Fix one of my mistake: I overrided some translations by the english one during file... 59/8759/2
Sylvestre Ledru [Tue, 21 Aug 2012 12:27:21 +0000 (14:27 +0200)]
Change-Id: Id73d3a8f63f82507561af8bfbbd5288c5efc7bfc

165 files changed:
scilab/modules/elementary_functions/help/en_US/exponential/expm.xml
scilab/modules/elementary_functions/help/fr_FR/exponential/expm.xml
scilab/modules/elementary_functions/help/fr_FR/exponential/polar.xml
scilab/modules/elementary_functions/help/fr_FR/matrixmanipulation/squeeze.xml
scilab/modules/elementary_functions/help/fr_FR/symbolic/cmb_lin.xml
scilab/modules/elementary_functions/help/ja_JP/exponential/expm.xml
scilab/modules/elementary_functions/help/ja_JP/exponential/polar.xml
scilab/modules/elementary_functions/help/ja_JP/matrixmanipulation/squeeze.xml
scilab/modules/elementary_functions/help/ja_JP/symbolic/cmb_lin.xml
scilab/modules/elementary_functions/help/pt_BR/exponential/expm.xml
scilab/modules/elementary_functions/help/pt_BR/exponential/polar.xml
scilab/modules/elementary_functions/help/pt_BR/matrixmanipulation/squeeze.xml
scilab/modules/linear_algebra/help/fr_FR/eigen/bdiag.xml
scilab/modules/linear_algebra/help/fr_FR/eigen/gspec.xml
scilab/modules/linear_algebra/help/fr_FR/eigen/hess.xml
scilab/modules/linear_algebra/help/fr_FR/eigen/pbig.xml
scilab/modules/linear_algebra/help/fr_FR/eigen/spec.xml
scilab/modules/linear_algebra/help/fr_FR/eigen/sva.xml
scilab/modules/linear_algebra/help/fr_FR/eigen/svd.xml
scilab/modules/linear_algebra/help/fr_FR/factorization/givens.xml
scilab/modules/linear_algebra/help/fr_FR/factorization/householder.xml
scilab/modules/linear_algebra/help/fr_FR/factorization/sqroot.xml
scilab/modules/linear_algebra/help/fr_FR/kernel/colcomp.xml
scilab/modules/linear_algebra/help/fr_FR/kernel/fullrf.xml
scilab/modules/linear_algebra/help/fr_FR/kernel/fullrfk.xml
scilab/modules/linear_algebra/help/fr_FR/kernel/kernel.xml
scilab/modules/linear_algebra/help/fr_FR/kernel/range.xml
scilab/modules/linear_algebra/help/fr_FR/kernel/rowcomp.xml
scilab/modules/linear_algebra/help/fr_FR/linear/chol.xml
scilab/modules/linear_algebra/help/fr_FR/linear/inv.xml
scilab/modules/linear_algebra/help/fr_FR/linear/linsolve.xml
scilab/modules/linear_algebra/help/fr_FR/linear/lu.xml
scilab/modules/linear_algebra/help/fr_FR/linear/pinv.xml
scilab/modules/linear_algebra/help/fr_FR/linear/qr.xml
scilab/modules/linear_algebra/help/fr_FR/matrix/cond.xml
scilab/modules/linear_algebra/help/fr_FR/matrix/det.xml
scilab/modules/linear_algebra/help/fr_FR/matrix/orth.xml
scilab/modules/linear_algebra/help/fr_FR/matrix/rank.xml
scilab/modules/linear_algebra/help/fr_FR/matrix/rcond.xml
scilab/modules/linear_algebra/help/fr_FR/matrix/trace.xml
scilab/modules/linear_algebra/help/fr_FR/pencil/companion.xml
scilab/modules/linear_algebra/help/fr_FR/pencil/glever.xml
scilab/modules/linear_algebra/help/fr_FR/pencil/lyap.xml
scilab/modules/linear_algebra/help/fr_FR/proj.xml
scilab/modules/linear_algebra/help/fr_FR/state_space/coff.xml
scilab/modules/linear_algebra/help/fr_FR/state_space/nlev.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/balanc.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/bdiag.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/gschur.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/gspec.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/hess.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/pbig.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/projspec.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/psmall.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/schur.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/spec.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/sva.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/svd.xml
scilab/modules/linear_algebra/help/ja_JP/factorization/givens.xml
scilab/modules/linear_algebra/help/ja_JP/factorization/householder.xml
scilab/modules/linear_algebra/help/ja_JP/factorization/sqroot.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/colcomp.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/fullrf.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/fullrfk.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/im_inv.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/kernel.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/range.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/rowcomp.xml
scilab/modules/linear_algebra/help/ja_JP/linear/aff2ab.xml
scilab/modules/linear_algebra/help/ja_JP/linear/chol.xml
scilab/modules/linear_algebra/help/ja_JP/linear/inv.xml
scilab/modules/linear_algebra/help/ja_JP/linear/linsolve.xml
scilab/modules/linear_algebra/help/ja_JP/linear/lsq.xml
scilab/modules/linear_algebra/help/ja_JP/linear/lu.xml
scilab/modules/linear_algebra/help/ja_JP/linear/pinv.xml
scilab/modules/linear_algebra/help/ja_JP/linear/qr.xml
scilab/modules/linear_algebra/help/ja_JP/linear/rankqr.xml
scilab/modules/linear_algebra/help/ja_JP/markov/classmarkov.xml
scilab/modules/linear_algebra/help/ja_JP/markov/eigenmarkov.xml
scilab/modules/linear_algebra/help/ja_JP/markov/genmarkov.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/cond.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/det.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/orth.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/rank.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/rcond.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/rref.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/trace.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/companion.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/ereduc.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/fstair.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/glever.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/kroneck.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/lyap.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/pencan.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/penlaur.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/quaskro.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/randpencil.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/rowshuff.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/sylv.xml
scilab/modules/linear_algebra/help/ja_JP/proj.xml
scilab/modules/linear_algebra/help/ja_JP/state_space/coff.xml
scilab/modules/linear_algebra/help/ja_JP/state_space/nlev.xml
scilab/modules/linear_algebra/help/ja_JP/subspaces/spaninter.xml
scilab/modules/linear_algebra/help/ja_JP/subspaces/spanplus.xml
scilab/modules/linear_algebra/help/ja_JP/subspaces/spantwo.xml
scilab/modules/linear_algebra/help/pt_BR/cmb_lin.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/balanc.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/bdiag.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/gschur.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/gspec.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/hess.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/pbig.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/projspec.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/psmall.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/schur.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/spec.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/sva.xml
scilab/modules/linear_algebra/help/pt_BR/eigen/svd.xml
scilab/modules/linear_algebra/help/pt_BR/factorization/givens.xml
scilab/modules/linear_algebra/help/pt_BR/factorization/householder.xml
scilab/modules/linear_algebra/help/pt_BR/factorization/sqroot.xml
scilab/modules/linear_algebra/help/pt_BR/kernel/colcomp.xml
scilab/modules/linear_algebra/help/pt_BR/kernel/fullrf.xml
scilab/modules/linear_algebra/help/pt_BR/kernel/fullrfk.xml
scilab/modules/linear_algebra/help/pt_BR/kernel/im_inv.xml
scilab/modules/linear_algebra/help/pt_BR/kernel/kernel.xml
scilab/modules/linear_algebra/help/pt_BR/kernel/range.xml
scilab/modules/linear_algebra/help/pt_BR/kernel/rowcomp.xml
scilab/modules/linear_algebra/help/pt_BR/linear/aff2ab.xml
scilab/modules/linear_algebra/help/pt_BR/linear/chol.xml
scilab/modules/linear_algebra/help/pt_BR/linear/inv.xml
scilab/modules/linear_algebra/help/pt_BR/linear/linsolve.xml
scilab/modules/linear_algebra/help/pt_BR/linear/lsq.xml
scilab/modules/linear_algebra/help/pt_BR/linear/lu.xml
scilab/modules/linear_algebra/help/pt_BR/linear/pinv.xml
scilab/modules/linear_algebra/help/pt_BR/linear/qr.xml
scilab/modules/linear_algebra/help/pt_BR/linear/rankqr.xml
scilab/modules/linear_algebra/help/pt_BR/markov/classmarkov.xml
scilab/modules/linear_algebra/help/pt_BR/markov/eigenmarkov.xml
scilab/modules/linear_algebra/help/pt_BR/markov/genmarkov.xml
scilab/modules/linear_algebra/help/pt_BR/matrix/cond.xml
scilab/modules/linear_algebra/help/pt_BR/matrix/det.xml
scilab/modules/linear_algebra/help/pt_BR/matrix/orth.xml
scilab/modules/linear_algebra/help/pt_BR/matrix/rank.xml
scilab/modules/linear_algebra/help/pt_BR/matrix/rcond.xml
scilab/modules/linear_algebra/help/pt_BR/matrix/rref.xml
scilab/modules/linear_algebra/help/pt_BR/matrix/trace.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/companion.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/ereduc.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/fstair.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/glever.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/kroneck.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/lyap.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/pencan.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/penlaur.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/quaskro.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/randpencil.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/rowshuff.xml
scilab/modules/linear_algebra/help/pt_BR/pencil/sylv.xml
scilab/modules/linear_algebra/help/pt_BR/proj.xml
scilab/modules/linear_algebra/help/pt_BR/state_space/coff.xml
scilab/modules/linear_algebra/help/pt_BR/state_space/nlev.xml
scilab/modules/linear_algebra/help/pt_BR/subspaces/spaninter.xml
scilab/modules/linear_algebra/help/pt_BR/subspaces/spanplus.xml
scilab/modules/linear_algebra/help/pt_BR/subspaces/spantwo.xml

index b4c281f..6cacde0 100644 (file)
  *
  -->
 <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" version="5.0-subset Scilab" xml:lang="en" xml:id="expm">
-    <refnamediv>
-        <refname>expm</refname>
-        <refpurpose> square matrix exponential</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>expm(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>square matrix with real or complex entries.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>X</literal> is a square matrix <literal>expm(X)</literal> is the matrix
-        </para>
-        <para>
-            <literal>expm(X) = I + X + X^2 /2 + ...</literal>
-        </para>
-        <para>
-            The computation is performed by first 
-            block-diagonalizing <literal>X</literal> and then applying a Pade approximation 
-            on each block.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+  <refnamediv>
+    <refname>expm</refname>
+    <refpurpose> square matrix exponential</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Calling Sequence</title>
+    <synopsis>expm(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Arguments</title>
+    <variablelist>
+      <varlistentry>
+        <term>X</term>
+        <listitem>
+          <para>square matrix with real or complex entries.</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>X</literal> is a square matrix <literal>expm(X)</literal> is the matrix
+    </para>
+    <para>
+      <literal>expm(X) = I + X + X^2 /2 + ...</literal>
+    </para>
+    <para>
+      The computation is performed by first 
+      block-diagonalizing <literal>X</literal> and then applying a Pade approximation 
+      on each block.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Examples</title>
+    <programlisting role="example"><![CDATA[ 
 X=[1 2;3 4]
 expm(X)
 logm(expm(X))    
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="logm">logm</link>
-            </member>
-            <member>
-                <link linkend="bdiag">bdiag</link>
-            </member>
-            <member>
-                <link linkend="coff">coff</link>
-            </member>
-            <member>
-                <link linkend="log">log</link>
-            </member>
-            <member>
-                <link linkend="exp">exp</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>See Also</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="logm">logm</link>
+      </member>
+      <member>
+        <link linkend="bdiag">bdiag</link>
+      </member>
+      <member>
+        <link linkend="coff">coff</link>
+      </member>
+      <member>
+        <link linkend="log">log</link>
+      </member>
+      <member>
+        <link linkend="exp">exp</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index b4c281f..ea7f61f 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="expm">
-    <refnamediv>
-        <refname>expm</refname>
-        <refpurpose> square matrix exponential</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>expm(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>square matrix with real or complex entries.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>X</literal> is a square matrix <literal>expm(X)</literal> is the matrix
-        </para>
-        <para>
-            <literal>expm(X) = I + X + X^2 /2 + ...</literal>
-        </para>
-        <para>
-            The computation is performed by first 
-            block-diagonalizing <literal>X</literal> and then applying a Pade approximation 
-            on each block.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="expm">
+  <refnamediv>
+    <refname>expm</refname>
+    <refpurpose> exponentielle de matrice  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>expm(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+    </para>
+    <para>
+      Pour <literal>X</literal> une matrice carrée <literal>expm(X)</literal> est la matrice
+    </para>
+    <para>
+      expm(X) = I + X + X^2 /2 + ...
+    </para>
+    <para>
+      Le calcul fait appel à une 
+      bloc-diagonalisation préliminaire de <literal>X</literal> suivie d'une approximation 
+      de Padé sur chaque bloc.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 X=[1 2;3 4]
 expm(X)
 logm(expm(X))    
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="logm">logm</link>
-            </member>
-            <member>
-                <link linkend="bdiag">bdiag</link>
-            </member>
-            <member>
-                <link linkend="coff">coff</link>
-            </member>
-            <member>
-                <link linkend="log">log</link>
-            </member>
-            <member>
-                <link linkend="exp">exp</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="logm">logm</link>
+      </member>
+      <member>
+        <link linkend="bdiag">bdiag</link>
+      </member>
+      <member>
+        <link linkend="coff">coff</link>
+      </member>
+      <member>
+        <link linkend="log">log</link>
+      </member>
+      <member>
+        <link linkend="exp">exp</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 2baa2ce..87b7fed 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="polar">
-    <refnamediv>
-        <refname>polar</refname>
-        <refpurpose> polar form</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Ro,Theta]=polar(A)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Ro,  </term>
-                <listitem>
-                    <para>real matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Theta,  </term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[Ro,Theta]=polar(A)</literal> returns the polar form of
-            <literal>A</literal> i.e.  <literal>A=Ro*expm(%i*Theta)</literal><literal>Ro</literal> symmetric &gt;=0 and <literal>Theta</literal> hermitian
-            &gt;=0.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="polar">
+  <refnamediv>
+    <refname>polar</refname>
+    <refpurpose> forme polaire  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[Ro,Theta]=polar(A)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Ro, Theta  </term>
+        <listitem>
+          <para>matrices réelles
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>[Ro,Theta]=polar(A)</literal> renvoie la forme polaire de
+      <literal>A</literal> c'est à dire :<literal>A=Ro*expm(%i*Theta)</literal>
+      <literal>Ro</literal> symétrique &gt;=0 et <literal>Theta</literal>
+      hermitienne &gt;=0.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,5);
 [Ro,Theta]=polar(A);
 norm(A-Ro*expm(%i*Theta),1)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="expm">expm</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="expm">expm</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index c9f3952..30c5204 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="squeeze">
-    <refnamediv>
-        <refname>squeeze</refname>
-        <refpurpose> squeeze</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>hypOut = squeeze(hypIn)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>hypIn</term>
-                <listitem>
-                    <para>hypermatrix or matrix of constant type.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>hypOut</term>
-                <listitem>
-                    <para>hypermatrix or matrix of constant type.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para> Remove singleton dimensions of a hypermatrix, that is any dimension for
-            which the size is 1. If the input is a matrix, it is unaffected.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
-       M1 = zeros(2,1,5)
-       squeeze(M1)
-       squeeze(M1(:,:,1))
-       
-       M2 = hypermat([2 1 2 1],1:4)
-       squeeze(M2)
-       ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="hypermat">hypermat</link>
-            </member>
-            <member>
-                <link linkend="hypermatrices">hypermatrices</link>
-            </member>
-        </simplelist>
-    </refsection>
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="squeeze">
+  <refnamediv>
+    <refname>squeeze</refname>
+    <refpurpose> squeeze</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>hypOut = squeeze(hypIn)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>hypIn</term>
+        <listitem>
+          <para>hypermatrice ou matrice réelle.</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>hypOut</term>
+        <listitem>
+          <para>hypermatrcex ou matrice réelle.</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para> Elimine les dimensions de type "singleton" d'une hypermatrice,
+      c'est-à -dire toutes les dimensions de taille 1.
+      Les matrices sont quant à  elles inchangées. 
+    </para>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="hypermat">hypermat</link>
+      </member>
+      <member>
+        <link linkend="hypermatrices">hypermatrices</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index c8eb1bf..249a38c 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="cmb_lin">
-    <refnamediv>
-        <refname>cmb_lin</refname>
-        <refpurpose> symbolic linear combination</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Evaluates <literal>alfa*x-beta*y</literal>. <literal> alfa, beta, x, y</literal> are character
-            strings. (low-level routine)
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="mulf">mulf</link>
-            </member>
-            <member>
-                <link linkend="addf">addf</link>
-            </member>
-        </simplelist>
-    </refsection>
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="cmb_lin">
+  <refnamediv>
+    <refname>cmb_lin</refname>
+    <refpurpose> combinaison linéaire symbolique  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Évalue <literal>alfa*x-beta*y</literal>. <literal> alfa, beta, x, y</literal> sont des chaînes de caractères (routine de bas niveau).
+    </para>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="mulf">mulf</link>
+      </member>
+      <member>
+        <link linkend="addf">addf</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 83783f1..2ac9c6e 100644 (file)
  *
  -->
 <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" version="5.0-subset Scilab" xml:lang="ja" xml:id="expm">
-    <refnamediv>
-        <refname>expm</refname>
-        <refpurpose> 正方行列の指数関数</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>呼び出し手順</title>
-        <synopsis>expm(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>パラメータ</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>実数または複素数のエントリを有する正方行列.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>説明</title>
-        <para>
-            <literal>X</literal> が正方行列の時,
-            <literal>expm(X)</literal> は以下の行列となります
-        </para>
-        <para>
-            <literal>expm(X) = I + X + X^2 /2 + ...</literal>
-        </para>
-        <para>
-            計算はまず<literal>X</literal>をブロック対角化した後,
-            各ブロックにパデ近似を適用します.
-        </para>
-    </refsection>
-    <refsection>
-        <title>例</title>
-        <programlisting role="example"><![CDATA[ 
+  <refnamediv>
+    <refname>expm</refname>
+    <refpurpose> 正方行列の指数関数</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>呼び出し手順</title>
+    <synopsis>expm(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>パラメータ</title>
+    <variablelist>
+      <varlistentry>
+        <term>X</term>
+        <listitem>
+          <para>実数または複素数のエントリを有する正方行列.</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>説明</title>
+    <para>
+      <literal>X</literal> が正方行列の時,
+      <literal>expm(X)</literal> は以下の行列となります
+    </para>
+    <para>
+      <literal>expm(X) = I + X + X^2 /2 + ...</literal>
+    </para>
+    <para>
+      計算はまず<literal>X</literal>をブロック対角化した後,
+      各ブロックにパデ近似を適用します.
+    </para>
+  </refsection>
+  <refsection>
+    <title>例</title>
+    <programlisting role="example"><![CDATA[ 
 X=[1 2;3 4]
 expm(X)
 logm(expm(X))    
  ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>参照</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="logm">logm</link>
-            </member>
-            <member>
-                <link linkend="bdiag">bdiag</link>
-            </member>
-            <member>
-                <link linkend="coff">coff</link>
-            </member>
-            <member>
-                <link linkend="log">log</link>
-            </member>
-            <member>
-                <link linkend="exp">exp</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>参照</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="logm">logm</link>
+      </member>
+      <member>
+        <link linkend="bdiag">bdiag</link>
+      </member>
+      <member>
+        <link linkend="coff">coff</link>
+      </member>
+      <member>
+        <link linkend="log">log</link>
+      </member>
+      <member>
+        <link linkend="exp">exp</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 8a61bed..8e85925 100644 (file)
  *
  -->
 <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" version="5.0-subset Scilab" xml:lang="ja" xml:id="polar">
-    <refnamediv>
-        <refname>polar</refname>
-        <refpurpose>極座標形式</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>呼び出し手順</title>
-        <synopsis>[Ro,Theta]=polar(A)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>パラメータ</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>実数または複素数の正方行列</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Ro,  </term>
-                <listitem>
-                    <para>実数行列</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Theta,  </term>
-                <listitem>
-                    <para>実数または複素数の行列</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>説明</title>
-        <para>
-            <literal>[Ro,Theta]=polar(A)</literal> は
-            <literal>A</literal>の極座標形式,すなわち,
-            <literal>A=Ro*expm(%i*Theta)</literal>,
-            対称行列 <literal>Ro</literal> &gt;=0
-            およびエルミート行列 <literal>Theta</literal> &gt;=0 を返します.
-        </para>
-    </refsection>
-    <refsection>
-        <title>例</title>
-        <programlisting role="example"><![CDATA[ 
+  <refnamediv>
+    <refname>polar</refname>
+    <refpurpose>極座標形式</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>呼び出し手順</title>
+    <synopsis>[Ro,Theta]=polar(A)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>パラメータ</title>
+    <variablelist>
+      <varlistentry>
+        <term>A</term>
+        <listitem>
+          <para>実数または複素数の正方行列</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Ro,  </term>
+        <listitem>
+          <para>実数行列</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Theta,  </term>
+        <listitem>
+          <para>実数または複素数の行列</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>説明</title>
+    <para>
+      <literal>[Ro,Theta]=polar(A)</literal> は
+      <literal>A</literal>の極座標形式,すなわち,
+      <literal>A=Ro*expm(%i*Theta)</literal>,
+      対称行列 <literal>Ro</literal> &gt;=0
+      およびエルミート行列 <literal>Theta</literal> &gt;=0 を返します.
+    </para>
+  </refsection>
+  <refsection>
+    <title>例</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,5);
 [Ro,Theta]=polar(A);
 norm(A-Ro*expm(%i*Theta),1)
  ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>参照</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="expm">expm</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>作者</title>
-        <para>F. Delebecque INRIA; ;   </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>参照</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="expm">expm</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index c9f3952..9180113 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="squeeze">
-    <refnamediv>
-        <refname>squeeze</refname>
-        <refpurpose> squeeze</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>hypOut = squeeze(hypIn)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>hypIn</term>
-                <listitem>
-                    <para>hypermatrix or matrix of constant type.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>hypOut</term>
-                <listitem>
-                    <para>hypermatrix or matrix of constant type.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para> Remove singleton dimensions of a hypermatrix, that is any dimension for
-            which the size is 1. If the input is a matrix, it is unaffected.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
-       M1 = zeros(2,1,5)
-       squeeze(M1)
-       squeeze(M1(:,:,1))
-       
-       M2 = hypermat([2 1 2 1],1:4)
-       squeeze(M2)
-       ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="hypermat">hypermat</link>
-            </member>
-            <member>
-                <link linkend="hypermatrices">hypermatrices</link>
-            </member>
-        </simplelist>
-    </refsection>
+<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" version="5.0-subset Scilab" xml:lang="ja" xml:id="squeeze">
+  <refnamediv>
+    <refname>squeeze</refname>
+    <refpurpose>スクイズ</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>呼び出し手順</title>
+    <synopsis>hypOut = squeeze(hypIn)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>パラメータ</title>
+    <variablelist>
+      <varlistentry>
+        <term>hypIn</term>
+        <listitem>
+          <para>定数型のハイパー行列または行列.</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>hypOut</term>
+        <listitem>
+          <para>定数型のハイパー行列または行列.</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>説明</title>
+    <para> 
+      ハイパー行列の単一次元,つまり,
+      大きさが1の次元を削除します.
+      入力が行列の場合,変更されません.
+    </para>
+  </refsection>
+  <refsection role="see also">
+    <title>参照</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="hypermat">hypermat</link>
+      </member>
+      <member>
+        <link linkend="hypermatrices">hypermatrices</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 8021c12..3916f6e 100644 (file)
  *
  -->
 <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" version="5.0-subset Scilab" xml:lang="ja" xml:id="cmb_lin">
-    <refnamediv>
-        <refname>cmb_lin</refname>
-        <refpurpose> シンボリックな線形結合計算</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>呼び出し手順</title>
-        <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>説明</title>
-        <para>
-            <literal>alfa*x-beta*y</literal>を評価します. 
-            <literal> alfa, beta, x, y</literal> は文字列です.
-            (低レベルルーチン)
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>参照</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="mulf">mulf</link>
-            </member>
-            <member>
-                <link linkend="addf">addf</link>
-            </member>
-        </simplelist>
-    </refsection>
+  <refnamediv>
+    <refname>cmb_lin</refname>
+    <refpurpose> シンボリックな線形結合</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>呼び出し手順</title>
+    <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>説明</title>
+    <para>
+      <literal>alfa*x-beta*y</literal>を評価します. <literal> alfa, beta, x, y</literal> 
+      は文字列です. (低レベルルーチン)
+    </para>
+  </refsection>
+  <refsection role="see also">
+    <title>参照</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="mulf">mulf</link>
+      </member>
+      <member>
+        <link linkend="addf">addf</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index b4c281f..acae35b 100644 (file)
@@ -1,4 +1,4 @@
-<?xml version="1.0" encoding="UTF-8"?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="expm">
-    <refnamediv>
-        <refname>expm</refname>
-        <refpurpose> square matrix exponential</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>expm(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>square matrix with real or complex entries.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>X</literal> is a square matrix <literal>expm(X)</literal> is the matrix
-        </para>
-        <para>
-            <literal>expm(X) = I + X + X^2 /2 + ...</literal>
-        </para>
-        <para>
-            The computation is performed by first 
-            block-diagonalizing <literal>X</literal> and then applying a Pade approximation 
-            on each block.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:id="expm" xml:lang="en">
+  <refnamediv>
+    <refname>expm</refname>
+    <refpurpose>exponencial de matriz quadrada (matriz
+      exponencial)
+    </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Seqüência de Chamamento</title>
+    <synopsis>expm(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Parâmetros</title>
+    <variablelist>
+      <varlistentry>
+        <term>X</term>
+        <listitem>
+          <para>square matrix with real or complex entries.</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Descrição</title>
+    <para>
+      <literal>X</literal> é uma matriz quadrada e
+      <literal>expm(X)</literal> é a matriz
+    </para>
+    <para>
+      <literal>expm(X) = I + X + X^2 /2 + ...</literal>
+    </para>
+    <para>A computação é realizada primeiro diagonalizando em blocos a matriz
+      <literal>X</literal> e, em seguida, aplicando uma aproximação de Pade em
+      cada bloco.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemplos</title>
+    <programlisting role="example"><![CDATA[ 
 X=[1 2;3 4]
 expm(X)
 logm(expm(X))    
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="logm">logm</link>
-            </member>
-            <member>
-                <link linkend="bdiag">bdiag</link>
-            </member>
-            <member>
-                <link linkend="coff">coff</link>
-            </member>
-            <member>
-                <link linkend="log">log</link>
-            </member>
-            <member>
-                <link linkend="exp">exp</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Ver Também</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="logm">logm</link>
+      </member>
+      <member>
+        <link linkend="bdiag">bdiag</link>
+      </member>
+      <member>
+        <link linkend="coff">coff</link>
+      </member>
+      <member>
+        <link linkend="log">log</link>
+      </member>
+      <member>
+        <link linkend="exp">exp</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 2baa2ce..bad23c2 100644 (file)
@@ -1,4 +1,4 @@
-<?xml version="1.0" encoding="UTF-8"?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="polar">
-    <refnamediv>
-        <refname>polar</refname>
-        <refpurpose> polar form</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Ro,Theta]=polar(A)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Ro,  </term>
-                <listitem>
-                    <para>real matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Theta,  </term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[Ro,Theta]=polar(A)</literal> returns the polar form of
-            <literal>A</literal> i.e.  <literal>A=Ro*expm(%i*Theta)</literal><literal>Ro</literal> symmetric &gt;=0 and <literal>Theta</literal> hermitian
-            &gt;=0.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:id="polar" xml:lang="en">
+  <refnamediv>
+    <refname>polar</refname>
+    <refpurpose>forma polar</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Seqüência de Chamamento</title>
+    <synopsis>[Ro,Theta]=polar(A)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Parâmetros</title>
+    <variablelist>
+      <varlistentry>
+        <term>A</term>
+        <listitem>
+          <para> matriz quadrada de reais ou complexos </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Ro,</term>
+        <listitem>
+          <para>matriz de reais </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Theta,</term>
+        <listitem>
+          <para>matriz de reais ou complexos</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Descrição</title>
+    <para>
+      <literal>[Ro,Theta]=polar(A)</literal> retorna a forma polar de
+      <literal>A</literal> i.e.
+      <literal>A=Ro*expm(%i*Theta)</literal><literal>Ro</literal> simétrico
+      &gt;= 0 e <literal>Theta</literal> hermitiano &gt;=0.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemplos</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,5);
 [Ro,Theta]=polar(A);
 norm(A-Ro*expm(%i*Theta),1)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="expm">expm</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Ver Também</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="expm">expm</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index c9f3952..5c371a0 100644 (file)
@@ -1,4 +1,4 @@
-<?xml version="1.0" encoding="UTF-8"?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="squeeze">
-    <refnamediv>
-        <refname>squeeze</refname>
-        <refpurpose> squeeze</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>hypOut = squeeze(hypIn)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>hypIn</term>
-                <listitem>
-                    <para>hypermatrix or matrix of constant type.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>hypOut</term>
-                <listitem>
-                    <para>hypermatrix or matrix of constant type.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para> Remove singleton dimensions of a hypermatrix, that is any dimension for
-            which the size is 1. If the input is a matrix, it is unaffected.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
-       M1 = zeros(2,1,5)
-       squeeze(M1)
-       squeeze(M1(:,:,1))
-       
-       M2 = hypermat([2 1 2 1],1:4)
-       squeeze(M2)
-       ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="hypermat">hypermat</link>
-            </member>
-            <member>
-                <link linkend="hypermatrices">hypermatrices</link>
-            </member>
-        </simplelist>
-    </refsection>
+<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" version="5.0-subset Scilab" xml:id="squeeze" xml:lang="en">
+  <refnamediv>
+    <refname>squeeze</refname>
+    <refpurpose>remoção de dimensões singletons</refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Seqüência de Chamamento</title>
+    <synopsis>hypOut = squeeze(hypIn)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Parâmetros</title>
+    <variablelist>
+      <varlistentry>
+        <term>hypIn</term>
+        <listitem>
+          <para>hipermatriz ou matriz do tipo constante.</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>hypOut</term>
+        <listitem>
+          <para>hipermatriz ou matriz do tipo constante.</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Descrição</title>
+    <para>Remove dimensões singletons de uma hipermatriz, i.e., qualquer
+      dimensão para a qual o tamanho é 1. Se a entrada é uma matriz, ela não é
+      afetada.
+    </para>
+  </refsection>
+  <refsection role="see also">
+    <title>Ver Também</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="hypermat">hypermat</link>
+      </member>
+      <member>
+        <link linkend="hypermatrices">hypermatrices</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Autores</title>
+    <para>Eric Dubois, Jean-Baptiste Silvy</para>
+  </refsection>
 </refentry>
index 29102fe..5200bb2 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="bdiag">
-    <refnamediv>
-        <refname>bdiag</refname>
-        <refpurpose> block diagonalization, generalized eigenvectors</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rmax</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Ab</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex non-singular matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>bs</term>
-                <listitem>
-                    <para>vector of integers</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <programlisting role=""><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="bdiag">
+  <refnamediv>
+    <refname>bdiag</refname>
+    <refpurpose> bloc-diagonalisation, vecteurs propres généralisés  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>rmax  </term>
+        <listitem>
+          <para>nombre réel
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Ab  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice régulière, réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>bs  </term>
+        <listitem>
+          <para>vecteur d'entiers
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <programlisting role=""><![CDATA[ 
 [Ab [,X [,bs]]]=bdiag(A [,rmax]) 
  ]]></programlisting>
-        <para>
-            performs the block-diagonalization of matrix <literal>A</literal>.  bs
-            gives the structure of the blocks (respective sizes of the
-            blocks).  <literal>X</literal> is the change of basis i.e 
-            <literal>Ab = inv(X)*A*X</literal>is block diagonal.
-        </para>
-        <para>
-            <literal>rmax</literal> controls the conditioning of <literal>X</literal>; the
-            default value is the l1 norm of <literal>A</literal>.
-        </para>
-        <para>
-            To get a diagonal form (if it exists) choose a large value for
-            <literal>rmax</literal> (<literal>rmax=1/%eps</literal> for example).
-            Generically (for real random A) the blocks are (1x1) and (2x2) and
-            <literal>X</literal> is the matrix of eigenvectors.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
-//Real case: 1x1 and 2x2 blocks
+    <para>
+      <literal>[Ab [,X [,bs]]]=bdiag(A [,rmax])</literal> calcule la forme
+      bloc-diagonale de <literal>A</literal>.  bs précise la structure des
+      blocs (tailles respectives des blocs).  <literal>X</literal> est la
+      matrice de changement de base, c'est à dire que <literal>Ab =
+        inv(X)*A*X 
+      </literal>
+      est bloc-diagonale.
+    </para>
+    <para>
+      <literal>rmax</literal> contrôle le conditionnement de <literal>X</literal>;
+      la valeur par défaut est la norme l1 de <literal>A</literal>.
+    </para>
+    <para>
+      Pour obtenir une forme diagonale (si celle-ci existe) choisissez
+      une valeur élevée de <literal>rmax</literal> (<literal>rmax=1/%eps</literal>
+      par exemple).  Pour une matrice réelle quelconque, les blocs sont
+      de taille (1x1) ou (2x2) et <literal>X</literal> est la matrice des
+      vecteurs propres.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
+// Cas réel: blocs 1x1 et 2x2
 a=rand(5,5);[ab,x,bs]=bdiag(a);ab
-
-//Complex case: complex 1x1 blocks
+// Cas complexe : blocs complexes 1x1
 [ab,x,bs]=bdiag(a+%i*0);ab
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="schur">schur</link>
-            </member>
-            <member>
-                <link linkend="sylv">sylv</link>
-            </member>
-            <member>
-                <link linkend="spec">spec</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="schur">schur</link>
+      </member>
+      <member>
+        <link linkend="sylv">sylv</link>
+      </member>
+      <member>
+        <link linkend="spec">spec</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index dbde0cb..16561cb 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="gspec">
-    <refnamediv>
-        <refname>gspec</refname>
-        <refpurpose>
-            eigenvalues of matrix pencil. <emphasis role="bold">This function is obsolete.</emphasis>
-        </refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[al,be]=gspec(A,E)
-            [al,be,Z]=gspec(A,E)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Description</title>
-        <para>
-            This function is now included in the <literal>spec</literal> function.
-            the calling syntax must be replaced by
-        </para>
-        <programlisting role=""><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="gspec">
+  <refnamediv>
+    <refname>gspec</refname>
+    <refpurpose> valeurs propres d'un faisceau de matrices (obsolete) </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[al,be]=gspec(A,E)
+      [al,be,Z]=gspec(A,E)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A, E  </term>
+        <listitem>
+          <para>matrices carrées réelles de mêmes dimensions
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>al, be  </term>
+        <listitem>
+          <para>vecteurs réels
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Z  </term>
+        <listitem>
+          <para>matrice carrée régulière
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Cette fonction est maintenant un cas particulier de la fonction
+      <literal>spec</literal>. La syntaxe d'appel doit être remplacée par 
+    </para>
+    <programlisting role=""><![CDATA[ 
 [al,be]=spec(A,E)
 [al,be,Z]=spec(A,E)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="spec">spec</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="spec">spec</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index f9cc5c5..6af47de 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="hess">
-    <refnamediv>
-        <refname>hess</refname>
-        <refpurpose> Hessenberg form</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>H = hess(A)
-            [U,H] = hess(A)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>H</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>U</term>
-                <listitem>
-                    <para>orthogonal or unitary square matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[U,H] = hess(A)</literal> produces a unitary matrix
-            <literal>U</literal> and a Hessenberg matrix <literal>H</literal> so that
-            <literal>A = U*H*U'</literal> and <literal>U'*U</literal> =
-            Identity.  By itself, <literal>hess(A)</literal> returns <literal>H</literal>.
-        </para>
-        <para>
-            The Hessenberg form of a matrix is zero below the first
-            subdiagonal. If the matrix is symmetric or Hermitian, the form is
-            tridiagonal.
-        </para>
-    </refsection>
-    <refsection>
-        <title>References</title>
-        <para>
-            hess function is based on the Lapack routines
-            DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the complex case.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="hess">
+  <refnamediv>
+    <refname>hess</refname>
+    <refpurpose> Forme de Hessenberg  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>H = hess(A)
+      [U,H] = hess(A)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>H  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>U  </term>
+        <listitem>
+          <para>matrice carrée unitaire
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>[U,H] = hess(A)</literal> Calcule une matrice unitaire <literal>U</literal>
+      et une matrice de Hessenberg <literal>H</literal> telles que <literal>A =
+        U*H*U'
+      </literal>
+      et <literal>U'*U</literal> = Identité. La syntaxe
+      <literal>H=hess(A)</literal> ne renvoie que la matrice de Hessenberg.
+    </para>
+    <para>
+      Les coefficients d'une matrice sous forme de Hessenberg sont nuls
+      sous la première sous-diagonale. Si la matrice est symétrique ou
+      hermitienne, la forme est tridiagonale.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(3,3);[U,H]=hess(A);
 and( abs(U*H*U'-A)<1.d-10 )
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="contr">contr</link>
-            </member>
-            <member>
-                <link linkend="schur">schur</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            <literal>hess</literal> function is based on the Lapack routines
-            DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the
-            complex  case.
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="contr">contr</link>
+      </member>
+      <member>
+        <link linkend="schur">schur</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      Le calcul de la forme de Hessenberg determinant est basé sur les routines Lapack :
+      DGEHRD, DORGHR  pour les matrices réelles et ZGEHRD, ZORGHR pour le cas complexe.
+    </para>
+  </refsection>
 </refentry>
index 9291150..21542bf 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="pbig">
-    <refnamediv>
-        <refname>pbig</refname>
-        <refpurpose> eigen-projection</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>thres</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag</term>
-                <listitem>
-                    <para>
-                        character string (<literal>'c'</literal> or <literal>'d'</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Q,M</term>
-                <listitem>
-                    <para>real matrices</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Projection on eigen-subspace associated with eigenvalues with real
-            part &gt;= <literal>thres</literal> (<literal>flag='c'</literal>) or
-            with magnitude &gt;= <literal>thres</literal>
-            (<literal>flag='d'</literal>).
-        </para>
-        <para>
-            The projection is defined by <literal>Q*M</literal>, <literal>Q</literal> is
-            full column rank, <literal>M</literal> is full row rank and
-            <literal>M*Q=eye</literal>.
-        </para>
-        <para>
-            If <literal>flag='c'</literal>, the eigenvalues of
-            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with real part
-            &gt;= <literal>thres</literal>.
-        </para>
-        <para>
-            If <literal>flag='d'</literal>, the eigenvalues of
-            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with magnitude
-            &gt;= <literal>thres</literal>.
-        </para>
-        <para>
-            If <literal>flag='c'</literal> and if <literal>[Q1,M1]</literal> =
-            full rank factorization (<literal>fullrf</literal>) of
-            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
-            eigenvalues of <literal>A</literal> with real part &lt;
-            <literal>thres</literal>.
-        </para>
-        <para>
-            If <literal>flag='d'</literal> and if <literal>[Q1,M1]</literal> =
-            full rank factorization (<literal>fullrf</literal>) of
-            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
-            eigenvalues of <literal>A</literal> with magnitude &lt;
-            <literal>thres</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="pbig">
+  <refnamediv>
+    <refname>pbig</refname>
+    <refpurpose> projection sur des sous-espaces propres   </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle carrée
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>thres  </term>
+        <listitem>
+          <para>nombre réel
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>flag  </term>
+        <listitem>
+          <para>
+            chaîne de caractères (<literal>'c'</literal> ou <literal>'d'</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Q,M  </term>
+        <listitem>
+          <para>matrices réelles
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Projection sur des sous-espaces propres de A associés aux valeurs
+      propres avec partie réelle &gt;= <literal>thres</literal>
+      (<literal>flag='c'</literal>) ou avec module &gt;=
+      <literal>thres</literal> (<literal>flag='d'</literal>).
+    </para>
+    <para>
+      La projection est définie par <literal>Q*M</literal>, où <literal>Q</literal>
+      est de rang maximal, les lignes de <literal>M</literal> sont
+      linéairement indépendantes et <literal>M*Q=eye</literal>.
+    </para>
+    <para>
+      Si <literal>flag='c'</literal>, les valeurs propres de
+      <literal>M*A*Q</literal> = valeurs propres de <literal>A</literal> avec partie
+      réelle &gt;= <literal>thres</literal>.
+    </para>
+    <para>
+      Si <literal>flag='d'</literal>, les valeurs propres de
+      <literal>M*A*Q</literal> = valeurs propres de <literal>A</literal> avec module
+      &gt;= <literal>thres</literal>.
+    </para>
+    <para>
+      Si <literal>flag='c'</literal> et si <literal>[Q1,M1]</literal> =
+      factorisation de rang maximal (<literal>fullrf</literal>) de
+      <literal>eye()-Q*M</literal> alors les valeurs propres de
+      <literal>M1*A*Q1</literal> = valeurs propres de <literal>A</literal> avec
+      partie réelle &lt; <literal>thres</literal>.
+    </para>
+    <para>
+      Si <literal>flag='d'</literal> et si <literal>[Q1,M1]</literal> =
+      factorisation de rang maximal (<literal>fullrf</literal>) de
+      <literal>eye()-Q*M</literal> alors les valeurs propres de
+      <literal>M1*A*Q1</literal> = valeurs propres de <literal>A</literal> avec
+      module &lt; <literal>thres</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
 [Q,M]=pbig(A,1.5,'d');
 spec(M*A*Q)
 [Q1,M1]=fullrf(eye()-Q*M);
 spec(M1*A*Q1)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="psmall">psmall</link>
-            </member>
-            <member>
-                <link linkend="projspec">projspec</link>
-            </member>
-            <member>
-                <link linkend="fullrf">fullrf</link>
-            </member>
-            <member>
-                <link linkend="schur">schur</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            <literal>pbig</literal> is based on the ordered schur form (scilab
-            function <literal>schur</literal>).
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="psmall">psmall</link>
+      </member>
+      <member>
+        <link linkend="projspec">projspec</link>
+      </member>
+      <member>
+        <link linkend="fullrf">fullrf</link>
+      </member>
+      <member>
+        <link linkend="schur">schur</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      <literal>pbig</literal> est basée sur la forme de Schur ordonnée
+      (fonction Scilab <literal>schur</literal>).
+    </para>
+  </refsection>
 </refentry>
index 20bd852..229aef7 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:id="spec" xml:lang="en">
-    <refnamediv>
-        <refname>spec</refname>
-        <refpurpose>eigenvalues of matrices and pencils</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>evals=spec(A)
-            [R,diagevals]=spec(A)
-            
-            evals=spec(A,B)
-            [alpha,beta]=spec(A,B)
-            [alpha,beta,Z]=spec(A,B)
-            [alpha,beta,Q,Z]=spec(A,B)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>B</term>
-                <listitem>
-                    <para>real or complex square matrix with same dimensions as
-                        <literal> A</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>evals</term>
-                <listitem>
-                    <para>real or complex vector, the eigenvalues</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>diagevals</term>
-                <listitem>
-                    <para>real or complex diagonal matrix (eigenvalues along the
-                        diagonal)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>alpha</term>
-                <listitem>
-                    <para>real or complex vector, al./be gives the eigenvalues</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>beta</term>
-                <listitem>
-                    <para>real vector, al./be gives the eigenvalues</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>R</term>
-                <listitem>
-                    <para>real or complex invertible square matrix, matrix right
-                        eigenvectors.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>L</term>
-                <listitem>
-                    <para>real or complex invertible square matrix, pencil left
-                        eigenvectors.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>R</term>
-                <listitem>
-                    <para>real or complex invertible square matrix, pencil right
-                        eigenvectors.
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <variablelist>
-            <varlistentry>
-                <term>evals=spec(A)</term>
-                <listitem>
-                    <para>
-                        returns in vector <literal>evals</literal> the
-                        eigenvalues.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[R,diagevals] =spec(A)</term>
-                <listitem>
-                    <para>
-                        returns in the diagonal matrix <literal>evals</literal> the
-                        eigenvalues and in <literal>R</literal> the right
-                        eigenvectors.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>evals=spec(A,B)</term>
-                <listitem>
-                    <para>returns the spectrum of the matrix pencil A - s B, i.e. the
-                        roots of the polynomial matrix s B - A.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[alpha,beta] = spec(A,B)</term>
-                <listitem>
-                    <para>
-                        returns the spectrum of the matrix pencil <literal>A- s
-                            B
-                        </literal>
-                        ,i.e. the roots of the polynomial matrix <literal>A - s
-                            B
-                        </literal>
-                        .Generalized eigenvalues alpha and beta are so that the
-                        matrix <literal>A - alpha./beta B</literal> is a singular matrix.
-                        The eigenvalues are given by <literal>al./be</literal> and if
-                        <literal>beta(i) = 0</literal> the ith eigenvalue is at infinity.
-                        (For <literal>B = eye(A), alpha./beta</literal> is
-                        <literal>spec(A)</literal>). It is usually represented as the pair
-                        (alpha,beta), as there is a reasonable interpretation for beta=0,
-                        and even for both being zero.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[alpha,beta,R] = spec(A,B)</term>
-                <listitem>
-                    <para>
-                        returns in addition the matrix <literal>R</literal> of
-                        generalized right eigenvectors of the pencil.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[al,be,L,R] = spec(A,B)</term>
-                <listitem>
-                    <para>
-                        returns in addition the matrix <literal>L</literal> and
-                        <literal>R</literal> of generalized left and right eigenvectors of
-                        the pencil.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[al,be,Z] = spec(A,E)</term>
-                <listitem>
-                    <para>
-                        returns the matrix <literal>Z</literal> of right
-                        generalized eigen vectors.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[al,be,Q,Z] = spec(A,E)</term>
-                <listitem>
-                    <para>
-                        returns the matrices <literal>Q</literal>
-                        and <literal>Z</literal> of right and left generalized
-                        eigen vectors.
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-        <para>For big full / sparse matrix, you can use the Arnoldi module.</para>
-    </refsection>
-    <refsection>
-        <title>References</title>
-        <para>Matrix eigenvalues computations are based on the Lapack
-            routines
-        </para>
-        <itemizedlist>
-            <listitem>
-                <para>DGEEV and ZGEEV when the matrix are not symmetric,</para>
-            </listitem>
-            <listitem>
-                <para>DSYEV and ZHEEV when the matrix are symmetric.</para>
-            </listitem>
-        </itemizedlist>
-        <para>A complex symmetric matrix has conjugate offdiagonal terms and real
-            diagonal terms.
-        </para>
-        <para>Pencil eigenvalues computations are based on the Lapack routines
-            DGGEV and ZGGEV.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Real and complex matrices</title>
-        <para>It must be noticed that the type of the output variables, such as
-            evals or R for example, is not necessarily the same as the type of the
-            input matrices A and B. In the following paragraph, we analyse the type of
-            the output variables in the case where one computes the eigenvalues and
-            eigenvectors of one single matrix A.
-        </para>
-        <itemizedlist>
-            <listitem>
-                <para>Real A matrix</para>
-                <itemizedlist>
-                    <listitem>
-                        <para>Symetric</para>
-                        <para>The eigenvalues and the eigenvectors are real.</para>
-                    </listitem>
-                    <listitem>
-                        <para>Not symmetric</para>
-                        <para>The eigenvalues and eigenvectors are complex.</para>
-                    </listitem>
-                </itemizedlist>
-            </listitem>
-            <listitem>
-                <para>Complex A matrix</para>
-                <itemizedlist>
-                    <listitem>
-                        <para>Symetric</para>
-                        <para>The eigenvalues are real but the eigenvectors are
-                            complex.
-                        </para>
-                    </listitem>
-                    <listitem>
-                        <para>Not symmetric</para>
-                        <para>The eigenvalues and the eigenvectors are complex.</para>
-                    </listitem>
-                </itemizedlist>
-            </listitem>
-        </itemizedlist>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="spec">
+  <refnamediv>
+    <refname>spec</refname>
+    <refpurpose> valeurs propres d'une matrice  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>evals=spec(A)
+      [X,diagevals]=spec(A)
+      
+      evals=spec(A,E)
+      [al,be]=spec(A,E)
+      [al,be,Z]=spec(A,E)
+      [al,be]=spec(A,E)
+      [al,be,Q,Z]=spec(A,E)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>E  </term>
+        <listitem>
+          <para>
+            matrice carrée réelle ou complexe de même dimensions que  <literal> A</literal>
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>evals  </term>
+        <listitem>
+          <para>vecteur réel ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>diagevals  </term>
+        <listitem>
+          <para> matrice carrée diagonale réelle ou complexe (les éléments
+            diagonaux sont les valeurs propres)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>al  </term>
+        <listitem>
+          <para>vecteur réel ou complexe, al./be donnes les valeurs propres
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>be  </term>
+        <listitem>
+          <para>vecteur réel ou complexe, al./be donnes les valeurs propres
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice carrée inversible réelle ou complexe, matrices des
+            vecteurs propres.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Q  </term>
+        <listitem>
+          <para>matrice carrée inversible réelle ou complexe, matrices des
+            vecteurs propres à gauche.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Z  </term>
+        <listitem>
+          <para>atrice carrée inversible réelle ou complexe, matrices des
+            vecteurs propres à droite.
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <variablelist>
+      <varlistentry>
+        <term>spec(A)</term>
+        <listitem>
+          <para>
+            <literal> evals=spec(A)</literal>  retourne dans le vecteur
+            <literal>evals</literal> les valeurs propres de <literal>A</literal>.
+          </para>
+          <para>
+            <literal> [evals,X] =spec(A)</literal> retourne de plus les vecteurs
+            propres (s'ils existent). Voir Aussi <literal>bdiag</literal>
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>spec(A,B)</term>
+        <listitem>
+          <para>
+            <literal>evals=spec(A,E)</literal> retourne le  spectre du faisceau
+            <literal>s E - A</literal>, c'est à dire les racines du déterminant de
+            la matrice de polynômes <literal>s E - A</literal>.
+          </para>
+          <para>
+            <literal>[al,be] = spec(A,E)</literal> retourne le  spectre du faisceau
+            <literal>s E - A</literal>, c'est à dire les racines du déterminant de
+            la matrice de polynômes <literal>s E - A</literal>. Les valeurs propres
+            sont données par <literal>al./be</literal>. Si <literal>be(i) = 0</literal> la
+            <literal>i</literal>ième valeur propres est à l'infini. (Pour <literal>E =
+              eye(A), al./be
+            </literal>
+            est <literal>spec(A)</literal>).
+          </para>
+          <para>
+            <literal> [al,be,Z] = spec(A,E)</literal> retourne de plus la matrice
+            <literal>Z</literal> des vecteurs propres généralisés à droite.
+          </para>
+          <para>
+            <literal> [al,be,Q,Z] = spec(A,E)</literal> retourne de plus les matrices
+            <literal>Q</literal> et <literal>Z</literal> des vecteurs propres généralisés à
+            droite et à gauche.
+          </para>
+          <para>Pour les grosses matrices pleines / creuses, vous
+            pouvez utiliser le module Arnoldi.
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 // MATRIX EIGENVALUES
-A=diag([1,2,3]);
-X=rand(3,3);
-A=inv(X)*A*X;
+A=diag([1,2,3]);X=rand(3,3);A=inv(X)*A*X;
 spec(A)
 
 x=poly(0,'x');
@@ -264,38 +166,46 @@ clean(inv(X)*A*X)
 
 // PENCIL EIGENVALUES
 A=rand(3,3);
-[al,be,R] = spec(A,eye(A));
-al./be
-clean(inv(R)*A*R)  //displaying the eigenvalues (generic matrix)
-A=A+%i*rand(A);
-E=rand(A);
-roots(det(A-%s*E))   //complex case
+[al,be,Z] = spec(A,eye(A));al./be
+clean(inv(Z)*A*Z)  //displaying the eigenvalues (generic matrix)
+A=A+%i*rand(A);E=rand(A);
+roots(det(%s*E-A))   //complex case
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="poly">poly</link>
-            </member>
-            <member>
-                <link linkend="det">det</link>
-            </member>
-            <member>
-                <link linkend="schur">schur</link>
-            </member>
-            <member>
-                <link linkend="bdiag">bdiag</link>
-            </member>
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-            <member>
-                <link linkend="dsaupd">dsaupd</link>
-            </member>
-            <member>
-                <link linkend="dnaupd">dnaupd</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="poly">poly</link>
+      </member>
+      <member>
+        <link linkend="det">det</link>
+      </member>
+      <member>
+        <link linkend="gspec">gspec</link>
+      </member>
+      <member>
+        <link linkend="schur">schur</link>
+      </member>
+      <member>
+        <link linkend="bdiag">bdiag</link>
+      </member>
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+      <member>
+        <link linkend="dsaupd">dsaupd</link>
+      </member>
+      <member>
+        <link linkend="dnaupd">dnaupd</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      Le calcul des valeurs propres des matrices est basé sur les
+      routines Lapack DGEEV and ZGEEV.
+    </para>
+  </refsection>
 </refentry>
index 77d0a4c..f07726c 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="sva">
-    <refnamediv>
-        <refname>sva</refname>
-        <refpurpose> singular value approximation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[U,s,V]=sva(A,k)
-            [U,s,V]=sva(A,tol)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>k</term>
-                <listitem>
-                    <para>integer</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>nonnegative real number</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Singular value approximation.
-        </para>
-        <para>
-            <literal>[U,S,V]=sva(A,k)</literal> with <literal>k</literal> an integer
-            &gt;=1, returns <literal>U,S</literal> and <literal>V</literal> such that
-            <literal>B=U*S*V'</literal> is the best L2 approximation of
-            <literal>A</literal> with rank(<literal>B</literal>)=<literal>k</literal>.
-        </para>
-        <para>
-            <literal>[U,S,V]=sva(A,tol)</literal> with <literal>tol</literal> a real
-            number, returns <literal>U,S</literal> and <literal>V</literal> such that
-            <literal>B=U*S*V'</literal> such that L2-norm of <literal>A-B</literal>
-            is at most <literal>tol</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="sva">
+  <refnamediv>
+    <refname>sva</refname>
+    <refpurpose> approximation de valeurs singulières  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[U,s,V]=sva(A,k)
+      [U,s,V]=sva(A,tol)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>k  </term>
+        <listitem>
+          <para>entier
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel positif
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Approximation de valeurs singulières.
+    </para>
+    <para>
+      <literal>[U,S,V]=sva(A,k)</literal> avec <literal>k</literal> un entier
+      &gt;=1, renvoie <literal>U,S</literal> et <literal>V</literal> telles que
+      <literal>B=U*S*V'</literal> est la meilleure approximation au sens
+      l_2 de <literal>A</literal> avec rang(<literal>B</literal>)=<literal>k</literal>.
+    </para>
+    <para>
+      <literal>[U,S,V]=sva(A,tol)</literal> où <literal>tol</literal> est un réel
+      positif, renvoie <literal>U,S</literal> et <literal>V</literal> tels que
+      <literal>B=U*S*V'</literal> et la norme l_2 de <literal>A-B</literal> est
+      inférieure à <literal>tol</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,4)*rand(4,5);
 [U,s,V]=sva(A,2);
 B=U*s*V';
@@ -72,13 +75,13 @@ svd(A)
 svd(B)
 clean(svd(A-B))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 105a3c8..81fb8d1 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="svd">
-    <refnamediv>
-        <refname>svd</refname>
-        <refpurpose>  singular value decomposition</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>s=svd(X)
-            [U,S,V]=svd(X)
-            [U,S,V]=svd(X,0) (obsolete)
-            [U,S,V]=svd(X,"e")
-            [U,S,V,rk]=svd(X [,tol])
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>a real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>s</term>
-                <listitem>
-                    <para>real vector (singular values)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>S</term>
-                <listitem>
-                    <para>real diagonal matrix (singular values)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>U,V</term>
-                <listitem>
-                    <para>orthogonal or unitary square matrices (singular vectors).</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[U,S,V] = svd(X)</literal> produces a diagonal matrix
-            <literal>S</literal> , of the same dimension as <literal>X</literal> and with
-            nonnegative diagonal elements in decreasing order, and unitary
-            matrices <literal>U</literal> and <literal>V</literal> so that <literal>X = U*S*V'</literal>.
-        </para>
-        <para>
-            <literal>[U,S,V] = svd(X,0)</literal> produces the "economy
-            size" decomposition. If <literal>X</literal> is m-by-n with m &gt;
-            n, then only the first n columns of <literal>U</literal> are computed
-            and <literal>S</literal> is n-by-n.
-        </para>
-        <para>
-            <literal>s= svd(X)</literal> by itself, returns a vector <literal>s</literal>
-            containing the singular values.
-        </para>
-        <para>
-            <literal>[U,S,V,rk]=svd(X,tol)</literal> gives in addition <literal>rk</literal>, the numerical rank of <literal>X</literal> i.e. the number of 
-            singular values larger than <literal>tol</literal>.
-        </para>
-        <para>
-            The default value of <literal>tol</literal> is the same as in <literal>rank</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="svd">
+  <refnamediv>
+    <refname>svd </refname>
+    <refpurpose>  décomposition en valeurs singulières  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>s=svd(X)
+      [U,S,V]=svd(X)
+      [U,S,V]=svd(X,0) (obsolete)
+      [U,S,V]=svd(X,"e")
+      [U,S,V,rk]=svd(X [,tol])
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>s  </term>
+        <listitem>
+          <para>vecteur réel (valeurs singulières)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>S  </term>
+        <listitem>
+          <para>matrice réelle diagonale (valeurs singulières sur la diagonale)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>U,V  </term>
+        <listitem>
+          <para>matrices carrées unitaires (vecteurs singuliers).
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel positif
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>[U,S,V]=svd(X)</literal> renvoie une matrice diagonale <literal>S</literal>, de même
+      dimension que <literal>X</literal> avec des éléments diagonaux positifs classés
+      par ordre décroissant, ainsi que deux matrices unitaires <literal>U</literal>
+      et <literal>V</literal> telles que 
+      <literal>X = U*S*V'</literal>.<literal>[U,S,V]=svd(X,"e")</literal>
+      renvoie la décomposition réduite : si <literal>X</literal> est une
+      matrice <literal>m x n </literal> et que <literal>m &gt; n </literal> alors
+      seulement les n premières colonnes de <literal>U</literal> sont
+      calculées et <literal>S</literal> est <literal>n x n </literal>.
+    </para>
+    <para>
+      <literal>s=svd(X)</literal> renvoie un vecteur <literal>s</literal> contenant
+      les valeurs singulières.
+    </para>
+    <para>
+      <literal>[U,S,V,rk]=svd(X [,tol])</literal> renvoie de plus
+      <literal>rk</literal>, le rang "numérique" de <literal>X</literal>
+      c'est à dire le nombre de valeurs singulières plus grandes
+      que <literal>tol</literal>.
+    </para>
+    <para>
+      La valeur par défaut de <literal>tol</literal> est la même que pour la fonction <literal>rank</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 X=rand(4,2)*rand(2,4)
 svd(X)
 sqrt(spec(X*X'))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="rank">rank</link>
-            </member>
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-            <member>
-                <link linkend="rowcomp">rowcomp</link>
-            </member>
-            <member>
-                <link linkend="sva">sva</link>
-            </member>
-            <member>
-                <link linkend="spec">spec</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            svd decompositions are based on  the Lapack routines DGESVD for
-            real matrices and  ZGESVD for the complex case.
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="rank">rank</link>
+      </member>
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+      <member>
+        <link linkend="rowcomp">rowcomp</link>
+      </member>
+      <member>
+        <link linkend="sva">sva</link>
+      </member>
+      <member>
+        <link linkend="spec">spec</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      la décomposition svd est basée sur les routines  DGESVD pour les
+      matrices réelles et  ZGESVD pour le cas complexe.
+    </para>
+  </refsection>
 </refentry>
index 4c6b6e2..98ecca2 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="givens">
-    <refnamediv>
-        <refname>givens</refname>
-        <refpurpose> Givens transformation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>U=givens(xy)
-            U=givens(x,y)
-            [U,c]=givens(xy)
-            [U,c]=givens(x,y)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>x,y</term>
-                <listitem>
-                    <para>two real or complex numbers</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>xy</term>
-                <listitem>
-                    <para> real or complex size 2 column vector</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>U</term>
-                <listitem>
-                    <para>2x2 unitary matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>c</term>
-                <listitem>
-                    <para> real or complex size 2 column vector</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>U= givens(x, y)</literal> or <literal>U = givens(xy)</literal> with <literal>xy = [x;y]</literal>
-            returns a <literal>2</literal>x<literal>2</literal> unitary matrix <literal>U</literal> such that:
-        </para>
-        <para>
-            <literal>U*xy=[r;0]=c</literal>.
-        </para>
-        <para>
-            Note that <literal>givens(x,y)</literal> and <literal>givens([x;y])</literal> are equivalent.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="givens">
+  <refnamediv>
+    <refname>givens</refname>
+    <refpurpose> Transformation de Givens  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>U=givens(xy)
+      U=givens(x,y)
+      [U,c]=givens(xy)
+      [U,c]=givens(x,y)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>x,y  </term>
+        <listitem>
+          <para>deux nombres réels ou complexes
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>xy  </term>
+        <listitem>
+          <para> vecteur colonne réel ou complexe à deux composantes
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>U  </term>
+        <listitem>
+          <para>matrice unitaire 2 x 2
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>c  </term>
+        <listitem>
+          <para> vecteur colonne réel ou complexe à deux composantes
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>U= givens(x, y)</literal> ou <literal>U = givens(xy)</literal> avec <literal>xy = [x;y]</literal>
+      renvoie <literal>U</literal> une matrice unitaire <literal>2</literal>x<literal>2</literal> telle que :
+    </para>
+    <para>
+      <literal>U*xy=[r;0]=c</literal>.
+    </para>
+    <para>
+      Notez que <literal>givens(x,y)</literal> et <literal>givens([x;y])</literal> sont équivalents.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=[3,4;5,6];
 U=givens(A(:,1));
 U*A
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 04113d9..186b184 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="householder">
-    <refnamediv>
-        <refname>householder</refname>
-        <refpurpose> Householder orthogonal reflexion matrix</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>u=householder(v [,w])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>v</term>
-                <listitem>
-                    <para>real or complex column vector</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>w</term>
-                <listitem>
-                    <para>
-                        real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>u</term>
-                <listitem>
-                    <para>real or complex column vector</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary 
-            column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>.
-            <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix .
-        </para>
-        <para>
-            <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the 
-            vector  <literal> eye(v)*norm(v)</literal>.
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="givens">givens</link>
-            </member>
-        </simplelist>
-    </refsection>
+<refentry 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" version="5.0-subset Scilab" xml:lang="fr" xml:id="householder">
+  <refnamediv>
+    <refname>householder</refname>
+    <refpurpose> Matrice de Householder  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>u=householder(v [,w])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>v  </term>
+        <listitem>
+          <para>vecteur colonne réel ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>w  </term>
+        <listitem>
+          <para>
+            vecteur colonne réel ou complexe de même taille que <literal>v</literal> (la valeur par défaut est <literal>eye(v)</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>u  </term>
+        <listitem>
+          <para>vecteur colonne réel ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Etant donnés deux vecteurs colonnes <literal>v</literal> et <literal>w</literal> de même taille, <literal>householder(v,w)</literal> renvoie un vecteur normé <literal>u</literal>, tel que 
+      <literal>(eye()-2*u*u')*v</literal> est colinéaire à <literal>w</literal>.
+      <literal>(eye()-2*u*u')</literal> est la matrice de la transformation de Householder correspondante.
+    </para>
+    <para>
+      La valeur par défaut de <literal>w</literal> est <literal> eye(v)</literal>. Dans ce cas le vecteur <literal> (eye()-2*u*u')*v</literal> est égal à <literal> eye(v)*norm(v)</literal>.
+    </para>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="givens">givens</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 0ab7a1d..4db48f6 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="sqroot">
-    <refnamediv>
-        <refname>sqroot</refname>
-        <refpurpose> W*W' hermitian factorization</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>sqroot(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>symmetric non negative definite real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            returns W such that  <literal>X=W*W'</literal> (uses SVD).
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="sqroot">
+  <refnamediv>
+    <refname>sqroot</refname>
+    <refpurpose> factorisation hermitienne W*W'  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>sqroot(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice complexe ou réelle, symétrique définie non-négative
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      renvoie W telle que <literal>X=W*W'</literal> (en utilisant svd).
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 X=rand(5,2)*rand(2,5);X=X*X';
 W=sqroot(X)
 norm(W*W'-X,1)
@@ -47,16 +48,16 @@ X=rand(5,2)+%i*rand(5,2);X=X*X';
 W=sqroot(X)
 norm(W*W'-X,1)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="chol">chol</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="chol">chol</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 48c89e8..8a67bf5 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="colcomp">
-    <refnamediv>
-        <refname>colcomp</refname>
-        <refpurpose> column compression, kernel, nullspace</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag</term>
-                <listitem>
-                    <para>character string</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>W</term>
-                <listitem>
-                    <para>square non-singular matrix (change of basis)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rk</term>
-                <listitem>
-                    <para>
-                        integer (rank of <literal>A</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Column compression of <literal>A</literal>: <literal>Ac = A*W</literal> is 
-            column compressed i.e
-        </para>
-        <para>
-            <literal>Ac=[0,Af]</literal> with <literal>Af</literal> full column rank, 
-            rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>.
-        </para>
-        <para>
-            <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> 
-            or <literal>'svd'</literal> (default is <literal>'svd'</literal>).
-        </para>
-        <para>
-            <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value).
-        </para>
-        <para>
-            The <literal>ma-rk</literal> first columns of <literal>W</literal> span the kernel of <literal>A</literal> 
-            when <literal>size(A)=(na,ma)</literal>
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="colcomp">
+  <refnamediv>
+    <refname>colcomp</refname>
+    <refpurpose> compression de colonnes, noyau  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>flag  </term>
+        <listitem>
+          <para>chaîne de caractères
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>W  </term>
+        <listitem>
+          <para>matrice carré régulière (matrice de changement de base)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>rk  </term>
+        <listitem>
+          <para>
+            entier (rang de"<literal>A</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Compression des colonnes de <literal>A</literal> : <literal>Ac = A*W</literal> est à colonnes compressées, c'est à dire
+    </para>
+    <para>
+      <literal>Ac=[0,Af]</literal> et <literal>Af</literal> est de rang maximal
+      rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>.
+    </para>
+    <para>
+      <literal>flag</literal> et <literal>tol</literal> sont des paramètres optionnels : <literal>flag = 'qr'</literal> 
+      ou <literal>'svd'</literal> (<literal>'svd'</literal> par défaut).
+    </para>
+    <para>
+      <literal>tol</literal> = paramètre de tolérance (de l'ordre de <literal>%eps</literal> par défaut).
+    </para>
+    <para>
+      Les <literal>ma-rk</literal> premières colonnes de <literal>W</literal> forment une base du noyau de <literal>A</literal> quand <literal>size(A)=[na,ma]</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,5);
 [X,r]=colcomp(A);
 norm(A*X(:,1:$-r),1)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="rowcomp">rowcomp</link>
-            </member>
-            <member>
-                <link linkend="fullrf">fullrf</link>
-            </member>
-            <member>
-                <link linkend="fullrfk">fullrfk</link>
-            </member>
-            <member>
-                <link linkend="kernel">kernel</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="rowcomp">rowcomp</link>
+      </member>
+      <member>
+        <link linkend="fullrf">fullrf</link>
+      </member>
+      <member>
+        <link linkend="fullrfk">fullrfk</link>
+      </member>
+      <member>
+        <link linkend="kernel">kernel</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index be5baae..23fa67d 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="fullrf">
-    <refnamediv>
-        <refname>fullrf</refname>
-        <refpurpose> full rank factorization</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>real number (threshold for rank determination)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Q,M</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rk</term>
-                <listitem>
-                    <para>
-                        integer (rank of <literal>A</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Full rank factorization : <literal>fullrf</literal> returns <literal>Q</literal> and <literal>M</literal> such
-            that <literal>A = Q*M</literal>
-            with range(<literal>Q</literal>)=range(<literal>A</literal>) and ker(<literal>M</literal>)=ker(<literal>A</literal>),
-            <literal>Q</literal> full column rank , <literal>M</literal> full row rank,
-            <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>.
-        </para>
-        <para>
-            <literal>tol</literal> is an optional real parameter (default value is <literal>sqrt(%eps)</literal>).
-            The rank <literal>rk</literal> of <literal>A</literal> is defined as the number of singular values
-            larger than <literal>norm(A)*tol</literal>.
-        </para>
-        <para>
-            If A is symmetric, <literal>fullrf</literal> returns <literal>M=Q'</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="fullrf">
+  <refnamediv>
+    <refname>fullrf</refname>
+    <refpurpose> factorisation de rang plein  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel (tolérance pour le calcul du rang)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Q,M  </term>
+        <listitem>
+          <para>matrices réelles ou complexes
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>rk  </term>
+        <listitem>
+          <para>
+            entier (rang de <literal>A</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Cette fonction calcule la factorisation de rang plein de <literal>A</literal> : <literal>fullrf</literal> renvoie <literal>Q</literal> et <literal>M</literal> telles que <literal>A = Q*M</literal>
+      avec Im(<literal>Q</literal>)=Im(<literal>A</literal>) et ker(<literal>M</literal>)=ker(<literal>A</literal>),
+      <literal>Q</literal> de rang maximal, et les lignes de <literal>M</literal> sont linéairement indépendantes, 
+      <literal>rk</literal> = rank(<literal>A</literal>) = nombre de colonnes de <literal>Q</literal> =  nombre de lignes de <literal>M</literal>.
+    </para>
+    <para>
+      <literal>tol</literal> = paramètre de tolérance (de l'ordre de <literal>%eps</literal> par défaut).
+      Le rang <literal>rk</literal> de <literal>A</literal> est considéré égal au nombre de ses valeurs singulières plus grandes que <literal>norm(A)*tol</literal>.
+    </para>
+    <para>
+      Si A est symétrique, <literal>fullrf</literal> renvoie <literal>M=Q'</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,5);
 [Q,M]=fullrf(A);
 norm(Q*M-A,1)
 [X,d]=rowcomp(A);Y=X';
-svd([A,Y(:,1:d),Q])        //span(Q) = span(A) = span(Y(:,1:2))
+svd([A,Y(:,1:d),Q])        // Im(Q) = Im(A) = Im(Y(:,1:2))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="fullrfk">fullrfk</link>
-            </member>
-            <member>
-                <link linkend="rowcomp">rowcomp</link>
-            </member>
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="fullrfk">fullrfk</link>
+      </member>
+      <member>
+        <link linkend="rowcomp">rowcomp</link>
+      </member>
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 1063130..67117dc 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="fullrfk">
-    <refnamediv>
-        <refname>fullrfk</refname>
-        <refpurpose> full rank factorization of A^k</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>k</term>
-                <listitem>
-                    <para>integer</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Bk,Ck</term>
-                <listitem>
-                    <para>real or complex matrices</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            This function computes the full rank factorization of <literal>A^k</literal> i.e.
-            <literal>Bk*Ck=A^k</literal> where <literal>Bk</literal> is full column rank and <literal>Ck</literal> full row rank.
-            One has range(<literal>Bk</literal>)=range(<literal>A^k</literal>) and ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>).
-        </para>
-        <para>
-            For <literal>k=1</literal>, <literal>fullrfk</literal> is equivalent to <literal>fullrf</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="fullrfk">
+  <refnamediv>
+    <refname>fullrfk</refname>
+    <refpurpose> factorisation de rang plein de A^k  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[Q,M]=fullrfk(A,k)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>k  </term>
+        <listitem>
+          <para>entier
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Q,M  </term>
+        <listitem>
+          <para>matrices réelles ou complexes
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Cette fonction calcule la factorisation de rang plein de <literal>A^k</literal> : <literal>fullrfk</literal> renvoie <literal>Q</literal> et <literal>M</literal> telles que <literal>A^k = Q*M</literal>
+      avec Im(<literal>Q</literal>)=Im(<literal>A^k</literal>) et ker(<literal>M</literal>)=ker(<literal>A^k</literal>),
+      <literal>Q</literal> de rang maximal, et les lignes de <literal>M</literal> sont linéairement indépendantes, 
+    </para>
+    <para>
+      Pour <literal>k=1</literal>, <literal>fullrfk</literal> est équivalent à <literal>fullrf</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3);
 norm(Bk*Ck-A^3,1)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="fullrf">fullrf</link>
-            </member>
-            <member>
-                <link linkend="range">range</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="fullrf">fullrf</link>
+      </member>
+      <member>
+        <link linkend="range">range</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index c2627af..081f372 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="kernel">
-    <refnamediv>
-        <refname>kernel</refname>
-        <refpurpose> kernel, nullspace</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>W=kernel(A [,tol,[,flag])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>full real or complex matrix or real sparse matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag</term>
-                <listitem>
-                    <para>
-                        character string <literal>'svd'</literal> (default) or <literal>'qr'</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>W</term>
-                <listitem>
-                    <para>full column rank matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>W=kernel(A)</literal> returns the kernel (nullspace) of <literal>A</literal>. If A has full column rank then an empty matrix [] is returned.
-        </para>
-        <para>
-            <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> 
-            or <literal>'svd'</literal> (default is <literal>'svd'</literal>).
-        </para>
-        <para>
-            <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value).
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="kernel">
+  <refnamediv>
+    <refname>kernel</refname>
+    <refpurpose> noyau  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>W=kernel(A [,tol,[,flag])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe (pleine ou creuse)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>flag  </term>
+        <listitem>
+          <para>chaîne de caractères
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>W  </term>
+        <listitem>
+          <para>matrice régulière
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>W=kernel(A)</literal> calcule le noyau de <literal>A</literal>. Les colonnes de <literal>W</literal> forment une base du noyau de <literal>A</literal>. Si A est régulière, alors W=[].
+    </para>
+    <para>
+      <literal>flag</literal> et <literal>tol</literal> sont des paramètres optionnels : <literal>flag = 'qr'</literal> 
+      or <literal>'svd'</literal> (<literal>'svd'</literal> par défaut).
+    </para>
+    <para>
+      <literal>tol</literal> = paramètre de tolérance (de l'ordre de <literal>%eps</literal> par défaut).
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(3,1)*rand(1,3);
 A*kernel(A)
 A=sparse(A);
 clean(A*kernel(A))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-            <member>
-                <link linkend="fullrf">fullrf</link>
-            </member>
-            <member>
-                <link linkend="fullrfk">fullrfk</link>
-            </member>
-            <member>
-                <link linkend="linsolve">linsolve</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+      <member>
+        <link linkend="fullrf">fullrf</link>
+      </member>
+      <member>
+        <link linkend="fullrfk">fullrfk</link>
+      </member>
+      <member>
+        <link linkend="linsolve">linsolve</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 5ae81b7..8b457cb 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="range">
-    <refnamediv>
-        <refname>range</refname>
-        <refpurpose> range (span) of A^k</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[X,dim]=range(A,k)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>k</term>
-                <listitem>
-                    <para>integer</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>orthonormal real matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>dim</term>
-                <listitem>
-                    <para>integer (dimension of subspace)</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Computation of Range <literal>A^k</literal> ; the first dim rows of <literal>X</literal> span the
-            range of <literal>A^k</literal>. The last rows of <literal>X</literal> span the
-            orthogonal complement of the range. <literal>X*X'</literal> is the Identity matrix
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
-A=rand(4,2)*rand(2,4);   // 4 column vectors, 2 independent.
-[X,dim]=range(A,1);dim   // compute the range
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="range">
+  <refnamediv>
+    <refname>range</refname>
+    <refpurpose> Image de A^k  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[X,dim]=range(A,k)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle carrée</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>k  </term>
+        <listitem>
+          <para>entier non négatif, La valeur par défaut est 1</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice réelle orthonormale.</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>dim</term>
+        <listitem>
+          <para>entier (dimension du sous-espace image)</para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Calcul de l'image de <literal>A^k</literal>; les <literal>dim</literal>
+      premières colonnes de <literal>X</literal> forment une base de
+      <literal>A^k</literal>. Les dernières lignes de  <literal>X</literal> forment une
+      base de l'orthogonal de l'image. 
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
+A=rand(4,2)*rand(2,4);   // Matrice de rang 2.
+[X,dim]=range(A,1);dim   // Calcul de l'image
 
-y1=A*rand(4,1);          //a vector which is in the range of A
-y2=rand(4,1);            //a vector which is not  in the range of A
-norm(X(dim+1:$,:)*y1)    //the last entries are zeros, y1 is in the range of A
-norm(X(dim+1:$,:)*y2)    //the last entries are not zeros
+y1=A*rand(4,1);          // un vecteur dans l'image de A
+y2=rand(4,1);            // un vecteur qui n'est pas dans l'image
+norm(X(dim+1:$,:)*y1)    // les derniéres composante sont nulles, y1 est dans l'image
+norm(X(dim+1:$,:)*y2)    // Les dernieres composantes ne sont pas nulles
 
-I=X(1:dim,:)'            //I is a basis of the range
-coeffs=X(1:dim,:)*y1     // components of y1 relative to the I basis
+I=X(1:dim,:)'            // I une base de l'image
+coeffs=X(1:dim,:)*y1     // les composante de y1 dans la base I
 
-norm(I*coeffs-y1)        //check
+norm(I*coeffs-y1)        // test
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="fullrfk">fullrfk</link>
-            </member>
-            <member>
-                <link linkend="rowcomp">rowcomp</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            The <literal>range</literal> function is based on the <link linkend="rowcomp">rowcomp</link> function
-            which uses the <link linkend="svd">svd</link> decomposition.
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="fullrfk">fullrfk</link>
+      </member>
+      <member>
+        <link linkend="rowcomp">rowcomp</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      La fonction <literal>range</literal> est basée sue la fonction <link linkend="rowcomp">rowcomp</link>
+      qui utilise la décomposition <link linkend="svd">svd</link>.
+    </para>
+  </refsection>
 </refentry>
index 0f0db63..1ebe926 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="rowcomp">
-    <refnamediv>
-        <refname>rowcomp</refname>
-        <refpurpose> row compression, range</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[W,rk]=rowcomp(A [,flag [,tol]])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag</term>
-                <listitem>
-                    <para>optional character string, with possible values
-                        <literal>'svd'</literal> or <literal>'qr'</literal>. The default value is  <literal>'svd'</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>optional real non negative number. The default value is 
-                        <literal>sqrt(%eps)*norm(A,1)</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>W</term>
-                <listitem>
-                    <para>square non-singular matrix (change of basis)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rk</term>
-                <listitem>
-                    <para>
-                        integer (rank of <literal>A</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Row compression of <literal>A</literal>. <literal>Ac = W*A</literal> is a row compressed matrix: i.e. 
-            <literal>Ac=[Af;0]</literal> with <literal>Af</literal> full row rank.
-        </para>
-        <para>
-            <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag='qr'</literal> 
-            or <literal>'svd'</literal> (default <literal>'svd'</literal>).
-        </para>
-        <para>
-            <literal>tol</literal> is a tolerance parameter.
-        </para>
-        <para>
-            The <literal>rk</literal> first columns of <literal>W'</literal> span the range of
-            <literal>A</literal>.
-        </para>
-        <para>
-            The <literal>rk</literal> first (top) rows of <literal>W</literal> span the row
-            range of <literal>A</literal>.
-        </para>
-        <para>
-            A non zero vector <literal>x</literal> belongs to range(<literal>A</literal>) iff
-            <literal>W*x</literal> is row  compressed in accordance with <literal>Ac</literal>
-            i.e the norm of its last components is small w.r.t its first
-            components.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
-A=rand(5,2)*rand(2,4);              // 4 col. vectors, 2 independent.
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="rowcomp">
+  <refnamediv>
+    <refname>rowcomp</refname>
+    <refpurpose> compression de lignes, image  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[W,rk]=colcomp(A [,flag [,tol]])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe</para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>flag  </term>
+        <listitem>
+          <para>chaîne de caractères optionnelle qui peut prendre les valeurs
+            <literal>'svd'</literal> ou <literal>'qr'</literal>.  La valeur par
+            défaut est  <literal>sqrt(%eps)*norm(A,1)</literal>.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel non négatif. La valeur par
+            défaut est  <literal>sqrt(%eps)*norm(A,1)</literal>.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>W  </term>
+        <listitem>
+          <para>matrice carrée régulière (matrice de changement de base) </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>rk  </term>
+        <listitem>
+          <para>
+            entier (rang de"<literal>A</literal>).
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Compression des colonnes de <literal>A</literal>. <literal>Ac = W*A</literal> est à
+      lignes compressées, c'est à dire
+      <literal>Ac=[Af;0]</literal> et les lignes de <literal>Af</literal> sont linéairement
+      indépendantes.
+    </para>
+    <para>
+      <literal>flag</literal> et <literal>tol</literal> sont des paramètres optionnels :
+      <literal>flag = 'qr'</literal> ou <literal>'svd'</literal>
+      (<literal>'svd'</literal> par défaut). 
+    </para>
+    <para>
+      <literal>tol</literal> = paramètre de tolérance (de l'ordre de
+      <literal>%eps</literal> par défaut).
+    </para>
+    <para>
+      Les <literal>rk</literal> premières colonnes de <literal>W'</literal> forment
+      une base de l'image de <literal>A</literal>. 
+    </para>
+    <para>
+      Un vecteur non nul <literal>x</literal> appartient à Im(<literal>A</literal>) si
+      <literal>W*x</literal> est à lignes compressées en accord avec <literal>Ac</literal>
+      c'est à dire que la norme de ses dernières composantes est  nulle (à
+      la précision machine) par rapport à ses rk premières composantes.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
+A=rand(5,2)*rand(2,4);          // 4 vecteurs colonne dont 2 indépendants
 [X,dim]=rowcomp(A);Xp=X';
-svd([Xp(:,1:dim),A])                //span(A) = span(Xp(:,1:dim)
-x=A*rand(4,1);                      //x belongs to span(A)
+svd([Xp(:,1:dim),A])            // Im(A) = Im(Xp(:,1:dim)
+x=A*rand(4,1);                  // x appartient à Im(A)
 y=X*x  
-norm(y(dim+1:$))/norm(y(1:dim))     // small
+norm(y(dim+1:$))/norm(y(1:dim)) // la norme est petite
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-            <member>
-                <link linkend="fullrf">fullrf</link>
-            </member>
-            <member>
-                <link linkend="fullrfk">fullrfk</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            The <literal>rowcomp</literal> function is based on the <link linkend="svd">svd</link> or
-            <link linkend="qr">qr</link> decompositions.
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+      <member>
+        <link linkend="fullrf">fullrf</link>
+      </member>
+      <member>
+        <link linkend="fullrfk">fullrfk</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      La fonction <literal>rowcomp</literal> est basée sur les décompositions
+      <link linkend="svd">svd</link> ou <link linkend="qr">qr</link>.
+    </para>
+  </refsection>
 </refentry>
index 05080eb..b7c8a22 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="chol">
-    <refnamediv>
-        <refname>chol</refname>
-        <refpurpose> Cholesky factorization</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[R]=chol(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>a symmetric positive definite real or complex matrix.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            If <literal>X</literal> is positive definite, then <literal>R = chol(X)</literal> produces an upper 
-            triangular matrix <literal>R</literal> such that <literal>R'*R = X</literal>.
-        </para>
-        <para>
-            <literal>chol(X)</literal> uses only the diagonal and upper triangle of <literal>X</literal>.
-            The lower triangular is assumed to be the (complex conjugate) 
-            transpose of the upper.
-        </para>
-    </refsection>
-    <refsection>
-        <title>References</title>
-        <para>
-            Cholesky decomposition is based on  the Lapack routines
-            DPOTRF for  real matrices and  ZPOTRF for the complex case.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="chol">
+  <refnamediv>
+    <refname>chol</refname>
+    <refpurpose> Factorisation de Cholesky  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[R]=chol(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Si <literal>X</literal> est hermitienne (symétrique dans le cas réel) définie positive, alors <literal>R = chol(X)</literal> renvoie une matrice triangulaire supérieure <literal>R</literal> telle que <literal>R'*R = X</literal>.
+    </para>
+    <para>
+      <literal>chol(X)</literal> utilise uniquement la partie triangulaire supérieure de <literal>X</literal> dont la
+      partie triangulaire inférieure est supposée être la transposée (transposée conjuguée dans le cas complexe).
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 W=rand(5,5)+%i*rand(5,5);
 X=W*W';
 R=chol(X);
 norm(R'*R-X)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="spchol">spchol</link>
-            </member>
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-            <member>
-                <link linkend="bdiag">bdiag</link>
-            </member>
-            <member>
-                <link linkend="fullrf">fullrf</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="spchol">spchol</link>
+      </member>
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+      <member>
+        <link linkend="bdiag">bdiag</link>
+      </member>
+      <member>
+        <link linkend="fullrf">fullrf</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      La décomposition de Cholesky est basée sur les routines Lapack
+      DPOTRF pour les matrices réelles et  ZPOTRF pour le cas complexe.
+    </para>
+  </refsection>
 </refentry>
index 2da37a3..7106ebc 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="inv">
-    <refnamediv>
-        <refname>inv</refname>
-        <refpurpose> matrix inverse</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>inv(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex square matrix, polynomial matrix, rational matrix in transfer or state-space representation.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>inv(X)</literal> is the inverse of the square matrix <literal>X</literal>. A warning
-            message is printed if <literal>X</literal> is badly scaled or nearly singular.
-        </para>
-        <para>
-            For polynomial matrices or rational matrices in transfer representation,
-            <literal>inv(X)</literal> is equivalent to <literal>invr(X)</literal>.
-        </para>
-        <para>
-            For linear systems in state-space representation (<literal>syslin</literal> list),
-            <literal>invr(X)</literal> is equivalent to <literal>invsyslin(X)</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>References</title>
-        <para>
-            <literal>inv</literal> function for matrices of numbers is  based on the Lapack routines
-            DGETRF, DGETRI for  real matrices and  ZGETRF, ZGETRI for the complex case.
-            For polynomial matrix and rational function matrix <literal>inv</literal> is based on the <literal>invr</literal>
-            Scilab function.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="inv">
+  <refnamediv>
+    <refname>inv</refname>
+    <refpurpose> inverse d'une matrice  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>inv(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice carrée réelle, complexe, polynomiale ou rationnelle,
+            liste de type "syslin"
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>inv(X)</literal> est l'inverse de la matrice carrée
+      <literal>X</literal>. Un message de mise en garde est affiché si <literal>X</literal>
+      est mal équilibrée (termes très petits et termes très grands) ou
+      singulière à la précision machine.
+    </para>
+    <para>
+      Pour les matrices polynomiales ou rationnelles, <literal>inv(X)</literal> est
+      équivalent à <literal>invr(X)</literal>.
+    </para>
+    <para>
+      Pour les systèmes dynamiques linéaires sous forme de leur représentation
+      d'état (liste de type <literal>syslin</literal>), <literal>inv(X)</literal> est
+      équivalent à <literal>invsyslin(X)</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(3,3);inv(A)*A
 
 x=poly(0,'x');
@@ -69,37 +65,48 @@ A=ssrand(2,2,3);
 W=inv(A)*A
 clean(ss2tf(W))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="slash">slash</link>
-            </member>
-            <member>
-                <link linkend="backslash">backslash</link>
-            </member>
-            <member>
-                <link linkend="pinv">pinv</link>
-            </member>
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="lufact">lufact</link>
-            </member>
-            <member>
-                <link linkend="lusolve">lusolve</link>
-            </member>
-            <member>
-                <link linkend="invr">invr</link>
-            </member>
-            <member>
-                <link linkend="coff">coff</link>
-            </member>
-            <member>
-                <link linkend="coffg">coffg</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="slash">slash</link>
+      </member>
+      <member>
+        <link linkend="backslash">backslash</link>
+      </member>
+      <member>
+        <link linkend="pinv">pinv</link>
+      </member>
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="lufact">lufact</link>
+      </member>
+      <member>
+        <link linkend="lusolve">lusolve</link>
+      </member>
+      <member>
+        <link linkend="invr">invr</link>
+      </member>
+      <member>
+        <link linkend="coff">coff</link>
+      </member>
+      <member>
+        <link linkend="coffg">coffg</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      La fonction <literal>inv</literal> pour les matrices de  nombres est basée
+      sur les routines Lapack :
+      DGETRF, DGETRI pour les matrices réelles et  ZGETRF, ZGETRI pour le
+      cas complexe.
+      Pour les matrices de polynomes et de fractions rationnelles
+      <literal>inv</literal>  est basée sur la fonction Scilab  <literal>invr</literal>.
+    </para>
+  </refsection>
 </refentry>
index ecf06f9..0dc7d6b 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="linsolve">
-    <refnamediv>
-        <refname>linsolve</refname>
-        <refpurpose> linear equation solver</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>
-                        a <literal>na x ma</literal> real matrix (possibly sparse)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>b</term>
-                <listitem>
-                    <para>
-                        a <literal>na x 1</literal> vector (same row dimension as <literal>A</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>x0</term>
-                <listitem>
-                    <para>a real vector</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>kerA</term>
-                <listitem>
-                    <para>
-                        a <literal>ma x k</literal> real matrix
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>linsolve</literal>  computes all the solutions to <literal> A*x+b=0</literal>.
-        </para>
-        <para>
-            <literal>x0</literal> is a particular solution (if any) and <literal> kerA= </literal>nullspace
-            of <literal>A</literal>. Any <literal>x=x0+kerA*w</literal> with arbitrary <literal>w</literal> satisfies
-            <literal> A*x+b=0</literal>.
-        </para>
-        <para>
-            If compatible <literal>x0</literal> is given on entry, <literal>x0</literal> is returned. If not
-            a compatible <literal>x0</literal>, if any, is returned.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="linsolve">
+  <refnamediv>
+    <refname>linsolve</refname>
+    <refpurpose> solveur d'équation linéaire  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>
+            une matrice réelle <literal>na x ma</literal> (éventuellement creuse)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>b  </term>
+        <listitem>
+          <para>
+            un vecteur <literal>na x 1</literal> 
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>x0  </term>
+        <listitem>
+          <para>un vecteur réel
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>kerA  </term>
+        <listitem>
+          <para>
+            une matrice réelle <literal>ma x k </literal>
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>linsolve</literal> donne toutes les solutions de <literal> A*x+b=0</literal>.
+    </para>
+    <para>
+      <literal>x0</literal> est une solution particulière (s'il en existe une) et <literal>kerA</literal> est le noyau de <literal>A</literal>. Tout vecteur de la forme <literal>x=x0+kerA*w</literal> avec <literal>w</literal> quelconque vérifie
+      <literal> A*x+b=0</literal>.
+    </para>
+    <para>
+      Si un <literal>x0</literal> compatible est donné en entrée, <literal>x0</literal> est renvoyé. Dans le cas contraire un <literal>x0</literal> compatible, s'il en existe un, est renvoyé.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,3)*rand(3,8);
-b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
-b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //uncompatible b
-A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x is unique
+b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   // b compatible
+b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   // b incompatible
+A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  // x est unique
+
+// Une comparaison des différentes méthode de résolution de systèmes linéaire creux
 
-// Benchmark with other linear sparse solver:
 [A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa"); 
 
 b = zeros(size(A,1),1);
 
 tic();
 res = umfpack(A,'\',b);
-mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc());
+mprintf('\ntemps nécessaire à la résolution du système avec umfpack: %.3f\n',toc());
 
 tic();
 res = linsolve(A,b);
-mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc());
+mprintf('\ntemps nécessaire à la résolution du système avec linsolve: %.3f\n',toc());
 
 tic();
 res = A\b;
-mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());
+mprintf('\ntemps nécessaire à la résolution du système avec l'opérateur backslash: %.3f\n',toc());
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="inv">inv</link>
-            </member>
-            <member>
-                <link linkend="pinv">pinv</link>
-            </member>
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-            <member>
-                <link linkend="im_inv">im_inv</link>
-            </member>
-            <member>
-                <link linkend="umfpack">umfpack</link>
-            </member>
-            <member>
-                <link linkend="backslash">backslash</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="inv">inv</link>
+      </member>
+      <member>
+        <link linkend="pinv">pinv</link>
+      </member>
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+      <member>
+        <link linkend="im_inv">im_inv</link>
+      </member>
+      <member>
+        <link linkend="umfpack">umfpack</link>
+      </member>
+      <member>
+        <link linkend="backslash">backslash</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 31d074c..9996cd0 100644 (file)
@@ -2,7 +2,6 @@
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
- * Copyright (C) 2009 - Digiteo - Michael Baudin
  * 
  * This file must be used under the terms of the CeCILL.
  * This source file is licensed as described in the file COPYING, which
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="lu">
-    <refnamediv>
-        <refname>lu</refname>
-        <refpurpose> LU factorization with pivoting</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[L,U]= lu(A)
-            [L,U,E]= lu(A)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex  matrix (m x n).</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>L</term>
-                <listitem>
-                    <para> real or complex matrices  (m x min(m,n)).</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>U</term>
-                <listitem>
-                    <para>real or complex matrices  (min(m,n) x n ).</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>E</term>
-                <listitem>
-                    <para>a (n x n) permutation matrix.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[L,U]= lu(A)</literal> produces two matrices <literal>L</literal> and
-            <literal>U</literal> such that <literal>A = L*U</literal> with <literal>U</literal>
-            upper triangular and <literal>L</literal> a general matrix without any particular 
-            structure. In fact, the matrix <literal>A</literal> is factored as <literal>E*A=B*U</literal>
-            where the matrix <literal>B</literal> is lower triangular 
-            and the matrix <literal>L</literal> is computed from <literal>L=E'*B</literal>.
-        </para>
-        <para>
-            If <literal>A</literal> has rank <literal>k</literal>, rows <literal>k+1</literal> to
-            <literal>n</literal> of <literal>U</literal> are zero.
-        </para>
-        <para>
-            <literal>[L,U,E]= lu(A)</literal> produces three matrices <literal>L</literal>, <literal>U</literal> and
-            <literal>E</literal> such that <literal>E*A = L*U</literal> with
-            <literal>U</literal> upper triangular and <literal>E*L</literal> lower
-            triangular for a permutation matrix <literal>E</literal>.
-        </para>
-        <para>
-            If <literal>A</literal> is a real matrix, using the function
-            <literal>lufact</literal> and  <literal>luget</literal> it is possible to obtain
-            the permutation matrices and also when <literal>A</literal> is not full
-            rank the column compression of the matrix <literal>L</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Example #1</title>
-        <para>
-            In the following example, we create the Hilbert matrix of size 4 and
-            factor it with A=LU. Notice that the matrix L is not lower triangular.
-            To get a lower triangular L matrix, we should have given the 
-            output argument E to Scilab.
-        </para>
-        <programlisting role="example"><![CDATA[ 
-a = testmatrix("hilb",4);
-[l,u]=lu(a)
-norm(l*u-a)
- ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>Example #2</title>
-        <para>
-            In the following example, we create the Hilbert matrix of size 4 and
-            factor it with EA=LU. Notice that the matrix L is lower triangular.
-        </para>
-        <programlisting role="example"><![CDATA[ 
-a = testmatrix("hilb",4);
-[l,u,e]=lu(a)
-norm(l*u-e*a)
- ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>Example #3</title>
-        <para>
-            The following example shows how to use the lufact and luget functions.
-        </para>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="lu">
+  <refnamediv>
+    <refname>lu</refname>
+    <refpurpose> factorisation LU  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[L,U]= lu(A)
+      [L,U,E]= lu(A)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe (m x n).
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>L,U  </term>
+        <listitem>
+          <para>matrices carrées réelles ou complexes (n x n).
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>E  </term>
+        <listitem>
+          <para>une matrice de permutation.
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>[L,U]= lu(A)</literal> calcule deux matrices <literal>L</literal> et
+      <literal>U</literal> telles que <literal>A = L*U</literal> avec <literal>U</literal>
+      triangulaire supérieure et <literal>L</literal> triangulaire inférieure
+      à une permutation des lignes près.
+    </para>
+    <para>
+      Si <literal>A</literal> est de rang <literal>k</literal>, les lignes
+      <literal>k+1</literal> à <literal>n</literal> de <literal>U</literal> sont nulles.
+    </para>
+    <para>
+    </para>
+    <para>
+      <literal>[L,U,E]= lu(A)</literal> calcule trois matrices <literal>L</literal>,
+      <literal>U</literal> et <literal>E</literal> telles que <literal>E*A = L*U</literal>
+      avec <literal>U</literal> triangulaire supérieure, <literal>L</literal>
+      triangulaire inférieure et <literal>E</literal> une matrice de
+      permutation.
+    </para>
+    <para>
+      Si <literal>A</literal> est une matrice réelle, il est possible en
+      utilisant <literal>lufact</literal> et <literal>luget</literal>
+      d'obtenir les matrices de permutations et quand
+      <literal>A</literal> n'est pas inversible la compression des
+      colonnes de la matrice <literal>L</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 a=rand(4,4);
 [l,u]=lu(a)
 norm(l*u-a)
 
-[h,rk]=lufact(sparse(a))
+[h,rk]=lufact(sparse(a))  // lufact fonctionne avec des matrices creuses 
 [P,L,U,Q]=luget(h);
 ludel(h)
-P=full(P);
-L=full(L);
-U=full(U);
-Q=full(Q);
-norm(P*L*U*Q-a)
+P=full(P);L=full(L);U=full(U);Q=full(Q); 
+norm(P*L*U*Q-a) // P,Q sont des matrices de permutation
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lufact">lufact</link>
-            </member>
-            <member>
-                <link linkend="luget">luget</link>
-            </member>
-            <member>
-                <link linkend="lusolve">lusolve</link>
-            </member>
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            lu decompositions are based on the Lapack routines DGETRF for real
-            matrices and ZGETRF for the complex case.
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="lufact">lufact</link>
+      </member>
+      <member>
+        <link linkend="luget">luget</link>
+      </member>
+      <member>
+        <link linkend="lusolve">lusolve</link>
+      </member>
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>La décomposition LU est basée sur les routines Lapack  DGETRF pour
+      les matrices réelles et ZGETRF pour le cas complexe. 
+    </para>
+  </refsection>
 </refentry>
index 820ddc1..30b491b 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="pinv">
-    <refnamediv>
-        <refname>pinv</refname>
-        <refpurpose> pseudoinverse</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>pinv(A,[tol])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>X= pinv(A)</literal> produces a matrix <literal>X</literal> of the
-            same dimensions as <literal>A'</literal> such that:
-        </para>
-        <para>
-            <literal>A*X*A = A, X*A*X = X</literal>  and both
-            <literal>A*X</literal> and <literal>X*A</literal> are Hermitian .
-        </para>
-        <para>
-            The computation is  based  on SVD and  any  singular values 
-            lower than a tolerance are treated   as zero: this  tolerance 
-            is accessed by <literal>X=pinv(A,tol)</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="pinv">
+  <refnamediv>
+    <refname>pinv</refname>
+    <refpurpose> pseudo-inverse  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>pinv(A,[tol])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>X= pinv(A)</literal>  renvoie une matrice <literal>X</literal> de mêmes dimensions que <literal>A'</literal> telle que :
+    </para>
+    <para>
+      <literal>A*X*A = A, X*A*X = X</literal> avec
+      <literal>A*X</literal> et <literal>X*A</literal> Hermitiennes.
+    </para>
+    <para>
+      Le calcul est basé sur une décomposition en valeurs singulières et
+      les valeurs singulières plus petites qu'une tolérance donnée
+      sont considérées comme nulles : pour cela utiliser la syntaxe
+      <literal>X=pinv(A,tol)</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,4);
 norm(A*pinv(A)*A-A,1)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="rank">rank</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            <literal>pinv</literal> function is  based on the singular value decomposition
-            (Scilab function <literal>svd</literal>).
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="rank">rank</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      La fonction <literal>pinv</literal> est basée sur la decomposition en valeurs
+      singulières (fonction Scilab  <literal>svd</literal>).
+    </para>
+  </refsection>
 </refentry>
index 6f24c66..24288c8 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="qr">
-    <refnamediv>
-        <refname>qr</refname>
-        <refpurpose> QR decomposition</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Q,R]=qr(X [,"e"])
-            [Q,R,E]=qr(X [,"e"])
-            [Q,R,rk,E]=qr(X [,tol])
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>nonnegative real number</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Q</term>
-                <listitem>
-                    <para>square orthogonal or unitary matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>R</term>
-                <listitem>
-                    <para>
-                        matrix with same dimensions as <literal>X</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>E</term>
-                <listitem>
-                    <para>permutation matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rk</term>
-                <listitem>
-                    <para>
-                        integer (QR-rank of <literal>X</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <variablelist>
-            <varlistentry>
-                <term>[Q,R] = qr(X)</term>
-                <listitem>
-                    <para>
-                        produces an upper triangular matrix <literal>R</literal> of the same dimension as <literal>X</literal> and an orthogonal (unitary in the complex case) matrix <literal>Q</literal> so that <literal>X = Q*R</literal>. <literal>[Q,R] = qr(X,"e")</literal> produces an "economy size": If <literal>X</literal> is m-by-n with m &gt; n, then only the first n columns of <literal>Q</literal>  are computed as well as the first n rows of <literal>R</literal>.
-                    </para>
-                    <para>
-                        From <literal>Q*R = X</literal> , it follows that
-                        the kth column of the matrix <literal>X</literal>, is expressed as a linear combination
-                        of the k first columns of <literal>Q</literal> (with coefficients <literal> R(1,k), ..., R(k,k) </literal>). The  k first columns of <literal>Q</literal> make an orthogonal basis
-                        of the subspace spanned by the k first comumns of <literal>X</literal>. If column <literal>k</literal>
-                        of <literal>X</literal> (i.e. <literal>X(:,k)</literal> ) is a linear combination of the first 
-                        <literal>p</literal> columns of <literal>X</literal>, then the entries <literal>R(p+1,k), ..., R(k,k)</literal>
-                        are zero. It this situation, <literal>R</literal> is upper trapezoidal. If <literal>X</literal> has
-                        rank <literal>rk</literal>, rows <literal>R(rk+1,:), R(rk+2,:), ...</literal> are zeros.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[Q,R,E] = qr(X)</term>
-                <listitem>
-                    <para>
-                        produces a (column) permutation matrix <literal>E</literal>, an upper
-                        triangular <literal>R</literal> with decreasing diagonal elements and an
-                        orthogonal (or unitary) <literal>Q</literal> so that <literal>X*E =    Q*R</literal>. 
-                        If <literal>rk</literal> is the rank of <literal>X</literal>, the
-                        <literal>rk</literal> first  entries along the main diagonal of
-                        <literal>R</literal>, i.e. <literal>R(1,1), R(2,2), ..., R(rk,rk)</literal>
-                        are all different from zero.  <literal>[Q,R,E] =  qr(X,"e")</literal> 
-                        produces an "economy size":
-                        If <literal>X</literal> is m-by-n with m &gt; n, then only the first n
-                        columns of <literal>Q</literal>  are computed as well as the first n
-                        rows of <literal>R</literal>. 
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[Q,R,rk,E] = qr(X ,tol)</term>
-                <listitem>
-                    <para>
-                        returns <literal>rk</literal> = rank estimate of <literal>X</literal> i.e. <literal>rk</literal> is the number of diagonal elements in <literal>R</literal> which are larger than a given threshold <literal>tol</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>[Q,R,rk,E] = qr(X) </term>
-                <listitem>
-                    <para>
-                        returns <literal>rk</literal> = rank estimate of <literal>X</literal>
-                        i.e. <literal>rk</literal> is the number of diagonal elements in
-                        <literal>R</literal> which are larger than
-                        <literal>tol=R(1,1)*%eps*max(size(R))</literal>. See <literal>rankqr</literal>
-                        for a rank revealing QR factorization, using the condition number
-                        of <literal>R</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="qr">
+  <refnamediv>
+    <refname>qr</refname>
+    <refpurpose> factorisation QR  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[Q,R]=qr(X [,"e"])
+      [Q,R,E]=qr(X [,"e"])
+      [Q,R,rk,E]=qr(X [,tol])
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel positif
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Q  </term>
+        <listitem>
+          <para>matrice carrée unitaire
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>R  </term>
+        <listitem>
+          <para>
+            matrice de même dimensions que <literal>X</literal>
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>E  </term>
+        <listitem>
+          <para>matrice de permutation
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>rk  </term>
+        <listitem>
+          <para>
+            entier (rang de <literal>X</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>[Q,R] = qr(X)</literal> renvoie une matrice triangulaire supérieure
+      <literal>R</literal> de même
+      dimensions que <literal>X</literal> et une matrice carrée othogonale
+      (unitaire dans le cas complexe) <literal>Q</literal> telles que
+      <literal>X = Q*R</literal>.
+      
+      <literal>[Q,R] = qr(X,"e")</literal>  renvoie une decomposition de
+      taille réduite: si <literal>X</literal> est une matrice <literal>m x
+        n
+      </literal>
+      avec <literal>m &gt; n</literal> alors seulement les
+      <literal>n</literal> premières colonnes de <literal>Q</literal> sont calculées
+      ainsi que les <literal>n</literal> premières lignes de
+      <literal>R</literal>.   
+    </para>
+    <para>
+      Il découle de <literal>Q*R = X</literal> que la
+      <literal>k</literal>ième colonne de <literal>X</literal> peut s'exprimer comme
+      une combinaison linéaire des <literal>k</literal> premieres colonnes de
+      <literal>Q</literal> (avec les coefficients <literal>R(1,k), ...,
+        R(k,k)
+      </literal>
+      .Les <literal>k</literal> premieres colonnes de
+      <literal>Q</literal> forment une base orthogonale du sous espace généré
+      par les Les <literal>k</literal> premieres colonnes de
+      <literal>X</literal>. Si la colonne <literal>k</literal> de <literal>X</literal> est
+      une combinaison linéaire des <literal>p</literal> premiéres colonnes de
+      <literal>X</literal> alors les éléments <literal>R(p+1,k), ...,
+        R(k,k)
+      </literal>
+      sont nuls. Dans cette situation <literal>R</literal> est
+      une matrice trapézoidale supérieure. Si <literal>X</literal> est de rang
+      <literal>rk</literal> alors les lignes  <literal>R(rk+1,:), R(rk+2,:),
+        ...
+      </literal>
+      sont nulles.
+      
+    </para>
+    <para>
+      <literal>[Q,R,E] = qr(X)</literal> renvoie une matrice de permutations (de
+      colonnes) <literal>E</literal>,
+      une matrice triangulaire supérieure <literal>R</literal> dont les
+      éléments diagonaux sont classés par ordre décroissant et une
+      matrice unitaire <literal>Q</literal> telles que <literal>X*E = Q*R</literal>.
+      si <literal>rk</literal> est le rang de <literal>X</literal> les
+      <literal>rk</literal> premiers éléménts diagonaux de <literal>R</literal> sont
+      tous non nuls. <literal>[Q,R,E] = qr(X,"e")</literal>  renvoie une decomposition de
+      taille réduite: si <literal>X</literal> est une matrice <literal>m x
+        n
+      </literal>
+      avec <literal>m &gt; n</literal> alors seulement les
+      <literal>n</literal> premières colonnes de <literal>Q</literal> sont calculées
+      ainsi que les <literal>n</literal> premières lignes de
+      <literal>R</literal>.   
+    </para>
+    <para>
+      <literal>[Q,R,rk,E] = qr(X [,tol])</literal>renvoie de plus 
+      <literal>rk</literal> =rang estimé de <literal>X</literal>. 
+      Plus précisément, 
+      <literal>rk</literal> est le nombre d'éléments diagonaux de
+      <literal>R</literal> supérieurs à <literal>tol</literal>. La valeur par défaut
+      de <literal>tol</literal> est <literal>R(1,1)*%eps*max(size(R))</literal> 
+    </para>
+    <para>
+      renvoie <literal>rk</literal> = rang estimé de <literal>X</literal>. Ici,
+      <literal>rk</literal> est le nombre d'éléments diagonaux de <literal>R</literal>
+      supérieurs à <literal>R(1,1)*%eps*max(size(R)</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 // QR factorization, generic case
 // X is tall (full rank)
 X=rand(5,2);[Q,R]=qr(X); [Q'*X R]
@@ -152,33 +166,29 @@ A=rand(5,2)*rand(2,5);
 norm(Q'*A-R)
 svd([A,Q(:,1:rk)])    //span(A) =span(Q(:,1:rk))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="rankqr">rankqr</link>
-            </member>
-            <member>
-                <link linkend="rank">rank</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-            <member>
-                <link linkend="rowcomp">rowcomp</link>
-            </member>
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Used Functions</title>
-        <para>
-            qr decomposition is based  the Lapack routines DGEQRF, DGEQPF,
-            DORGQR for the real matrices and  ZGEQRF, ZGEQPF, ZORGQR for the
-            complex case.
-        </para>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="rank">rank</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+      <member>
+        <link linkend="rowcomp">rowcomp</link>
+      </member>
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>La décomposition QR est basée sur les routines Lapack  DGEQRF, DGEQPF,
+      DORGQR pour les matrices réelles et ZGEQRF, ZGEQPF, ZORGQR pour le cas
+      complexe.
+    </para>
+  </refsection>
 </refentry>
index de19ad2..ded811c 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="cond">
-    <refnamediv>
-        <refname>cond</refname>
-        <refpurpose> condition number</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>cond(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Condition number in 2-norm.  <literal>cond(X)</literal> is the  ratio  of  the
-            largest singular value of  <literal>X</literal>  to the smallest.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="cond">
+  <refnamediv>
+    <refname>cond</refname>
+    <refpurpose> conditionnement  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>cond(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Conditionnement en norme 2. <literal>cond(X)</literal> est le quotient entre la plus grande et la plus petite valeur singulière de <literal>X</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=testmatrix('hilb',6);
 cond(A)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="rcond">rcond</link>
-            </member>
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="rcond">rcond</link>
+      </member>
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index a649899..01a46cb 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="det">
-    <refnamediv>
-        <refname>det</refname>
-        <refpurpose> determinant</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>det(X)
-            [e,m]=det(X)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex square matrix, polynomial or rational matrix.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>m</term>
-                <listitem>
-                    <para>real or complex number, the determinant base 10 mantissae</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>e</term>
-                <listitem>
-                    <para>integer, the determinant base 10 exponent</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>det(X)</literal> ( <literal>m*10^e</literal> is the determinant of the square matrix <literal>X</literal>.
-        </para>
-        <para>
-            For polynomial matrix <literal>det(X)</literal> is equivalent to <literal>determ(X)</literal>.
-        </para>
-        <para>
-            For rational matrices <literal>det(X)</literal> is equivalent to <literal>detr(X)</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>References</title>
-        <para>
-            det computations are based on the Lapack routines
-            DGETRF for  real matrices and  ZGETRF for the complex case.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="det">
+  <refnamediv>
+    <refname>det </refname>
+    <refpurpose> déterminant  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>det(X)
+      [e,m]=det(X)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice réelle, complexe, polynomiale, rationnelle
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>m  </term>
+        <listitem>
+          <para>nombre réel ou complexe, mantisse du déterminant en base 10
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>e  </term>
+        <listitem>
+          <para>entier, exposant du déterminant en base 10 
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>det(X)</literal> ( <literal>m*10^e</literal> est le déterminant de la matrice carrée <literal>X</literal>.
+    </para>
+    <para>
+      Pour les matrices polynomiales <literal>det(X)</literal> est équivalent à <literal>determ(X)</literal>.
+    </para>
+    <para>
+      Pour les matrices rationnelles <literal>det(X)</literal> est équivalent à <literal>detr(X)</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 x=poly(0,'x');
 det([x,1+x;2-x,x^2])
-w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w)   //zeros of linear system
+w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w)   // zéros du système linéaire
 A=rand(3,3);
 det(A), prod(spec(A))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="detr">detr</link>
-            </member>
-            <member>
-                <link linkend="determ">determ</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="detr">detr</link>
+      </member>
+      <member>
+        <link linkend="determ">determ</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Fonctions Utilisées</title>
+    <para>
+      Le calcul du determinant est basé sur les routines Lapack :
+      DGETRF pour les matrices réelles et  ZGETRF pour le cas complexe.
+    </para>
+  </refsection>
 </refentry>
index e84d0ea..e91f4e0 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="orth">
-    <refnamediv>
-        <refname>orth</refname>
-        <refpurpose> orthogonal basis</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>Q=orth(A)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Q</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>Q=orth(A)</literal> returns <literal>Q</literal>, an orthogonal
-            basis for the span of <literal>A</literal>.  Range(<literal>Q</literal>) =
-            Range(<literal>A</literal>) and <literal>Q'*Q=eye</literal>.
-        </para>
-        <para>
-            The number of columns of <literal>Q</literal> is the rank of
-            <literal>A</literal> as determined by the QR algorithm.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="orth">
+  <refnamediv>
+    <refname>orth</refname>
+    <refpurpose> calcul d'une base orthogonale  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>Q=orth(A)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Q  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>Q=orth(A)</literal> renvoie <literal>Q</literal>, une base
+      orthogonale de l'image de <literal>A</literal>.  Im(<literal>Q</literal>)
+      = Im(<literal>A</literal>) et <literal>Q'*Q = I</literal>.
+    </para>
+    <para>
+      Le nombre de colonnes de <literal>Q</literal> est égal au rang de
+      <literal>A</literal>, comme déterminé par l'algorithme QR.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(5,3)*rand(3,4);
 [X,dim]=rowcomp(A);X=X';
 svd([orth(A),X(:,1:dim)])
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="rowcomp">rowcomp</link>
-            </member>
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-            <member>
-                <link linkend="range">range</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="rowcomp">rowcomp</link>
+      </member>
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+      <member>
+        <link linkend="range">range</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 4848dd0..64477b0 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="rank">
-    <refnamediv>
-        <refname>rank</refname>
-        <refpurpose> rank</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[i]=rank(X)
-            [i]=rank(X,tol)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>nonnegative real number</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>rank(X)</literal> is the numerical rank of <literal>X</literal>
-            i.e. the number of singular values of X that are larger than
-            <literal>norm(size(X),'inf') * norm(X) * %eps</literal>.
-        </para>
-        <para>
-            <literal>rank(X,tol)</literal> is the number of singular values of
-            <literal>X</literal> that are larger than <literal>tol</literal>.
-        </para>
-        <para>
-            Note that the default value of <literal>tol</literal> is proportional to
-            <literal>norm(X)</literal>. As a consequence
-            <literal>rank([1.d-80,0;0,1.d-80])</literal> is 2 !.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="rank">
+  <refnamediv>
+    <refname>rank</refname>
+    <refpurpose> rang  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[i]=rank(X)
+      [i]=rank(X,tol)
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>tol  </term>
+        <listitem>
+          <para>nombre réel positif
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal> rank(X)</literal> calcule le rang "numérique" de
+      <literal>X</literal> c'est à dire le nombre de ses valeurs
+      singulières supérieures à <literal>norm(size(X),'inf') *
+        norm(X) * %eps
+      </literal>
+      .
+    </para>
+    <para>
+      <literal>rank(X,tol)</literal> est le nombre de valeurs singulières de
+      <literal>X</literal> supérieures à <literal>tol</literal>.
+    </para>
+    <para>
+      Notez que la valeur par défaut de <literal>tol</literal> est
+      proportionnelle à <literal>norm(X)</literal>. Par exemple
+    </para>
+    <para>
+      <literal>rank([1.d-80,0;0,1.d-80])</literal> vaut 2 !.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 rank([1.d-80,0;0,1.d-80])
 rank([1,0;0,1.d-80])
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-            <member>
-                <link linkend="qr">qr</link>
-            </member>
-            <member>
-                <link linkend="rowcomp">rowcomp</link>
-            </member>
-            <member>
-                <link linkend="colcomp">colcomp</link>
-            </member>
-            <member>
-                <link linkend="lu">lu</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+      <member>
+        <link linkend="qr">qr</link>
+      </member>
+      <member>
+        <link linkend="rowcomp">rowcomp</link>
+      </member>
+      <member>
+        <link linkend="colcomp">colcomp</link>
+      </member>
+      <member>
+        <link linkend="lu">lu</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index f6a1972..7db5496 100644 (file)
@@ -2,7 +2,6 @@
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
- * Copyright (C) 2010 - DIGITEO - Michael Baudin
  * 
  * This file must be used under the terms of the CeCILL.
  * This source file is licensed as described in the file COPYING, which
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="rcond">
-    <refnamediv>
-        <refname>rcond</refname>
-        <refpurpose>  inverse condition number</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>rcond(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex square matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>rcond(X)</literal> is an estimate for the reciprocal of the
-            condition of <literal>X</literal> in the 1-norm.
-        </para>
-        <para>
-            If <literal>X</literal> is well conditioned, <literal>rcond(X)</literal> is close to 1.
-            If not, <literal>rcond(X)</literal> is close to 0.
-        </para>
-        <para>
-            We compute the 1-norm of A with Lapack/DLANGE, compute its LU decomposition with Lapack/DGETRF 
-            and finally estimate the condition with Lapack/DGECON.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="rcond">
+  <refnamediv>
+    <refname>rcond</refname>
+    <refpurpose>  estimation de l'inverse du conditionnement  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>rcond(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice carrée réelle ou complexe
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>rcond(X)</literal> est une estimation de l'inverse du conditionnement de <literal>X</literal> pour la norme l_1.
+    </para>
+    <para>
+      Si <literal>X</literal> est bien conditionnée, <literal>rcond(X)</literal> est proche 1.
+      Sinon, <literal>rcond(X)</literal> est proche de 0.
+    </para>
+    <para>
+      <literal>[r,z]=rcond(X)</literal> renvoie <literal>rcond(X)</literal> dans
+      <literal>r</literal> et renvoie aussi <literal>z</literal> tel que <literal>norm(X*z,1) = r*norm(X,1)*norm(z,1)</literal> 
+    </para>
+    <para>
+      Ainsi,  si <literal>rcond</literal> est très petit <literal>z</literal> est un vecteur se trouvant dans le noyau de X.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=diag([1:10]);
 rcond(A)
 A(1,1)=0.000001;
 rcond(A)
  ]]></programlisting>
-        <para>
-            Estimating the 1-norm inverse condition number with <literal>rcond</literal> is 
-            much faster than computing the 2-norm condition number with <literal>cond</literal>.
-            As a trade-off, <literal>rcond</literal> may be less reliable.
-        </para>
-        <programlisting role="example"><![CDATA[ 
-    A=ones(1000,1000);
-    timer();cond(A);timer()
-    timer();1/rcond(A);timer()
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="svd">svd</link>
-            </member>
-            <member>
-                <link linkend="cond">cond</link>
-            </member>
-            <member>
-                <link linkend="inv">inv</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="svd">svd</link>
+      </member>
+      <member>
+        <link linkend="cond">cond</link>
+      </member>
+      <member>
+        <link linkend="inv">inv</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 56af8a0..fb5ec47 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="trace">
-    <refnamediv>
-        <refname>trace</refname>
-        <refpurpose> trace</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>trace(X)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>real or complex square matrix, polynomial or rational matrix.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>trace(X)</literal> is the trace of the matrix <literal>X</literal>.
-        </para>
-        <para>
-            Same as <literal>sum(diag(X))</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="trace">
+  <refnamediv>
+    <refname>trace </refname>
+    <refpurpose> trace d'une matrice  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>trace(X)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X  </term>
+        <listitem>
+          <para>matrice carrée, réelle, complexe, polynomiale ou rationnelle.
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>trace(X)</literal> calcule la trace de <literal>X</literal>.
+    </para>
+    <para>
+      Identique à <literal>sum(diag(X))</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(3,3);
 trace(A)-sum(spec(A))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="det">det</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="det">det</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index e03e86b..390b543 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="companion">
-    <refnamediv>
-        <refname>companion</refname>
-        <refpurpose> companion matrix</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>A=companion(p)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>p</term>
-                <listitem>
-                    <para>polynomial or vector of polynomials</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>square matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Returns a matrix <literal>A</literal> with characteristic polynomial equal
-            to <literal>p</literal> if <literal>p</literal> is monic. If <literal>p</literal> is not monic
-            the characteristic polynomial of <literal>A</literal> is equal to
-            <literal>p/c</literal> where <literal>c</literal> is the coefficient of largest degree
-            in <literal>p</literal>.
-        </para>
-        <para>
-            If <literal>p</literal> is a vector of monic polynomials, <literal>A</literal> is block diagonal,
-            and the characteristic polynomial of the ith block is <literal>p(i)</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="companion">
+  <refnamediv>
+    <refname>companion</refname>
+    <refpurpose> matrice compagnon  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>A=companion(p)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>p  </term>
+        <listitem>
+          <para>polynôme ou vecteur de polynômes
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>A  </term>
+        <listitem>
+          <para>matrice carrée
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Renvoie une matrice <literal>A</literal> dont le polynôme caractéristique est
+      <literal>p</literal> si <literal>p</literal> est unitaire (le coefficient de plus haut degré est égal à un). Si <literal>p</literal> n'est pas unitaire
+      le polynôme caractéristique de <literal>A</literal> est égal à
+      <literal>p/c</literal> où <literal>c</literal> est le coefficient de plus haut degré de <literal>p</literal>.
+    </para>
+    <para>
+      Si <literal>p</literal> est un vecteur de polynômes unitaires, <literal>A</literal> est bloc-diagonale,
+      et le polynôme caractéristique du i-ème bloc est égal à <literal>p(i)</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 s=poly(0,'s');
 p=poly([1,2,3,4,1],'s','c')
 det(s*eye()-companion(p))
 roots(p)
 spec(companion(p))
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="spec">spec</link>
-            </member>
-            <member>
-                <link linkend="poly">poly</link>
-            </member>
-            <member>
-                <link linkend="randpencil">randpencil</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="spec">spec</link>
+      </member>
+      <member>
+        <link linkend="poly">poly</link>
+      </member>
+      <member>
+        <link linkend="randpencil">randpencil</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index baa3bdc..b3d7857 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="glever">
-    <refnamediv>
-        <refname>glever</refname>
-        <refpurpose> inverse of matrix pencil</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>E, A</term>
-                <listitem>
-                    <para>two real square matrices of same dimensions</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>s</term>
-                <listitem>
-                    <para>
-                        character string (default value '<literal>s</literal>')
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Bfs,Bis</term>
-                <listitem>
-                    <para>two polynomial matrices</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>chis</term>
-                <listitem>
-                    <para>polynomial</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Computation of
-        </para>
-        <para>
-            <literal>(s*E-A)^-1</literal>
-        </para>
-        <para>
-            by generalized Leverrier's algorithm for a matrix pencil.
-        </para>
-        <programlisting role=""><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="glever">
+  <refnamediv>
+    <refname>glever</refname>
+    <refpurpose> inverse d'un faisceau de matrices  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>E, A  </term>
+        <listitem>
+          <para>matrices carrées réelles de même dimensions
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>s  </term>
+        <listitem>
+          <para>
+            chaîne de caractères (indéterminée des polynômes, '<literal>s</literal>' par défaut )
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>Bfs,Bis  </term>
+        <listitem>
+          <para>deux matrices polynomiales
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>chis  </term>
+        <listitem>
+          <para>polynôme
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      Calcul de 
+    </para>
+    <para>
+      (s*E-A)^-1
+    </para>
+    <para>
+      par l'algorithme généralisé de Leverrier pour un faisceau de matrices.
+    </para>
+    <programlisting role=""><![CDATA[ 
 (s*E-A)^-1 = (Bfs/chis) - Bis.
  ]]></programlisting>
-        <para>
-            <literal>chis</literal> = characteristic polynomial (up to a multiplicative constant).
-        </para>
-        <para>
-            <literal>Bfs</literal>  = numerator polynomial matrix.
-        </para>
-        <para>
-            <literal>Bis</literal>
-            = polynomial matrix ( - expansion of <literal>(s*E-A)^-1</literal> at infinity).
-        </para>
-        <para>
-            Note the - sign before <literal>Bis</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Caution</title>
-        <para>
-            This function uses <literal>cleanp</literal> to simplify <literal>Bfs,Bis</literal> and <literal>chis</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+    <para>
+      <literal>chis</literal> = polynôme caractéristique (à une constante multiplicative près).
+    </para>
+    <para>
+      <literal>Bfs</literal>  = matrice polynomiale de numérateurs
+    </para>
+    <para>
+      <literal>Bis</literal>
+      = matrice polynomiale ( - développement de <literal>(s*E-A)^-1</literal> à l'infini).
+    </para>
+    <para>
+      Noter le signe - devant <literal>Bis</literal>.
+    </para>
+    <para>
+    </para>
+  </refsection>
+  <refsection>
+    <title>Attention</title>
+    <para>
+      Cette fonction utilise <literal>cleanp</literal> pour simplifier <literal>Bfs,Bis</literal> et <literal>chis</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1];
 [Bfs,Bis,chis]=glever(F)
 inv(F)-((Bfs/chis) - Bis)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="rowshuff">rowshuff</link>
-            </member>
-            <member>
-                <link linkend="det">det</link>
-            </member>
-            <member>
-                <link linkend="invr">invr</link>
-            </member>
-            <member>
-                <link linkend="coffg">coffg</link>
-            </member>
-            <member>
-                <link linkend="pencan">pencan</link>
-            </member>
-            <member>
-                <link linkend="penlaur">penlaur</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="rowshuff">rowshuff</link>
+      </member>
+      <member>
+        <link linkend="det">det</link>
+      </member>
+      <member>
+        <link linkend="invr">invr</link>
+      </member>
+      <member>
+        <link linkend="coffg">coffg</link>
+      </member>
+      <member>
+        <link linkend="pencan">pencan</link>
+      </member>
+      <member>
+        <link linkend="penlaur">penlaur</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index e0ed560..179088e 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="lyap">
-    <refnamediv>
-        <refname>lyap</refname>
-        <refpurpose> Lyapunov equation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[X]=lyap(A,C,'c')
-            [X]=lyap(A,C,'d')
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A, C</term>
-                <listitem>
-                    <para>
-                        real square matrices, <literal>C</literal> must be symmetric
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>X= lyap(A,C,flag)</literal> solves the continuous time or
-            discrete time matrix Lyapunov matrix equation:
-        </para>
-        <programlisting role=""><![CDATA[ 
-A'*X + X*A = C       ( flag='c' )
-A'*X*A - X = C       ( flag='d' )
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="lyap">
+  <refnamediv>
+    <refname>lyap </refname>
+    <refpurpose> Equation de Lyapunov  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[X]=lyap(A,C,flag)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>A, C  </term>
+        <listitem>
+          <para>
+            matrices réelles, <literal>C</literal> doit être symétrique
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>flag  </term>
+        <listitem>
+          <para>chaîne de caractères, 'c' ou 'd'
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>X= lyap(A,C,flag)</literal> résout l'équation matricielle de
+      Lyapunov en temps continu ou discret
+    </para>
+    <programlisting role=""><![CDATA[ 
+A'*X + X*A = C       ( flag = 'c' )
+A'*X*A - X = C       ( flag = 'd' )
  ]]></programlisting>
-        <para>
-            Note that a unique solution exist if and only if an eigenvalue of <literal>A</literal> is
-            not an eigenvalue of <literal>-A</literal> (<literal>flag='c'</literal>)  or 1 over an eigenvalue of <literal>A</literal> 
-            (<literal>flag='d'</literal>).
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+    <para>
+      Une solution unique existe si <literal>A</literal> n'a pas de valeur propre
+      sur l'axe imaginaire (<literal>flag='c'</literal>) ou si 1 n'est pas
+      valeur propre de <literal>A</literal> (<literal>flag='d'</literal>).
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 A=rand(4,4);C=rand(A);C=C+C';
 X=lyap(A,C,'c');
 A'*X + X*A -C
 X=lyap(A,C,'d');
 A'*X*A - X -C
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="sylv">sylv</link>
-            </member>
-            <member>
-                <link linkend="ctr_gram">ctr_gram</link>
-            </member>
-            <member>
-                <link linkend="obs_gram">obs_gram</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="sylv">sylv</link>
+      </member>
+      <member>
+        <link linkend="ctr_gram">ctr_gram</link>
+      </member>
+      <member>
+        <link linkend="obs_gram">obs_gram</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 57aa597..9f280c0 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="proj">
-    <refnamediv>
-        <refname>proj</refname>
-        <refpurpose> projection</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>P = proj(X1,X2)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>X1,X2</term>
-                <listitem>
-                    <para>two real matrices with equal number of columns</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>
-                        real projection matrix (<literal>P^2=P</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>P</literal> is the projection on <literal>X2</literal> parallel to <literal>X1</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="proj">
+  <refnamediv>
+    <refname>proj</refname>
+    <refpurpose> projection  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>P = proj(X1,X2)</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>X1,X2  </term>
+        <listitem>
+          <para>deux matrices réelles avec un nombre identique de colonnes.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>P  </term>
+        <listitem>
+          <para>
+            matrice réelle de projection (<literal>P^2=P</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>P</literal> est la projection sur <literal>X2</literal> parallèlement à <literal>X1</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 X1=rand(5,2);X2=rand(5,3);
 P=proj(X1,X2);
 norm(P^2-P,1)
-trace(P)    // This is dim(X2)
+trace(P)    // il s'agit de dim(X2)
 [Q,M]=fullrf(P);
-svd([Q,X2])   // span(Q) = span(X2)
+svd([Q,X2])   // Im(Q) = Im(X2)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="projspec">projspec</link>
-            </member>
-            <member>
-                <link linkend="orth">orth</link>
-            </member>
-            <member>
-                <link linkend="fullrf">fullrf</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="projspec">projspec</link>
+      </member>
+      <member>
+        <link linkend="orth">orth</link>
+      </member>
+      <member>
+        <link linkend="fullrf">fullrf</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index 07ffc43..f9f3cb8 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="coff">
-    <refnamediv>
-        <refname>coff</refname>
-        <refpurpose> resolvent (cofactor method)  </refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[N,d]=coff(M [,var])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>M</term>
-                <listitem>
-                    <para>square real matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>var</term>
-                <listitem>
-                    <para>character string</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>N</term>
-                <listitem>
-                    <para>
-                        polynomial matrix (same size as <literal>M</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>d</term>
-                <listitem>
-                    <para>
-                        polynomial (characteristic polynomial <literal>poly(A,'s')</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>coff</literal> computes R=<literal>(s*eye()-M)^-1</literal> for <literal>M</literal> a real matrix. 
-            R is given by <literal>N/d</literal>.
-        </para>
-        <para>
-            <literal>N</literal> = numerator polynomial matrix.
-        </para>
-        <para>
-            <literal>d</literal> = common denominator.
-        </para>
-        <para>
-            <literal>var</literal> character string ('<literal>s</literal>' if omitted)
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="coff">
+  <refnamediv>
+    <refname>coff</refname>
+    <refpurpose> résolvante (méthode des cofacteurs)  </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[N,d]=coff(M [,var])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+        <term>M  </term>
+        <listitem>
+          <para>matrice carrée réelle
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>var  </term>
+        <listitem>
+          <para>chaîne de caractères (indéterminée des polynômes)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>N  </term>
+        <listitem>
+          <para>
+            matrice de polynômes (de même taille que <literal>M</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>d  </term>
+        <listitem>
+          <para>
+            polynôme (polynôme caractéristique de M : <literal>poly(M,var)</literal>)
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      <literal>coff</literal> calcule R=<literal>(s*eye()-M)^-1</literal> pour <literal>M</literal> une matrice réelle. 
+      R est donnée par <literal>N/d</literal>.
+    </para>
+    <para>
+      <literal>N</literal> = matrice des numérateurs (polynômes).
+    </para>
+    <para>
+      <literal>d</literal> = dénominateur commun.
+    </para>
+    <para>
+      <literal>var</literal> chaîne de caractères (indéterminée des polynômes, '<literal>s</literal>' par défaut)
+    </para>
+  </refsection>
+  <refsection>
+    <title>Exemples</title>
+    <programlisting role="example"><![CDATA[ 
 M=[1,2;0,3];
 [N,d]=coff(M)
 N/d
 inv(%s*eye()-M)
  ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See Also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="coffg">coffg</link>
-            </member>
-            <member>
-                <link linkend="ss2tf">ss2tf</link>
-            </member>
-            <member>
-                <link linkend="nlev">nlev</link>
-            </member>
-            <member>
-                <link linkend="poly">poly</link>
-            </member>
-        </simplelist>
-    </refsection>
+  </refsection>
+  <refsection role="see also">
+    <title>Voir aussi</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="coffg">coffg</link>
+      </member>
+      <member>
+        <link linkend="ss2tf">ss2tf</link>
+      </member>
+      <member>
+        <link linkend="nlev">nlev</link>
+      </member>
+      <member>
+        <link linkend="poly">poly</link>
+      </member>
+    </simplelist>
+  </refsection>
 </refentry>
index f0fdeb0..e89bfb1 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="nlev">
-    <refnamediv>
-        <refname>nlev</refname>
-        <refpurpose> Leverrier's algorithm</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Calling Sequence</title>
-        <synopsis>[num,den]=nlev(A,z [,rmax])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>real square matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>z</term>
-                <listitem>
-                    <para>character string</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rmax</term>
-                <listitem>
-                    <para>
-                        optional parameter (see <literal>bdiag</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[num,den]=nlev(A,z [,rmax])</literal> computes
-            <literal>(z*eye()-A)^(-1)</literal>
-        </para>
-        <para>
-            by block diagonalization of A followed by Leverrier's algorithm
-            on each block.
-        </para>
-        <para>
-            This algorithm is better than the usual leverrier algorithm but
-            still not perfect!
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[ 
+<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="nlev">
+  <refnamediv>
+    <refname>nlev</refname>
+    <refpurpose> Algorithme de Leverrier   </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Séquence d'appel</title>
+    <synopsis>[num,den]=nlev(A,z [,rmax])</synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Paramètres</title>
+    <variablelist>
+      <varlistentry>
+