help/ja_JP/calerf.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="calerf" xml:lang="ja"> + <refnamediv> + <refname>calerf</refname> + <refpurpose>誤差関数を計算する.</refpurpose> + </refnamediv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>実数ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para>整数インジケータ</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>(xと同じ大きさの)実数ベクトルまたは行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>calerf(x,0)</literal> は誤差関数 + <literal>erf(x)</literal>を計算します + </para> + <para> + <literal>calerf(x,1)</literal> は相補誤差関数 + <literal>erfc(x)</literal>を計算します + </para> + <para> + <literal>calerf(x,2)</literal> はスケーリング付き相補誤差関数 + <literal>erfcx(x)</literal>を計算します + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +calerf(1,0) +2/sqrt(%pi)*intg(0,1,f) + ]]></programlisting> + </refsection> + <refsection> + <title>アルゴリズム</title> + <para> + この関数は<ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeevaパッケージ</ulink>ライブラリ + に基づきます. + </para> + </refsection> + <refsection> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>calerf関数はfadddeevaパッケージを使用しています</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/dawson.xml b/modules/special_functions/help/ja_JP/dawson.xml new file mode 100755 index 000000000..8204c1ae2 --- /dev/null +++ b/modules/special_functions/help/ja_JP/dawson.xml @@ -0,0 +1,87 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="dawson" xml:lang="ja"> + <refnamediv> + <refname>dawson</refname> + <refpurpose>Dawson (スケーリングされた虚数の誤差) 関数を計算.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = dawson(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>(xと同じ大きさ)ベクトルまたは行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>dawson</literal> はスケーリングされた虚数の誤差関数を計算します: + </para> + <para> + <latex> + \mathrm{Dawson}(z) = \frac{\sqrt{\pi}}{2} e^{-z^2} \mathrm{erfi}(z) + </latex> + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +x = [0.1, 1, 1+2*%i,-1+2*%i,1e-4+2e-4*%i,0+2*%i]; +dawson(x) +dawson(-x) + ]]></programlisting> + </refsection> + <refsection> + <title>アルゴリズム</title> + <para> + この関数は <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeevaパッケージ</ulink> ライブラリにもとづいています. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>関数dawsonが追加されました</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/delip.xml b/modules/special_functions/help/ja_JP/delip.xml new file mode 100755 index 000000000..ddecaa243 --- /dev/null +++ b/modules/special_functions/help/ja_JP/delip.xml @@ -0,0 +1,150 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="delip" xml:lang="ja"> + <refnamediv> + <refname>delip</refname> + <refpurpose> + 第一種の完全および不完全楕円積分 + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[r]=delip(x,ck)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>非負の要素を有する実数ベクトル</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ck</term> + <listitem> + <para>-1 と 1の間の実数</para> + </listitem> + </varlistentry> + <varlistentry> + <term>r</term> + <listitem> + <para> + <literal>x</literal>と同じ大きさの + 実数または複素数(またはベクトル) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 引数<literal>ck</literal>の + 第一種の楕円積分は以下のように定義されます: + </para> + <para> + <inlinemediaobject> + <imageobject> + <imagedata align="center"> + <mml:math> + <mml:semantics> + <mml:mrow> + <mml:munderover> + <mml:mo mml:stretchy="false">∫</mml:mo> + <mml:mn>0</mml:mn> + <mml:mi>x</mml:mi> + </mml:munderover> + <mml:mfrac> + <mml:mi mml:fontstyle="italic">dt</mml:mi> + <mml:msqrt> + <mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msubsup> + <mml:mi>c</mml:mi> + <mml:mi>k</mml:mi> + <mml:mn>2</mml:mn> + </mml:msubsup> + </mml:mrow> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + </mml:mrow> + </mml:msqrt> + </mml:mfrac> + </mml:mrow> + <mml:annotation mml:encoding="StarMath 5.0">int from{0} to{x} {{dt} over sqrt{ + (1-t^2)(1-c_k^2 t^2)}} + </mml:annotation> + </mml:semantics> + </mml:math> + </imagedata> + </imageobject> + </inlinemediaobject> + </para> + <para> + ただし, <literal>x</literal> は実数および正で, + <literal>ck</literal> は <literal>[-1 1]</literal>の範囲となります. + </para> + <para>x が1より小さい場合,結果は実数となります.</para> + <para> + <literal>x</literal>を指定して + コールされた場合,<literal>x</literal>の各エントリについて + ベクトル<literal>r</literal>が評価されます. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +ck=0.5; +delip([1,2],ck) +deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))') +intg(0,1,f) //OK since real solution! + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="amell">amell</link> + </member> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/dlgamma.xml b/modules/special_functions/help/ja_JP/dlgamma.xml new file mode 100755 index 000000000..4cfb3fc81 --- /dev/null +++ b/modules/special_functions/help/ja_JP/dlgamma.xml @@ -0,0 +1,86 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="dlgamma" xml:lang="ja"> +<refnamediv> +<refname>dlgamma</refname> +<refpurpose>ガンマ関数, psi関数の微分</refpurpose> +</refnamediv> +<refsynopsisdiv> +<title>呼び出し手順</title> +<synopsis>y = dlgamma(x)</synopsis> +</refsynopsisdiv> +<refsection> +<title>引数</title> +<variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>実数ベクトル</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>同じ大きさの実数ベクトル.</para> + </listitem> + </varlistentry> +</variablelist> +</refsection> +<refsection> +<title>説明</title> +<para> + <literal>dlgamma(x)</literal> は,<literal>x</literal> + の全ての要素について,ガンマ関数の対数微分を計算します. + この値はgammaln関数の微分に一致します: +</para> +<informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/dlgamma_equation1.mml"/> + </imageobject> + </mediaobject> +</informalequation> +<para> + <literal>x</literal> は実数である必要があります. + psi 関数としても知られています. +</para> +</refsection> +<refsection> +<title>例</title> +<programlisting role="example"><![CDATA[ +dlgamma(0.5) + ]]></programlisting> +</refsection> +<refsection role="see also"> +<title>参照</title> +<simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="gammaln">gammaln</link> + </member> +</simplelist> +</refsection> +<refsection> +<title>履歴</title> +<revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark>list, mlist, tlist およびハイパー行列型の + オーバーロードが可能となりました. + </revremark> + </revision> +</revhistory> +</refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/erf.xml b/modules/special_functions/help/ja_JP/erf.xml new file mode 100755 index 000000000..c2280daac --- /dev/null +++ b/modules/special_functions/help/ja_JP/erf.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="erf" xml:lang="ja"> + <refnamediv> + <refname>erf</refname> + <refpurpose>誤差関数.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = erf(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>(xと同じ大きさの)ベクトルまたは行列 </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>erf</literal> は誤差関数を計算します: <latex> + \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt + </latex> + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +erf(0.5)-2/sqrt(%pi)*intg(0,0.5,f) +x = [1+2*%i, -1+2*%i, 1e-6+2e-6*%i,0+2*%i]; +a=erf(x) +// 以下と等価 +1-erfc(x) +]]></programlisting> + </refsection> + <refsection> + <title>アルゴリズム</title> + <para> + この関数は <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeevaパッケージ</ulink> + ライブラリに基づきます. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="calerf">calerf</link> + </member> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="erfinv">erfinv</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>erf関数が複素数の要素をサポート</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/erfc.xml b/modules/special_functions/help/ja_JP/erfc.xml new file mode 100755 index 000000000..a36e33bfb --- /dev/null +++ b/modules/special_functions/help/ja_JP/erfc.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="erfc" xml:lang="ja"> + <refnamediv> + <refname>erfc</refname> + <refpurpose>相補誤差関数.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = erfc(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>(xと同じ大きさの)ベクトルまたは行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>erfc</literal> は相補誤差関数を計算します: <latex>1- \operatorname{erf}(x)</latex> + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +erf([0.5,0.2])+erfc([0.5,0.2]) +x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfc(x) + ]]></programlisting> + </refsection> + <refsection> + <title>アルゴリズム</title> + <para> + この関数は <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeevaパッケージ</ulink> + ライブラリに基づきます. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>erfc関数が複素数の要素をサポート</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/erfcx.xml b/modules/special_functions/help/ja_JP/erfcx.xml new file mode 100755 index 000000000..1f3dcaa76 --- /dev/null +++ b/modules/special_functions/help/ja_JP/erfcx.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="erfcx" xml:lang="ja"> + <refnamediv> + <refname>erfcx</refname> + <refpurpose>スケーリング付き相補誤差関数.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = erfcx(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>(xと同じ大きさの)ベクトルまたは行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>erfcx</literal> はスケーリング付き相互関数を計算します:<latex>e^{x^2} \operatorname{erfc}(x)</latex> + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfcx(x) +// 以下と等価 +exp (x.^2) .* erfc(x) + ]]></programlisting> + </refsection> + <refsection> + <title>アルゴリズム</title> + <para> + この関数は <ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeevaパッケージ</ulink> + ライブラリに基づきます. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>erfcx関数が複素数の要素をサポート</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/erfi.xml b/modules/special_functions/help/ja_JP/erfi.xml new file mode 100755 index 000000000..b7d89a505 --- /dev/null +++ b/modules/special_functions/help/ja_JP/erfi.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="erfi" xml:lang="ja"> + <refnamediv> + <refname>erfi</refname> + <refpurpose>虚数の誤差関数.</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = erfi(z)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>z</term> + <listitem> + <para>ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>ベクトルまたは行列 (xと同じ大きさ)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>erfi</literal> は,<latex>-i \operatorname{erf}(ix)</latex> + で定義される xの虚数誤差関数を計算します. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +erfi(1.234) +x = [-0.1, 0.1, 1, 1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i]; +erfi(x) +// 以下と同じ +-%i * erf(%i*x) + ]]></programlisting> + </refsection> + <refsection> + <title>アルゴリズム</title> + <para> + この関数は<ulink url="http://ab-initio.mit.edu/Faddeeva">Faddeevaパッケージ</ulink> ライブラリにもとづいています. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>関数erfiが複素数引数をサポート</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/erfinv.xml b/modules/special_functions/help/ja_JP/erfinv.xml new file mode 100755 index 000000000..361de6acb --- /dev/null +++ b/modules/special_functions/help/ja_JP/erfinv.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2010 - Digiteo - Vincent LIARD + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<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="erfinv"> + <refnamediv> + <refname>erfinv</refname> + <refpurpose>逆誤差関数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = erfinv(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>実数ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>(xと同じ大きさの)実数ベクトルまたは行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>erfinv</literal> 関数は<literal>erf</literal> + 誤差関数の逆, + つまり,<literal>-1 ≤ x ≤ 1</literal> となるような + 任意の<literal>x</literal>について + erf(erfinv(x)) = x を計算します. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +x = linspace(-0.99, 0.99, 100); +y = erfinv(x); +plot2d(x, y) +]]></programlisting> + <scilab:image> + x = linspace(-0.99, 0.99, 100); + y = erfinv(x); + plot2d(x, y); + </scilab:image> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>参考文献</title> + <para> + Milton Abramowitz and Irene A. Stegun, eds. Handbook of + Mathematical Functions with Formulas, Graphs, and Mathematical + Tables. New York: Dover, 1972. + </para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/findm.xml b/modules/special_functions/help/ja_JP/findm.xml new file mode 100755 index 000000000..a6a2539e0 --- /dev/null +++ b/modules/special_functions/help/ja_JP/findm.xml @@ -0,0 +1,27 @@ +<?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: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="findm"> + <refnamediv> + <refname>findm</refname> + <refpurpose>楕円フィルタ設計用</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[m]=findm(chi)</synopsis> + </refsynopsisdiv> + <refsection> + <title>説明</title> + <para> + <literal>chi = %k(1-m)/%k(m)</literal>となるような<literal>m</literal>を + 探索します + (<literal>find_freq</literal>で使用されます). + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="percentk">%k</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/gamma.xml b/modules/special_functions/help/ja_JP/gamma.xml new file mode 100755 index 000000000..efd331ca4 --- /dev/null +++ b/modules/special_functions/help/ja_JP/gamma.xml @@ -0,0 +1,108 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="gamma" xml:lang="ja"> +<refnamediv> +<refname>gamma</refname> +<refpurpose>ガンマ関数.</refpurpose> +</refnamediv> +<refsynopsisdiv> +<title>呼び出し手順</title> +<synopsis>y = gamma(x)</synopsis> +</refsynopsisdiv> +<refsection> +<title>引数</title> +<variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>実数ベクトルまたは行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>(xと同じ大きさの)実数ベクトルまたは行列.</para> + </listitem> + </varlistentry> +</variablelist> +</refsection> +<refsection> +<title>説明</title> +<para> + <literal>gamma(x)</literal> は, + <literal>x</literal>の全要素についてガンマ関数を計算します. + ガンマ関数は以下のように定義されます: +</para> +<informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/gamma_equation1.mml"/> + </imageobject> + </mediaobject> +</informalequation> +<para>そして,階乗関数を実数に一般化します. + (<literal>gamma(n+1) = n!</literal>). +</para> +</refsection> +<refsection> +<title>例</title> +<programlisting role="example"><![CDATA[ +// 簡単な例 +gamma(0.5) +gamma(6)-prod(1:5) + ]]></programlisting> +<programlisting role="example"><![CDATA[ +// [a,b]のガンマ関数のグラフ +a = -3; b = 5; +x = linspace(a,b,40000)'; +y = gamma(x); +clf() +c=xget("color") +xset("color",2) +plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10]) +xset("color",c) +xtitle("The gamma function on ["+string(a)+","+string(b)+"]") +show_window() + ]]></programlisting> +<scilab:image> + a = -3; b = 5; + x = linspace(a,b,40000)'; + y = gamma(x); + plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10]) + xtitle("The gamma function on ["+string(a)+","+string(b)+"]") +</scilab:image> +</refsection> +<refsection role="see also"> +<title>参照</title> +<simplelist type="inline"> + <member> + <link linkend="gammaln">gammaln</link> + </member> + <member> + <link linkend="dlgamma">dlgamma</link> + </member> +</simplelist> +</refsection> +<refsection> +<title>履歴</title> +<revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark> + list, mlist, tlistおよびハイパー行列型のオーバーロードが + 可能となりました. + </revremark> + </revision> +</revhistory> +</refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/gammaln.xml b/modules/special_functions/help/ja_JP/gammaln.xml new file mode 100755 index 000000000..d4e0f31ee --- /dev/null +++ b/modules/special_functions/help/ja_JP/gammaln.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="gammaln" xml:lang="ja"> +<refnamediv> +<refname>gammaln</refname> +<refpurpose>ガンマ関数の対数.</refpurpose> +</refnamediv> +<refsynopsisdiv> +<title>呼び出し手順</title> +<synopsis>y = gammaln(x)</synopsis> +</refsynopsisdiv> +<refsection> +<title>引数</title> +<variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>実数ベクトル</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>同じ大きさの実数ベクトル.</para> + </listitem> + </varlistentry> +</variablelist> +</refsection> +<refsection> +<title>説明</title> +<para> + <literal>gammaln(x)</literal> は<literal>x</literal> + の全ての要素に関してオーバーフローおよびアンダーフローを回避しつつ + ガンマ関数の対数を計算します. + <literal>x</literal>は実数とする必要があります. +</para> +</refsection> +<refsection> +<title>例</title> +<programlisting role="example"><![CDATA[ +gammaln(0.5) + ]]></programlisting> +</refsection> +<refsection role="see also"> +<title>参照</title> +<simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="dlgamma">dlgamma</link> + </member> +</simplelist> +</refsection> +<refsection> +<title>履歴</title> +<revhistory> + <revision> + <revnumber>5.4.0</revnumber> + <revremark> + list, mlist, tlistおよびハイパー行列型のオーバーロードが + 可能となりました. + </revremark> + </revision> +</revhistory> +</refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/legendre.xml b/modules/special_functions/help/ja_JP/legendre.xml new file mode 100755 index 000000000..70e82303a --- /dev/null +++ b/modules/special_functions/help/ja_JP/legendre.xml @@ -0,0 +1,181 @@ +<?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: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="legendre" xml:lang="ja"> + <refnamediv> + <refname>legendre</refname> + <refpurpose>随伴ルジャンドル関数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = legendre(n,m,x [,normflag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>n</term> + <listitem> + <para>非負の整数または等間隔で増分刻みが1の + 非負の整数のベクトル + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>m</term> + <listitem> + <para>非負の整数または等間隔で増分刻みが1の + 非負の整数のベクトル + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para> + 実数 (行) ベクトル (<literal>x</literal>の要素は + <literal>(-1,1)</literal>の範囲にある必要があります) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>normflag</term> + <listitem> + <para>(オプション) スカラー文字列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>n</literal> および <literal>m</literal> がスカラーの場合, + <literal>legendre(n,m,x)</literal> は, + <literal>x</literal>の全要素について + 随伴ルジャンドル関数Pnm(x)を計算します. + 使用される定義を以下に示します: + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/legendre_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para> + ただし,<literal>Pn</literal>は<literal>n</literal>次の + ルジャンドル多項式です. + <literal>legendre(n,0,x)</literal> は + <literal>x</literal>の全要素について + ルジャンドル関数Pn(x)を計算します. + </para> + <para> + normflagが"norm"に等しい時, + (<literal>(-1)^m</literal>係数を付けずに) + 正規化された出力が得られます : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/legendre_equation2.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>これは,球面調和関数を計算する際に有用です(例3参照):</para> + <para>効率化のため, + 最初の2つの引数の一つをベクトルとすることができ, + 例えば,<literal>legendre(n1:n2,0,x)</literal>は + <literal>x</literal>の要素における + <emphasis>n1, n1+1, ..., n2</emphasis>次の + ルジャンドル多項式を全て計算します. + また, + <literal>legendre(n,m1:m2,x)</literal> は + <literal>x</literal>において<emphasis>m=m1, m1+1, ..., m2</emphasis> + に関する随伴ルジャンドル関数Pnmを全て計算します. + </para> + </refsection> + <refsection> + <title>出力形式</title> + <para> + どの場合でも, <literal>y</literal>の形式は以下のようになります : + </para> + <programlisting role=""><![CDATA[ +max(length(n),length(m)) x length(x) + ]]></programlisting> + <para>and :</para> + <programlisting role=""><![CDATA[ +y(i,j) = P(n(i),m;x(j)) n がベクトルの場合 +y(i,j) = P(n,m(i);x(j)) m がベクトルの場合 +y(1,j) = P(n,m;x(j)) n と m が共にスカラーの場合 + ]]></programlisting> + <para> + <literal>x</literal>は行ベクトルの方が好ましいですが, + 任意の<literal>mx x nx</literal>行列を指定すると, + <literal>1 x (mx * nx)</literal>行列とみなされ, + 以下のように列順に成形されます. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +// 例 1 : 最初の6個のルジャンドル多項式を(-1,1)の範囲でプロット +l = nearfloat("pred",1); +x = linspace(-l,l,200)'; +y = legendre(0:5, 0, x); +clf() +plot2d(x,y', leg="p0@p1@p2@p3@p4@p5@p6") +xtitle("the 6 th first Legendre polynomials") +// 例2 : 5次の随伴ルジャンドル関数をプロット +l = nearfloat("pred",1); +x = linspace(-l,l,200)'; +y = legendre(5, 0:5, x, "norm"); +clf() +plot2d(x,y', leg="p5,0@p5,1@p5,2@p5,3@p5,4@p5,5") +xtitle("the (normalized) associated Legendre functions of degree 5") +// 例3 : 球面調和関数を定義,プロット +// 3-1 : 関数Ylmを定義 +function [y] = Y(l,m,theta,phi) + // theta はスカラーまたは行ベクトル + // phi はスカラーまたは列ベクトル + if m >= 0 then + y = (-1)^m/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, m, cos(theta), "norm") + else + y = 1/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, -m, cos(theta), "norm") + end +endfunction +// 3.2 : 他の有用な関数を定義 +function [x,y,z] = sph2cart(theta,phi,r) + // theta 行ベクトル 1 x nt + // phi 列ベクトル np x 1 + // r スカラーまたは np x nt 行列 (r(i,j) phi(i) theta(j)) における長さ + x = r.*(cos(phi)*sin(theta)); + y = r.*(sin(phi)*sin(theta)); + z = r.*(ones(phi)*cos(theta)); +endfunction +// 3-3 Y31(theta,phi)をプロット +l = 3; m = 1; +theta = linspace(0.1,%pi-0.1,60); +phi = linspace(0,2*%pi,120)'; +f = Y(l,m,theta,phi); +[x1,y1,z1] = sph2cart(theta,phi,abs(f)); [xf1,yf1,zf1] = nf3d(x1,y1,z1); +[x2,y2,z2] = sph2cart(theta,phi,abs(real(f))); [xf2,yf2,zf2] = nf3d(x2,y2,z2); +[x3,y3,z3] = sph2cart(theta,phi,abs(imag(f))); [xf3,yf3,zf3] = nf3d(x3,y3,z3); +clf() +subplot(1,3,1) +plot3d(xf1,yf1,zf1,flag=[2 4 4]); xtitle("|Y31(theta,phi)|") +subplot(1,3,2) +plot3d(xf2,yf2,zf2,flag=[2 4 4]); xtitle("|Real(Y31(theta,phi))|") +subplot(1,3,3) +plot3d(xf3,yf3,zf3,flag=[2 4 4]); xtitle("|Imag(Y31(theta,phi))|") + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/oldbessel.xml b/modules/special_functions/help/ja_JP/oldbessel.xml new file mode 100755 index 000000000..c0f309507 --- /dev/null +++ b/modules/special_functions/help/ja_JP/oldbessel.xml @@ -0,0 +1,186 @@ +<?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: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="oldbessel" xml:lang="ja"> + <refnamediv xml:id="oldbesseli"> + <refname>oldbesseli</refname> + <refpurpose>第1種の修正ベッセル関数 (I_alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="oldbesselj"> + <refname>oldbesselj</refname> + <refpurpose>第1種のベッセル関数 (J_alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="oldbesselk"> + <refname>oldbesselk</refname> + <refpurpose>第2種の修正ベッセル関数 (K_alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="oldbessely"> + <refname>oldbessely</refname> + <refpurpose>第2種のベッセル関数 (Y_alpha).</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>y = oldbesseli(alpha,x) + y = oldbesseli(alpha,x,ice) + y = oldbesselj(alpha,x) + y = oldbesselk(alpha,x) + y = oldbesselk(alpha,x,ice) + y = oldbessely(alpha,x) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real vector with non negative entries</para> + </listitem> + </varlistentry> + <varlistentry> + <term>alpha</term> + <listitem> + <para>real vector with non negative entries regularly spaced with + increment equal to one + <literal>alpha=alpha0+(n1:n2)</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ice</term> + <listitem> + <para>integer flag, with default value 1</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para>これらの関数は古い関数であり, + <link linkend="besseli">besseli</link>, <link linkend="besselj">besselj</link>, + <link linkend="besselk">besselk</link>, <link linkend="bessely">bessely</link> を代わりに使用してください. + しかし,これらの2組の関数の構文は異なっていることに注意してください. + </para> + <para> + <literal>oldbesseli(alpha,x)</literal> computes modified Bessel + functions of the first kind (I sub alpha), for real, non-negative order + <literal>alpha</literal> and real non negative argument + <literal>x</literal>. <literal>besseli(alpha,x,2)</literal> computes + <literal>besseli(alpha,x).*exp(-x)</literal>. + </para> + <para> + <literal>oldbesselj(alpha,x)</literal> computes Bessel functions of + the first kind (J sub alpha), for real, non-negative order + <literal>alpha</literal> and real non negative argument + <literal>x</literal>. + </para> + <para> + <literal>oldbesselk(alpha,x)</literal> computes modified Bessel + functions of the second kind (K sub alpha), for real, non-negative order + <literal>alpha</literal> and real non negative argument + <literal>x</literal>. <literal>besselk(alpha,x,2)</literal> computes + <literal>besselk(alpha,x).*exp(x)</literal>. + </para> + <para> + <literal>oldbessely(alpha,x)</literal> computes Bessel functions of + the second kind (Y sub alpha), for real, non-negative order + <literal>alpha</literal> and real non negative argument + <literal>x</literal>. + </para> + <para> + <literal>alpha</literal> and <literal>x</literal> may be vectors. + The output is <literal>m</literal>-by-<literal>n</literal> with <literal>m + = size(x,'*') + </literal> + ,<literal>n = size(alpha,'*')</literal> whose + <literal>(i,j)</literal> entry is + <literal>oldbessel?(alpha(j),x(i))</literal>. + </para> + </refsection> + <refsection> + <title>Remarks</title> + <para>Y_alpha and J_alpha Bessel functions are 2 independant solutions of + the Bessel 's differential equation : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation1.mml"/> + </imageobject> + </mediaobject> + </informalequation> + <para>K_alpha and I_alpha modified Bessel functions are 2 independant + solutions of the modified Bessel 's differential equation : + </para> + <informalequation> + <mediaobject> + <imageobject> + <imagedata align="center" fileref="../mml/bessel_equation2.mml"/> + </imageobject> + </mediaobject> + </informalequation> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// example #1: display some I Bessel functions +x = linspace(0.01,10,5000)'; +y = oldbesseli(0:4,x); +ys = oldbesseli(0:4,x,2); +clf() +subplot(2,1,1) +plot2d(x,y, style=2:6, leg="I0@I1@I2@I3@I4", rect=[0,0,6,10]) +xtitle("Some modified Bessel functions of the first kind") +subplot(2,1,2) +plot2d(x,ys, style=2:6, leg="I0s@I1s@I2s@I3s@I4s", rect=[0,0,6,1]) +xtitle("Some modified scaled Bessel functions of the first kind") +// example #2 : display some J Bessel functions +x = linspace(0,40,5000)'; +y = besselj(0:4,x); +clf() +plot2d(x,y, style=2:6, leg="J0@J1@J2@J3@J4") +xtitle("Some Bessel functions of the first kind") +// example #3 : use the fact that J_(1/2)(x) = sqrt(2/(x pi)) sin(x) +// to compare the algorithm of besselj(0.5,x) with +// a more direct formula +x = linspace(0.1,40,5000)'; +y1 = besselj(0.5, x); +y2 = sqrt(2 ./(%pi*x)).*sin(x); +er = abs((y1-y2)./y2); +ind = find(er > 0 & y2 ~= 0); +clf() +subplot(2,1,1) +plot2d(x,y1,style=2) +xtitle("besselj(0.5,x)") +subplot(2,1,2) +plot2d(x(ind), er(ind), style=2, logflag="nl") +xtitle("relative error between 2 formulae for besselj(0.5,x)") +// example #4: display some K Bessel functions +x = linspace(0.01,10,5000)'; +y = besselk(0:4,x); +ys = besselk(0:4,x,1); +clf() +subplot(2,1,1) +plot2d(x,y, style=0:4, leg="K0@K1@K2@K3@K4", rect=[0,0,6,10]) +xtitle("Some modified Bessel functions of the second kind") +subplot(2,1,2) +plot2d(x,ys, style=0:4, leg="K0s@K1s@K2s@K3s@K4s", rect=[0,0,6,10]) +xtitle("Some modified scaled Bessel functions of the second kind") +// example #5: plot severals Y Bessel functions +x = linspace(0.1,40,5000)'; // Y Bessel functions are unbounded for x -> 0+ +y = bessely(0:4,x); +clf() +plot2d(x,y, style=0:4, leg="Y0@Y1@Y2@Y3@Y4", rect=[0,-1.5,40,0.6]) +xtitle("Some Bessel functions of the second kind") + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/percentk.xml b/modules/special_functions/help/ja_JP/percentk.xml new file mode 100755 index 000000000..3e6513f3f --- /dev/null +++ b/modules/special_functions/help/ja_JP/percentk.xml @@ -0,0 +1,61 @@ +<?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: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="percentk"> + <refnamediv> + <refname>%k</refname> + <refpurpose>ヤコビの完全楕円積分</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[K]=%k(m)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>m</term> + <listitem> + <para> + 楕円積分のパラメータ <literal>0<m<1</literal> + (<literal>m</literal> はベクトルとすることができます) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>K</term> + <listitem> + <para> + 実軸上の 0 から 1までの楕円積分の値 + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + ヤコビの第一種完全楕円積分を計算します : + </para> + </refsection> + <refsection> + <title>参考文献</title> + <para> + Abramowitz and Stegun page 598 + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +m=0.4; +delip(1,sqrt(m)) +%k(m) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ja_JP/percentsn.xml b/modules/special_functions/help/ja_JP/percentsn.xml new file mode 100755 index 000000000..d5f454a1c --- /dev/null +++ b/modules/special_functions/help/ja_JP/percentsn.xml @@ -0,0 +1,80 @@ +<?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: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="percentsn"> + <refnamediv> + <refname>%sn</refname> + <refpurpose>ヤコビ楕円関数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[y]=%sn(x,m)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para> + 楕円積分により定義される基本矩形の中の点; + <literal>x</literal> は複素数ベクトル + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>m</term> + <listitem> + <para> + 楕円積分のパラメータ (<literal>0<m<1</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>結果</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + パラメータ<literal>m</literal>を指定した + ヤコビの楕円関数: + パラメータ<literal>m</literal>の楕円積分の逆. + </para> + <para> + ゲインamはFortran形式で計算され, + 楕円関数用の加算式が適用されます. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +m=0.36; +K=%k(m); +P=4*K; //実周期 +real_val=0:(P/50):P; +plot(real_val,real(%sn(real_val,m))) +clf(); +KK=%k(1-m); +Ip=2*KK; +ima_val1=0:(Ip/50):KK-0.001; +ima_val2=(KK+0.05):(Ip/25):(Ip+KK); +z1=%sn(%i*ima_val1,m);z2=%sn(%i*ima_val2,m); +plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']); +xgrid(3) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentk">%k</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/mml/bessel_equation1.mml b/modules/special_functions/help/mml/bessel_equation1.mml new file mode 100755 index 000000000..39878a051 --- /dev/null +++ b/modules/special_functions/help/mml/bessel_equation1.mml @@ -0,0 +1,71 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:mrow> + <math:mrow> + <math:mrow> + <math:mrow> + <math:msup> + <math:mi>x</math:mi> + <math:mn>2</math:mn> + </math:msup> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mfrac> + <math:mrow> + <math:msup> + <math:mi>d</math:mi> + <math:mn>2</math:mn> + </math:msup> + <math:mi>y</math:mi> + </math:mrow> + <math:msup> + <math:mi math:fontstyle="italic">dx</math:mi> + <math:mn>2</math:mn> + </math:msup> + </math:mfrac> + </math:mrow> + <math:mo math:stretchy="false">+</math:mo> + <math:mrow> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mfrac> + <math:mi math:fontstyle="italic">dy</math:mi> + <math:mi math:fontstyle="italic">dx</math:mi> + </math:mfrac> + </math:mrow> + </math:mrow> + <math:mo math:stretchy="false">+</math:mo> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:msup> + <math:mi>x</math:mi> + <math:mn>2</math:mn> + </math:msup> + <math:mo math:stretchy="false">−</math:mo> + <math:msup> + <math:mo math:stretchy="false">α</math:mo> + <math:mn>2</math:mn> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mi>y</math:mi> + </math:mrow> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:mn>0,</math:mn> + </math:mrow> + <math:mrow> + <math:mo math:stretchy="false">α</math:mo> + <math:mo math:stretchy="false">≥</math:mo> + <math:mn>0</math:mn> + </math:mrow> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">x^2 cdot {{d^2 y} over {dx^2}} + x cdot {{dy} over {dx}} + (x^2 - %alpha^2) cdot y = 0, %alpha>=0</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/mml/bessel_equation2.mml b/modules/special_functions/help/mml/bessel_equation2.mml new file mode 100755 index 000000000..f62d24698 --- /dev/null +++ b/modules/special_functions/help/mml/bessel_equation2.mml @@ -0,0 +1,71 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:mrow> + <math:mrow> + <math:mrow> + <math:mrow> + <math:msup> + <math:mi>x</math:mi> + <math:mn>2</math:mn> + </math:msup> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mfrac> + <math:mrow> + <math:msup> + <math:mi>d</math:mi> + <math:mn>2</math:mn> + </math:msup> + <math:mi>y</math:mi> + </math:mrow> + <math:msup> + <math:mi math:fontstyle="italic">dx</math:mi> + <math:mn>2</math:mn> + </math:msup> + </math:mfrac> + </math:mrow> + <math:mo math:stretchy="false">+</math:mo> + <math:mrow> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mfrac> + <math:mi math:fontstyle="italic">dy</math:mi> + <math:mi math:fontstyle="italic">dx</math:mi> + </math:mfrac> + </math:mrow> + </math:mrow> + <math:mo math:stretchy="false">−</math:mo> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:msup> + <math:mi>x</math:mi> + <math:mn>2</math:mn> + </math:msup> + <math:mo math:stretchy="false">+</math:mo> + <math:msup> + <math:mo math:stretchy="false">α</math:mo> + <math:mn>2</math:mn> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mi>y</math:mi> + </math:mrow> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:mn>0,</math:mn> + </math:mrow> + <math:mrow> + <math:mo math:stretchy="false">α</math:mo> + <math:mo math:stretchy="false">≥</math:mo> + <math:mn>0</math:mn> + </math:mrow> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">x^2 cdot {{d^2 y} over {dx^2}} + x cdot {{dy} over {dx}} - (x^2 + %alpha^2) cdot y = 0, %alpha >= 0</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/mml/bessel_equation3.mml b/modules/special_functions/help/mml/bessel_equation3.mml new file mode 100755 index 000000000..de5200b16 --- /dev/null +++ b/modules/special_functions/help/mml/bessel_equation3.mml @@ -0,0 +1,98 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:mtable> + <math:mtr> + <math:mrow> + <math:msubsup> + <math:mi>H</math:mi> + <math:mo math:stretchy="false">α</math:mo> + <math:mn>1</math:mn> + </math:msubsup> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>z</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:msub> + <math:mi>J</math:mi> + <math:mo math:stretchy="false">α</math:mo> + </math:msub> + </math:mrow> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>z</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">+</math:mo> + <math:mrow> + <math:mi>i</math:mi> + <math:mo math:stretchy="false">⋅</math:mo> + <math:msub> + <math:mi>Y</math:mi> + <math:mo math:stretchy="false">α</math:mo> + </math:msub> + </math:mrow> + </math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>z</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + </math:mtr> + <math:mtr> + <math:mrow> + <math:msubsup> + <math:mi>H</math:mi> + <math:mo math:stretchy="false">α</math:mo> + <math:mn>2</math:mn> + </math:msubsup> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>z</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:msub> + <math:mi>J</math:mi> + <math:mo math:stretchy="false">α</math:mo> + </math:msub> + </math:mrow> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>z</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">−</math:mo> + <math:mrow> + <math:mi>i</math:mi> + <math:mo math:stretchy="false">⋅</math:mo> + <math:msub> + <math:mi>Y</math:mi> + <math:mo math:stretchy="false">α</math:mo> + </math:msub> + </math:mrow> + </math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>z</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + </math:mtr> + </math:mtable> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">alignl stack { +H^1_%alpha(z) = J_%alpha(z) + i cdot Y_%alpha(z) # +H^2_%alpha(z) = J_%alpha(z) - i cdot Y_%alpha(z) +}</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/mml/beta_equation1.mml b/modules/special_functions/help/mml/beta_equation1.mml new file mode 100755 index 000000000..531704422 --- /dev/null +++ b/modules/special_functions/help/mml/beta_equation1.mml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:mi>B</math:mi> + <math:mrow> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mi>x</math:mi> + <math:mi>,</math:mi> + <math:mi>y</math:mi> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:mrow> + <math:mrow> + <math:mrow> + <math:munderover> + <math:mo math:stretchy="false">∫</math:mo> + <math:mn>0</math:mn> + <math:mn>1</math:mn> + </math:munderover> + <math:msup> + <math:mi>t</math:mi> + <math:mrow> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">−</math:mo> + <math:mn>1</math:mn> + </math:mrow> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:msup> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mn>1</math:mn> + <math:mo math:stretchy="false">−</math:mo> + <math:mi>t</math:mi> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mrow> + <math:mi>y</math:mi> + <math:mo math:stretchy="false">−</math:mo> + <math:mn>1</math:mn> + </math:mrow> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mi math:fontstyle="italic">dt</math:mi> + </math:mrow> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:mfrac> + <math:mrow> + <math:mo math:stretchy="false">Γ</math:mo> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mo math:stretchy="false">Γ</math:mo> + </math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>y</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + <math:mrow> + <math:mo math:stretchy="false">Γ</math:mo> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">+</math:mo> + <math:mi>y</math:mi> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + </math:mfrac> + </math:mrow> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">B(x,y) = int from 0 to 1 t^{x-1} cdot (1-t)^{y-1} cdot dt = {{%GAMMA(x) cdot %GAMMA(y)} over {%GAMMA(x + y)}}</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/mml/dlgamma_equation1.mml b/modules/special_functions/help/mml/dlgamma_equation1.mml new file mode 100755 index 000000000..5b70cb34c --- /dev/null +++ b/modules/special_functions/help/mml/dlgamma_equation1.mml @@ -0,0 +1,58 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:mfrac> + <math:mn>1</math:mn> + <math:mrow> + <math:mo math:stretchy="false">Γ</math:mo> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + </math:mfrac> + <math:mrow> + <math:mfrac> + <math:mrow> + <math:mi>d</math:mi> + <math:mo math:stretchy="false">Γ</math:mo> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + <math:mi math:fontstyle="italic">dx</math:mi> + </math:mfrac> + <math:mo math:stretchy="false">=</math:mo> + <math:mfrac> + <math:mi>d</math:mi> + <math:mi math:fontstyle="italic">dx</math:mi> + </math:mfrac> + </math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mi>ln</math:mi> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mo math:stretchy="false">Γ</math:mo> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">{1 over {%GAMMA(x)}}{{d %GAMMA(x)} over {dx}} = {d over dx} (ln(%GAMMA(x)))</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/mml/gamma_equation1.mml b/modules/special_functions/help/mml/gamma_equation1.mml new file mode 100755 index 000000000..85df2557b --- /dev/null +++ b/modules/special_functions/help/mml/gamma_equation1.mml @@ -0,0 +1,50 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:mo math:stretchy="false">Γ</math:mo> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:mrow> + <math:mrow> + <math:mrow> + <math:munderover> + <math:mo math:stretchy="false">∫</math:mo> + <math:mn>0</math:mn> + <math:mrow> + <math:mo math:stretchy="false">+</math:mo> + <math:mo math:stretchy="false">∞</math:mo> + </math:mrow> + </math:munderover> + <math:msup> + <math:mi>t</math:mi> + <math:mrow> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">−</math:mo> + <math:mn>1</math:mn> + </math:mrow> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:msup> + <math:mi>e</math:mi> + <math:mrow> + <math:mo math:stretchy="false">−</math:mo> + <math:mi>t</math:mi> + </math:mrow> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mi math:fontstyle="italic">dt</math:mi> + </math:mrow> + </math:mrow> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">%GAMMA(x) = int from 0 to {+infty} t^{x-1} cdot e^{-t} cdot dt</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/mml/legendre_equation1.mml b/modules/special_functions/help/mml/legendre_equation1.mml new file mode 100755 index 000000000..50c88a10a --- /dev/null +++ b/modules/special_functions/help/mml/legendre_equation1.mml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:msubsup> + <math:mi>P</math:mi> + <math:mi>n</math:mi> + <math:mi>m</math:mi> + </math:msubsup> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:mrow> + <math:mrow> + <math:msup> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mo math:stretchy="false">−</math:mo> + <math:mn>1</math:mn> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mi>m</math:mi> + </math:msup> + <math:mo math:stretchy="false">⋅</math:mo> + <math:msup> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mn>1</math:mn> + <math:mo math:stretchy="false">−</math:mo> + <math:msup> + <math:mi>x</math:mi> + <math:mn>2</math:mn> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mrow> + <math:mi>m</math:mi> + <math:mo math:stretchy="false">/</math:mo> + <math:mn>2</math:mn> + </math:mrow> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mfrac> + <math:msup> + <math:mi>d</math:mi> + <math:mi>m</math:mi> + </math:msup> + <math:msup> + <math:mi math:fontstyle="italic">dx</math:mi> + <math:mi>m</math:mi> + </math:msup> + </math:mfrac> + </math:mrow> + </math:mrow> + <math:msub> + <math:mi>P</math:mi> + <math:mi>n</math:mi> + </math:msub> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">P_n^m(x) = (-1)^m cdot (1-x^2)^{m/2} cdot {d^m over dx^m}P_n(x)</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/mml/legendre_equation2.mml b/modules/special_functions/help/mml/legendre_equation2.mml new file mode 100755 index 000000000..8ce2da506 --- /dev/null +++ b/modules/special_functions/help/mml/legendre_equation2.mml @@ -0,0 +1,113 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"> +<math:math xmlns:math="http://www.w3.org/1998/Math/MathML"> + <math:semantics> + <math:mrow> + <math:msubsup> + <math:mi>P</math:mi> + <math:mi>n</math:mi> + <math:mi>m</math:mi> + </math:msubsup> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mi>x</math:mi> + <math:mi>,</math:mi> + <math:mtext>norm</math:mtext> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mo math:stretchy="false">=</math:mo> + <math:mrow> + <math:mrow> + <math:msqrt> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mfrac> + <math:mrow> + <math:mn>2n</math:mn> + <math:mo math:stretchy="false">+</math:mo> + <math:mn>1</math:mn> + </math:mrow> + <math:mn>2</math:mn> + </math:mfrac> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mfrac> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mi>n</math:mi> + <math:mo math:stretchy="false">−</math:mo> + <math:mi>m</math:mi> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mi>!</math:mi> + </math:mrow> + <math:mrow> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mi>n</math:mi> + <math:mo math:stretchy="false">+</math:mo> + <math:mi>m</math:mi> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mi>!</math:mi> + </math:mrow> + </math:mfrac> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:msqrt> + <math:mo math:stretchy="false">⋅</math:mo> + <math:msup> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mrow> + <math:mn>1</math:mn> + <math:mo math:stretchy="false">−</math:mo> + <math:msup> + <math:mi>x</math:mi> + <math:mn>2</math:mn> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + <math:mrow> + <math:mi>m</math:mi> + <math:mo math:stretchy="false">/</math:mo> + <math:mn>2</math:mn> + </math:mrow> + </math:msup> + </math:mrow> + <math:mo math:stretchy="false">⋅</math:mo> + <math:mfrac> + <math:msup> + <math:mi>d</math:mi> + <math:mi>m</math:mi> + </math:msup> + <math:msup> + <math:mi math:fontstyle="italic">dx</math:mi> + <math:mi>m</math:mi> + </math:msup> + </math:mfrac> + </math:mrow> + </math:mrow> + <math:msub> + <math:mi>P</math:mi> + <math:mi>n</math:mi> + </math:msub> + <math:mrow> + <math:mo math:stretchy="false">(</math:mo> + <math:mi>x</math:mi> + <math:mo math:stretchy="false">)</math:mo> + </math:mrow> + </math:mrow> + <math:annotation math:encoding="StarMath 5.0">P_n^m(x,"norm") = {sqrt({{2n+1} over {2}} cdot {{(n-m)!} over {(n+m)!}})} cdot (1-x^2)^{m/2} cdot {d^m over dx^m}P_n(x)</math:annotation> + </math:semantics> +</math:math>
\ No newline at end of file diff --git a/modules/special_functions/help/pt_BR/addchapter.sce b/modules/special_functions/help/pt_BR/addchapter.sce new file mode 100755 index 000000000..891fde6e7 --- /dev/null +++ b/modules/special_functions/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("Funções Especiais",SCI+"/modules/special_functions/help/pt_BR",%T); + diff --git a/modules/special_functions/help/pt_BR/amell.xml b/modules/special_functions/help/pt_BR/amell.xml new file mode 100755 index 000000000..0a63ccc9e --- /dev/null +++ b/modules/special_functions/help/pt_BR/amell.xml @@ -0,0 +1,66 @@ +<?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="amell" xml:lang="en"> + <refnamediv> + <refname>amell</refname> + <refpurpose>funo "am" de Jacobi</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>[sn]=amell(u,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>u</term> + <listitem> + <para>escalar real ou vetor de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>escalar </para> + </listitem> + </varlistentry> + <varlistentry> + <term>sn</term> + <listitem> + <para>escalar real ou vetor de reais</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Computa a funo elptica de Jacobi <literal>am(u,k)</literal> onde + <literal>k</literal> o parmetro e <literal>u</literal> o argumento. + Se <literal>u</literal> um vetor <literal>sn</literal> o vetor dos + valores computados (elemento a elemento) . Usado na funo + <literal>%sn</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/bessel.xml b/modules/special_functions/help/pt_BR/bessel.xml new file mode 100755 index 000000000..ce6abc8c9 --- /dev/null +++ b/modules/special_functions/help/pt_BR/bessel.xml @@ -0,0 +1,256 @@ +<?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="bessel" xml:lang="en"> + <refnamediv xml:id="besseli"> + <refname>besseli</refname> + <refpurpose>funes modificadas de Bessel do primeiro tipo (I sub + alfa). + </refpurpose> + </refnamediv> + <refnamediv xml:id="besselj"> + <refname>besselj</refname> + <refpurpose>funes de Bessel do primeiro tipo (J sub alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="besselk"> + <refname>besselk</refname> + <refpurpose>funes modificadas de Bessel do segundo tipo (K sub + alpha). + </refpurpose> + </refnamediv> + <refnamediv xml:id="bessely"> + <refname>bessely</refname> + <refpurpose>funes de Bessel do segundo tipo (Y sub alpha).</refpurpose> + </refnamediv> + <refnamediv xml:id="besselh"> + <refname>besselh</refname> + <refpurpose>funes de Bessel do terceiro tipo (tambm conhecidas como + funes de Hankel) + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = besseli(alpha,x [,ice]) + y = besselj(alpha,x [,ice]) + y = besselk(alpha,x [,ice]) + y = bessely(alpha,x [,ice]) + y = besselh(alpha,x) + y = besselh(alpha,K,x [,ice]) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor de reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>alpha</term> + <listitem> + <para>vetor de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>ice</term> + <listitem> + <para>flag (sinalizador) inteiro, com valor padro 0 </para> + </listitem> + </varlistentry> + <varlistentry> + <term>K</term> + <listitem> + <para>inteiro, com valores possveis 1 ou 2, a funo do tipo de + Hankel. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <itemizedlist> + <listitem> + <para> + <literal>besseli(alpha,x)</literal> computa as funes de Bessel + modificadas do primeiro tipo (I sub alfa), para ordem real + <literal>alpha</literal> e argumento <literal>x</literal>. + <literal>besseli(alpha,x,1)</literal> computa + <literal>besseli(alpha,x).*exp(-abs(real(x)))</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>besselj(alpha,x)</literal> computa as funes de Bessel + do primeiro tipo (J sub alfa), para ordem real + <literal>alpha</literal> e argumento <literal>x</literal>. + <literal>besselj(alpha,x,1)</literal> computa + <literal>besselj(alpha,x).*exp(-abs(imag(x)))</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>besselk(alpha,x)</literal> computa as funes de Bessel + modificadas do segundo tipo (K sub alfa), para ordem real + <literal>alpha</literal> e argumento <literal>x</literal>. + <literal>besselk(alpha,x,1)</literal> computa + <literal>besselk(alpha,x).*exp(x)</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>bessely(alpha,x)</literal> computa as funes de Bessel + do segundo tipo (Y sub alfa), para ordem real <literal>alpha</literal> + e argumento <literal>x</literal>. + <literal>bessely(alpha,x,1)</literal> computa + <literal>bessely(alpha,x).*exp(-abs(imag(x)))</literal>. + </para> + </listitem> + <listitem> + <para> + <literal>besselh(alpha [,K] ,x)</literal> computa as funes de + Bessel do terceiro tipo (funo de Hankel H1 ou H2, dependendo do + <literal>K</literal>), para ordem real <literal>alpha</literal> e + argumentot <literal>x</literal>. Se omitido, <literal>K</literal> + suposto como sendo 1. <literal>besselh(alpha,1,x,1)</literal> computa + <literal>besselh(alpha,1,x).*exp(-%i*x)</literal> e + <literal>besselh(alpha,2,x,1)</literal> computa + <literal>besselh(alpha,2,x).*exp(%i*x)</literal> + </para> + </listitem> + </itemizedlist> + </refsection> + <refsection> + <title>Observaes </title> + <para> + Se <literal>alpha</literal> e <literal>x</literal> so arrays de + mesmo tamanho, o resultado <literal>y</literal> tambm ter este tamanho. + Se uma entrada um escalar, ela expandida para o tamanho da outra + entrada. Se uma entrada um vetor linha e a outra um vetor coluna, o + resultado <literal>y</literal> um table 2-dimensional ("tabela") de + valores de funes. + </para> + <para>As funes de Bessel Y_alfa e J_alfa so duas solues independentes + da equao diferencial de Bessel: + </para> + <programlisting role=""><![CDATA[ +2 2 2 x y" + x y' + (x - alfa ) y = 0 , alfa >= 0 + ]]></programlisting> + <para>As funes modificadas de Bessel K_alfa e I_alfa so duas solues + independentes para a equao diferencial de Bessel : + </para> + <programlisting role=""><![CDATA[ +2 2 2 x y" + x y' - (x + alfa ) y = 0 , alfa >= 0 + ]]></programlisting> + <para>As funes de Hankel de primeiro e segundo tipos H^1_alfa e + H^2_alfa, so combinaes lineares das funes de Bessel de primeiro e + segundo tipos: + </para> + <programlisting role=""><![CDATA[ +H^1_alfa(z) = J_alfa(z) + i Y_alfa(z) H^2_alfa(z) = J_alfa(z) - i Y_alfa(z) + ]]></programlisting> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// Funes I de Bessel +// ================== +x = linspace(0.01,10,5000)'; +clf() +subplot(2,1,1) +plot2d(x,besseli(0:4,x), style=2:6) +legend('I'+string(0:4),2); +xtitle("Algumas funes modificadas de Bessel do primeiro tipo") +subplot(2,1,2) +plot2d(x,besseli(0:4,x,1), style=2:6) +legend('I'+string(0:4),1); +xtitle("Algumas funes modificadas de Bessel do primeiro tipo escaladas") + +// Funes J de Bessel +// ================= +x = linspace(0,40,5000)'; +clf() +plot2d(x,besselj(0:4,x), style=2:6, leg="J0@J1@J2@J3@J4") +legend('I'+string(0:4),1); +xtitle("Algumas funes de Bessel do primeiro tipo") + +// Usando o fato de que J_(1/2)(x) = sqrt(2/(x pi)) sin(x) +// Para comparar o algoritmo de besselj(0.5,x) com uma frmula mais direta +x = linspace(0.1,40,5000)'; +y1 = besselj(0.5, x); +y2 = sqrt(2 ./(%pi*x)).*sin(x); +er = abs((y1-y2)./y2); +ind = find(er > 0 & y2 ~= 0); +clf() +subplot(2,1,1) +plot2d(x,y1,style=2) +xtitle("besselj(0.5,x)") +subplot(2,1,2) +plot2d(x(ind), er(ind), style=2, logflag="nl") +xtitle("Erro relativo entre as duas frmulas para besselj(0.5,x)") + +// Funes K de Bessel +// ================= +x = linspace(0.01,10,5000)'; +clf() +subplot(2,1,1) +plot2d(x,besselk(0:4,x), style=0:4, rect=[0,0,6,10]) +legend('K'+string(0:4),1); +xtitle("Algumas funes modificadas de Bessel do segundo tipo") +subplot(2,1,2) +plot2d(x,besselk(0:4,x,1), style=0:4, rect=[0,0,6,10]) +legend('K'+string(0:4),1); +xtitle("Algumas funes modificadas de Bessel do segundo tipo escaladas") + +// Funes Y de Bessel +// ================= +x = linspace(0.1,40,5000)'; // funes Y de Bessel no possuem limite para x -> 0+ +clf() +plot2d(x,bessely(0:4,x), style=0:4, rect=[0,-1.5,40,0.6]) +legend('Y'+string(0:4),4); +xtitle("Algumas funes de Bessel do segundo tipo") + +// Funes H de Bessel +// ================= +x=-4:0.025:2; y=-1.5:0.025:1.5; +[X,Y] = ndgrid(x,y); +H = besselh(0,1,X+%i*Y); +clf();f=gcf(); +xset("fpf"," ") +f.color_map=jetcolormap(16); +contour2d(x,y,abs(H),0.2:0.2:3.2,strf="034",rect=[-4,-1.5,3,1.5]) +legends(string(0.2:0.2:3.2),1:16,"ur") +xtitle("Curvas de nvel de |H1(0,z)|") + ]]></programlisting> + </refsection> + <refsection> + <title>Autores</title> + <simplelist type="vert"> + <member>Amos, D. E., (SNLA)</member> + <member>Daniel, S. L., (SNLA)</member> + <member>Weston, M. K., (SNLA)</member> + </simplelist> + </refsection> + <refsection> + <title>Funo Usada</title> + <para>Os cdigos-fontes podem ser achados em SCI/modules/special_functions/src/fortran/slatec e SCI/modules/special_functions/src/fortran</para> + <para>Slatec : dbesi.f, zbesi.f, dbesj.f, zbesj.f, dbesk.f, zbesk.f, + dbesy.f, zbesy.f, zbesh.f + </para> + <para>Drivers para estender a rea de definio (Serge Steer INRIA): + dbesig.f, zbesig.f, dbesjg.f, zbesjg.f, dbeskg.f, zbeskg.f, dbesyg.f, + zbesyg.f, zbeshg.f + </para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/beta.xml b/modules/special_functions/help/pt_BR/beta.xml new file mode 100755 index 000000000..51be052cd --- /dev/null +++ b/modules/special_functions/help/pt_BR/beta.xml @@ -0,0 +1,106 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="beta" xml:lang="en"> + <refnamediv> + <refname>beta</refname> + <refpurpose>funo beta</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>z = beta(x,y)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros </title> + <variablelist> + <varlistentry> + <term>x, y</term> + <listitem> + <para>dois reais positivos ou duas matrizes (ou vetores) de reais + positivos de mesmo tamanho + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>z</term> + <listitem> + <para>um real ou uma matriz de reais com mesmo tamanho que + <literal>x</literal> com <literal>z(i,j) = + beta(x(i,j),y(i,j)) + </literal> + . + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>Computa a funo beta completa : </para> + <programlisting role=""><![CDATA[ + /1 + | x-1 y-1 gamma(x) gamma(y) + beta(x,y) = | t (1-t) dt = ---------------- + /0 gamma(x+y) + ]]></programlisting> + <para> + Para <literal>x</literal> e <literal>y</literal> pequenos, o + algoritmo usa a expresso em funo da funo gama, de outro modo, ele + aplica a funo exponencial no resutado da funo + <literal>betaln</literal> function fornecido no DCDFLIB: Biblioteca de + Rotinas FORTRAN para Funes, Inversas e Outros Parmetros de Distribuio + Cumulativa (ver <link linkend="cdfbet">cdfbet</link> para maiores + informaes sobre DCDFLIB). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// exemplo 1 : +beta(5,2) - beta(2,5) // simetria (deve ser exatamente 0) +beta(0.5,0.5) // o valor exato pi + +// exemplo 2 : um estudo de erros baseado na relao B(1,x) = 1/x +// (a computao de 1/x deve levar apenas a um erro relativo de eps_m, ento +// pode ser usada como referncia para avaliar o erro em B(1,x)) +x = logspace(-8,8,20000)'; +e = beta(ones(x),x) - (1)./x; +er = abs(e) .* x; +ind = find(er ~= 0); +eps = ones(x(ind))*number_properties("eps"); +clf() +plot2d(x(ind),[er(ind) eps 2*eps],style=[1 2 3],logflag="ll",leg="er@eps_m@2 eps_m") +xtitle("erro relativo aproximado na computao de beta(1,x)") +show_window() + +// exemplo 3 : plotando a funo beta +t = linspace(0.2,10,60); +X = t'*ones(t); Y = ones(t')*t; +Z = beta(X,Y); +clf() +plot3d(t, t, Z, flag=[2 4 4], leg="x@y@z", alpha=75, theta=30) +xtitle("A funo beta em [0.2,10]x[0.2,10]") +show_window() + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="cdfbet">cdfbet</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/calerf.xml b/modules/special_functions/help/pt_BR/calerf.xml new file mode 100755 index 000000000..2d774eb79 --- /dev/null +++ b/modules/special_functions/help/pt_BR/calerf.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="calerf" xml:lang="en"> + <refnamediv> + <refname>calerf</refname> + <refpurpose>computa funes de erro</refpurpose> + </refnamediv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>matriz ou vetor de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para>indicador inteiro </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>matriz ou vetor de reais (de mesmo tamanho que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>calerf(x,0)</literal> computa a funo de erro + <literal>erf(x)</literal> + </para> + <para> + <literal>calerf(x,1)</literal> computa a funo de erro complementar + <literal>erfc(x)</literal> + </para> + <para> + <literal>calerf(x,2)</literal> computa a funo de erro complementar + escalada <literal>erfcx(x)</literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +calerf(1,0) +2/sqrt(%pi)*intg(0,1,f) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/delip.xml b/modules/special_functions/help/pt_BR/delip.xml new file mode 100755 index 000000000..f32677a42 --- /dev/null +++ b/modules/special_functions/help/pt_BR/delip.xml @@ -0,0 +1,143 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns: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="delip" xml:lang="en"> + <refnamediv> + <refname>delip</refname> + <refpurpose>Integral elíptica</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>[r]=delip(x,ck)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor real com elementos não-negativos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ck</term> + <listitem> + <para>número real entre -1 e 1 </para> + </listitem> + </varlistentry> + <varlistentry> + <term>r</term> + <listitem> + <para>número real ou complexo ou vetor de reais ou complexos com + mesmo tamanho que <literal>x</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para>A integral elíptica de primeira espécie com parâmetro + <literal>ck</literal> definido como segue: + </para> + <para> + <inlinemediaobject> + <imageobject> + <imagedata> + <mml:math> + <mml:semantics> + <mml:mrow> + <mml:munderover> + <mml:mo mml:stretchy="false">∫</mml:mo> + <mml:mn>0</mml:mn> + <mml:mi>x</mml:mi> + </mml:munderover> + <mml:mfrac> + <mml:mi mml:fontstyle="italic">dt</mml:mi> + <mml:msqrt> + <mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msubsup> + <mml:mi>c</mml:mi> + <mml:mi>k</mml:mi> + <mml:mn>2</mml:mn> + </mml:msubsup> + </mml:mrow> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + </mml:mrow> + </mml:msqrt> + </mml:mfrac> + </mml:mrow> + <mml:annotation mml:encoding="StarMath 5.0">int from{0} to{x} {{dt} over sqrt{ + (1-t^2)(1-c_k^2 t^2)}} + </mml:annotation> + </mml:semantics> + </mml:math> + </imagedata> + </imageobject> + </inlinemediaobject> + </para> + <para> + Onde <literal>x</literal> é real e positivo e <literal>ck</literal> + está em <literal>[-1 1]</literal>. + </para> + <para>Se x é menor do que ou igual a 1, o resultado é real.</para> + <para> + Quando chamado com <literal>x</literal>, um vetor real + <literal>r</literal> é avaliado para cada entrada de + <literal>x</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +ck=0.5; +delip([1,2],ck) +deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))') +intg(0,1,f) //OK, desde que a solução seja real! + ]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="amell">amell</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/dlgamma.xml b/modules/special_functions/help/pt_BR/dlgamma.xml new file mode 100755 index 000000000..af823e413 --- /dev/null +++ b/modules/special_functions/help/pt_BR/dlgamma.xml @@ -0,0 +1,71 @@ +<?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="dlgamma" xml:lang="en"> + <refnamediv> + <refname>dlgamma</refname> + <refpurpose>derivada da funo gammaln, funo psi</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = dlgamma(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vetor de reais com o mesmo tamanho</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>dlgamma(x)</literal> avalia, em todos os elementos de + <literal>x</literal> a derivada logartmica da funo gama (gamma), que + corresponde tambm derivada da funo ln(gama) (gammaln): + </para> + <programlisting role=""><![CDATA[ +d/dx (gamma(x)) / gamma(x) = d/dx (ln gamma(x)) + ]]></programlisting> + <para> + <literal>x</literal> deve ser real. Tambm conhecida como a funo + psi. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +dlgamma(0.5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="gammaln">gammaln</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/erf.xml b/modules/special_functions/help/pt_BR/erf.xml new file mode 100755 index 000000000..9cdca9cc1 --- /dev/null +++ b/modules/special_functions/help/pt_BR/erf.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="erf" xml:lang="en"> + <refnamediv> + <refname>erf</refname> + <refpurpose>funo de erro </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = erf(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor ou matriz de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vetor ou matriz de reais (de mesmo tamanho que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>erf</literal> computa a funo de erro: + </para> + <programlisting role=""><![CDATA[ + /x 2 + 2 | -t + y = ------- | e dt + sqrt(pi) /0 + ]]></programlisting> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +deff('y=f(t)','y=exp(-t^2)'); +erf(0.5)-2/sqrt(%pi)*intg(0,0.5,f) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="calerf">calerf</link> + </member> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="erfinv">erfinv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/erfc.xml b/modules/special_functions/help/pt_BR/erfc.xml new file mode 100755 index 000000000..551d01ad0 --- /dev/null +++ b/modules/special_functions/help/pt_BR/erfc.xml @@ -0,0 +1,75 @@ +<?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="erfc" xml:lang="en"> + <refnamediv> + <refname>erfc</refname> + <refpurpose>funo de erro complementar </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = erfc(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>real vector or matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>real vector or matrix (of same size than x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>erfc</literal> computa a funo de erro + complementar: + </para> + <programlisting role=""><![CDATA[ + /+oo 2 + 2 | -t + y = ------- | e dt + sqrt(pi) | + /x + + y = 1 - erf(x) + ]]></programlisting> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +erf([0.5,0.2])+erfc([0.5,0.2]) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/erfcx.xml b/modules/special_functions/help/pt_BR/erfcx.xml new file mode 100755 index 000000000..3337e7257 --- /dev/null +++ b/modules/special_functions/help/pt_BR/erfcx.xml @@ -0,0 +1,68 @@ +<?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="erfcx" xml:lang="en"> + <refnamediv> + <refname>erfcx</refname> + <refpurpose>funo de erro complementar escalada </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = erfcx(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parameters</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor ou matriz de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vetor ou matriz de reais (de mesmo tamanho que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>erfcx</literal> computa a funo de erro complementar + escalada: + </para> + <programlisting role=""><![CDATA[ + 2 + y = exp(x ) * erfc(x) + + 1 + y --> --------- quando x --> +oo + x sqrt(pi) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="calerf">calerf</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/erfinv.xml b/modules/special_functions/help/pt_BR/erfinv.xml new file mode 100755 index 000000000..ea8bdb039 --- /dev/null +++ b/modules/special_functions/help/pt_BR/erfinv.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA + * Copyright (C) 2010 - Digiteo - Vincent LIARD + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<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="erfinv" xml:lang="en"> + <refnamediv> + <refname>erfinv</refname> + <refpurpose>função inversa à função de erro</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqüência de Chamamento</title> + <synopsis>y = erfinv(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parâmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor ou matriz de reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vetor ou matriz de reais (de mesmo tamanho que x)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>erfinv</literal> computa a função inversa à função de + erro <literal>erf</literal>. <literal>x = erfinv(y)</literal> + satisfaz <literal>y = erf(x)</literal>, <literal>-1 ≤ y ≤ + 1 + </literal> + ,<literal>∞ ≤ x ≤ ∞</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +x=linspace(-0.99,0.99,100); +y=erfinv(x); +plot2d(x,y) +]]></programlisting> + </refsection> + <refsection> + <title>Ver Também</title> + <simplelist type="inline"> + <member> + <link linkend="cdfnor">cdfnor</link> + </member> + <member> + <link linkend="erf">erf</link> + </member> + <member> + <link linkend="erfc">erfc</link> + </member> + <member> + <link linkend="erfcx">erfcx</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Referências</title> + <para>Milton Abramowitz e Irene A. Stegun, eds. Handbook of Mathematical + Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, + 1972. + </para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/gamma.xml b/modules/special_functions/help/pt_BR/gamma.xml new file mode 100755 index 000000000..75cee9b3b --- /dev/null +++ b/modules/special_functions/help/pt_BR/gamma.xml @@ -0,0 +1,92 @@ +<?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="gamma" xml:lang="en"> + <refnamediv> + <refname>gamma</refname> + <refpurpose>funo gama </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = gamma(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor ou matriz de reais ou complexos </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vetor ou matriz de reais ou complexos de mesmo tamanho que + x + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>gamma(x)</literal> avalia a funo gama em todos os + elementos de <literal>x</literal>. A funo gama defininda por : + </para> + <programlisting role=""><![CDATA[ + /+oo + | x-1 -t +gamma(x) = | t e dt + /0 + ]]></programlisting> + <para>e generaliza a funo fatorial para os nmeros reais + (<literal>gamma(n+1) = n!</literal>). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// exemplos simples +gamma(0.5) +gamma(6)-prod(1:5) + +// o grfico da funo gama em [a,b] +a = -3; b = 5; +x = linspace(a,b,40000)'; +y = gamma(x); +clf() +c=xget("color") +xset("color",2) +plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10]) +xset("color",c) +xtitle("A funo gama em ["+string(a)+","+string(b)+"]") +show_window() + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="gammaln">gammaln</link> + </member> + <member> + <link linkend="dlgamma">dlgamma</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Autores</title> + <para>W. J. Cody e L. Stoltz (cdigo de Netlib (specfun))</para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/gammaln.xml b/modules/special_functions/help/pt_BR/gammaln.xml new file mode 100755 index 000000000..7dfdb4ece --- /dev/null +++ b/modules/special_functions/help/pt_BR/gammaln.xml @@ -0,0 +1,68 @@ +<?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="gammaln" xml:lang="en"> + <refnamediv> + <refname>gammaln</refname> + <refpurpose>o logaritmo (natural) da funo gama </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = gammaln(x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parameters</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor de reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>y</term> + <listitem> + <para>vetor de reais com o mesmo tamanho</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>gammaln(x)</literal> avalia o logaritmo (natural) da funo + gama em todos os elementos de <literal>x</literal>, evitando underflow e + overflow. <literal>x</literal> deve ser de reais. + </para> + </refsection> + <refsection> + <title>Exemplos </title> + <programlisting role="example"><![CDATA[ +gammaln(0.5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="gamma">gamma</link> + </member> + <member> + <link linkend="dlgamma">dlgamma</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Autores</title> + <para>W. J. Cody e L. Stoltz (cdigo de Netlib (specfun))</para> + </refsection> +</refentry> diff --git a/modules/special_functions/help/pt_BR/legendre.xml b/modules/special_functions/help/pt_BR/legendre.xml new file mode 100755 index 000000000..bd2a8f0e6 --- /dev/null +++ b/modules/special_functions/help/pt_BR/legendre.xml @@ -0,0 +1,189 @@ +<?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="legendre" xml:lang="en"> + <refnamediv> + <refname>legendre</refname> + <refpurpose>funes associadas de Legendre</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>y = legendre(n,m,x [,normflag])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>n</term> + <listitem> + <para>inteiro no-negativo ou vetor de inteiros no-negativos + igualmente espaados com incremento igual a 1 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>m</term> + <listitem> + <para>inteiro no-negativo ou vetor de inteiros no-negativos + igualmente espaados com incremento igual a 1 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para> + vetor (linha) de reais (os elementos de <literal>x</literal> + devem estar no intervalo <literal>(-1,1)</literal> ) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>normflag</term> + <listitem> + <para>(opcional) escalar string </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Quando <literal>n</literal> e <literal>m</literal> so escalares, + <literal>legendre(n,m,x)</literal> avalia a funo de Legendre associada + Pnm(x) em todos os elementos de <literal>x</literal>. A definio usada + : + </para> + <programlisting role=""><![CDATA[ + m + m m/2 d +Pnm(x) = (-1) (1-x^2) --- Pn(x) + m + dx + ]]></programlisting> + <para> + onde <literal>Pn</literal> o polinmio de Legendre de grau + <literal>n</literal>. Ento, <literal>legendre(n,0,x)</literal> avalia o + polinmio de Legendre Pn(x) em todos os elementos de + <literal>x</literal>. + </para> + <para>Quando normflag igual a "norm" o resultado uma verso + normalizada (sem o fator <literal>(-1)^m</literal> ), precisamente : + </para> + <programlisting role=""><![CDATA[ + _____________ m + /(2n+1)(n-m)! m/2 d +Pnm(x,"norm") = /-------------- (1-x^2) --- Pn(x) + \/ 2 (n+m)! m + dx + ]]></programlisting> + <para>que til para computar funes harmnicas esfricas (ver exemplo + 3): + </para> + <para>Por eficincia, um dos primeiros dois argumentos pode ser um vetor, + por exemplo <literal>legendre(n1:n2,0,x)</literal> avalia todos os + polinmios de Legendre de graus <emphasis>n1, n1+1, ..., n2</emphasis> nos + elementos de <literal>x</literal> e <literal>legendre(n,m1:m2,x)</literal> + avalia todas as funes de Legendre associadas Pnm para <emphasis>m=m1, + m1+1, ..., m2 + </emphasis> + em <literal>x</literal>. + </para> + </refsection> + <refsection> + <title>Formato de Sada </title> + <para> + Em qualquer caso, o formato <literal>y</literal> : + </para> + <programlisting role=""><![CDATA[ +max(length(n),length(m)) x length(x) + ]]></programlisting> + <para>e :</para> + <programlisting role=""><![CDATA[ +y(i,j) = P(n(i),m;x(j)) se n um vetor +y(i,j) = P(n,m(i);x(j)) se m um vetor +y(1,j) = P(n,m;x(j)) se ambos n e m so escalares + ]]></programlisting> + <para> + de tal modo que <literal>x</literal> preferivelmente um vetor + linha, mas qualquer matriz <literal>mx x nx</literal> excetuada e + considerada como uma matriz <literal>1 x (mx * nx)</literal> matrix, + reformada segundo a ordem das colunas. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// exemplo 1 : plot dos primeiros 6 polinmios de Legendre em (-1,1) +l = nearfloat("pred",1); +x = linspace(-l,l,200)'; +y = legendre(0:5, 0, x); +clf() +plot2d(x,y', leg="p0@p1@p2@p3@p4@p5@p6") +xtitle("Os 6 primeiros polinmios de Legendre") + +// exemplo 2 : plot das funes associadas de Legendre de grau 5 +l = nearfloat("pred",1); +x = linspace(-l,l,200)'; +y = legendre(5, 0:5, x, "norm"); +clf() +plot2d(x,y', leg="p5,0@p5,1@p5,2@p5,3@p5,4@p5,5") +xtitle("As funes associadas de Legendre (normalizadas) de grau 5") + +// exemplo 3 : definindo e plotando uma funo harmnica esfrica +// 3-1 : definindo a funo Ylm +function [y] = Y(l,m,theta,phi) + // teta pode ser um escalar ou um vetor linha + // phi pode ser um escalar ou um vetor coluna + if m >= 0 then + y = (-1)^m/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, m, cos(theta), "norm") + else + y = 1/(sqrt(2*%pi))*exp(%i*m*phi)*legendre(l, -m, cos(theta), "norm") + end +endfunction + +// 3.2 : definindo outra funo til +function [x,y,z] = sph2cart(theta,phi,r) + // vetor linha teta 1 x nt + // vetor coluna phi np x 1 + // r escalar ou matriz np x nt (r(i,j) o comprimento em phi(i) theta(j)) + x = r.*(cos(phi)*sin(theta)); + y = r.*(sin(phi)*sin(theta)); + z = r.*(ones(phi)*cos(theta)); +endfunction + +// 3-3 plot de Y31(theta,phi) +l = 3; m = 1; +theta = linspace(0.1,%pi-0.1,60); +phi = linspace(0,2*%pi,120)'; +f = Y(l,m,theta,phi); +[x1,y1,z1] = sph2cart(theta,phi,abs(f)); [xf1,yf1,zf1] = nf3d(x1,y1,z1); +[x2,y2,z2] = sph2cart(theta,phi,abs(real(f))); [xf2,yf2,zf2] = nf3d(x2,y2,z2); +[x3,y3,z3] = sph2cart(theta,phi,abs(imag(f))); [xf3,yf3,zf3] = nf3d(x3,y3,z3); + +clf() +subplot(1,3,1) +plot3d(xf1,yf1,zf1,flag=[2 4 4]); xtitle("|Y31(theta,phi)|") +subplot(1,3,2) +plot3d(xf2,yf2,zf2,flag=[2 4 4]); xtitle("|Real(Y31(theta,phi))|") +subplot(1,3,3) +plot3d(xf3,yf3,zf3,flag=[2 4 4]); xtitle("|Imag(Y31(theta,phi))|") + ]]></programlisting> + </refsection> + <refsection> + <title>Autores</title> + <simplelist type="vert"> + <member>Smith, John M. (cdigo dxlegf.f de Slatec) </member> + <member>B. Pincon (interface Scilab)</member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ru_RU/addchapter.sce b/modules/special_functions/help/ru_RU/addchapter.sce new file mode 100755 index 000000000..8fbedc933 --- /dev/null +++ b/modules/special_functions/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("Special Functions",SCI+"/modules/special_functions/help/ru_RU",%T); + diff --git a/modules/special_functions/help/ru_RU/amell.xml b/modules/special_functions/help/ru_RU/amell.xml new file mode 100755 index 000000000..b63795fb4 --- /dev/null +++ b/modules/special_functions/help/ru_RU/amell.xml @@ -0,0 +1,65 @@ +<?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="ru" xml:id="amell"> + <refnamediv> + <refname>amell</refname> + <refpurpose>Эллиптическая функция am Якоби</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Последовательность вызова</title> + <synopsis>[sn]=amell(u,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Аргументы</title> + <variablelist> + <varlistentry> + <term>u</term> + <listitem> + <para>вещественный скаляр или вектор</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>скаляр</para> + </listitem> + </varlistentry> + <varlistentry> + <term>sn</term> + <listitem> + <para>вещественный скаляр или вектор</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Описание</title> + <para> + Вычисляет эллиптическую функцию <literal>am(u,k)</literal> Якоби, где + <literal>k</literal> - параметр, а <literal>u</literal> - аргумент. Если + <literal>u</literal> является вектором, то <literal>sn</literal> является вектором + вычисленных (поэлементно) значений. Используется в функции <literal>%sn</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Смотрите также</title> + <simplelist type="inline"> + <member> + <link linkend="delip">delip</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/special_functions/help/ru_RU/delip.xml b/modules/special_functions/help/ru_RU/delip.xml new file mode 100755 index 000000000..7aecaf170 --- /dev/null +++ b/modules/special_functions/help/ru_RU/delip.xml @@ -0,0 +1,146 @@ +<?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: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="delip" xml:lang="ru"> + <refnamediv> + <refname>delip</refname> + <refpurpose>полный и неполный эллиптический интеграл первого рода</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Последовательность вызова</title> + <synopsis>[r]=delip(x,ck)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Аргументы</title> + <variablelist> + <varlistentry> + <term>x</term> + <listitem> + <para>вещественный вектор/матрица с неотрицательными элементами real vector with non negative elements</para> + </listitem> + </varlistentry> + <varlistentry> + <term>ck</term> + <listitem> + <para>вещественное число между -1 и 1</para> + </listitem> + </varlistentry> + <varlistentry> + <term>r</term> + <listitem> + <para> + вещественное или комплексное число (или вектор/матрица) того же + размера, что и <literal>x</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Описание</title> + <para> + Эллиптический интеграл первого рода с параметром <literal>ck</literal> + определяется как: + </para> + <para> + <inlinemediaobject> + <imageobject> + <imagedata align="center"> + <mml:math> + <mml:semantics> + <mml:mrow> + <mml:munderover> + <mml:mo mml:stretchy="false">∫</mml:mo> + <mml:mn>0</mml:mn> + <mml:mi>x</mml:mi> + </mml:munderover> + <mml:mfrac> + <mml:mi mml:fontstyle="italic">dt</mml:mi> + <mml:msqrt> + <mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + <mml:mrow> + <mml:mo mml:stretchy="false">(</mml:mo> + <mml:mrow> + <mml:mrow> + <mml:mn>1</mml:mn> + <mml:mo mml:stretchy="false">−</mml:mo> + <mml:msubsup> + <mml:mi>c</mml:mi> + <mml:mi>k</mml:mi> + <mml:mn>2</mml:mn> + </mml:msubsup> + </mml:mrow> + <mml:msup> + <mml:mi>t</mml:mi> + <mml:mn>2</mml:mn> + </mml:msup> + </mml:mrow> + <mml:mo mml:stretchy="false">)</mml:mo> + </mml:mrow> + </mml:mrow> + </mml:msqrt> + </mml:mfrac> + </mml:mrow> + <mml:annotation mml:encoding="StarMath 5.0">int from{0} to{x} {{dt} over sqrt{ + (1-t^2)(1-c_k^2 t^2)}} + </mml:annotation> + </mml:semantics> + </mml:math> + </imagedata> + </imageobject> + </inlinemediaobject> + </para> + <para> + Где <literal>x</literal> - вещественное положительное число, + <literal>ck</literal> - лежит на интервале <literal>[-1 1]</literal>. + </para> + <para> + Если <literal>x</literal> меньше 1, то результат вещественный. + </para> + <para> + Вектор/матрица <literal>r</literal> + вычисляется для каждого элемента <literal>x</literal>. + </para> + </refsection> + <refsection> + <title>Примеры</title> + <programlisting role="example"><![CDATA[ +ck=0.5; +delip([1,2],ck) +deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))') +intg(0,1,f) //OK так как решение вещественное! + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Смотрите также</title> + <simplelist type="inline"> + <member> + <link linkend="amell">amell</link> + </member> + <member> + <link linkend="percentsn">%sn</link> + </member> + </simplelist> + </refsection> +</refentry> |