<?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="power">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ * Copyright (C) 2020 - Samuel GOUGEON
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+-->
+<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="power">
<refnamediv>
<refname>power</refname>
<refpurpose>(^,.^) power operation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Syntax</title>
- <synopsis>t=A^b
- t=A**b
- t=A.^b
+ <synopsis>
+ t = A ^ b
+ t = A ** b
+ t = A .^ b
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
- <term>A,t</term>
+ <term>A, t</term>
<listitem>
- <para>scalar, polynomial or rational matrix.</para>
+ a scalar, vector, or matrix of encoded integers, decimal or complex numbers,
+ polynomials, or rationals.
+ <para/>
</listitem>
</varlistentry>
<varlistentry>
<term>b</term>
<listitem>
- <para>a scalar, a vector or a scalar matrix.</para>
+ a scalar, vector, or matrix of encoded integers, decimal or complex numbers.
+ <para/>
</listitem>
</varlistentry>
</variablelist>
- </refsection>
- <refsection>
- <title>Description</title>
- <itemizedlist>
- <listitem>
- <para>
- If <literal>A</literal> is a square matrix and <literal>b</literal> is a scalar then <literal>A^b</literal> is the matrix <literal>A</literal> to the power <literal>b</literal>.
- </para>
- </listitem>
- <listitem>
- <para>
- If <literal>b</literal> is a scalar and <literal>A</literal> a matrix then
- <literal>A.^b</literal> is the matrix formed by the element of
- <literal>A</literal> to the power <literal>b</literal> (element-wise power). If
- <literal>A</literal> is a vector and <literal>b</literal> is a scalar then
- <literal>A^b</literal> and <literal>A.^b</literal> performs the same operation
- (i.e. element-wise power).
- </para>
- </listitem>
- <listitem>
- <para>
- If <literal>A</literal> is a scalar and <literal>b</literal> is a square matrix <literal>A^b</literal> is the matrix <literal> expm(log(A) * b)</literal>.
- </para>
- <para>
- If <literal>A</literal> is a scalar and <literal>b</literal> is a vector <literal>A^b</literal> and <literal>A.^b</literal> are the vector formed by <literal> a^(b(i,j))</literal>.
- </para>
- <para>
- If <literal>A</literal> is a scalar and <literal>b</literal> is a matrix <literal>A.^b</literal> is the matrix formed by <literal> a^(b(i,j))</literal>.
- </para>
- </listitem>
- <listitem>
- <para>
- If <literal>A</literal> and <literal>b</literal> are vectors (matrices) of the same size <literal>A.^b</literal> is the <literal>A(i)^b(i)</literal> vector (<literal>A(i,j)^b(i,j)</literal> matrix).
- </para>
- </listitem>
- </itemizedlist>
- </refsection>
- <refsection>
- <title>Additional Remarks</title>
- <para>
- <note> Notes: </note>
- </para>
- <para>
- 1. For square matrices <literal>A^p</literal> is computed through successive matrices
- multiplications if <literal>p</literal> is a positive integer, and by <emphasis>diagonalization</emphasis> if not (see "note 2 and 3" below for details).
- </para>
- <para>
- 2. If <varname>A</varname> is a square and Hermitian matrix and <varname>p</varname> is a non-integer scalar,
- <literal>A^p</literal> is computed as:
- </para>
- <para>
- <code>A^p = u*diag(diag(s).^p)*u'</code> (For real matrix <varname>A</varname>, only the real part of the answer is taken into account).
- </para>
- <para>
- <varname>u</varname> and <varname>s</varname> are determined by <code>[u,s] = schur(A)</code> .
- </para>
- <para>
- 3. If <varname>A</varname> is not a Hermitian matrix and <varname>p</varname> is a non-integer scalar,
- <literal>A^p</literal> is computed as:
- </para>
- <para>
- <code>A^p = v*diag(diag(d).^p)*inv(v)</code> (For real matrix <varname>A</varname>, only the real part of the answer is taken into account).
- </para>
- <para>
- <varname>d</varname> and <varname>v</varname> are determined by <code>[d,v] = bdiag(A+0*%i)</code> .
- </para>
- <para>
- 4. If <varname>A</varname> and <varname>p</varname> are real or complex numbers,
- <literal>A^p</literal> is the <emphasis>principal value</emphasis> determined by:
- </para>
- <para>
- <code>A^p = exp(p*log(A))</code> (or <code>A^p = exp(p*(log(abs(A))+ %i*atan(imag(A)/real(A))))</code> ).
- </para>
<para>
- 5. If <varname>A</varname> is a square matrix and <varname>p</varname> is a real or complex number,
- <literal>A.^p</literal> is the <emphasis>principal value</emphasis> computed as:
+ If an operand are encoded integers, the other one can be only encoded integers or real
+ numbers.
</para>
<para>
- <code>A.^p = exp(p*log(A))</code> (same as case 4 above).
- </para>
- <para>
- 6. <literal>**</literal> and <literal>^</literal> operators are synonyms.
- </para>
- <para>
- <warning>
- Exponentiation is right-associative in Scilab contrarily to Matlab® and Octave.
- For example 2^3^4 is equal to 2^(3^4) in Scilab but is equal to (2^3)^4 in Matlab®
- and Octave.
- </warning>
+ If <varname>A</varname> are polynomials or rationals, <varname>b</varname> can only be
+ a single decimal (positive or negative) integer.
</para>
</refsection>
<refsection>
+ <title>Description</title>
+ <refsect3>
+ <title>.^ by-element power</title>
+ <para>
+ If <varname>A</varname> or <varname>b</varname> is scalar, it is first
+ replicated to the size of the other, with A*ones(b) or b*ones(A).
+ Otherwise, <varname>A</varname> and <varname>b</varname> must have the same size.
+ </para>
+ <para>
+ Then, for each element of index i, <literal>t(i) = A(i)^b(i)</literal>
+ is computed.
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>^ matricial power</title>
+ <para>
+ The ^ operator is equivalent to the .^ by-element power in the following cases:
+ <itemizedlist>
+ <listitem>
+ <varname>A</varname> is scalar and <varname>b</varname> is a vector.
+ </listitem>
+ <listitem>
+ <varname>A</varname> is a vector and <varname>b</varname> is scalar.
+ </listitem>
+ </itemizedlist>
+ Otherwise, <varname>A</varname> or <varname>b</varname> must be a scalar,
+ and the other one must be a square matrix:
+ <itemizedlist>
+ <listitem>
+ <para>
+ If <varname>A</varname> is scalar and <varname>b</varname> is
+ a square matrix, then <literal>A^b</literal> is the matrix
+ <literal>expm(log(A) * b)</literal>
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is a square matrix and <varname>b</varname>
+ is scalar, then <literal>A^b</literal> is the matrix
+ <varname>A</varname> to the power <varname>b</varname>.
+ </para>
+ </listitem>
+ </itemizedlist>
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>Remarks</title>
+ <orderedlist>
+ <listitem>
+ <para>
+ For square matrices <literal>A^p</literal> is computed through successive
+ matrices multiplications if <literal>p</literal> is a positive integer, and by
+ <emphasis>diagonalization</emphasis> if not (see "note 2 and 3" below for details).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is a square and Hermitian matrix and <literal>p</literal>
+ is a non-integer scalar, <literal>A^p</literal> is computed as:
+ </para>
+ <para>
+ <code>A^p = u*diag(diag(s).^p)*u'</code> (For real matrix <varname>A</varname>,
+ only the real part of the answer is taken into account).
+ </para>
+ <para>
+ <literal>u</literal> and <literal>s</literal> are determined by
+ <code>[u,s] = schur(A)</code> .
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is not a Hermitian matrix and <literal>p</literal> is a
+ non-integer scalar, <literal>A^p</literal> is computed as:
+ </para>
+ <para>
+ <code>A^p = v*diag(diag(d).^p)*inv(v)</code> (For real matrix <varname>A</varname>,
+ only the real part of the answer is taken into account).
+ </para>
+ <para>
+ <literal>d</literal> and <literal>v</literal> are determined by
+ <code>[d,v] = bdiag(A+0*%i)</code>.
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> and <literal>p</literal> are real or complex numbers,
+ <literal>A^p</literal> is the <emphasis>principal value</emphasis> determined by
+ </para>
+ <para>
+ <code>A^p = exp(p*log(A))</code>
+ </para>
+ <para>
+ (or <code>A^p = exp(p*(log(abs(A))+ %i*atan(imag(A)/real(A))))</code> ).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is a square matrix and <literal>p</literal> is a real or
+ complex number, <literal>A.^p</literal> is the <emphasis>principal value</emphasis>
+ computed as:
+ </para>
+ <para>
+ <code>A.^p = exp(p*log(A))</code> (same as case 4 above).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ <literal>**</literal> and <literal>^</literal> operators are synonyms.
+ </para>
+ </listitem>
+ </orderedlist>
+ <para>
+ <warning>
+ Exponentiation is right-associative in Scilab, contrarily to Matlab® and Octave.
+ For example 2^3^4 is equal to 2^(3^4) in Scilab, but to (2^3)^4 in Matlab® and Octave.
+ </warning>
+ </para>
+ </refsect3>
+ </refsection>
+ <refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
-A=[1 2;3 4];
-A^2.5,
-A.^2.5
-(1:10)^2
-(1:10).^2
+A = [1 2 ; 3 4];
+A ^ 2.5,
+A .^ 2.5
+(1:10) ^ 2
+(1:10) .^ 2
-A^%i
-A.^%i
+A ^ %i
+A .^ %i
exp(%i*log(A))
-s=poly(0,'s')
-s^(1:10)
+s = poly(0,'s')
+s ^ (1:10)
]]></programlisting>
</refsection>
<refsection role="see also">
<link linkend="exp">exp</link>
</member>
<member>
+ <link linkend="expm">expm</link>
+ </member>
+ <member>
<link linkend="hat">hat</link>
</member>
+ <member>
+ <link linkend="inv">inv</link>
+ </member>
</simplelist>
</refsection>
+ <refsection role="history">
+ <title>History</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.0.0</revnumber>
+ <revdescription>
+ With decimal or complex numbers, <literal>scalar ^ squareMat</literal> now
+ yields <literal>expm(log(scalar)*squareMat)</literal> instead of
+ <literal>scalar .^ squareMat</literal>
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
</refentry>
<?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="power">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ * Copyright (C) 2020 - Samuel GOUGEON
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+-->
+<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="power">
<refnamediv>
<refname>power</refname>
<refpurpose>élévation à la puissance (^,.^) </refpurpose>
<refsynopsisdiv>
<title>Séquence d'appel</title>
<synopsis>
- t=A^b
- t=A**b
- t=A.^b
+ t = A ^ b
+ t = A ** b
+ t = A .^ b
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Paramètres</title>
<variablelist>
<varlistentry>
- <term>A,t </term>
+ <term>A, t </term>
<listitem>
- <para>matrice réelle, complexe, polynomiale ou rationnelle
- </para>
+ scalaire, vecteur, ou matrice de nombres entiers encodés, de nombres
+ ou polynômes ou fractions rationnelles à coefficients réels ou complexes.
+ <para/>
</listitem>
</varlistentry>
<varlistentry>
<term>b </term>
<listitem>
- <para>matrice réelle, complexe, polynomiale ou rationnelle
- </para>
+ scalaire, vecteur, ou matrice d'entiers encodés, de nombres décimaux,
+ ou de nombres complexes.
+ <para/>
</listitem>
</varlistentry>
</variablelist>
- </refsection>
- <refsection>
- <title>Description</title>
- <itemizedlist>
- <listitem>
- <para>
- Si <literal>A</literal> est une matrice carrée et <literal>b</literal> un scalaire alors <literal>A^b</literal> est la matrice <literal>A</literal> élevée à la puissance <literal>b</literal>.
- </para>
- </listitem>
- <listitem>
- <para>
- Si <literal>b</literal> est un un scalaire et <literal>A</literal> une matrice alors <literal>A.^b</literal> est la matrice formée par les éléments de <literal>A</literal> élevés à la puissance <literal>b</literal> (puissance élément par élément). Si <literal>A</literal> est un vecteur et <literal>b</literal> un scalaire alors <literal>A^b</literal> et <literal>A.^b</literal> donnent le même résultat (puissance élément par élément).
- </para>
- </listitem>
- <listitem>
- <para>
- Si <literal>A</literal> est un scalaire et <literal>b</literal> est une matrice carrée <literal>A^b</literal> est la matrice <literal>expm(log(A)*b)</literal>.
- </para>
- <para>
- Si <literal>A</literal> est un scalaire et <literal>b</literal> est une matrice <literal>A.^b</literal> est une matrice de même taille que b dont les termes sont égaux à <literal> a^(b(i,j))</literal>.
- </para>
- </listitem>
- <listitem>
- <para>
- Si <literal>A</literal> et <literal>b</literal> sont des matrices de même taille <literal>A.^b</literal> est la matrice dont les termes sont égaux à <literal>A(i,j)^b(i,j)</literal>.
- </para>
- </listitem>
- </itemizedlist>
<para>
- Notes :
+ Si un opérande sont des entiers encodés, l'autre peut être uniquement des entiers
+ encodés ou des nombres réels.
</para>
<para>
- -
- Pour les matrices carrées <literal>A^p</literal> est calculé par multiplications successives si <literal>p</literal> est un entier positif, et par diagonalisation sinon.
- </para>
- <para>
- -
- Les opérateurs <literal>**</literal> et <literal>^</literal> sont synonymes.
- </para>
- <para>
- <warning>
- L'élévation à la puissance est associative à droite dans Scilab contrairement à
- Matlab® et Octave. Par exemple 2^3^4 est égal à 2^(3^4) dans Scilab mais est égal à
- (2^3)^4 dans Matlab® et Octave.
- </warning>
+ Si <varname>A</varname> sont des polynômes ou des fractions rationnelles,
+ <varname>b</varname> peut uniquement être un entier décimal (positif ou négatif).
</para>
</refsection>
<refsection>
+ <title>Description</title>
+ <refsect3>
+ <title>.^ : puissances respectives par élément</title>
+ <para>
+ Si <varname>A</varname> ou <varname>b</varname> est scalaire, il est préalablement
+ répliqué à la taille de l'autre, par A*ones(b) ou b*ones(A).
+ Sinon, <varname>A</varname> et <varname>b</varname> doivent avoir la même taille.
+ </para>
+ <para>
+ Alors, pour chaque élément numéro i, <literal>t(i) = A(i)^b(i)</literal>
+ est calculé.
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>^ : puissance matricielle</title>
+ <para>
+ L'opérateur ^ est équivalent à .^ dans les cas suivants :
+ <itemizedlist>
+ <listitem>
+ <varname>A</varname> est scalaire et <varname>b</varname> est un vecteur.
+ </listitem>
+ <listitem>
+ <varname>A</varname> est un vecteur et <varname>b</varname> est scalaire.
+ </listitem>
+ </itemizedlist>
+ Sinon, <varname>A</varname> ou <varname>b</varname> doit être scalaire, et l'autre
+ opérande doit être une matrice carrée :
+ <itemizedlist>
+ <listitem>
+ <para>
+ Si <varname>A</varname> est scalaire et <varname>b</varname> est carrée,
+ alors <literal>A^b</literal> est la matrice
+ <literal>expm(log(A) * b)</literal>
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ Si <varname>A</varname> est carrée et <varname>b</varname> est scalaire,
+ alors <literal>A^b</literal> est la matrice
+ <varname>A</varname> à la puissane <varname>b</varname>.
+ </para>
+ </listitem>
+ </itemizedlist>
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>Autres remarques</title>
+ <orderedlist>
+ <listitem>
+ <para>
+ Si <varname>A</varname> est une matrice carrée, <literal>A^p</literal> est
+ calculé par multiplications successives si <literal>p</literal> est un
+ entier positif, et par diagonalisation sinon (détails en remarques n°2 et 3
+ ci-dessous).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is a square and Hermitian matrix and <literal>p</literal>
+ is a non-integer scalar, <literal>A^p</literal> is computed as:
+ </para>
+ <para>
+ <code>A^p = u*diag(diag(s).^p)*u'</code> (For real matrix <varname>A</varname>,
+ only the real part of the answer is taken into account).
+ </para>
+ <para>
+ <literal>u</literal> and <literal>s</literal> are determined by
+ <code>[u,s] = schur(A)</code> .
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is not a Hermitian matrix and <literal>p</literal> is a
+ non-integer scalar, <literal>A^p</literal> is computed as:
+ </para>
+ <para>
+ <code>A^p = v*diag(diag(d).^p)*inv(v)</code> (For real matrix <varname>A</varname>,
+ only the real part of the answer is taken into account).
+ </para>
+ <para>
+ <literal>d</literal> and <literal>v</literal> are determined by
+ <code>[d,v] = bdiag(A+0*%i)</code>.
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> and <literal>p</literal> are real or complex numbers,
+ <literal>A^p</literal> is the <emphasis>principal value</emphasis> determined by
+ </para>
+ <para>
+ <code>A^p = exp(p*log(A))</code>
+ </para>
+ <para>
+ (or <code>A^p = exp(p*(log(abs(A))+ %i*atan(imag(A)/real(A))))</code> ).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is a square matrix and <literal>p</literal> is a real or
+ complex number, <literal>A.^p</literal> is the <emphasis>principal value</emphasis>
+ computed as:
+ </para>
+ <para>
+ <code>A.^p = exp(p*log(A))</code> (same as case 4 above).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ Les opérateurs <literal>**</literal> et <literal>^</literal> sont équivalents.
+ </para>
+ </listitem>
+ </orderedlist>
+ <para>
+ <warning>
+ L'élévation à la puissance est associative à droite dans Scilab contrairement à
+ Matlab® et Octave. Par exemple 2^3^4 est égal à 2^(3^4) dans Scilab mais est égal à
+ (2^3)^4 dans Matlab® et Octave.
+ </warning>
+ </para>
+ </refsect3>
+ </refsection>
+ <refsection>
<title>Exemples</title>
<programlisting role="example"><![CDATA[
-A=[1 2;3 4];
-A^2.5,
-A.^2.5
-(1:10)^2
-(1:10).^2
+A = [1 2 ; 3 4];
+A ^ 2.5,
+A .^ 2.5
+(1:10) ^ 2
+(1:10) .^ 2
+
+A ^ %i
+A .^ %i
+exp(%i*log(A))
-s=poly(0,'s')
-s^(1:10)
+s = poly(0,'s')
+s ^ (1:10)
]]></programlisting>
</refsection>
<refsection role="see also">
<link linkend="exp">exp</link>
</member>
<member>
+ <link linkend="expm">expm</link>
+ </member>
+ <member>
<link linkend="hat">hat</link>
</member>
+ <member>
+ <link linkend="inv">inv</link>
+ </member>
</simplelist>
</refsection>
+ <refsection role="history">
+ <title>Historique</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.0.0</revnumber>
+ <revdescription>
+ Avec des nombres décimaux ou complexes, <literal>scalaire ^ matriceCarrée</literal>
+ produit désormais <literal>expm(log(scalaire)*matriceCarrée)</literal> au lieu
+ de <literal>scalaire .^ matriceCarrée</literal>.
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
</refentry>
<?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="power">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ * Copyright (C) 2020 - Samuel GOUGEON
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+-->
+<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="power">
<refnamediv>
<refname>power</refname>
<refpurpose>指数演算子 (^,.^) </refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>呼出し手順</title>
- <synopsis>t=A^b
- t=A**b
- t=A.^b
+ <synopsis>
+ t = A ^ b
+ t = A ** b
+ t = A .^ b
</synopsis>
</refsynopsisdiv>
<refsection>
<title>引数</title>
<variablelist>
<varlistentry>
- <term>A,t</term>
+ <term>A, t</term>
<listitem>
- <para>スカラー, 多項式または有理行列.</para>
+ a scalar, vector, or matrix of encoded integers, decimal or complex numbers,
+ polynomials, or rationals.
+ <para/>
</listitem>
</varlistentry>
<varlistentry>
<term>b</term>
<listitem>
- <para>スカラー, ベクトルまたはスカラーの行列.</para>
+ a scalar, vector, or matrix of encoded integers, decimal or complex numbers.
+ <para/>
</listitem>
</varlistentry>
</variablelist>
- </refsection>
- <refsection>
- <title>説明</title>
- <itemizedlist>
- <listitem>
- <para>
- <literal>A</literal> が正方行列で<literal>b</literal> がスカラーの場合,
- <literal>A^b</literal>は行列<literal>A</literal>の<literal>b</literal>乗に
- なります.
- </para>
- </listitem>
- <listitem>
- <para>
- <literal>b</literal> がスカラーで<literal>A</literal>が行列の場合,
- <literal>A.^b</literal>は<literal>A</literal>の各要素を<literal>b</literal>乗
- (要素毎の累乗)にした行列となります.
- <literal>A</literal> がベクトルで <literal>b</literal> がスカラーの場合,
- <literal>A^b</literal> と <literal>A.^b</literal> は同じ意味となります
- (すなわち,要素毎の累乗).
- </para>
- </listitem>
- <listitem>
- <para>
- <literal>A</literal> がスカラーで,<literal>b</literal> が行列 (またはベクトル)の場合,
- <literal>A^b</literal> および <literal>A.^b</literal> は,
- <literal> a^(b(i,j))</literal> により構成される行列 (またはベクトル) となります.
- </para>
- </listitem>
- <listitem>
- <para>
- <literal>A</literal> および <literal>b</literal> が同じ大きさのベクトル (行列) の場合,
- <literal>A.^b</literal> はベクトル <literal>A(i)^b(i)</literal>
- (行列<literal>A(i,j)^b(i,j)</literal>)となります.
- </para>
- </listitem>
- </itemizedlist>
- </refsection>
- <refsection>
- <title>追加の注記</title>
- <para>
- <note>注意:</note>
- </para>
- <para>
- 1.正方行列の場合, <literal>A^p</literal>は,
- <literal>p</literal>が正のスカラーの場合は行列の逐次乗算により計算され,
- それ以外の場合,<emphasis>対角化</emphasis>により計算されます
- (詳細は"注記2および3"を参照).
- </para>
- <para>
- 2. <varname>A</varname>が正方かつエルミート行列で
- <varname>p</varname> が整数でないスカラーの場合,
- <literal>A^p</literal> は以下の様に計算されます:
- </para>
- <para>
- <code>A^p = u*diag(diag(s).^p)*u'</code> (<varname>A</varname>が実数行列の場合,
- 答えの実部のみが考慮されます).
- </para>
- <para>
- <varname>u</varname>および<varname>s</varname> は, <code>[u,s] = schur(A)</code>
- により定義されます.
- </para>
- <para>
- 3. <varname>A</varname> がエルミート行列でなく,
- <varname>p</varname> が非整数スカラーの場合,
- <literal>A^p</literal> は以下の様に計算されます:
- </para>
- <para>
- <code>A^p = v*diag(diag(d).^p)*inv(v)</code>
- (<varname>A</varname>が実数行列の場合, 答えの実部のみが考慮されます).
- </para>
- <para>
- <varname>d</varname> および <varname>v</varname> は,
- <code>[d,v] = bdiag(A+0*%i)</code>により定義されます.
- </para>
<para>
- 4. <varname>A</varname> および <varname>p</varname> が実数または複素数の場合,
- <literal>A^p</literal> は以下のように計算される
- <emphasis>主値</emphasis>となります:
+ If an operand are encoded integers, the other one can be only encoded integers or real
+ numbers.
</para>
<para>
- <code>A^p = exp(p*log(A))</code> (または<code>A^p = exp(p*(log(abs(A))+ %i*atan(imag(A)/real(A))))</code> ).
- </para>
- <para>
- 5. <varname>A</varname> が正方行列で
- <varname>p</varname> が実数または複素数の場合,
- <literal>A.^p</literal> は以下のように計算される
- <emphasis>主値</emphasis> となります:
- </para>
- <para>
- <code>A.^p = exp(p*log(A))</code> (上記のケース4と同じ).
- </para>
- <para>
- 6. <literal>**</literal> および <literal>^</literal> 演算子は同義です.
+ If <varname>A</varname> are polynomials or rationals, <varname>b</varname> can only be
+ a single decimal (positive or negative) integer.
</para>
</refsection>
<refsection>
+ <title>説明</title>
+ <refsect3>
+ <title>.^ by-element power</title>
+ <para>
+ If <varname>A</varname> or <varname>b</varname> is scalar, it is first
+ replicated to the size of the other, with A*ones(b) or b*ones(A).
+ Otherwise, <varname>A</varname> and <varname>b</varname> must have the same size.
+ </para>
+ <para>
+ Then, for each element of index i, <literal>t(i) = A(i)^b(i)</literal>
+ is computed.
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>^ matricial power</title>
+ <para>
+ The ^ operator is equivalent to the .^ by-element power in the following cases:
+ <itemizedlist>
+ <listitem>
+ <varname>A</varname> is scalar and <varname>b</varname> is a vector.
+ </listitem>
+ <listitem>
+ <varname>A</varname> is a vector and <varname>b</varname> is scalar.
+ </listitem>
+ </itemizedlist>
+ Otherwise, <varname>A</varname> or <varname>b</varname> must be a scalar,
+ and the other one must be a square matrix:
+ <itemizedlist>
+ <listitem>
+ <para>
+ If <varname>A</varname> is scalar and <varname>b</varname> is
+ a square matrix, then <literal>A^b</literal> is the matrix
+ <literal>expm(log(A) * b)</literal>
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ If <varname>A</varname> is a square matrix and <varname>b</varname>
+ is scalar, then <literal>A^b</literal> is the matrix
+ <varname>A</varname> to the power <varname>b</varname>.
+ </para>
+ </listitem>
+ </itemizedlist>
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>追加の注記</title>
+ <orderedlist>
+ <listitem> <!-- #1 -->
+ <para>
+ 正方行列の場合, <literal>A^p</literal>は,
+ <literal>p</literal>が正のスカラーの場合は行列の逐次乗算により計算され,
+ それ以外の場合,<emphasis>対角化</emphasis>により計算されます
+ (詳細は"注記2および3"を参照).
+ </para>
+ </listitem>
+ <listitem> <!-- #2 -->
+ <para>
+ <varname>A</varname>が正方かつエルミート行列で
+ <literal>p</literal> が整数でないスカラーの場合,
+ <literal>A^p</literal> は以下の様に計算されます:
+ </para>
+ <para>
+ <code>A^p = u*diag(diag(s).^p)*u'</code> (<varname>A</varname>が実数行列の場合,
+ 答えの実部のみが考慮されます).
+ </para>
+ <para>
+ <literal>u</literal>および<literal>s</literal> は, <code>[u,s] = schur(A)</code>
+ により定義されます.
+ </para>
+ </listitem>
+ <listitem> <!-- #3 -->
+ <para>
+ <varname>A</varname> がエルミート行列でなく,
+ <literal>p</literal> が非整数スカラーの場合,
+ <literal>A^p</literal> は以下の様に計算されます:
+ </para>
+ <para>
+ <code>A^p = v*diag(diag(d).^p)*inv(v)</code>
+ (<varname>A</varname>が実数行列の場合, 答えの実部のみが考慮されます).
+ </para>
+ <para>
+ <literal>d</literal> および <literal>v</literal> は,
+ <code>[d,v] = bdiag(A+0*%i)</code>により定義されます.
+ </para>
+ </listitem>
+ <listitem> <!-- #4 -->
+ <para>
+ <varname>A</varname> および <literal>p</literal> が実数または複素数の場合,
+ <literal>A^p</literal> は以下のように計算される
+ <emphasis>主値</emphasis>となります:
+ </para>
+ <para>
+ <code>A^p = exp(p*log(A))</code>
+ </para>
+ <para>
+ (または<code>A^p = exp(p*(log(abs(A))+ %i*atan(imag(A)/real(A))))</code> ).
+ </para>
+ </listitem>
+ <listitem> <!-- #5 -->
+ <para>
+ <varname>A</varname> が正方行列で
+ <literal>p</literal> が実数または複素数の場合,
+ <literal>A.^p</literal> は以下のように計算される
+ <emphasis>主値</emphasis> となります:
+ </para>
+ <para>
+ <code>A.^p = exp(p*log(A))</code> (上記のケース4と同じ).
+ </para>
+ </listitem>
+ <listitem> <!-- #6 -->
+ <para>
+ <literal>**</literal> および <literal>^</literal> 演算子は同義です.
+ </para>
+ </listitem>
+ </orderedlist>
+ <para>
+ <warning>
+ Exponentiation is right-associative in Scilab, contrarily to Matlab® and Octave.
+ For example 2^3^4 is equal to 2^(3^4) in Scilab, but to (2^3)^4 in Matlab® and
+ Octave.
+ </warning>
+ </para>
+ </refsect3>
+ </refsection>
+ <refsection>
<title>例</title>
<programlisting role="example"><![CDATA[
-A=[1 2;3 4];
-A^2.5,
-A.^2.5
-(1:10)^2
-(1:10).^2
+A = [1 2 ; 3 4];
+A ^ 2.5,
+A .^ 2.5
+(1:10) ^ 2
+(1:10) .^ 2
-A^%i
-A.^%i
+A ^ %i
+A .^ %i
exp(%i*log(A))
-s=poly(0,'s')
-s^(1:10)
+s = poly(0,'s')
+s ^ (1:10)
]]></programlisting>
</refsection>
<refsection role="see also">
<link linkend="exp">exp</link>
</member>
<member>
+ <link linkend="expm">expm</link>
+ </member>
+ <member>
<link linkend="hat">hat</link>
</member>
+ <member>
+ <link linkend="inv">inv</link>
+ </member>
</simplelist>
</refsection>
+ <refsection role="history">
+ <title>履歴</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.0.0</revnumber>
+ <revdescription>
+ With decimal or complex numbers, <literal>scalar ^ squareMat</literal> now
+ yields <literal>expm(log(scalar)*squareMat)</literal> instead of
+ <literal>scalar .^ squareMat</literal>
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
</refentry>
+++ /dev/null
-<?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="power" xml:lang="pt">
- <refnamediv>
- <refname>power</refname>
- <refpurpose>operação de potenciação(^,.^)</refpurpose>
- </refnamediv>
- <refsynopsisdiv>
- <title>Seqüência de Chamamento</title>
- <synopsis>t=A^b
- t=A**b
- t=A.^b
- </synopsis>
- </refsynopsisdiv>
- <refsection>
- <title>Parâmetros</title>
- <variablelist>
- <varlistentry>
- <term>A,t</term>
- <listitem>
- <para>matriz de escalares, polinômios ou razões de
- polinômios.
- </para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>b</term>
- <listitem>
- <para>um escalar ou um vetor ou matriz de escalares.</para>
- </listitem>
- </varlistentry>
- </variablelist>
- </refsection>
- <refsection>
- <title>Descrição</title>
- <itemizedlist>
- <listitem>
- <para>
- <literal>"(A:square)^(b:scalar)"</literal>Se
- <literal>A</literal> é uma matriz quadrada e <literal>b</literal> é um
- escalar, então <literal>A^b</literal> é a matriz <literal>A</literal>
- elevada à potência <literal>b</literal>.
- </para>
- </listitem>
- <listitem>
- <para>
- <literal>"(A:matrix).^(b:scalar)"</literal>Se
- <literal>b</literal> é um escalar e <literal>A</literal> uma matriz,
- então <literal>A.^b</literal> é formada pelos elementos de
- <literal>A</literal> elevados à potência <literal>b</literal>
- (potenciação elemento a elemento). Se <literal>A</literal> é um vetor
- e <literal>b</literal> é um escalar, então <literal>A^b</literal> e
- <literal>A.^b</literal> realizam a mesma operação (i.e., potenciação
- elemento a elemento).
- </para>
- </listitem>
- <listitem>
- <para>
- <literal>"(A:scalar).^(b:matrix)"</literal> Se
- <literal>A</literal> é um escalar e <literal>b</literal> é uma matriz
- (ou vetor) então <literal>A^b</literal> e <literal>A.^b</literal> são
- as matrizes (ou vetores) formados por<literal>
- a^(b(i,j))
- </literal>
- .
- </para>
- </listitem>
- <listitem>
- <para>
- <literal>"(A:matrix).^(b:matrix)"</literal> Se
- <literal>A</literal> e <literal>b</literal> são vetores (matrizes) de
- mesmo tamanho <literal>A.^b</literal> é o vetor
- <literal>A(i)^b(i)</literal> (matriz
- <literal>A(i,j)^b(i,j)</literal>).
- </para>
- </listitem>
- </itemizedlist>
- <para>Notas:</para>
- <para>
- - Para matrizes quadradas <literal>A^p</literal> é computada através
- de sucessivas multiplicações de matrizes se <literal>p</literal> is é um
- número inteiro positivo e por diagonalização se não for.
- </para>
- <para>- Os operadores ** e ^ são sinônimos.</para>
- </refsection>
- <refsection>
- <title>Exemplos</title>
- <programlisting role="example"><![CDATA[
-A=[1 2;3 4];
-A^2.5,
-A.^2.5
-(1:10)^2
-(1:10).^2
-
-s=poly(0,'s')
-s^(1:10)
- ]]></programlisting>
- </refsection>
- <refsection>
- <title> Ver Também </title>
- <simplelist type="inline">
- <member>
- <link linkend="exp">exp</link>
- </member>
- </simplelist>
- </refsection>
-</refentry>
<?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="ru" xml:id="power">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ * Copyright (C) 2020 - Samuel GOUGEON
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+-->
+<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="power">
<refnamediv>
<refname>возведение в степень</refname>
<refpurpose>операция возведения в степень (^, .^)</refpurpose>
<refsynopsisdiv>
<title>Синтаксис</title>
<synopsis>
- t=A^b
- t=A**b
- t=A.^b
+ t = A ^ b
+ t = A ** b
+ t = A .^ b
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Аргументы</title>
<variablelist>
<varlistentry>
- <term>A,t</term>
+ <term>A, t</term>
<listitem>
- <para>
- скаляр или вектор/матрица числовых, полиномиальных или рациональных значений
- </para>
+ скаляр, вектор или матрица кодированных целых чисел, десятичных или
+ комплексных чисел, полиномов или дробно-рациональных выражений.
+ <para/>
</listitem>
</varlistentry>
<varlistentry>
<term>b</term>
<listitem>
- <para>скаляр, вектор или матрица.</para>
+ скаляр, вектор или матрица кодированных целых чисел, десятичных или
+ комплексных чисел.
+ <para/>
</listitem>
</varlistentry>
</variablelist>
- </refsection>
- <refsection>
- <title>Описание</title>
- <itemizedlist>
- <listitem>
- <para>
- Если <literal>A</literal> -- квадратная матрица, а <literal>b</literal> -- скаляр, то <literal>A^b</literal>
- является матрицей <literal>A</literal> в степени <literal>b</literal>.
- </para>
- </listitem>
- <listitem>
- <para>
- Если <literal>A</literal> -- матрица, а <literal>b</literal> -- скаляр, то матрица
- <literal>A.^b</literal> формируется элементами матрицы <literal>A</literal>
- в степени <literal>b</literal> (поэлементное возведение в степень).
- Если <literal>A</literal> -- вектор, а <literal>b</literal> -- скаляр, то
- <literal>A^b</literal> и <literal>A.^b</literal> выполняют одну и ту же операцию
- (т. е. поэлементное возведение в степень).
- </para>
- </listitem>
- <listitem>
- <para>
- Если <literal>A</literal> -- скаляр, а <literal>b</literal> -- матрица (или вектор), то
- <literal>A^b</literal> и <literal>A.^b</literal> являются матрицами (или векторами), сформированными
- элементами <literal> a^(b(i,j))</literal>.
- </para>
- </listitem>
- <listitem>
- <para>
- Если <literal>A</literal> и <literal>b</literal> -- векторы (матрицы) одного размера, то
- <literal>A.^b</literal> равно <literal>A(i)^b(i)</literal> (векторы) или <literal>A(i,j)^b(i,j)</literal> (матрицы).
- </para>
- </listitem>
- </itemizedlist>
- <para>
- Примечания:
- </para>
<para>
- -
- Для квадратных матриц <literal>A^p</literal> вычисляется через последовательное
- перемножение матриц, если <literal>p</literal> является положительным числом, а иначе --
- через диагонализацию.
+ Если операндом являются кодированные целые числа, то другие числа могут
+ быть только кодированными целыми числами или вещественными числами.
</para>
<para>
- -
- операторы <literal>**</literal> и <literal>^</literal> являются синонимами.
+ Если <varname>A</varname> является полиномами или дробно-рациональными
+ выражениями, то <varname>b</varname> может быть только одиночным десятичным
+ (положительным или отрицательным) числом.
</para>
</refsection>
<refsection>
+ <title>Описание</title>
+ <refsect3>
+ <title>.^ поэлементное возведение в степень</title>
+ <para>
+ Если <varname>A</varname> или <varname>b</varname> скаляр,
+ то он сначала реплицируется до размера другого с помощью
+ <literal>A*ones(b)</literal> или <literal>b*ones(A)</literal>.
+ В противном случае <varname>A</varname> и <varname>b</varname>
+ должны быть одинакового размера.
+ </para>
+ <para>
+ Затем для каждого элемента с индексом <literal>i</literal>
+ вычисляется <literal>t(i) = A(i)^b(i)</literal>.
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>^ матричное возведение в степень</title>
+ <para>
+ Оператор <literal>^</literal> эквивалентен поэлементному возведению
+ в степень <literal>.^</literal> в следующих случаях:
+ <itemizedlist>
+ <listitem>
+ <varname>A</varname> скаляр, а <varname>b</varname> вектор;
+ </listitem>
+ <listitem>
+ <varname>A</varname> вектор, а <varname>b</varname> скаляр.
+ </listitem>
+ </itemizedlist>
+ В противном случае <varname>A</varname> либо <varname>b</varname>
+ должен быть скаляром, а другой должен быть квадратной матрицей:
+ <itemizedlist>
+ <listitem>
+ <para>
+ если <varname>A</varname> скаляр, а <varname>b</varname>
+ квадратная матрица, то <literal>A^b</literal> является
+ матрицей <literal>expm(log(A) * b)</literal>;
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ если <varname>A</varname> квадратная матрица, а <varname>b</varname>
+ скаляр, то <literal>A^b</literal> является матрицей
+ <varname>A</varname> в степени <varname>b</varname>.
+ </para>
+ </listitem>
+ </itemizedlist>
+ </para>
+ </refsect3>
+ <refsect3>
+ <title>Примечания</title>
+ <orderedlist>
+ <listitem>
+ <para>
+ Для квадратных матриц <varname>A</varname>, <literal>A^p</literal>
+ вычисляется через последовательное перемножение матриц, если
+ <literal>p</literal> является положительным числом, а иначе -
+ через диагонализацию (см. примечания №2 и №3 ниже).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ Если <varname>A</varname> квадратная и эрмитова матрица, а
+ <literal>p</literal> нецелый скаляр, то <literal>A^p</literal>
+ вычисляется как:
+ </para>
+ <para>
+ <code>A^p = u*diag(diag(s).^p)*u'</code> (для вещественной
+ матрицы <varname>A</varname> во внимание принимается только
+ вещественная часть ответа).
+ </para>
+ <para>
+ <literal>u</literal> и <literal>s</literal> определяются как
+ <code>[u,s] = schur(A)</code> .
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ Если <varname>A</varname> не является эрмитовой матрицей,
+ а <literal>p</literal> является нецелым скаляром, то
+ <literal>A^p</literal> вычисляется как:
+ </para>
+ <para>
+ <code>A^p = v*diag(diag(d).^p)*inv(v)</code> (для вещественной
+ матрицы <varname>A</varname> во внимание принимается только
+ вещественная часть ответа).
+ </para>
+ <para>
+ <literal>d</literal> и <literal>v</literal> определяются
+ как <code>[d,v] = bdiag(A+0*%i)</code>.
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ Если <varname>A</varname> и <literal>p</literal> вещественные
+ или комплексные числа, то <literal>A^p</literal> является
+ <emphasis>главным значением</emphasis>, определяемым как
+ </para>
+ <para>
+ <code>A^p = exp(p*log(A))</code>
+ </para>
+ <para>
+ (или <code>A^p = exp(p*(log(abs(A))+ %i*atan(imag(A)/real(A))))</code> ).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ Если <varname>A</varname> является квадратной матрице, а
+ <literal>p</literal> вещественным или комплексным числом, то
+ <literal>A.^p</literal> является <emphasis>главным значением</emphasis>
+ вычисленным как:
+ </para>
+ <para>
+ <code>A.^p = exp(p*log(A))</code> (то же самое, что и в случае 4 выше).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ операторы <literal>**</literal> и <literal>^</literal> являются
+ синонимами.
+ </para>
+ </listitem>
+ </orderedlist>
+ <para>
+ <warning>
+ Возведение в степень в Scilab является оператором с ассоциативностью
+ справа, в отличие от Matlab® и Octave.
+ Например <literal>2^3^4</literal> в Scilab равно <literal>2^(3^4)</literal>,
+ а в Matlab® и Octave равно <literal>(2^3)^4</literal>.
+ </warning>
+ </para>
+ </refsect3>
+ </refsection>
+ <refsection>
<title>Примеры</title>
<programlisting role="example"><![CDATA[
-A=[1 2;3 4];
-A^2.5,
-A.^2.5
-(1:10)^2
-(1:10).^2
+A = [1 2 ; 3 4];
+A ^ 2.5,
+A .^ 2.5
+(1:10) ^ 2
+(1:10) .^ 2
-s=poly(0,'s')
-s^(1:10)
+A ^ %i
+A .^ %i
+exp(%i*log(A))
+
+s = poly(0,'s')
+s ^ (1:10)
]]></programlisting>
</refsection>
<refsection role="see also">
<link linkend="exp">exp</link>
</member>
<member>
+ <link linkend="expm">expm</link>
+ </member>
+ <member>
<link linkend="hat">крышечка</link>
</member>
+ <member>
+ <link linkend="inv">inv</link>
+ </member>
</simplelist>
</refsection>
+ <refsection role="history">
+ <title>История</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.0.0</revnumber>
+ <revdescription>
+ С десятичным или комплексным числами <literal>scalar ^ squareMat</literal>
+ теперь даёт <literal>expm(log(scalar)*squareMat)</literal> вместо
+ <literal>scalar .^ squareMat</literal>.
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
</refentry>
projects / scilab.git / commitdiff