[doc] replace MathML with LaTeX (continue) 07/21507/12
Samuel GOUGEON [Sat, 20 Jun 2020 21:17:42 +0000 (23:17 +0200)]
Change-Id: I0f1e697b17717699fda0e042b99852e028fcb63c

124 files changed:
scilab/modules/cacsd/help/en_US/linear_system_representation/syslin.xml
scilab/modules/cacsd/help/fr_FR/linear_system_representation/syslin.xml
scilab/modules/cacsd/help/ja_JP/linear_system_representation/syslin.xml
scilab/modules/cacsd/help/mml/syslin_equation_1.mml [deleted file]
scilab/modules/cacsd/help/pt_BR/linear_system_representation/syslin.xml
scilab/modules/cacsd/help/ru_RU/linear_system_representation/syslin.xml
scilab/modules/helptools/etc/images_md5.txt
scilab/modules/helptools/images/_LaTeX_INTEGRAL_m.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_beta.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_binomial.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_bsplin3val.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_dlgamma.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_gamma.xml_1.png
scilab/modules/helptools/images/_LaTeX_interp.xml_1.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_10.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_11.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_12.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_13.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_14.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_15.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_16.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_17.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_18.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_19.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_2.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_20.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_3.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_4.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_5.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_6.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_7.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_8.png [deleted file]
scilab/modules/helptools/images/_LaTeX_interp.xml_9.png [deleted file]
scilab/modules/helptools/images/_LaTeX_legendre.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_legendre.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lsq_splin.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_splin.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_splin2d.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/beta_equation1.mml.png [deleted file]
scilab/modules/helptools/images/binomial_equation_1_en_US.mml.png [deleted file]
scilab/modules/helptools/images/binomial_equation_1_ru_RU.mml.png [deleted file]
scilab/modules/helptools/images/bsplin3val_equation1.mml.png [deleted file]
scilab/modules/helptools/images/dlgamma_equation1.mml.png [deleted file]
scilab/modules/helptools/images/integral_m.mml.png [deleted file]
scilab/modules/helptools/images/legendre_equation1.mml.png [deleted file]
scilab/modules/helptools/images/legendre_equation2.mml.png [deleted file]
scilab/modules/helptools/images/linear_interpn_equation1.mml.png [deleted file]
scilab/modules/helptools/images/linear_interpn_equation2.mml.png [deleted file]
scilab/modules/helptools/images/linear_interpn_equation3.mml.png [deleted file]
scilab/modules/helptools/images/lsq_splin_equation1.mml.png [deleted file]
scilab/modules/helptools/images/splin2d_equation_1.mml.png [deleted file]
scilab/modules/helptools/images/splin3d_equation1.mml.png [deleted file]
scilab/modules/helptools/images/splin3d_pt_BR_1.png [new file with mode: 0644]
scilab/modules/helptools/images/splin_equation1.mml.png [deleted file]
scilab/modules/helptools/images/splin_equation2.mml.png [deleted file]
scilab/modules/helptools/images/splin_equation3.mml.png [deleted file]
scilab/modules/helptools/images/splin_equation4.mml.png [deleted file]
scilab/modules/helptools/images/splin_equation5.mml.png [deleted file]
scilab/modules/helptools/images/syslin_equation_1.mml.png [deleted file]
scilab/modules/interpolation/help/en_US/bsplin3val.xml
scilab/modules/interpolation/help/en_US/interp.xml
scilab/modules/interpolation/help/en_US/linear_interpn.xml
scilab/modules/interpolation/help/en_US/lsq_splin.xml
scilab/modules/interpolation/help/en_US/splin.xml
scilab/modules/interpolation/help/en_US/splin2d.xml
scilab/modules/interpolation/help/en_US/splin3d.xml
scilab/modules/interpolation/help/ja_JP/bsplin3val.xml
scilab/modules/interpolation/help/ja_JP/interp.xml
scilab/modules/interpolation/help/ja_JP/linear_interpn.xml
scilab/modules/interpolation/help/ja_JP/lsq_splin.xml
scilab/modules/interpolation/help/ja_JP/splin.xml
scilab/modules/interpolation/help/ja_JP/splin2d.xml
scilab/modules/interpolation/help/ja_JP/splin3d.xml
scilab/modules/interpolation/help/mml/bsplin3val_equation1.mml [deleted file]
scilab/modules/interpolation/help/mml/interp_equation1.mml [deleted file]
scilab/modules/interpolation/help/mml/interp_equation2.mml [deleted file]
scilab/modules/interpolation/help/mml/interp_equation3.mml [deleted file]
scilab/modules/interpolation/help/mml/interp_equation4.mml [deleted file]
scilab/modules/interpolation/help/mml/linear_interpn_equation1.mml [deleted file]
scilab/modules/interpolation/help/mml/linear_interpn_equation2.mml [deleted file]
scilab/modules/interpolation/help/mml/linear_interpn_equation3.mml [deleted file]
scilab/modules/interpolation/help/mml/lsq_splin_equation1.mml [deleted file]
scilab/modules/interpolation/help/mml/splin2d_equation_1.mml [deleted file]
scilab/modules/interpolation/help/mml/splin3d_equation1.mml [deleted file]
scilab/modules/interpolation/help/mml/splin_equation1.mml [deleted file]
scilab/modules/interpolation/help/mml/splin_equation2.mml [deleted file]
scilab/modules/interpolation/help/mml/splin_equation3.mml [deleted file]
scilab/modules/interpolation/help/mml/splin_equation4.mml [deleted file]
scilab/modules/interpolation/help/mml/splin_equation5.mml [deleted file]
scilab/modules/interpolation/help/pt_BR/bsplin3val.xml
scilab/modules/interpolation/help/pt_BR/interp.xml
scilab/modules/interpolation/help/pt_BR/linear_interpn.xml
scilab/modules/interpolation/help/pt_BR/lsq_splin.xml
scilab/modules/interpolation/help/pt_BR/splin.xml
scilab/modules/interpolation/help/pt_BR/splin2d.xml
scilab/modules/interpolation/help/pt_BR/splin3d.xml
scilab/modules/special_functions/help/en_US/beta.xml
scilab/modules/special_functions/help/en_US/dlgamma.xml
scilab/modules/special_functions/help/en_US/gamma.xml
scilab/modules/special_functions/help/en_US/legendre.xml
scilab/modules/special_functions/help/fr_FR/dlgamma.xml
scilab/modules/special_functions/help/ja_JP/beta.xml
scilab/modules/special_functions/help/ja_JP/dlgamma.xml
scilab/modules/special_functions/help/ja_JP/gamma.xml [new file with mode: 0644]
scilab/modules/special_functions/help/ja_JP/legendre.xml
scilab/modules/special_functions/help/mml/beta_equation1.mml [deleted file]
scilab/modules/special_functions/help/mml/dlgamma_equation1.mml [deleted file]
scilab/modules/special_functions/help/mml/legendre_equation1.mml [deleted file]
scilab/modules/special_functions/help/mml/legendre_equation2.mml [deleted file]
scilab/modules/special_functions/help/pt_BR/beta.xml
scilab/modules/special_functions/help/pt_BR/dlgamma.xml
scilab/modules/special_functions/help/pt_BR/gamma.xml [new file with mode: 0644]
scilab/modules/special_functions/help/pt_BR/legendre.xml
scilab/modules/statistics/help/en_US/1_cdf/binomial.xml
scilab/modules/statistics/help/ja_JP/1_cdf/binomial.xml
scilab/modules/statistics/help/mml/binomial_equation_1_en_US.mml [deleted file]
scilab/modules/statistics/help/mml/binomial_equation_1_fr_FR.mml [deleted file]
scilab/modules/statistics/help/mml/binomial_equation_1_ru_RU.mml [deleted file]
scilab/modules/statistics/help/pt_BR/1_cdf/binomial.xml
scilab/modules/statistics/help/ru_RU/1_cdf/binomial.xml
scilab/modules/xcos/help/en_US/palettes/Continuous_pal/INTEGRAL_m.xml
scilab/modules/xcos/help/fr_FR/palettes/Continuous_pal/INTEGRAL_m.xml
scilab/modules/xcos/help/ja_JP/palettes/Continuous_pal/INTEGRAL_m.xml
scilab/modules/xcos/help/mml/integral_m.mml [deleted file]

index 020c85f..179ca85 100644 (file)
@@ -14,8 +14,8 @@
  -->
 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
           xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
-          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
-          xmlns:scilab="http://www.scilab.org" xml:id="syslin" xml:lang="en">
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="syslin" xml:lang="en">
     <refnamediv>
         <refname>syslin</refname>
         <refpurpose>linear system definition</refpurpose>
         </para>
         <para>State-space representation:</para>
         <programlisting><![CDATA[
-sl=syslin(dom,A,B,C [,D [,x0] ])
+sl = syslin(dom,A,B,C [,D [,x0] ])
  ]]></programlisting>
-        <para>represents the system :</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../../mml/syslin_equation_1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            represents the system
+        </para>
+        <para>
+            <table align="center">
+            <tr><td align="right">s.X</td><td>= A.X + B.u</td></tr>
+            <tr><td align="right">y</td><td>= C.X + D.u</td></tr>
+            <tr><td align="right">x(0)</td><td>= x0</td></tr>
+            </table>
+        </para>
         <para>
             The output of <literal>syslin</literal> is a list of the following
             form:
index 616aa9f..7462980 100644 (file)
@@ -1,14 +1,20 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="syslin" xml:lang="fr">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="syslin" xml:lang="fr">
     <refnamediv>
         <refname>syslin</refname>
         <refpurpose>définition d'un système dynamique linéaire</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Séquence d'appel</title>
-        <synopsis>[sl]=syslin(dom,A,B,C [,D [,x0] ])
-            [sl]=syslin(dom,N,D)
-            [sl]=syslin(dom,H)
+        <synopsis>
+            sl = syslin(dom, A, B, C)
+            sl = syslin(dom, A, B, C, D)
+            sl = syslin(dom, A, B, C, D, x0)
+            sl = syslin(dom, N, D)
+            sl = syslin(dom, H)
         </synopsis>
     </refsynopsisdiv>
     <refsection>
         </para>
         <para>Représentation d'état :</para>
         <programlisting role=""><![CDATA[
-sl=syslin(dom,A,B,C [,D [,x0] ])
+sl = syslin(dom,A,B,C [,D [,x0] ])
  ]]></programlisting>
-        <para>représente le système :</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../../mml/syslin_equation_1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            représente le système
+        </para>
+        <para>
+            <table align="center">
+            <tr><td align="right">s.X</td><td>= A.X + B.u</td></tr>
+            <tr><td align="right">y</td><td>= C.X + D.u</td></tr>
+            <tr><td align="right">x(0)</td><td>= x0</td></tr>
+            </table>
+        </para>
         <para>
             La sortie de <literal>syslin</literal> est une liste de la forme
             suivante : <literal>
index f0075f6..f78f6bd 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="syslin" xml:lang="ja">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="syslin" xml:lang="ja">
     <refnamediv>
         <refname>syslin</refname>
         <refpurpose>線形システムを定義する</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>[sl]=syslin(dom,A,B,C [,D [,x0] ])
-            [sl]=syslin(dom,N,D)
-            [sl]=syslin(dom,H)
+        <synopsis>
+            sl = syslin(dom, A, B, C)
+            sl = syslin(dom, A, B, C, D)
+            sl = syslin(dom, A, B, C, D, x0)
+            sl = syslin(dom, N, D)
+            sl = syslin(dom, H)
         </synopsis>
     </refsynopsisdiv>
     <refsection>
         </para>
         <para>状態空間表現:</para>
         <programlisting role=""><![CDATA[
-sl=syslin(dom,A,B,C [,D [,x0] ])
+sl  =syslin(dom,A,B,C [,D [,x0] ])
  ]]></programlisting>
-        <para>は次のシステムを定義します :</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../../mml/syslin_equation_1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            は次のシステムを定義します
+        </para>
+        <para>
+            <table align="center">
+            <tr><td align="right">s.X</td><td>= A.X + B.u</td></tr>
+            <tr><td align="right">y</td><td>= C.X + D.u</td></tr>
+            <tr><td align="right">x(0)</td><td>= x0</td></tr>
+            </table>
+        </para>
         <para>
             <literal>syslin</literal> の出力は以下の形式のリストとなります:
             <literal>sl=tlist(['lss','A','B','C','D','X0','dt'],A,B,C,D,x0,dom)</literal>
diff --git a/scilab/modules/cacsd/help/mml/syslin_equation_1.mml b/scilab/modules/cacsd/help/mml/syslin_equation_1.mml
deleted file mode 100644 (file)
index 140e6ba..0000000
+++ /dev/null
@@ -1,69 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mtable>
-   <math:mtr>
-    <math:mrow>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mo math:stretchy="false">⋅</math:mo>
-      <math:mi>x</math:mi>
-     </math:mrow>
-     <math:mo math:stretchy="false">=</math:mo>
-     <math:mrow>
-      <math:mrow>
-       <math:mi>A</math:mi>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:mi>x</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">+</math:mo>
-      <math:mrow>
-       <math:mi>B</math:mi>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:mi>u</math:mi>
-      </math:mrow>
-     </math:mrow>
-    </math:mrow>
-   </math:mtr>
-   <math:mtr>
-    <math:mrow>
-     <math:mi>y</math:mi>
-     <math:mo math:stretchy="false">=</math:mo>
-     <math:mrow>
-      <math:mrow>
-       <math:mi>C</math:mi>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:mi>x</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">+</math:mo>
-      <math:mrow>
-       <math:mi>D</math:mi>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:mi>u</math:mi>
-      </math:mrow>
-     </math:mrow>
-    </math:mrow>
-   </math:mtr>
-   <math:mtr>
-    <math:mrow>
-     <math:mi>x</math:mi>
-     <math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mn>0</math:mn>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mo math:stretchy="false">=</math:mo>
-      <math:mi math:fontstyle="italic">x0</math:mi>
-     </math:mrow>
-    </math:mrow>
-   </math:mtr>
-  </math:mtable>
-  <math:annotation math:encoding="StarMath 5.0">stack {
-s cdot x = A cdot x + B cdot u #
-y = C cdot x + D cdot u #
-x(0) = x0
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
index 038d5f9..9fe5287 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="syslin" xml:lang="pt">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="syslin" xml:lang="pt">
     <refnamediv>
         <refname>syslin</refname>
         <refpurpose>definição de sistemas lineares</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>[sl]=syslin(dom,A,B,C [,D [,x0] ])
-            [sl]=syslin(dom,N,D)
-            [sl]=syslin(dom,H)
+        <synopsis>
+            sl = syslin(dom, A, B, C)
+            sl = syslin(dom, A, B, C, D)
+            sl = syslin(dom, A, B, C, D, x0)
+            sl = syslin(dom, N, D)
+            sl = syslin(dom, H)
         </synopsis>
     </refsynopsisdiv>
     <refsection>
         </para>
         <para>Representação em espaço de estados:</para>
         <programlisting><![CDATA[
-sl=syslin(dom,A,B,C [,D [,x0] ])
- ]]></programlisting>
-        <para>Representa o sistema :</para>
-        <programlisting><![CDATA[
-      s x  = A*x + B*u
-        y  = C*x + D*u
-      x(0) = x0
+sl = syslin(dom,A,B,C [,D [,x0] ])
  ]]></programlisting>
         <para>
+            Representa o sistema
+        </para>
+        <para>
+            <table align="center">
+            <tr><td align="right">s.X</td><td>= A.X + B.u</td></tr>
+            <tr><td align="right">y</td><td>= C.X + D.u</td></tr>
+            <tr><td align="right">x(0)</td><td>= x0</td></tr>
+            </table>
+        </para>
+        <para>
             A saída de <literal>syslin</literal> é uma lista da seguinte forma:
             <literal>sl=tlist(['lss','A','B','C','D','X0','dt'],A,B,C,D,x0,dom)</literal>
             . Note que <literal>D</literal> pode ser uma matriz de polinômios
index ea83365..b9192e8 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="syslin" xml:lang="ru">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="syslin" xml:lang="ru">
     <refnamediv>
         <refname>syslin</refname>
         <refpurpose>определение линейной системы</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Синтаксис</title>
-        <synopsis>[sl]=syslin(dom,A,B,C [,D [,x0] ])
-            [sl]=syslin(dom,N,D)
-            [sl]=syslin(dom,H)
+        <synopsis>
+            sl = syslin(dom, A, B, C)
+            sl = syslin(dom, A, B, C, D)
+            sl = syslin(dom, A, B, C, D, x0)
+            sl = syslin(dom, N, D)
+            sl = syslin(dom, H)
         </synopsis>
     </refsynopsisdiv>
     <refsection>
         </para>
         <para>Представление в виде пространства состояний:</para>
         <programlisting><![CDATA[
-sl=syslin(dom,A,B,C [,D [,x0] ])
+sl = syslin(dom,A,B,C [,D [,x0] ])
  ]]></programlisting>
-        <para>представляет систему :</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../../mml/syslin_equation_1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            представляет систему
+        </para>
+        <para>
+            <table align="center">
+            <tr><td align="right">s.X</td><td>= A.X + B.u</td></tr>
+            <tr><td align="right">y</td><td>= C.X + D.u</td></tr>
+            <tr><td align="right">x(0)</td><td>= x0</td></tr>
+            </table>
+        </para>
         <para>
             Выход <literal>syslin</literal> является списком следующей формы:
             <literal>sl=tlist(['lss','A','B','C','D','X0','dt'],A,B,C,D,x0,dom)</literal>
index c26157f..2d74ff9 100644 (file)
@@ -232,6 +232,7 @@ _LaTeX_FROMWSB.xml_5.png=12ceba0046931ee8cf25df2f71f06a57
 _LaTeX_FROMWSB.xml_6.png=edd38b21f4afb3b9bd3022d6594bc04d
 _LaTeX_GENSIN_f.xml_1.png=df7110d93d01f93f0b54d9aa298e9635
 _LaTeX_GENSQR_f.xml_1.png=746f663ac5f83b108763d9273b5f0e21
+_LaTeX_INTEGRAL_m.xml_1.png=a5506c60abcfda2944a96cba27140390
 _LaTeX_INTRP2BLK_f.xml_1.png=205995f88b807b2f5268f7ef4053f049
 _LaTeX_Inductor.xml_1.png=4e69417e6e0001a48e9abb40adf4be71
 _LaTeX_PerteDP.xml_1.png=0aaa66cecfcbc25a73e52eb804020799
@@ -251,7 +252,10 @@ _LaTeX_assert_computedigits.xml_2.png=27dba5ee1401d31d2106736651e99140
 _LaTeX_bessel.xml_1.png=75b18324986d95f0ce739c723eff803f
 _LaTeX_bessel.xml_2.png=91604506c2c5f30b0fab1ef9da180a89
 _LaTeX_bessel.xml_3.png=5e4298e19e224d62ecbd7b6db2a80a31
+_LaTeX_beta.xml_1.png=985c0d6227e43f606488047fc5cd7ed0
+_LaTeX_binomial.xml_1.png=9f650a3f2c46ae011aa0d0e88f6f7ea4
 _LaTeX_blockdiag.xml_1.png=26bcad469ac051064707c071f102456c
+_LaTeX_bsplin3val.xml_1.png=53180456233c6fead6c34e6f97a34b22
 _LaTeX_bvode.xml_1.png=7d919bf8f33698749d88e30e99c33d7c
 _LaTeX_bvode.xml_2.png=417a5301693b60807fa658e5ef9f9535
 _LaTeX_bvode.xml_3.png=7e3c241c2dec821bd6c6fbd314fe4762
@@ -287,6 +291,7 @@ _LaTeX_dct.xml_8.png=f28152d5910cdadab309239834b072b3
 _LaTeX_delip.xml_1.png=37cb84bfae9d9238643106ec09d43388
 _LaTeX_derivat.xml_1.png=884753c7c6265a65bb3803b66a0fec59
 _LaTeX_derivat.xml_2.png=1f26913a320e0f43588894e762729d16
+_LaTeX_dlgamma.xml_1.png=0ea9c92ae3d7b2b814d8a4f769773cd8
 _LaTeX_dst.xml_1.png=9cd22909f8eca591c252c206124e482f
 _LaTeX_dst.xml_2.png=d35f934540a4804eb1475655fa5bd72b
 _LaTeX_dst.xml_3.png=caa2ed7797bbc39b3a28cb86ce6ce771
@@ -303,7 +308,7 @@ _LaTeX_fft.xml_1.png=b16d8d250dade64a45e1e557c4673442
 _LaTeX_fft.xml_2.png=fa418662faf728120edcfff2a838bc8e
 _LaTeX_filter.xml_1.png=f5eab130f2e7fd10b80a402952421a05
 _LaTeX_floor.xml_ru_RU_1.png=1d5ba78bbbafd3226f371146bc348363
-_LaTeX_gamma.xml_1.png=960350f434595f88477814ea577e1359
+_LaTeX_gamma.xml_1.png=b5b5605d75f6d03d1d4dc6a8d817f78f
 _LaTeX_gamma.xml_2.png=3c98a6fd836c18394e05939979158ebf
 _LaTeX_gamma.xml_3.png=7aeff606c2524edc54dd085a53d673af
 _LaTeX_gamma.xml_4.png=92502c47ca464eaea97178b3a176595d
@@ -347,6 +352,8 @@ _LaTeX_lattn.xml_1.png=7ba64bdfad2c53fb336f12443f4926c6
 _LaTeX_lattn.xml_2.png=9b7ed107c9acb432bc04c8505b9d96ce
 _LaTeX_lattp.xml_1.png=7ba64bdfad2c53fb336f12443f4926c6
 _LaTeX_leastsq.xml_1.png=3d52f8613fe5a2330979b844cd60da0b
+_LaTeX_legendre.xml_1.png=901934bfc7bb9f760c29ed2d475cd9e4
+_LaTeX_legendre.xml_2.png=7fb916ea1d3380604237466209a0e2f4
 _LaTeX_levin.xml_1.png=7ba64bdfad2c53fb336f12443f4926c6
 _LaTeX_levin.xml_2.png=f524fdf11d769933d7138962185e2606
 _LaTeX_lft.xml_1.png=dc31caa4ca7b8e599933934a98dc2262
@@ -395,6 +402,7 @@ _LaTeX_lqr.xml_6.png=4f6dd247e1f511ea66298c4c2a76bb94
 _LaTeX_lqr.xml_7.png=c5cd7e3f5ea453e798ef0d5e0cbe734c
 _LaTeX_lqr.xml_8.png=1645328711c5c5406c0bff794c3afd40
 _LaTeX_lqr.xml_9.png=c76c57d5a1f43cdcb78069c14fac2e48
+_LaTeX_lsq_splin.xml_1.png=2397b9dd603fb440564750130da26127
 _LaTeX_nchoosek.xml_1.png=135b3c20a094e91dbe86ffaf4db0ffcc
 _LaTeX_nchoosek.xml_2.png=5070bc471485a78578069bb4405225b4
 _LaTeX_number_properties.xml_1.png=e44429416209c43ee6736fc6e4fb475e
@@ -427,6 +435,8 @@ _LaTeX_semidef.xml_1.png=69da8dee51aab98296232a5bc939053a
 _LaTeX_semidef.xml_2.png=9852782930e4e21c7115f35f70ab0966
 _LaTeX_semidef.xml_3.png=2098b9e5e447ece7cd838247adcb262b
 _LaTeX_semidef.xml_4.png=44e43279e4a6173003d2e27d996c92e5
+_LaTeX_splin.xml_1.png=af0a8f6474a7254de0fc7ea25a388f66
+_LaTeX_splin2d.xml_1.png=d8560d407972da202ab8e2e081ed5e7b
 _LaTeX_ss2zp.xml_1.png=b03e0f26548784f834e2978d640ded24
 _LaTeX_sum.xml_1.png=ef9aafe044823d17d08371770fa73e9f
 _LaTeX_sum.xml_2.png=b4f505fff21a34a842c50a707dd320ee
@@ -1063,7 +1073,7 @@ sinh_1.png=a6d9cd67d383e2b737257c4a18317abe
 smooth_1.png=ebef37585006626b34e13b95a3667e9d
 splin2d_1.png=6e186e7bcf5d848fd9d8f354282f6489
 splin2d_2.png=f36065c49f29e782c8b49e2958ad75c0
-splin3d_en_US_1.png=13b170241470ca4af84f26b2b0faf91c
+splin3d_en_US_1.png=924b5de4c3968e33949dd67fbeac437d
 splin3d_fr_FR_1.png=13b170241470ca4af84f26b2b0faf91c
 splin3d_ja_JP_1.png=13b170241470ca4af84f26b2b0faf91c
 splin3d_pt_BR_1.png=13b170241470ca4af84f26b2b0faf91c
diff --git a/scilab/modules/helptools/images/_LaTeX_INTEGRAL_m.xml_1.png b/scilab/modules/helptools/images/_LaTeX_INTEGRAL_m.xml_1.png
new file mode 100644 (file)
index 0000000..0dcc06f
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_INTEGRAL_m.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_beta.xml_1.png b/scilab/modules/helptools/images/_LaTeX_beta.xml_1.png
new file mode 100644 (file)
index 0000000..5f5f8dc
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_beta.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_binomial.xml_1.png b/scilab/modules/helptools/images/_LaTeX_binomial.xml_1.png
new file mode 100644 (file)
index 0000000..e597c03
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_binomial.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_bsplin3val.xml_1.png b/scilab/modules/helptools/images/_LaTeX_bsplin3val.xml_1.png
new file mode 100644 (file)
index 0000000..7897616
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_bsplin3val.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_dlgamma.xml_1.png b/scilab/modules/helptools/images/_LaTeX_dlgamma.xml_1.png
new file mode 100644 (file)
index 0000000..84af1e7
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_dlgamma.xml_1.png differ
index cfd6439..9a3ecaa 100644 (file)
Binary files a/scilab/modules/helptools/images/_LaTeX_gamma.xml_1.png and b/scilab/modules/helptools/images/_LaTeX_gamma.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_1.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_1.png
deleted file mode 100644 (file)
index 821fc07..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_1.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_10.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_10.png
deleted file mode 100644 (file)
index bcfa62c..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_10.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_11.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_11.png
deleted file mode 100644 (file)
index 821fc07..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_11.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_12.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_12.png
deleted file mode 100644 (file)
index 8249c9d..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_12.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_13.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_13.png
deleted file mode 100644 (file)
index adc12d2..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_13.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_14.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_14.png
deleted file mode 100644 (file)
index 45d8b77..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_14.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_15.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_15.png
deleted file mode 100644 (file)
index 764a626..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_15.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_16.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_16.png
deleted file mode 100644 (file)
index 9d403dc..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_16.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_17.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_17.png
deleted file mode 100644 (file)
index 2781cf7..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_17.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_18.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_18.png
deleted file mode 100644 (file)
index c1ed2ee..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_18.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_19.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_19.png
deleted file mode 100644 (file)
index 7651aef..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_19.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_2.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_2.png
deleted file mode 100644 (file)
index 821fc07..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_2.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_20.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_20.png
deleted file mode 100644 (file)
index 3922dfb..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_20.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_3.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_3.png
deleted file mode 100644 (file)
index 8b7e2fa..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_3.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_4.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_4.png
deleted file mode 100644 (file)
index add2d2f..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_4.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_5.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_5.png
deleted file mode 100644 (file)
index 5776d58..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_5.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_6.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_6.png
deleted file mode 100644 (file)
index 9df245f..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_6.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_7.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_7.png
deleted file mode 100644 (file)
index 27d470a..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_7.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_8.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_8.png
deleted file mode 100644 (file)
index d1cbc11..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_8.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_interp.xml_9.png b/scilab/modules/helptools/images/_LaTeX_interp.xml_9.png
deleted file mode 100644 (file)
index 0d53561..0000000
Binary files a/scilab/modules/helptools/images/_LaTeX_interp.xml_9.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/_LaTeX_legendre.xml_1.png b/scilab/modules/helptools/images/_LaTeX_legendre.xml_1.png
new file mode 100644 (file)
index 0000000..7dc5332
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_legendre.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_legendre.xml_2.png b/scilab/modules/helptools/images/_LaTeX_legendre.xml_2.png
new file mode 100644 (file)
index 0000000..348c693
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_legendre.xml_2.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_lsq_splin.xml_1.png b/scilab/modules/helptools/images/_LaTeX_lsq_splin.xml_1.png
new file mode 100644 (file)
index 0000000..26c9c2e
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_lsq_splin.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_splin.xml_1.png b/scilab/modules/helptools/images/_LaTeX_splin.xml_1.png
new file mode 100644 (file)
index 0000000..66de6f1
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_splin.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_splin2d.xml_1.png b/scilab/modules/helptools/images/_LaTeX_splin2d.xml_1.png
new file mode 100644 (file)
index 0000000..085a505
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_splin2d.xml_1.png differ
diff --git a/scilab/modules/helptools/images/beta_equation1.mml.png b/scilab/modules/helptools/images/beta_equation1.mml.png
deleted file mode 100644 (file)
index 324ad8a..0000000
Binary files a/scilab/modules/helptools/images/beta_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/binomial_equation_1_en_US.mml.png b/scilab/modules/helptools/images/binomial_equation_1_en_US.mml.png
deleted file mode 100644 (file)
index 5df9d52..0000000
Binary files a/scilab/modules/helptools/images/binomial_equation_1_en_US.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/binomial_equation_1_ru_RU.mml.png b/scilab/modules/helptools/images/binomial_equation_1_ru_RU.mml.png
deleted file mode 100644 (file)
index 269d670..0000000
Binary files a/scilab/modules/helptools/images/binomial_equation_1_ru_RU.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/bsplin3val_equation1.mml.png b/scilab/modules/helptools/images/bsplin3val_equation1.mml.png
deleted file mode 100644 (file)
index 0e97c8a..0000000
Binary files a/scilab/modules/helptools/images/bsplin3val_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/dlgamma_equation1.mml.png b/scilab/modules/helptools/images/dlgamma_equation1.mml.png
deleted file mode 100644 (file)
index 63e760d..0000000
Binary files a/scilab/modules/helptools/images/dlgamma_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/integral_m.mml.png b/scilab/modules/helptools/images/integral_m.mml.png
deleted file mode 100644 (file)
index 459c456..0000000
Binary files a/scilab/modules/helptools/images/integral_m.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/legendre_equation1.mml.png b/scilab/modules/helptools/images/legendre_equation1.mml.png
deleted file mode 100644 (file)
index b910602..0000000
Binary files a/scilab/modules/helptools/images/legendre_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/legendre_equation2.mml.png b/scilab/modules/helptools/images/legendre_equation2.mml.png
deleted file mode 100644 (file)
index ec805a2..0000000
Binary files a/scilab/modules/helptools/images/legendre_equation2.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/linear_interpn_equation1.mml.png b/scilab/modules/helptools/images/linear_interpn_equation1.mml.png
deleted file mode 100644 (file)
index 271b699..0000000
Binary files a/scilab/modules/helptools/images/linear_interpn_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/linear_interpn_equation2.mml.png b/scilab/modules/helptools/images/linear_interpn_equation2.mml.png
deleted file mode 100644 (file)
index 5a0f7e6..0000000
Binary files a/scilab/modules/helptools/images/linear_interpn_equation2.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/linear_interpn_equation3.mml.png b/scilab/modules/helptools/images/linear_interpn_equation3.mml.png
deleted file mode 100644 (file)
index 9b383d8..0000000
Binary files a/scilab/modules/helptools/images/linear_interpn_equation3.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/lsq_splin_equation1.mml.png b/scilab/modules/helptools/images/lsq_splin_equation1.mml.png
deleted file mode 100644 (file)
index 6089046..0000000
Binary files a/scilab/modules/helptools/images/lsq_splin_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/splin2d_equation_1.mml.png b/scilab/modules/helptools/images/splin2d_equation_1.mml.png
deleted file mode 100644 (file)
index f84e14a..0000000
Binary files a/scilab/modules/helptools/images/splin2d_equation_1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/splin3d_equation1.mml.png b/scilab/modules/helptools/images/splin3d_equation1.mml.png
deleted file mode 100644 (file)
index 285d2f4..0000000
Binary files a/scilab/modules/helptools/images/splin3d_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/splin3d_pt_BR_1.png b/scilab/modules/helptools/images/splin3d_pt_BR_1.png
new file mode 100644 (file)
index 0000000..e0989fc
Binary files /dev/null and b/scilab/modules/helptools/images/splin3d_pt_BR_1.png differ
diff --git a/scilab/modules/helptools/images/splin_equation1.mml.png b/scilab/modules/helptools/images/splin_equation1.mml.png
deleted file mode 100644 (file)
index c69235e..0000000
Binary files a/scilab/modules/helptools/images/splin_equation1.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/splin_equation2.mml.png b/scilab/modules/helptools/images/splin_equation2.mml.png
deleted file mode 100644 (file)
index 595f295..0000000
Binary files a/scilab/modules/helptools/images/splin_equation2.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/splin_equation3.mml.png b/scilab/modules/helptools/images/splin_equation3.mml.png
deleted file mode 100644 (file)
index e5c0f8a..0000000
Binary files a/scilab/modules/helptools/images/splin_equation3.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/splin_equation4.mml.png b/scilab/modules/helptools/images/splin_equation4.mml.png
deleted file mode 100644 (file)
index ca96e6b..0000000
Binary files a/scilab/modules/helptools/images/splin_equation4.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/splin_equation5.mml.png b/scilab/modules/helptools/images/splin_equation5.mml.png
deleted file mode 100644 (file)
index cb75d03..0000000
Binary files a/scilab/modules/helptools/images/splin_equation5.mml.png and /dev/null differ
diff --git a/scilab/modules/helptools/images/syslin_equation_1.mml.png b/scilab/modules/helptools/images/syslin_equation_1.mml.png
deleted file mode 100644 (file)
index 09acda8..0000000
Binary files a/scilab/modules/helptools/images/syslin_equation_1.mml.png and /dev/null differ
index d579ac5..02e62fb 100644 (file)
@@ -1,5 +1,8 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bsplin3val" xml:lang="en">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="bsplin3val" xml:lang="en">
     <refnamediv>
         <refname>bsplin3val</refname>
         <refpurpose>3d spline arbitrary derivative evaluation
@@ -8,7 +11,7 @@
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>[dfp]=bsplin3val(xp,yp,zp,tl,der)</synopsis>
+        <synopsis>dfp = bsplin3val(xp, yp, zp, tl, der)</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
             <literal>s</literal>. The derivative to compute is specified by the
             argument <literal>der=[ox,oy,oz]</literal> :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/bsplin3val_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18"
+                alt="dfp(i)=∂^{oxoyoz}/(∂^ox.∂^oy.∂^oz) s(xp(i),yp(i),zp(i))">
+                dfp(i)=\frac{\partial^{ox\,oy\,oz}}{\partial ^{ox}\,\partial ^{oy}\,\partial ^{oz}}
+                        s\left(xp(i),yp(i),zp(i)\right)
+            </latex>
+        </para>
         <para>
             So <literal>der=[0 0 0]</literal> corresponds to
             <emphasis>s</emphasis>, <literal>der=[1 0 0]</literal> to
@@ -123,13 +126,4 @@ fxxyz_i = bsplin3val(xp,yp,zp,tl,[2 1 1])
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 49ad16f..dcb89e5 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="interp" xml:lang="en">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="interp" xml:lang="en">
     <refnamediv>
         <refname>interp</refname>
         <refpurpose>cubic spline evaluation function</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>[ yp [,yp1 [,yp2 [,yp3]]]] = interp(xp, x, y, d [, out_mode])</synopsis>
+        <synopsis>
+            [yp, yp1, yp2, yp3] = interp(xp, x, y, d)
+            [yp, yp1, yp2, yp3] = interp(xp, x, y, d, out_mode)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
                 <term>x,y</term>
                 <listitem>
                     <para>
-                        real vectors of same size <literal>n</literal>: Coordinates of data points on which the interpolation and the related cubic spline (called <literal>s(X)</literal> in the following) or sub-spline function is based and built.
+                        real vectors of same size <literal>n</literal>: Coordinates of data points on
+                        which the interpolation and the related cubic spline (called <literal>s(X)</literal>
+                        in the following) or sub-spline function is based and built.
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>d</term>
                 <listitem>
-                    <para>real vector of size(x): The derivative s'(x). Most often, s'(x) will be priorly estimated through the function splin(x, y,..)
+                    <para>
+                        real vector of size(x): The derivative s'(x). Most often, s'(x) will be
+                        priorly estimated through the function splin(x, y,..)
                     </para>
                 </listitem>
             </varlistentry>
@@ -30,7 +40,8 @@
                 <term>out_mode</term>
                 <listitem>
                     <para>
-                        (optional) string defining <literal>s(X)</literal> for <literal>X</literal>  outside <latex>[x_1,\ x_n]</latex>.
+                        (optional) string defining <literal>s(X)</literal> for <literal>X</literal>
+                        outside [x<subscript>1</subscript>, x<subscript>n</subscript>].
                         Possible values: "by_zero" | "by_nan" | "C0" | "natural" | "linear" | "periodic"
                     </para>
                 </listitem>
@@ -39,7 +50,8 @@
                 <term>xp</term>
                 <listitem>
                     <para>
-                        real vector or matrix: abscissae at which <literal>Y</literal> is unknown and must be estimated with <literal>s(xp)</literal>
+                        real vector or matrix: abscissae at which <literal>Y</literal> is unknown
+                        and must be estimated with <literal>s(xp)</literal>
                     </para>
                 </listitem>
             </varlistentry>
@@ -47,7 +59,8 @@
                 <term>yp</term>
                 <listitem>
                     <para>
-                        vector or matrix of size(xp): <literal>yp(i) = s(xp(i))</literal> or <literal>yp(i,j) = s(xp(i,j))</literal>
+                        vector or matrix of size(xp): <literal>yp(i) = s(xp(i))</literal> or
+                        <literal>yp(i,j) = s(xp(i,j))</literal>
                     </para>
                 </listitem>
             </varlistentry>
@@ -55,7 +68,8 @@
                 <term>yp1, yp2, yp3</term>
                 <listitem>
                     <para>
-                        vectors (or matrices) of size(x): elementwise evaluation of the derivatives <literal>s'(xp)</literal>, <literal>s''(xp)</literal> and <literal>s'''(xp)</literal>.
+                        vectors (or matrices) of size(x): elementwise evaluation of the derivatives
+                        <literal>s'(xp)</literal>, <literal>s''(xp)</literal> and <literal>s'''(xp)</literal>.
                     </para>
                 </listitem>
             </varlistentry>
     <refsection>
         <title>Description</title>
         <para>
-            The cubic spline function <literal>s(X)</literal> interpolating the <literal>(x,y)</literal> set of given points is a continuous and derivable piece-wise function defined over <latex>[x_1,\ x_n]</latex>. It consists of a set of cubic polynomials, each one <latex>p_k(X)</latex> being defined on <latex>[x_k,\ x_{k+1}]</latex> and connected in values and slopes to both its neighbours. Thus, we can state that for each <latex>X\ \in\ [x_k,\ x_{k+1}],\ s(X) = p_k(X)</latex>, such that
-            <latex>s(x_i) = y_i,\quad \mbox{and}\quad s'(x_i) = d_i</latex>.  Then, interp() evaluates <literal>s(X)</literal> (and <literal>s'(X), s''(X), s'''(X)</literal> if needed) at <literal>xp(i)</literal>, such that
+            The cubic spline function <literal>s(X)</literal> interpolating the <literal>(x,y)</literal>
+            set of given points is a continuous and derivable piece-wise function defined over
+            [x<subscript>1</subscript>, x<subscript>n</subscript>]. It consists of a set of cubic polynomials, each one
+            p<subscript>k</subscript>(X) being defined on [x<subscript>k</subscript>, x<subscript>k+1</subscript>]
+            and connected in values and slopes to both its neighbours. Thus, we can state that for each
+            <emphasis>
+                X &#8712; [x<subscript>k</subscript>, x<subscript>k+1</subscript>],
+                s(X) = p<subscript>k</subscript>(X)
+            </emphasis>, such that
+            <emphasis>
+                s(x<subscript>i</subscript>) = y<subscript>i</subscript>,  and  
+                s'(x<subscript>i</subscript>) = d<subscript>i</subscript>
+            </emphasis>.
+            Then, interp() evaluates <literal>s(X)</literal> (and <literal>s'(X), s''(X), s'''(X)</literal>
+            if needed) at <literal>xp(i)</literal>, such that
+        </para>
+        <para>
+            <table align="center">
+            <tr align="center">
+                <td><emphasis>
+                        yp<subscript>i</subscript> = s(xp<subscript>i</subscript>)
+                           or   
+                        yp<subscript>ij</subscript> = s(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp1<subscript>i</subscript> = s'(xp<subscript>i</subscript>)
+                           or   
+                        yp1<subscript>ij</subscript> = s'(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp2<subscript>i</subscript> = s''(xp<subscript>i</subscript>)
+                           or   
+                        yp2<subscript>ij</subscript> = s''(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp3<subscript>i</subscript> = s'''(xp<subscript>i</subscript>)
+                           or   
+                        yp3<subscript>ij</subscript> = s'''(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            </table>
         </para>
-        <latex style="display" align="center"><![CDATA[ yp_i = s(xp_i) \quad or \quad yp_{i,j} = s(xp_{i,j})  ]]></latex>
-        <latex style="display" align="center"><![CDATA[ yp1_i = s'(xp_i) \quad or \quad yp1_{i,j} = s'(xp_{i,j})  ]]></latex>
-        <latex style="display" align="center"><![CDATA[ yp2_i = s''(xp_i) \quad or \quad yp2_{i,j} = s''(xp_{i,j})  ]]></latex>
-        <latex style="display" align="center"><![CDATA[ yp3_i = s'''(xp_i) \quad or \quad yp3_{i,j} = s'''(xp_{i,j})  ]]></latex>
         <para>
             The <literal>out_mode</literal> parameter set the evaluation rule
-            for extrapolation, i.e. for <literal>xp(i)</literal> outside <latex>[x_1,\ x_n]</latex> :
+            for extrapolation, i.e. for <literal>xp(i)</literal> outside [x<subscript>1</subscript>, x<subscript>n</subscript>] :
         </para>
         <variablelist>
             <varlistentry>
             <varlistentry>
                 <term>"C0"</term>
                 <listitem>
-                    <para>the extrapolation is defined as follows :</para>
-                    <latex style="display" align="center"><![CDATA[ xp_i < x_1   \Rightarrow  yp_i = y_1 ]]></latex>
-                    <latex style="display" align="center"><![CDATA[ xp_i > x_n   \Rightarrow  yp_i = y_n ]]></latex>
+                    <para>the extrapolation is defined as follows :
+                        <table align="center">
+                        <tr align="center"><td><emphasis>
+                            xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                            yp<subscript>i</subscript> = y<subscript>1</subscript>
+                            </emphasis></td></tr>
+                        <tr align="center"><td><emphasis>
+                            xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                            yp<subscript>i</subscript> = y<subscript>n</subscript>
+                            </emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"natural"</term>
                 <listitem>
                     <para>
-                        the extrapolation is defined as follows (<latex>p_i(x)</latex> being the polynomial defining
-                        <literal>s(X)</literal> on <latex>[x_i,\ x_{i+1}]</latex>)
+                        the extrapolation is defined as follows (p<subscript>i</subscript>(x) being the polynomial defining
+                        <literal>s(X)</literal> on [x<subscript>i</subscript>, x<subscript>i+1</subscript>]):
                     </para>
-                    <latex style="display" align="center"><![CDATA[ xp_i < x_1   \Rightarrow  yp_i = p_1(xp_i) ]]></latex>
-                    <latex style="display" align="center"><![CDATA[ xp_i > x_n   \Rightarrow  yp_i = p_{n-1}(xp_i) ]]></latex>
+                    <table align="center">
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = p<subscript>1</subscript>(xp<subscript>i</subscript>)
+                        </emphasis></td></tr>
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = p<subscript>n-1</subscript>(xp<subscript>i</subscript>)
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"linear"</term>
                 <listitem>
                     <para>the extrapolation is defined as follows :</para>
-                    <latex style="display" align="center"><![CDATA[ xp_i < x_1   \Rightarrow  yp_i = y_1 + d_1.(xp_i - x_1) ]]></latex>
-                    <latex style="display" align="center"><![CDATA[ xp_i > x_n   \Rightarrow  yp_i = y_n + d_n.(xp_i - x_n) ]]></latex>
+                    <table align="center">
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = y<subscript>1</subscript> +
+                            d<subscript>1</subscript>.(xp<subscript>i</subscript> - x<subscript>1</subscript>)
+                        </emphasis></td></tr>
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = y<subscript>n</subscript> +
+                            d<subscript>n</subscript>.(xp<subscript>i</subscript> - x<subscript>n</subscript>)
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
             <varlistentry>
                     <para>
                         <literal>s(X)</literal> is extended by periodicity:
                     </para>
-                    <latex style="display" align="center"><![CDATA[ yp_i = s( x_1 + ( (xp_i-x_1)\ \mbox{modulo}\ [x_n-x_1] ) ) ]]></latex>
+                    <table align="center">
+                    <tr><td><emphasis>
+                        yp<subscript>i</subscript> = s( x<subscript>1</subscript> + 
+                         (xp<subscript>i</subscript> - x<subscript>1</subscript>) modulo 
+                         (x<subscript>n</subscript>-x<subscript>1</subscript>) )
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
         </variablelist>
@@ -220,13 +312,4 @@ xtitle(" different way to evaluate a spline outside its domain")
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 0668b72..501e1d2 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="en">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="en">
     <refnamediv>
         <refname>linear_interpn</refname>
         <refpurpose>n dimensional linear interpolation</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>vp = linear_interpn(xp1,xp2,..,xpn, x1, ..., xn, v [,out_mode])</synopsis>
+        <synopsis>
+            vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v)
+            vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v, out_mode)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
@@ -46,8 +52,7 @@
                 <term>vp</term>
                 <listitem>
                     <para>
-                        vector or matrix of same size than <literal>xp1, ...,
-                            xpn
+                        vector or matrix of same size than <literal>xp1, ..., xpn
                         </literal>
                     </para>
                 </listitem>
             and the values <literal>v</literal> of a function (says
             <emphasis>f</emphasis>) at the grid points :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/linear_interpn_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <table align="center">
+            <tr><td>
+                    v(i<subscript>1</subscript>,
+                      i<subscript>2</subscript>,…,
+                      i<subscript>n</subscript>) =
+                      <emphasis>f</emphasis>(x1(i<subscript>1</subscript>),
+                                             x2(i<subscript>2</subscript>),…,
+                                             xn(i<subscript>n</subscript>))
+                </td>
+            </tr>
+            </table>
+        </para>
         <para>this function computes the linear interpolant of
             <emphasis>f</emphasis> from the grid (called <emphasis>s</emphasis> in the
             following) at the points which coordinates are defined by the vectors (or
             matrices) <literal>xp1, xp2, ..., xpn</literal>:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/linear_interpn_equation2.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <table align="center">
+            <tr align="center">
+                <td>vp(i) = <emphasis>s</emphasis>(xp1(i), xp2(i), …, xpn(i))</td></tr>
+            <tr align="center"><td>or</td></tr>
+            <tr align="center">
+                <td>vp(i,j) = <emphasis>s</emphasis>(xp1(i,j), xp2(i,j), …, xpn(i,j))</td>
+            </tr>
+            </table>
+            in case the xpk are matrices.
+        </para>
         <para>
             The <literal>out_mode</literal> parameter set the evaluation rule
             for extrapolation: if we note
             <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> then
             <literal>out_mode</literal> defines the evaluation rule when:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/linear_interpn_equation3.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <table align="center">
+            <tr><td>P(i) ∉ [x1(1), x1($)] × [x2(1), x2($)] × … × [xn(1), xn($)]</td></tr>
+            </table>
+        </para>
         <para>The different choices are:</para>
         <variablelist>
             <varlistentry>
@@ -285,13 +298,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 5da6902..40298ca 100644 (file)
@@ -1,12 +1,31 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lsq_splin" xml:lang="en">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="lsq_splin" xml:lang="en">
     <refnamediv>
         <refname>lsq_splin</refname>
         <refpurpose>weighted least squares cubic spline fitting</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>[y, d] = lsq_splin(xd, yd [, wd], x)</synopsis>
+        <synopsis>
+            [y, d] = lsq_splin(xd, yd, x)
+            [y, d] = lsq_splin(xd, yd, wd, x)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
             breakpoints <emphasis>x1 &lt; x2 &lt; ... &lt; xn</emphasis> then the
             resulting spline <emphasis>s</emphasis> is such that:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/lsq_splin_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
         <para>
-            for all <emphasis>fin S</emphasis>, i.e. realizes the minimum of
+            <latex style="display" fontsize="18" alt="∑_k=1→m wd(k).[s(xd(k))-yd(k)]² ⬅ ∑_k=1→m wd(k).[f(xd(k))-yd(k)]²">
+                \sum_{k=1}^m wd(k)\left(s(xd(k))-yd(k)\right)^2 \,\leftarrow\,
+                \sum_{k=1}^m wd(k)\left(f(xd(k))-yd(k)\right)^2
+            </latex>
+        </para>
+        <para>
+            for all <emphasis>f in S</emphasis>, i.e. realizes the minimum of
             the sum of the squared errors over all functions of
             <emphasis>S</emphasis>.
         </para>
@@ -161,6 +179,12 @@ show_window()
         <title>See also</title>
         <simplelist type="inline">
             <member>
+                <link linkend="backslash">backslash</link>
+            </member>
+            <member>
+                <link linkend="datafit">datafit</link>
+            </member>
+            <member>
                 <link linkend="interp">interp</link>
             </member>
             <member>
index 050925c..fe2adad 100644 (file)
@@ -1,12 +1,32 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin" xml:lang="en">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) F. N. Fritsch (pchim.f Slatec routine is used for monotonous interpolation)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin" xml:lang="en">
     <refnamediv>
         <refname>splin</refname>
         <refpurpose>cubic spline interpolation</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>d = splin(x, y [,spline_type [, der]])</synopsis>
+        <synopsis>
+            d = splin(x, y)
+            d = splin(x, y, spline_type)
+            d = splin(x, y, spline_type, der)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
                         using the following conditions (considering n points
                         x1,...,xn):
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation1.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <latex fontsize="18" alt="s′′′(x₂⁻)=s′′′(x₂⁺), s′′′(x{n-1}⁻)=s′′′(x{n-1}⁺)">
+                            s'''(x_2^-) = s'''(x_2^+) \\
+                            s'''(x_{n-1}^-) = s'''(x_{n-1}^+)
+                        </latex>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                         points derivatives which must be provided as the last argument
                         <literal>der</literal>:
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation2.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <table align="center">
+                        <tr align="center"><td><emphasis>s'(x<subscript>1</subscript>) = der(1)</emphasis></td></tr>
+                        <tr align="center"><td><emphasis>s'(x<subscript>n</subscript>) = der(2)</emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"natural"</term>
                 <listitem>
                     <para>the cubic spline is computed by using the conditions:</para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation3.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <table align="center">
+                        <tr align="center"><td><emphasis>s''(x<subscript>1</subscript>) = 0</emphasis></td></tr>
+                        <tr align="center"><td><emphasis>s''(x<subscript>n</subscript>) = 0</emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                         a periodic cubic spline is computed (<literal>y</literal> must
                         verify <emphasis>y1=yn</emphasis>) by using the conditions:
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation4.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <table align="center">
+                        <tr align="center">
+                            <td>
+                            <emphasis>s'(x<subscript>1</subscript>) = s'(x<subscript>n</subscript>)</emphasis>
+                            </td>
+                        </tr>
+                        <tr align="center">
+                            <td>
+                            <emphasis>s''(x<subscript>1</subscript>) = s''(x<subscript>n</subscript>)</emphasis>
+                            </td>
+                        </tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                         the <emphasis>di</emphasis> such that <emphasis>s</emphasis> is
                         monotone on each interval:
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation5.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                If y(i) ≤ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
+                            </listitem>
+                            <listitem>
+                                If y(i) ≥ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
+                            </listitem>
+                        </itemizedlist>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
     <refsection>
         <title>Remarks</title>
         <para>
-            From an accuracy point of view use essentially the <emphasis role="bold">clamped</emphasis> type if you know the end point derivatives,
-            else use <emphasis role="bold">not_a_knot</emphasis>. But if the
-            underlying approximated function is periodic use the <emphasis role="bold">periodic</emphasis> type. Under the good assumptions these
+            From an accuracy point of view use essentially the <emphasis role="bold">clamped</emphasis>
+            type if you know the end point derivatives, else use <emphasis role="bold">not_a_knot</emphasis>.
+            But if the underlying approximated function is periodic use the
+            <emphasis role="bold">periodic</emphasis> type. Under the good assumptions these
             kind of splines got an <literal>O(h^4)</literal> asymptotic behavior of
             the error. Don't use the <emphasis role="bold">natural</emphasis> type
             unless the underlying function have zero second end points
             derivatives.
         </para>
         <para>
-            The <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis> (or <emphasis role="bold">fast_periodic</emphasis>) type may be useful in some cases,
+            The <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis>
+            (or <emphasis role="bold">fast_periodic</emphasis>) type may be useful in some cases,
             for instance to limit oscillations (these kind of sub-splines have an
             <literal>O(h^3)</literal> asymptotic behavior of the error).
         </para>
             If <emphasis>n=2</emphasis> (and <literal>spline_type</literal> is
             not <emphasis role="bold">clamped</emphasis>) linear interpolation is
             used. If <emphasis>n=3</emphasis> and <literal>spline_type</literal> is
-            <emphasis role="bold">not_a_knot</emphasis>, then a <emphasis role="bold">fast</emphasis> sub-spline type is in fact computed.
+            <emphasis role="bold">not_a_knot</emphasis>, then a <emphasis role="bold">fast</emphasis>
+            sub-spline type is in fact computed.
         </para>
     </refsection>
     <refsection>
@@ -274,13 +304,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 91f8c18..8c88f38 100644 (file)
@@ -1,50 +1,52 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin2d" xml:lang="en">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+         xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+         xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+         xmlns:scilab="http://www.scilab.org" xml:id="splin2d" xml:lang="en">
     <refnamediv>
         <refname>splin2d</refname>
         <refpurpose>bicubic spline gridded 2d interpolation</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>C = splin2d(x, y, z, [,spline_type])</synopsis>
+        <synopsis>
+            C = splin2d(x, y, z)
+            C = splin2d(x, y, z, spline_type)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
         <variablelist>
             <varlistentry>
-                <term>x</term>
+                <term>x, y</term>
                 <listitem>
-                    <para> a 1-by-nx matrix of doubles, the x coordinate of the interpolation points. We must have x(i)&lt;x(i+1), for i=1,2,...,nx-1.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>y</term>
-                <listitem>
-                    <para>a 1-by-ny matrix of doubles, the y coordinate of the interpolation points.
-                        We must have y(i)&lt;y(i+1), for i=1,2,...,ny-1.
+                    <para>
+                        rows of nx and ny real numbers, in strictly increasing order: the
+                        <varname>x</varname> and <varname>y</varname> coordinates building
+                        the grid of the interpolation points (nodes).
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>z</term>
                 <listitem>
-                    <para>a nx-by-ny matrix of doubles, the function values.
+                    <para>a nx-by-ny matrix of real numbers: the function values.
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>spline_type</term>
                 <listitem>
-                    <para>a 1-by-1 matrix of strings, the typof of spline to compute.
-                        Available values are spline_type="not_a_knot" and spline_type="periodic".
+                    <para>"not_a_knot" or "periodic" string: the type of spline to compute.
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>C</term>
                 <listitem>
-                    <para>the coefficients of the bicubic patches. This output argument of splin2d is the input argument of the interp2d function.
+                    <para>
+                        the coefficients of the bicubic patches. This output argument of splin2d
+                        is the input argument of the interp2d function.
                     </para>
                 </listitem>
             </varlistentry>
         <title>Description</title>
         <para>This function computes a bicubic spline or sub-spline
             <emphasis>s</emphasis> which interpolates the
-            <emphasis>(xi,yj,zij)</emphasis> points, ie, we have
-            <emphasis>s(xi,yj)=zij</emphasis> for all <emphasis>i=1,..,nx</emphasis>
+            <emphasis>(x<subscript>i </subscript>,y<subscript>j </subscript>,z<subscript>ij </subscript>)</emphasis>
+            points, ie, we have
+            <emphasis>s(x<subscript>i </subscript>,y<subscript>j </subscript>)=z<subscript>ij </subscript></emphasis>
+            for all <emphasis>i=1,..,nx</emphasis>
             and <emphasis>j=1,..,ny</emphasis>. The resulting spline
             <emphasis>s</emphasis> is defined by the triplet
-            <literal>(x,y,C)</literal> where <literal>C</literal> is the vector (of
+            <literal>(x,y,C)</literal> where <varname>C</varname> is the vector (of
             length 16(nx-1)(ny-1)) with the coefficients of each of the (nx-1)(ny-1)
-            bicubic patches : on <emphasis>[x(i) x(i+1)]x[y(j) y(j+1)]</emphasis>,
-            <emphasis>s</emphasis> is defined by :
+            bicubic patches : on <emphasis>[x(i),x(i+1)] × [y(j),y(j+1)]</emphasis>,
+            <emphasis>s</emphasis> is defined by
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/splin2d_equation_1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <latex style="display" fontsize="18"
+              alt="s(x,y) = ∑_m=1→4 ∑_n=1→4 c_ij(m,n).(x-x_i)^{m-1}.(y-y_j)^{n-1}">
+                s(x,y)=\sum_{k=1}^4\sum_{l=1}^4 c_{ij}(k,l)\cdot(x-x_i)^{k-1}\cdot(y-y_j)^{l-1}
+        </latex>
         <para>
-            The evaluation of <emphasis>s</emphasis> at some points must be done
-            by the <link linkend="interp2d">interp2d</link> function. Several kind of
-            splines may be computed by selecting the appropriate
-            <literal>spline_type</literal> parameter. The method used to compute the
-            bicubic spline (or sub-spline) is the old fashioned one 's, i.e. to
-            compute on each grid point <emphasis>(xi,yj)</emphasis> an approximation
-            of the first derivatives <emphasis>ds/dx(xi,yj)</emphasis> and
-            <emphasis>ds/dy(xi,yj)</emphasis> and of the cross derivative
-            <emphasis>d2s/dxdy(xi,yj)</emphasis>. Those derivatives are computed by
-            the mean of 1d spline schemes leading to a C2 function
-            (<emphasis>s</emphasis> is twice continuously differentiable) or by the
-            mean of a local approximation scheme leading to a C1 function only. This
-            scheme is selected with the <literal>spline_type</literal> parameter (see
-            <link linkend="splin">splin</link> for details) :
+            The evaluation of <emphasis>s</emphasis> at some points must be done by the
+            <link linkend="interp2d">interp2d</link> function. Several kind of splines may be
+            computed by selecting the appropriate <varname>spline_type</varname> parameter.
+            The method used to compute the bicubic spline (or sub-spline) is the old fashioned
+            one's, i.e. to compute on each grid point
+            <emphasis>(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis>
+            an approximation of the first derivatives
+            <emphasis>ds/dx(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis> and
+            <emphasis>ds/dy(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis> and
+            of the cross derivative
+            <emphasis>d2s/dxdy(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis>.
+            Those derivatives are computed by the mean of 1d spline schemes leading to a C2 function
+            (<emphasis>s</emphasis> is twice continuously differentiable) or by the  mean of a local
+            approximation scheme leading to a C1 function only. This scheme is selected with the
+            <varname>spline_type</varname> parameter (see <link linkend="splin">splin</link> for
+            details) :
         </para>
         <variablelist>
             <varlistentry>
     <refsection>
         <title>Remarks</title>
         <para>
-            From an accuracy point of view use essentially the <emphasis role="bold">not_a_knot</emphasis> type or <emphasis role="bold">periodic</emphasis> type if the underlying interpolated
-            function is periodic.
+            From an accuracy point of view use essentially the
+            <emphasis role="bold">not_a_knot</emphasis> type or
+            <emphasis role="bold">periodic</emphasis> type if the underlying interpolated function
+            is periodic.
         </para>
         <para>
-            The <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis> (or
-            <emphasis role="bold">fast_periodic</emphasis>) type may be useful in some
-            cases, for instance to limit oscillations (<emphasis role="bold">monotone</emphasis> being the most powerful for that).
+            The <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>,
+            <emphasis role="bold">fast</emphasis> (or <emphasis role="bold">fast_periodic</emphasis>)
+            type may be useful in some cases, for instance to limit oscillations
+            (<emphasis role="bold">monotone</emphasis> being the most powerful for that).
         </para>
         <para>To get the coefficients of the bi-cubic patches in a more friendly
             way you can use <literal>c = matrix(C, [4,4,nx-1,ny-1])</literal> then
             the coefficient <emphasis>(k,l)</emphasis> of the patch
             <emphasis>(i,j)</emphasis> (see equation here before) is stored at
-            <literal>c(k,l,i,j)</literal>. Nevertheless the <link linkend="interp2d">interp2d</link> function wait for the big vector
-            <literal>C</literal> and not for the hypermatrix <literal>c</literal>
-            (note that one can easily retrieve <literal>C</literal> from
+            <literal>c(k,l,i,j)</literal>. Nevertheless the <link linkend="interp2d">interp2d</link>
+            function wait for the big vector <varname>C</varname> and not for the hypermatrix
+            <literal>c</literal> (note that one can easily retrieve <varname>C</varname> from
             <literal>c</literal> with <literal>C=c(:)</literal>).
         </para>
     </refsection>
@@ -194,7 +200,6 @@ xtitle("natural")
 subplot(2,2,4)
 plot3d1(xp, yp, ZP4, flag=[2 2 4])
 xtitle("monotone")
-show_window()
  ]]></programlisting>
         <scilab:image>
             // example 2 : different interpolation functions on random data
@@ -265,13 +270,4 @@ xtitle("subspline (monotone)")
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 7538ff9..0265541 100644 (file)
@@ -1,12 +1,31 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin3d" xml:lang="en">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin3d" xml:lang="en">
     <refnamediv>
         <refname>splin3d</refname>
         <refpurpose>spline gridded 3d interpolation</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>tl = splin3d(x, y, z, v, [order])</synopsis>
+        <synopsis>
+            tl = splin3d(x, y, z, v)
+            tl = splin3d(x, y, z, v, order)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
             in a B-spline-tensor representation of <emphasis>s</emphasis>. The
             evaluation of <emphasis>s</emphasis> at some points must be done by the
             <link linkend="interp3d">interp3d</link> function (to compute
-            <emphasis>s</emphasis> and its first derivatives) or by the <link linkend="bsplin3val">bsplin3val</link> function (to compute an arbitrary
+            <emphasis>s</emphasis> and its first derivatives) or by the
+            <link linkend="bsplin3val">bsplin3val</link> function (to compute an arbitrary
             derivative of <emphasis>s</emphasis>) . Several kind of splines may be
             computed by selecting the order of the spline in each direction
             <literal>order=[kx,ky,kz]</literal>.
         </para>
-    </refsection>
-    <refsection>
-        <title>Remark</title>
-        <para>This function works under the conditions:</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/splin3d_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
-        <para>an error being issued when they are not respected.</para>
+        <para>
+            Remark : This function works under the conditions
+            <table align="center"  style="float:center">
+                <tr><td>nx, ny, nz ≥ 3</td></tr>
+                <tr><td>2 ≤ kx &lt; nx</td></tr>
+                <tr><td>2 ≤ ky &lt; ny</td></tr>
+                <tr><td>2 ≤ kz &lt; nz</td></tr>
+            </table>
+        </para>
+        <para>An error is yielded when they are not respected.</para>
     </refsection>
     <refsection>
         <title>Examples</title>
@@ -95,15 +113,14 @@ vp_exact = f(xp,yp,zp);
 vp_interp = interp3d(xp,yp,zp, tl);
 er = max(abs(vp_exact - vp_interp))
 // now retry with n=20 and see the error
- ]]></programlisting>
-
+     ]]></programlisting>
+        <para/>
         <programlisting role="example"><![CDATA[
-
 // example 2 (see linear_interpn help page which have the
 //            same example with trilinear interpolation)
 // =============================================================================
 
-exec("SCI/modules/interpolation/demos/interp_demo.sci")
+exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
 func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
 deff("v=f(x,y,z)",func);
 n = 5;
@@ -116,7 +133,7 @@ m = 41;
 direction = ["z="  "z="  "z="  "x="  "y="];
 val = [ 0.1   0.5   0.9   0.5   0.5];
 ebox = [0 1 0 1 0 1];
-XF=[]; YF=[]; ZF=[]; VF=[];
+[XF, YF, ZF, VF] = ([], [], [], []);
 for i = 1:length(val)
   [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(direction(i), val(i), ebox, m, m, m);
   Vm = interp3d(Xm,Ym,Zm, tl);
@@ -126,19 +143,18 @@ for i = 1:length(val)
   [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
 end
-nb_col = 128;
-vmin = min(VF); vmax = max(VF);
+
+clf
+[nb_col, vmin, vmax] = (128, min(VF), max(VF));
 color_example = dsearch(VF,linspace(vmin,vmax,nb_col+1));
 gcf().color_map = jetcolormap(nb_col);
-clf();
 gca().hiddencolor = gca().background;
 colorbar(vmin,vmax)
 plot3d(XF, YF, list(ZF,color_example), flag=[-1 6 4])
-xtitle("3d spline interpolation of "+func)
-show_window()
- ]]></programlisting>
+title("3d spline interpolation of "+func, "fontsize",3)
+     ]]></programlisting>
         <scilab:image localized="true">
-            exec("SCI/modules/interpolation/demos/interp_demo.sci")
+            exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
             func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
             deff("v=f(x,y,z)",func);
             n = 5;
@@ -185,13 +201,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 1bdbf7f..555d738 100644 (file)
@@ -1,12 +1,15 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bsplin3val" xml:lang="ja">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="bsplin3val" xml:lang="ja">
     <refnamediv>
         <refname>bsplin3val</refname>
         <refpurpose>3次元スプラインの任意微分評価関数</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>[dfp]=bsplin3val(xp,yp,zp,tl,der)</synopsis>
+        <synopsis>dfp = bsplin3val(xp, yp, zp, tl, der)</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>引数</title>
             計算する微分値は引数<literal>der=[ox,oy,oz]</literal>で
             指定されます  :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/bsplin3val_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18"
+                alt="dfp(i)=∂^{oxoyoz}/(∂^ox.∂^oy.∂^oz) s(xp(i),yp(i),zp(i))">
+                dfp(i)=\frac{\partial^{ox\,oy\,oz}}{\partial ^{ox}\,\partial ^{oy}\,\partial ^{oz}}
+                        s\left(xp(i),yp(i),zp(i)\right)
+            </latex>
+        </para>
         <para>
             この場合,<literal>der=[0 0 0]</literal> は
             <emphasis>s</emphasis>, <literal>der=[1 0 0]</literal>は
@@ -115,15 +118,4 @@ fxxyz_i = bsplin3val(xp,yp,zp,tl,[2 1 1])
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>履歴</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    以前は,入力引数の虚部は暗黙的に無視されていました.
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index e0b9a11..dce04d5 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="interp" xml:lang="ja">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="interp" xml:lang="ja">
     <refnamediv>
         <refname>interp</refname>
         <refpurpose>3次スプライン評価関数</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>[yp [,yp1 [,yp2 [,yp3]]]]=interp(xp, x, y, d [, out_mode])</synopsis>
+        <synopsis>
+            [yp, yp1, yp2, yp3] = interp(xp, x, y, d)
+            [yp, yp1, yp2, yp3] = interp(xp, x, y, d, out_mode)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>引数</title>
@@ -35,7 +41,7 @@
                 <term>out_mode</term>
                 <listitem>
                     <para>
-                        (オプション)<latex>[x_1,\ x_n]</latex>の外側で.
+                        (オプション)[x<subscript>1</subscript>, x<subscript>n</subscript>]の外側で.
                         <literal>X</literal> に対する<literal>s(X)</literal>を定義します.
                         利用可能な値: "by_zero" | "by_nan" | "C0" | "natural" | "linear" | "periodic"
                     </para>
         <title>説明</title>
         <para>
             指定した点の<literal>(x,y)</literal> 集合を補間する3次スプライン関数 <literal>s(X)</literal>
-            は,<latex>[x_1,\ x_n]</latex>の範囲で定義された,連続で微分可能な関数です.
-            これは,3次元多項式の集合からなり,その各々は<latex>p_k(X)</latex>が
-            <latex>[x_k,\ x_{k+1}]</latex>で定義され,
-            隣接する多項式と値と傾きで接続されています.
-            つまり, <latex>X\ \in\ [x_k,\ x_{k+1}],\ s(X) = p_k(X)</latex>の各々について,
-            <latex>s(x_i) = y_i,\quad \mbox{and}\quad s'(x_i) = d_i</latex>を記述できます.
+            は,[x<subscript>1</subscript>, x<subscript>n</subscript>]の範囲で定義された,連続で微分可能な関数です.
+            これは,3次元多項式の集合からなり,その各々はp<subscript>k</subscript>(X)が
+            [x<subscript>k</subscript>, x<subscript>k+1</subscript>]で定義され,
+            隣接する多項式と値と傾きで接続されています. つまり,
+            <emphasis>
+                X &#8712; [x<subscript>k</subscript>, x<subscript>k+1</subscript>],
+                s(X) = p<subscript>k</subscript>(X)
+            </emphasis> の各々について,
+            <emphasis>
+                s(x<subscript>i</subscript>) = y<subscript>i</subscript>,  and  
+                s'(x<subscript>i</subscript>) = d<subscript>i</subscript>
+            </emphasis>
+            を記述できます.
+        </para>
+        <para>
+            <table align="center">
+            <tr align="center">
+                <td><emphasis>
+                        yp<subscript>i</subscript> = s(xp<subscript>i</subscript>)
+                           or   
+                        yp<subscript>ij</subscript> = s(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp1<subscript>i</subscript> = s'(xp<subscript>i</subscript>)
+                           or   
+                        yp1<subscript>ij</subscript> = s'(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp2<subscript>i</subscript> = s''(xp<subscript>i</subscript>)
+                           or   
+                        yp2<subscript>ij</subscript> = s''(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp3<subscript>i</subscript> = s'''(xp<subscript>i</subscript>)
+                           or   
+                        yp3<subscript>ij</subscript> = s'''(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            </table>
         </para>
-        <latex style="display" align="center"><![CDATA[ yp_i = s(xp_i) \quad or \quad yp_{i,j} = s(xp_{i,j})  ]]></latex>
-        <latex style="display" align="center"><![CDATA[ yp1_i = s'(xp_i) \quad or \quad yp1_{i,j} = s'(xp_{i,j})  ]]></latex>
-        <latex style="display" align="center"><![CDATA[ yp2_i = s''(xp_i) \quad or \quad yp2_{i,j} = s''(xp_{i,j})  ]]></latex>
-        <latex style="display" align="center"><![CDATA[ yp3_i = s'''(xp_i) \quad or \quad yp3_{i,j} = s'''(xp_{i,j})  ]]></latex>
         <para>
             <literal>out_mode</literal>パラメータは
-            補外,すなわち,<literal>xp(i)</literal>が<latex>[x_1,\ x_n]</latex> の範囲にない場合
+            補外,すなわち,<literal>xp(i)</literal>が[x<subscript>1</subscript>, x<subscript>n</subscript>] の範囲にない場合
             の評価規則を設定します :
         </para>
         <variablelist>
             <varlistentry>
                 <term>"C0"</term>
                 <listitem>
-                    <para>以下のように定義される補外 :</para>
-                    <latex style="display" align="center"><![CDATA[ xp_i < x_1   \Rightarrow  yp_i = y_1 ]]></latex>
-                    <latex style="display" align="center"><![CDATA[ xp_i > x_n   \Rightarrow  yp_i = y_n ]]></latex>
+                    <para>以下のように定義される補外 :
+                        <table align="center">
+                        <tr align="center"><td><emphasis>
+                            xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                            yp<subscript>i</subscript> = y<subscript>1</subscript>
+                            </emphasis></td></tr>
+                        <tr align="center"><td><emphasis>
+                            xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                            yp<subscript>i</subscript> = y<subscript>n</subscript>
+                            </emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"natural"</term>
                 <listitem>
                     <para>以下のように定義される補外
-                        (<latex>p_i(x)</latex> は,<latex>[x_i,\ x_{i+1}]</latex>
+                        (p<subscript>i</subscript>(x) は,[x<subscript>i</subscript>, x<subscript>i+1</subscript>]
                         において<literal>s(X)</literal>を定義する多項式です)
                     </para>
-                    <latex style="display" align="center"><![CDATA[ xp_i < x_1   \Rightarrow  yp_i = p_1(xp_i) ]]></latex>
-                    <latex style="display" align="center"><![CDATA[ xp_i > x_n   \Rightarrow  yp_i = p_{n-1}(xp_i) ]]></latex>
+                    <table align="center">
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = p<subscript>1</subscript>(xp<subscript>i</subscript>)
+                        </emphasis></td></tr>
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = p<subscript>n-1</subscript>(xp<subscript>i</subscript>)
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"linear"</term>
                 <listitem>
                     <para>補外は以下のように定義されます :</para>
-                    <latex style="display" align="center"><![CDATA[ xp_i < x_1   \Rightarrow  yp_i = y_1 + d_1.(xp_i - x_1) ]]></latex>
-                    <latex style="display" align="center"><![CDATA[ xp_i > x_n   \Rightarrow  yp_i = y_n + d_n.(xp_i - x_n) ]]></latex>
+                    <table align="center">
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = y<subscript>1</subscript> +
+                            d<subscript>1</subscript>.(xp<subscript>i</subscript> - x<subscript>1</subscript>)
+                        </emphasis></td></tr>
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = y<subscript>n</subscript> +
+                            d<subscript>n</subscript>.(xp<subscript>i</subscript> - x<subscript>n</subscript>)
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
             <varlistentry>
                     <para>
                         <literal>s</literal> は周期性により拡張されます.
                     </para>
-                    <latex style="display" align="center"><![CDATA[ yp_i = s( x_1 + ( (xp_i-x_1)\ \mbox{modulo}\ [x_n-x_1] ) ) ]]></latex>
+                    <table align="center">
+                    <tr><td><emphasis>
+                        yp<subscript>i</subscript> = s( x<subscript>1</subscript> + (xp<subscript>i</subscript> - x<subscript>1</subscript>) modulo (x<subscript>n</subscript>-x<subscript>1</subscript>) )
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
         </variablelist>
@@ -237,13 +313,4 @@ xtitle(" different way to evaluate a spline outside its domain")
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>履歴</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 752ae52..db6acbb 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="ja">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="ja">
     <refnamediv>
         <refname>linear_interpn</refname>
         <refpurpose>n 次元線形補間</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>vp = linear_interpn(xp1,xp2,..,xpn, x1, ..., xn, v [,out_mode])</synopsis>
+        <synopsis>
+            vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v)
+            vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v, out_mode)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>引数</title>
             n個のベクトル<literal>x1 ,x2,..., xn</literal>で定義された n次元グリッド
             とそのグリッドにおける関数(例えば <emphasis>f</emphasis>)の値を次のように指定すると:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/linear_interpn_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <table align="center">
+            <tr><td>
+                    v(i<subscript>1</subscript>,
+                      i<subscript>2</subscript>,…,
+                      i<subscript>n</subscript>) =
+                      <emphasis>f</emphasis>(x1(i<subscript>1</subscript>),
+                                             x2(i<subscript>2</subscript>),…,
+                                             xn(i<subscript>n</subscript>))
+                </td>
+            </tr>
+            </table>
+        </para>
         <para>
             この関数は, ベクトル<literal>xp1, xp2, ..., xpn</literal>(または行列)により定義された座標にある
             (以下 <emphasis>s</emphasis> と呼ぶ)グリッドから次のように
             <emphasis>f</emphasis>の線形補間を計算します:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/linear_interpn_equation2.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <table align="center">
+            <tr align="center">
+                <td>vp(i) = <emphasis>s</emphasis>(xp1(i), xp2(i), …, xpn(i))</td></tr>
+            <tr align="center"><td>or</td></tr>
+            <tr align="center">
+                <td>vp(i,j) = <emphasis>s</emphasis>(xp1(i,j), xp2(i,j), …, xpn(i,j))</td>
+            </tr>
+            </table>
+            in case the xpk are matrices.
+        </para>
         <para>
             <literal>out_mode</literal> パラメータは捕外の評価規則を設定します:
             <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> とすると,
             <literal>out_mode</literal> は次の場合に評価規則を定義します:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/linear_interpn_equation3.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <table align="center">
+            <tr><td>P(i) ∉ [x1(1), x1($)] × [x2(1), x2($)] × … × [xn(1), xn($)]</td></tr>
+            </table>
+        </para>
         <para>その他の選択肢は以下があります:</para>
         <variablelist>
             <varlistentry>
@@ -280,13 +294,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>履歴</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index d0b2df4..549a9fc 100644 (file)
@@ -1,12 +1,31 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lsq_splin" xml:lang="ja">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="lsq_splin" xml:lang="ja">
     <refnamediv>
         <refname>lsq_splin</refname>
         <refpurpose>重み付き最小二乗三次スプラインフィッティング</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>[y, d] = lsq_splin(xd, yd [, wd], x)</synopsis>
+        <synopsis>
+            [y, d] = lsq_splin(xd, yd, x)
+            [y, d] = lsq_splin(xd, yd, wd, x)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>パラメータ</title>
             あらゆる3次スプライン関数の空間とする場合,
             得られるスプライン <emphasis>s</emphasis>は次のようになります:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/lsq_splin_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18" alt="∑_k=1→m wd(k).[s(xd(k))-yd(k)]² ⬅ ∑_k=1→m wd(k).[f(xd(k))-yd(k)]²">
+                \sum_{k=1}^m wd(k)\left(s(xd(k))-yd(k)\right)^2 \,\leftarrow\,
+                \sum_{k=1}^m wd(k)\left(f(xd(k))-yd(k)\right)^2
+            </latex>
+        </para>
         <para>
             ただし,<emphasis>fはSの中の任意の値</emphasis>.
             すなわち,<emphasis>S</emphasis>の任意の関数について,
@@ -148,6 +166,12 @@ show_window()
         <title>参照</title>
         <simplelist type="inline">
             <member>
+                <link linkend="backslash">backslash</link>
+            </member>
+            <member>
+                <link linkend="datafit">datafit</link>
+            </member>
+            <member>
                 <link linkend="interp">interp</link>
             </member>
             <member>
index 27e3cfd..b5458b0 100644 (file)
@@ -1,12 +1,32 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin" xml:lang="ja">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) F. N. Fritsch (pchim.f Slatec routine is used for monotonous interpolation)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin" xml:lang="ja">
     <refnamediv>
         <refname>splin</refname>
         <refpurpose>3次スプライン補間</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>d = splin(x, y [,spline_type [, der]])</synopsis>
+        <synopsis>
+            d = splin(x, y)
+            d = splin(x, y, spline_type)
+            d = splin(x, y, spline_type, der)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>引数</title>
                     <para>これはデフォルトで,
                         3次スプラインが以下の条件 (n個の点 x1,...,xnを考慮)により計算されます:
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation1.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <latex fontsize="18" alt="s′′′(x₂⁻)=s′′′(x₂⁺), s′′′(x{n-1}⁻)=s′′′(x{n-1}⁺)">
+                            s'''(x_2^-) = s'''(x_2^+) \\
+                            s'''(x_{n-1}^-) = s'''(x_{n-1}^+)
+                        </latex>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                         を用いて計算されます.この微係数は最後の引数<literal>der</literal>
                         で指定されます:
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation2.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <table align="center">
+                        <tr align="center"><td><emphasis>s'(x<subscript>1</subscript>) = der(1)</emphasis></td></tr>
+                        <tr align="center"><td><emphasis>s'(x<subscript>n</subscript>) = der(2)</emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"natural"</term>
                 <listitem>
                     <para>3次スプラインは次の条件により計算されます:</para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation3.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <table align="center">
+                        <tr align="center"><td><emphasis>s''(x<subscript>1</subscript>) = 0</emphasis></td></tr>
+                        <tr align="center"><td><emphasis>s''(x<subscript>n</subscript>) = 0</emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                     <para>周期的3次スプラインは次の条件により計算されます
                         (<literal>y</literal>は<emphasis>y1=yn</emphasis>を確認する必要があります):
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation4.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <table align="center">
+                        <tr align="center">
+                            <td>
+                            <emphasis>s'(x<subscript>1</subscript>) = s'(x<subscript>n</subscript>)</emphasis>
+                            </td>
+                        </tr>
+                        <tr align="center">
+                            <td>
+                            <emphasis>s''(x<subscript>1</subscript>) = s''(x<subscript>n</subscript>)</emphasis>
+                            </td>
+                        </tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                         各区間で単調となるような<emphasis>di</emphasis>
                         に関するローカルなスキームにより計算されます:
                     </para>
-                    <informalequation>
-                        <mediaobject>
-                            <imageobject>
-                                <imagedata align="center" fileref="../mml/splin_equation5.mml"/>
-                            </imageobject>
-                        </mediaobject>
-                    </informalequation>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                If y(i) ≤ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
+                            </listitem>
+                            <listitem>
+                                If y(i) ≥ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
+                            </listitem>
+                        </itemizedlist>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
@@ -281,13 +308,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>履歴</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index effe141..f5ebc84 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin2d" xml:lang="ja">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin2d" xml:lang="ja">
     <refnamediv>
         <refname>splin2d</refname>
         <refpurpose>双3次スプラインのグリッド2次元補間</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>C = splin2d(x, y, z, [,spline_type])</synopsis>
+        <synopsis>
+            C = splin2d(x, y, z)
+            C = splin2d(x, y, z, spline_type)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>引数</title>
             (長さ16(nx-1)(ny-1)の)ベクトルです,
             <emphasis>s</emphasis>は次のように定義されます :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/splin2d_equation_1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+        <latex style="display" fontsize="18"  alt="s(x,y) = ∑_m=1→4 ∑_n=1→4 c_ij(m,n).(x-x_i)^{m-1}.(y-y_j)^{n-1}">
+                s(x,y)=\sum_{k=1}^4\sum_{l=1}^4 c_{ij}(k,l)\cdot(x-x_i)^{k-1}\cdot(y-y_j)^{l-1}
+        </latex>
+        </para>
         <para>
             いくつかの点で<link linkend="interp2d">interp2d</link>関数により
             <emphasis>s</emphasis>の評価を行う必要があります.
             基本となる補間関数に周期性がある場合には<emphasis role="bold">periodic</emphasis>型を使用してください.
         </para>
         <para>
-            <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis> (または
+            <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>,
+            <emphasis role="bold">fast</emphasis> (または
             <emphasis role="bold">fast_periodic</emphasis>) 型は,
             例えば発振を防止したい場合(<emphasis role="bold">monotone</emphasis>
             がこの用途には最も強力です)に有用です.
@@ -207,7 +212,6 @@ xtitle("natural")
 subplot(2,2,4)
 plot3d1(xp, yp, ZP4, flag=[2 2 4])
 xtitle("monotone")
-show_window()
  ]]></programlisting>
         <scilab:image>
             // example 2 : different interpolation functions on random data
@@ -277,13 +281,4 @@ xtitle("subspline (monotone)")
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>履歴</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
index 9874aa6..6b0581c 100644 (file)
@@ -1,12 +1,31 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin3d" xml:lang="ja">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin3d" xml:lang="ja">
     <refnamediv>
         <refname>splin3d</refname>
         <refpurpose>3次元補間グリッドのスプライン</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>tl = splin3d(x, y, z, v, [order])</synopsis>
+        <synopsis>
+            tl = splin3d(x, y, z, v)
+            tl = splin3d(x, y, z, v, order)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>引数</title>
             <literal>order=[kx,ky,kz]</literal>を選択することにより
             計算することができます.
         </para>
-    </refsection>
-    <refsection>
-        <title>注意</title>
-        <para>この関数は以下の条件で動作します:</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/splin3d_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            注意 : この関数は以下の条件で動作します
+            <table align="center"  style="float:center">
+                <tr><td>nx, ny, nz ≥ 3</td></tr>
+                <tr><td>2 ≤ kx &lt; nx</td></tr>
+                <tr><td>2 ≤ ky &lt; ny</td></tr>
+                <tr><td>2 ≤ kz &lt; nz</td></tr>
+            </table>
+        </para>
         <para>これらの条件が考慮されない場合にエラーが発生します.</para>
     </refsection>
     <refsection>
@@ -98,12 +115,13 @@ vp_exact = f(xp,yp,zp);
 vp_interp = interp3d(xp,yp,zp, tl);
 er = max(abs(vp_exact - vp_interp))
 // n=20で再試行し,誤差を見る
- ]]></programlisting>
+     ]]></programlisting>
+        <para/>
         <programlisting role="example"><![CDATA[
 // 例 2 (linear_interpn のヘルプを参照ください,
 //       trilinear補間に関する同じ例があります)
 // =============================================================================
-exec("SCI/modules/interpolation/demos/interp_demo.sci")
+exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
 func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
 deff("v=f(x,y,z)",func);
 n = 5;
@@ -116,29 +134,28 @@ m = 41;
 dir = ["z="  "z="  "z="  "x="  "y="];
 val = [ 0.1   0.5   0.9   0.5   0.5];
 ebox = [0 1 0 1 0 1];
-XF=[]; YF=[]; ZF=[]; VF=[];
+[XF, YF, ZF, VF] = ([], [], [], []);
 for i = 1:length(val)
-  [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m);
-  Vm = interp3d(Xm,Ym,Zm, tl);
-  [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
-  XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
-  Vp = interp3d(Xp,Yp,Zp, tl);
-  [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
-  XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
+    [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m);
+    Vm = interp3d(Xm,Ym,Zm, tl);
+    [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
+    XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
+    Vp = interp3d(Xp,Yp,Zp, tl);
+    [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
+    XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
 end
-nb_col = 128;
-vmin = min(VF); vmax = max(VF);
+
+clf
+[nb_col, vmin, vmax] = (128, min(VF), max(VF));
 color = dsearch(VF,linspace(vmin,vmax,nb_col+1));
 gcf().color_map = jetcolormap(nb_col);
-clf();
 gca().hiddencolor = gca().background;
 colorbar(vmin,vmax)
 plot3d(XF, YF, list(ZF,color), flag=[-1 6 4])
-xtitle("3d spline interpolation of "+func)
-show_window()
+title("3d spline interpolation of "+func, "fontsize",3)
  ]]></programlisting>
         <scilab:image localized="true">
-            exec("SCI/modules/interpolation/demos/interp_demo.sci")
+            exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
             func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
             deff("v=f(x,y,z)",func);
             n = 5;
@@ -185,13 +202,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>履歴</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
-            </revision>
-        </revhistory>
-    </refsection>
 </refentry>
diff --git a/scilab/modules/interpolation/help/mml/bsplin3val_equation1.mml b/scilab/modules/interpolation/help/mml/bsplin3val_equation1.mml
deleted file mode 100644 (file)
index ee2292b..0000000
+++ /dev/null
@@ -1,77 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mi math:fontstyle="italic">dfp</math:mi>
-   <math:mrow>
-    <math:mrow>
-     <math:mo math:stretchy="false">(</math:mo>
-     <math:mi>i</math:mi>
-     <math:mo math:stretchy="false">)</math:mo>
-    </math:mrow>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mfrac>
-     <math:msup>
-      <math:mo math:stretchy="false">∂</math:mo>
-      <math:mrow>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">ox</math:mi>
-        <math:mo math:stretchy="false">×</math:mo>
-        <math:mi math:fontstyle="italic">ox</math:mi>
-       </math:mrow>
-       <math:mo math:stretchy="false">×</math:mo>
-       <math:mi math:fontstyle="italic">oz</math:mi>
-      </math:mrow>
-     </math:msup>
-     <math:mrow>
-      <math:mrow>
-       <math:msup>
-        <math:mo math:stretchy="false">∂</math:mo>
-        <math:mi math:fontstyle="italic">ox</math:mi>
-       </math:msup>
-       <math:mo math:stretchy="false">×</math:mo>
-       <math:msup>
-        <math:mo math:stretchy="false">∂</math:mo>
-        <math:mi math:fontstyle="italic">oy</math:mi>
-       </math:msup>
-      </math:mrow>
-      <math:mo math:stretchy="false">×</math:mo>
-      <math:msup>
-       <math:mo math:stretchy="false">∂</math:mo>
-       <math:mi math:fontstyle="italic">oz</math:mi>
-      </math:msup>
-     </math:mrow>
-    </math:mfrac>
-   </math:mrow>
-   <math:mi>s</math:mi>
-   <math:mrow>
-    <math:mo math:stretchy="false">(</math:mo>
-    <math:mrow>
-     <math:mi math:fontstyle="italic">xp</math:mi>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mi>i</math:mi>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mi>,</math:mi>
-     <math:mi math:fontstyle="italic">yp</math:mi>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mi>i</math:mi>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mi>,</math:mi>
-     <math:mi math:fontstyle="italic">zp</math:mi>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mi>i</math:mi>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-    </math:mrow>
-    <math:mo math:stretchy="false">)</math:mo>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">dfp(i) = {{partial^{ox times ox times oz} } over {partial^{ox} times partial ^{oy} times partial^{oz}}} s(xp(i),yp(i),zp(i))</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation1.mml b/scilab/modules/interpolation/help/mml/interp_equation1.mml
deleted file mode 100644 (file)
index aed72bf..0000000
+++ /dev/null
@@ -1,256 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi math:fontstyle="italic">yp</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> or </math:mtext>
-      <math:mi math:fontstyle="italic">yp</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mi>i</math:mi>
-         <math:mi>,</math:mi>
-         <math:mi>j</math:mi>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mi>,</math:mi>
-          <math:mi>j</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi math:fontstyle="italic">yp1</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> or </math:mtext>
-      <math:mi math:fontstyle="italic">yp1</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mi>i</math:mi>
-         <math:mi>,</math:mi>
-         <math:mi>j</math:mi>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mi>,</math:mi>
-          <math:mi>j</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi math:fontstyle="italic">yp2</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> or </math:mtext>
-      <math:mi math:fontstyle="italic">yp2</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mi>i</math:mi>
-         <math:mi>,</math:mi>
-         <math:mi>j</math:mi>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mi>,</math:mi>
-          <math:mi>j</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi math:fontstyle="italic">yp3</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> or </math:mtext>
-      <math:mi math:fontstyle="italic">yp3</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mi>i</math:mi>
-         <math:mi>,</math:mi>
-         <math:mi>j</math:mi>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mi>,</math:mi>
-          <math:mi>j</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-yp(i) = s(xp(i)) &quot; or &quot; yp(i,j) = s(xp(i,j)) #
-yp1(i) = s&apos;(xp(i)) &quot; or &quot; yp1(i,j) = s&apos;(xp(i,j)) #
-yp2(i) = s&apos;&apos;(xp(i)) &quot; or &quot; yp2(i,j) = s&apos;&apos;(xp(i,j)) #
-yp3(i) = s&apos;&apos;&apos;(xp(i)) &quot; or &quot; yp3(i,j) = s&apos;&apos;&apos;(xp(i,j))
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation2.mml b/scilab/modules/interpolation/help/mml/interp_equation2.mml
deleted file mode 100644 (file)
index 955f8e6..0000000
+++ /dev/null
@@ -1,66 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:msub>
-        <math:mi>y</math:mi>
-        <math:mn>1</math:mn>
-       </math:msub>
-      </math:mrow>
-      <math:mtext> for </math:mtext>
-      <math:mrow>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">&lt;</math:mo>
-       <math:msub>
-        <math:mi>x</math:mi>
-        <math:mn>1</math:mn>
-       </math:msub>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:msub>
-        <math:mi>y</math:mi>
-        <math:mi>n</math:mi>
-       </math:msub>
-      </math:mrow>
-      <math:mtext> for </math:mtext>
-      <math:mrow>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">&gt;</math:mo>
-       <math:msub>
-        <math:mi>x</math:mi>
-        <math:mi>n</math:mi>
-       </math:msub>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-s(x) = y_1 &quot; for &quot; x &lt; x_1 #
-s(x) = y_n &quot; for &quot; x &gt; x_n
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation3.mml b/scilab/modules/interpolation/help/mml/interp_equation3.mml
deleted file mode 100644 (file)
index 978121e..0000000
+++ /dev/null
@@ -1,80 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:msub>
-        <math:mi>p</math:mi>
-        <math:mn>1</math:mn>
-       </math:msub>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> for </math:mtext>
-      <math:mrow>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">&lt;</math:mo>
-       <math:msub>
-        <math:mi>x</math:mi>
-        <math:mn>1</math:mn>
-       </math:msub>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:msub>
-        <math:mi>p</math:mi>
-        <math:mrow>
-         <math:mi>n</math:mi>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:mn>1</math:mn>
-        </math:mrow>
-       </math:msub>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> for </math:mtext>
-      <math:mrow>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">&gt;</math:mo>
-       <math:msub>
-        <math:mi>x</math:mi>
-        <math:mi>n</math:mi>
-       </math:msub>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-s(x) = p_1(x) &quot; for &quot; x &lt; x_1 #
-s(x) = p_{n-1}(x) &quot; for &quot; x &gt; x_n
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation4.mml b/scilab/modules/interpolation/help/mml/interp_equation4.mml
deleted file mode 100644 (file)
index 039d20c..0000000
+++ /dev/null
@@ -1,122 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mrow>
-        <math:msub>
-         <math:mi>y</math:mi>
-         <math:mn>1</math:mn>
-        </math:msub>
-        <math:mo math:stretchy="false">+</math:mo>
-        <math:mi>s</math:mi>
-       </math:mrow>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:msub>
-         <math:mi>x</math:mi>
-         <math:mn>1</math:mn>
-        </math:msub>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mi>x</math:mi>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:msub>
-          <math:mi>x</math:mi>
-          <math:mn>1</math:mn>
-         </math:msub>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-      </math:mrow>
-      <math:mtext> for </math:mtext>
-      <math:mrow>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">&lt;</math:mo>
-       <math:msub>
-        <math:mi>x</math:mi>
-        <math:mn>1</math:mn>
-       </math:msub>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mrow>
-        <math:msub>
-         <math:mi>y</math:mi>
-         <math:mi>n</math:mi>
-        </math:msub>
-        <math:mo math:stretchy="false">+</math:mo>
-        <math:mi>s</math:mi>
-       </math:mrow>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:msub>
-         <math:mi>x</math:mi>
-         <math:mi>n</math:mi>
-        </math:msub>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mi>x</math:mi>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:msub>
-          <math:mi>x</math:mi>
-          <math:mi>n</math:mi>
-         </math:msub>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-      </math:mrow>
-      <math:mtext> for </math:mtext>
-      <math:mrow>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">&gt;</math:mo>
-       <math:msub>
-        <math:mi>x</math:mi>
-        <math:mi>n</math:mi>
-       </math:msub>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-s(x) = y_1 + s&apos;(x_1) cdot (x - x_1) &quot; for &quot; x &lt; x_1 #
-s(x) = y_n + s&apos;(x_n) cdot (x - x_n) &quot; for &quot; x &gt; x_n
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/linear_interpn_equation1.mml b/scilab/modules/interpolation/help/mml/linear_interpn_equation1.mml
deleted file mode 100644 (file)
index 0be654a..0000000
+++ /dev/null
@@ -1,59 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mi>v</math:mi>
-   <math:mrow>
-    <math:mrow>
-     <math:mo math:stretchy="false">(</math:mo>
-     <math:mrow>
-      <math:mi math:fontstyle="italic">i1</math:mi>
-      <math:mi>,</math:mi>
-      <math:mi math:fontstyle="italic">i2</math:mi>
-      <math:mi>,</math:mi>
-      <math:mo math:stretchy="false">⋯</math:mo>
-      <math:mi>,</math:mi>
-      <math:mi>i</math:mi>
-      <math:mi>n</math:mi>
-     </math:mrow>
-     <math:mo math:stretchy="false">)</math:mo>
-    </math:mrow>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mi>f</math:mi>
-   </math:mrow>
-   <math:mrow>
-    <math:mo math:stretchy="false">(</math:mo>
-    <math:mrow>
-     <math:mi math:fontstyle="italic">x1</math:mi>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mi math:fontstyle="italic">i1</math:mi>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mi>,</math:mi>
-     <math:mi math:fontstyle="italic">x2</math:mi>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mi math:fontstyle="italic">i2</math:mi>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mi>,</math:mi>
-     <math:mo math:stretchy="false">⋯</math:mo>
-     <math:mi>,</math:mi>
-     <math:mi math:fontstyle="italic">xn</math:mi>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mrow>
-       <math:mi>i</math:mi>
-       <math:mi>n</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-    </math:mrow>
-    <math:mo math:stretchy="false">)</math:mo>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">v(i1,i2, dotsaxis,i{n}) = f(x1(i1),x2(i2),dotsaxis,xn(i{n}))</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/linear_interpn_equation2.mml b/scilab/modules/interpolation/help/mml/linear_interpn_equation2.mml
deleted file mode 100644 (file)
index 4af9596..0000000
+++ /dev/null
@@ -1,116 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi math:fontstyle="italic">vp</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp1</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mi>,</math:mi>
-        <math:mi math:fontstyle="italic">xp2</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mi>,</math:mi>
-        <math:mo math:stretchy="false">⋯</math:mo>
-        <math:mi>,</math:mi>
-        <math:mi math:fontstyle="italic">xpn</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mtext>or </math:mtext>
-      <math:mi math:fontstyle="italic">vp</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mi>i</math:mi>
-         <math:mi>,</math:mi>
-         <math:mi>j</math:mi>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi math:fontstyle="italic">xp1</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mi>,</math:mi>
-          <math:mi>j</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mi>,</math:mi>
-        <math:mi math:fontstyle="italic">xp2</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mi>,</math:mi>
-          <math:mi>j</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mi>,</math:mi>
-        <math:mo math:stretchy="false">⋯</math:mo>
-        <math:mi>,</math:mi>
-        <math:mi math:fontstyle="italic">xpn</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mi>,</math:mi>
-          <math:mi>j</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> in case the xpk are matrices</math:mtext>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-vp(i) = s(xp1(i),xp2(i),dotsaxis,xpn(i)) #
-&quot;or &quot; vp(i,j) = s(xp1(i,j),xp2(i,j),dotsaxis,xpn(i,j)) &quot; in case the xpk are matrices&quot;
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/linear_interpn_equation3.mml b/scilab/modules/interpolation/help/mml/linear_interpn_equation3.mml
deleted file mode 100644 (file)
index 04f3d31..0000000
+++ /dev/null
@@ -1,85 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mi>P</math:mi>
-   <math:mrow>
-    <math:mrow>
-     <math:mo math:stretchy="false">(</math:mo>
-     <math:mi>i</math:mi>
-     <math:mo math:stretchy="false">)</math:mo>
-    </math:mrow>
-    <math:mo math:stretchy="false">∉</math:mo>
-    <math:mrow>
-     <math:mrow>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">[</math:mo>
-        <math:mrow>
-         <math:mi math:fontstyle="italic">x1</math:mi>
-         <math:mrow>
-          <math:mo math:stretchy="false">(</math:mo>
-          <math:mn>1</math:mn>
-          <math:mo math:stretchy="false">)</math:mo>
-         </math:mrow>
-         <math:mi>,</math:mi>
-         <math:mi math:fontstyle="italic">x1</math:mi>
-         <math:mrow>
-          <math:mo math:stretchy="false">(</math:mo>
-          <math:mi>$</math:mi>
-          <math:mo math:stretchy="false">)</math:mo>
-         </math:mrow>
-        </math:mrow>
-        <math:mo math:stretchy="false">]</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">×</math:mo>
-       <math:mrow>
-        <math:mo math:stretchy="false">[</math:mo>
-        <math:mrow>
-         <math:mi math:fontstyle="italic">x2</math:mi>
-         <math:mrow>
-          <math:mo math:stretchy="false">(</math:mo>
-          <math:mn>1</math:mn>
-          <math:mo math:stretchy="false">)</math:mo>
-         </math:mrow>
-         <math:mi>,</math:mi>
-         <math:mi math:fontstyle="italic">x2</math:mi>
-         <math:mrow>
-          <math:mo math:stretchy="false">(</math:mo>
-          <math:mi>$</math:mi>
-          <math:mo math:stretchy="false">)</math:mo>
-         </math:mrow>
-        </math:mrow>
-        <math:mo math:stretchy="false">]</math:mo>
-       </math:mrow>
-      </math:mrow>
-      <math:mo math:stretchy="false">×</math:mo>
-      <math:mo math:stretchy="false">⋯</math:mo>
-     </math:mrow>
-     <math:mo math:stretchy="false">×</math:mo>
-     <math:mrow>
-      <math:mo math:stretchy="false">[</math:mo>
-      <math:mrow>
-       <math:mi math:fontstyle="italic">xn</math:mi>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mn>1</math:mn>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mi>,</math:mi>
-       <math:mi math:fontstyle="italic">xn</math:mi>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>$</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-      </math:mrow>
-      <math:mo math:stretchy="false">]</math:mo>
-     </math:mrow>
-    </math:mrow>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">P(i) notin [x1(1), x1($)] times [x2(1), x2($)] times dotsaxis times [xn(1), xn($)] </math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/lsq_splin_equation1.mml b/scilab/modules/interpolation/help/mml/lsq_splin_equation1.mml
deleted file mode 100644 (file)
index eb50442..0000000
+++ /dev/null
@@ -1,112 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mrow>
-    <math:munderover>
-     <math:mo math:stretchy="false">∑</math:mo>
-     <math:mrow>
-      <math:mi>k</math:mi>
-      <math:mo math:stretchy="false">=</math:mo>
-      <math:mn>1</math:mn>
-     </math:mrow>
-     <math:mi>m</math:mi>
-    </math:munderover>
-    <math:mi math:fontstyle="italic">wd</math:mi>
-   </math:mrow>
-   <math:mrow>
-    <math:mo math:stretchy="false">(</math:mo>
-    <math:mi>k</math:mi>
-    <math:mo math:stretchy="false">)</math:mo>
-   </math:mrow>
-   <math:mover math:accent="true">
-    <math:msup>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mrow>
-       <math:mi>s</math:mi>
-       <math:mrow>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi math:fontstyle="italic">xd</math:mi>
-          <math:mrow>
-           <math:mo math:stretchy="false">(</math:mo>
-           <math:mi>k</math:mi>
-           <math:mo math:stretchy="false">)</math:mo>
-          </math:mrow>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mo math:stretchy="false">−</math:mo>
-        <math:mi math:fontstyle="italic">yd</math:mi>
-       </math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>k</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-      </math:mrow>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mn>2</math:mn>
-    </math:msup>
-    <math:mo math:stretchy="false">˙</math:mo>
-   </math:mover>
-   <math:mo math:stretchy="false">←</math:mo>
-   <math:mrow>
-    <math:munderover>
-     <math:mo math:stretchy="false">∑</math:mo>
-     <math:mrow>
-      <math:mi>k</math:mi>
-      <math:mo math:stretchy="false">=</math:mo>
-      <math:mn>1</math:mn>
-     </math:mrow>
-     <math:mi>m</math:mi>
-    </math:munderover>
-    <math:mi math:fontstyle="italic">wd</math:mi>
-   </math:mrow>
-   <math:mrow>
-    <math:mo math:stretchy="false">(</math:mo>
-    <math:mi>k</math:mi>
-    <math:mo math:stretchy="false">)</math:mo>
-   </math:mrow>
-   <math:mover math:accent="true">
-    <math:msup>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mrow>
-       <math:mi>f</math:mi>
-       <math:mrow>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi math:fontstyle="italic">xd</math:mi>
-          <math:mrow>
-           <math:mo math:stretchy="false">(</math:mo>
-           <math:mi>k</math:mi>
-           <math:mo math:stretchy="false">)</math:mo>
-          </math:mrow>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mo math:stretchy="false">−</math:mo>
-        <math:mi math:fontstyle="italic">yd</math:mi>
-       </math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>k</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-      </math:mrow>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mn>2</math:mn>
-    </math:msup>
-    <math:mo math:stretchy="false">˙</math:mo>
-   </math:mover>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">sum from {k=1} to m wd(k) dot (s(xd(k)) - yd(k))^2 leftarrow sum from {k=1} to m wd(k) dot (f(xd(k)) - yd(k))^2</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin2d_equation_1.mml b/scilab/modules/interpolation/help/mml/splin2d_equation_1.mml
deleted file mode 100644 (file)
index b77bd7d..0000000
+++ /dev/null
@@ -1,101 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mi>s</math:mi>
-   <math:mrow>
-    <math:mrow>
-     <math:mo math:stretchy="false">(</math:mo>
-     <math:mrow>
-      <math:mi>x</math:mi>
-      <math:mi>,</math:mi>
-      <math:mi>y</math:mi>
-     </math:mrow>
-     <math:mo math:stretchy="false">)</math:mo>
-    </math:mrow>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mrow>
-     <math:munderover>
-      <math:mo math:stretchy="false">∑</math:mo>
-      <math:mrow>
-       <math:mi>k</math:mi>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mn>1</math:mn>
-      </math:mrow>
-      <math:mn>4</math:mn>
-     </math:munderover>
-     <math:mrow>
-      <math:munderover>
-       <math:mo math:stretchy="false">∑</math:mo>
-       <math:mrow>
-        <math:mi>l</math:mi>
-        <math:mo math:stretchy="false">=</math:mo>
-        <math:mn>1</math:mn>
-       </math:mrow>
-       <math:mn>4</math:mn>
-      </math:munderover>
-      <math:msub>
-       <math:mi>c</math:mi>
-       <math:mi math:fontstyle="italic">ij</math:mi>
-      </math:msub>
-     </math:mrow>
-    </math:mrow>
-   </math:mrow>
-   <math:mrow>
-    <math:mrow>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mrow>
-       <math:mi>k</math:mi>
-       <math:mi>,</math:mi>
-       <math:mi>l</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mo math:stretchy="false">⋅</math:mo>
-     <math:msup>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">−</math:mo>
-        <math:msub>
-         <math:mi>x</math:mi>
-         <math:mi>i</math:mi>
-        </math:msub>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mrow>
-       <math:mi>k</math:mi>
-       <math:mo math:stretchy="false">−</math:mo>
-       <math:mn>1</math:mn>
-      </math:mrow>
-     </math:msup>
-    </math:mrow>
-    <math:mo math:stretchy="false">⋅</math:mo>
-    <math:msup>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mrow>
-       <math:mi>y</math:mi>
-       <math:mo math:stretchy="false">−</math:mo>
-       <math:msub>
-        <math:mi>y</math:mi>
-        <math:mi>i</math:mi>
-       </math:msub>
-      </math:mrow>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mrow>
-      <math:mi>l</math:mi>
-      <math:mo math:stretchy="false">−</math:mo>
-      <math:mn>1</math:mn>
-     </math:mrow>
-    </math:msup>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">s(x,y) = sum from {k=1} to 4 sum from {l=1} to 4 c_{ij}(k,l) cdot (x - x_i)^{k-1} cdot (y - y_i)^{l-1}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin3d_equation1.mml b/scilab/modules/interpolation/help/mml/splin3d_equation1.mml
deleted file mode 100644 (file)
index 5d449e5..0000000
+++ /dev/null
@@ -1,62 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi math:fontstyle="italic">nx</math:mi>
-      <math:mi>,</math:mi>
-      <math:mi math:fontstyle="italic">ny</math:mi>
-      <math:mi>,</math:mi>
-      <math:mrow>
-       <math:mi math:fontstyle="italic">nz</math:mi>
-       <math:mo math:stretchy="false">≥</math:mo>
-       <math:mn>3</math:mn>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mrow>
-       <math:mn>2</math:mn>
-       <math:mo math:stretchy="false">≤</math:mo>
-       <math:mi math:fontstyle="italic">kx</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">&lt;</math:mo>
-      <math:mi math:fontstyle="italic">nx</math:mi>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mrow>
-       <math:mn>2</math:mn>
-       <math:mo math:stretchy="false">≤</math:mo>
-       <math:mi math:fontstyle="italic">ky</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">&lt;</math:mo>
-      <math:mi math:fontstyle="italic">ny</math:mi>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mrow>
-       <math:mn>2</math:mn>
-       <math:mo math:stretchy="false">≤</math:mo>
-       <math:mi math:fontstyle="italic">kz</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">&lt;</math:mo>
-      <math:mi math:fontstyle="italic">nz</math:mi>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-nx,ny,nz &gt;= 3 #
-2 &lt;= kx &lt; nx #
-2 &lt;= ky &lt; ny #
-2 &lt;= kz &lt; nz
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation1.mml b/scilab/modules/interpolation/help/mml/splin_equation1.mml
deleted file mode 100644 (file)
index 059e9da..0000000
+++ /dev/null
@@ -1,86 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:msup>
-         <math:mi math:fontstyle="italic">x2</math:mi>
-         <math:mtext>-</math:mtext>
-        </math:msup>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:msup>
-        <math:mi math:fontstyle="italic">x2</math:mi>
-        <math:mtext>+</math:mtext>
-       </math:msup>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:msubsup>
-         <math:mi>x</math:mi>
-         <math:mrow>
-          <math:mi>n</math:mi>
-          <math:mo math:stretchy="false">−</math:mo>
-          <math:mn>1</math:mn>
-         </math:mrow>
-         <math:mtext>-</math:mtext>
-        </math:msubsup>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:msubsup>
-        <math:mi>x</math:mi>
-        <math:mrow>
-         <math:mi>n</math:mi>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:mn>1</math:mn>
-        </math:mrow>
-        <math:mtext>+</math:mtext>
-       </math:msubsup>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-s&apos;&apos;&apos;(x2^&quot;-&quot;) = s&apos;&apos;&apos;(x2^&quot;+&quot;) #
-s&apos;&apos;&apos;(x_{n-1}^&quot;-&quot;) = s&apos;&apos;&apos;(x_{n-1}^&quot;+&quot;)
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation2.mml b/scilab/modules/interpolation/help/mml/splin_equation2.mml
deleted file mode 100644 (file)
index f01e392..0000000
+++ /dev/null
@@ -1,54 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi math:fontstyle="italic">x1</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi math:fontstyle="italic">der</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mn>1</math:mn>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi math:fontstyle="italic">xn</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi math:fontstyle="italic">der</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mn>2</math:mn>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-s&apos;(x1) = der(1) #
-s&apos;(xn) = der(2)
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation3.mml b/scilab/modules/interpolation/help/mml/splin_equation3.mml
deleted file mode 100644 (file)
index 83989d2..0000000
+++ /dev/null
@@ -1,46 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi math:fontstyle="italic">x1</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mn>0</math:mn>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi math:fontstyle="italic">xn</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mn>0</math:mn>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-s&apos;&apos;(x1) = 0 #
-s&apos;&apos;(xn) = 0
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation4.mml b/scilab/modules/interpolation/help/mml/splin_equation4.mml
deleted file mode 100644 (file)
index 2f1984c..0000000
+++ /dev/null
@@ -1,58 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi math:fontstyle="italic">x1</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mi math:fontstyle="italic">xn</math:mi>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mi>s</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi math:fontstyle="italic">x1</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">=</math:mo>
-       <math:mi>s</math:mi>
-      </math:mrow>
-      <math:mi>&apos;</math:mi>
-      <math:mi>&apos;</math:mi>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mi math:fontstyle="italic">xn</math:mi>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-s&apos;(x1) = s&apos;(xn) #
-s&apos;&apos;(x1) = s&apos;&apos;(xn)
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation5.mml b/scilab/modules/interpolation/help/mml/splin_equation5.mml
deleted file mode 100644 (file)
index 8dff82d..0000000
+++ /dev/null
@@ -1,110 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mtable>
-    <math:mtr>
-     <math:mrow>
-      <math:mtext>if </math:mtext>
-      <math:mi>y</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">≤</math:mo>
-       <math:mi>y</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">+</math:mo>
-        <math:mn>1</math:mn>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> s is increasing on </math:mtext>
-      <math:mrow>
-       <math:mo math:stretchy="false">[</math:mo>
-       <math:mrow>
-        <math:mi>x</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mi>,</math:mi>
-        <math:mi>x</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mo math:stretchy="false">+</math:mo>
-          <math:mn>1</math:mn>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">]</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-    <math:mtr>
-     <math:mrow>
-      <math:mtext>if </math:mtext>
-      <math:mi>y</math:mi>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">≥</math:mo>
-       <math:mi>y</math:mi>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi>i</math:mi>
-        <math:mo math:stretchy="false">+</math:mo>
-        <math:mn>1</math:mn>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mtext> s is decreasing on </math:mtext>
-      <math:mrow>
-       <math:mo math:stretchy="false">[</math:mo>
-       <math:mrow>
-        <math:mi>x</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mi>i</math:mi>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mi>,</math:mi>
-        <math:mi>x</math:mi>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mi>i</math:mi>
-          <math:mo math:stretchy="false">+</math:mo>
-          <math:mn>1</math:mn>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-       </math:mrow>
-       <math:mo math:stretchy="false">]</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mtr>
-   </math:mtable>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">alignl stack {
-&quot;if &quot; y(i) &lt;= y(i+1) &quot; s is increasing on &quot; [x(i), x(i+1)]#
-&quot;if &quot; y(i) &gt;= y(i+1) &quot; s is decreasing on &quot; [x(i), x(i+1)]
-}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
index 9cad597..f0ecca4 100644 (file)
@@ -1,5 +1,8 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bsplin3val" xml:lang="pt">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="bsplin3val" xml:lang="pt">
     <refnamediv>
         <refname>bsplin3val</refname>
         <refpurpose>função de avaliação de derivada arbitrária de spline
@@ -8,7 +11,7 @@
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>[dfp]=bsplin3val(xp,yp,zp,tl,der)</synopsis>
+        <synopsis>dfp = bsplin3val(xp, yp, zp, tl, der)</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
             <literal>s</literal>. A derivada a ser computada é especificada pelo
             argumento <literal>der=[ox,oy,oz]</literal> :
         </para>
-        <programlisting role=""><![CDATA[
-            ox   oy   oz
-           d    d    d
-dfp(i) =  ---  ---  ---   s (xp(i),yp(i),zp(i))
-            ox   oy   oz
-          dx   dy   dz
- ]]></programlisting>
+        <para>
+            <latex style="display" fontsize="18"
+                alt="dfp(i)=∂^{oxoyoz}/(∂^ox.∂^oy.∂^oz) s(xp(i),yp(i),zp(i))">
+                dfp(i)=\frac{\partial^{ox\,oy\,oz}}{\partial ^{ox}\,\partial ^{oy}\,\partial ^{oz}}
+                        s\left(xp(i),yp(i),zp(i)\right)
+            </latex>
+        </para>
         <para>
             Então, <literal>der=[0 0 0]</literal> corresponde a
             <emphasis>s</emphasis>, <literal>der=[1 0 0]</literal> to
@@ -122,12 +125,4 @@ fxxyz_i = bsplin3val(xp,yp,zp,tl,[2 1 1])
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>Autores</title>
-        <simplelist type="vert">
-            <member>R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
-            </member>
-            <member>B. Pincon (interface Scilab)</member>
-        </simplelist>
-    </refsection>
 </refentry>
index 0d48395..7bed98f 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="interp" xml:lang="pt">
+<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:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="interp" xml:lang="pt">
     <refnamediv>
         <refname>interp</refname>
         <refpurpose>função de avaliação de spline cúbico</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>[yp [,yp1 [,yp2 [,yp3]]]]=interp(xp, x, y, d [, out_mode])</synopsis>
+        <synopsis>
+            [yp, yp1, yp2, yp3] = interp(xp, x, y, d)
+            [yp, yp1, yp2, yp3] = interp(xp, x, y, d, out_mode)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
@@ -31,7 +37,7 @@
                 <listitem>
                     <para>
                         (opcional) string definido a avaliação de <literal>s</literal>
-                        fora do intervalo [x1,xn]
+                        fora do intervalo [x<subscript>1</subscript>, x<subscript>n</subscript>].
                     </para>
                 </listitem>
             </varlistentry>
         <para>
             Dados três vetores <literal>(x,y,d)</literal> ddefinindo uma função
             de spline cúbico ou sup-spline (ver <link linkend="splin">splin</link>)
-            com <literal>yi=s(xi), di = s'(xi)</literal> esta função avalia
+            com
+            <emphasis>
+                s(x<subscript>i</subscript>) = y<subscript>i</subscript>,  e 
+                s'(x<subscript>i</subscript>) = d<subscript>i</subscript>
+            </emphasis>
+            esta função avalia
             <literal>s</literal> (e <literal>s', s'', s'''</literal> se necessário) em
             <literal>xp(i)</literal> :
         </para>
-        <programlisting role=""><![CDATA[
-yp(i) = s(xp(i))    ou  yp(i,j) = s(xp(i,j))
-yp1(i) = s'(xp(i))   ou  yp1(i,j) = s'(xp(i,j))
-yp2(i) = s''(xp(i))   ou  yp2(i,j) = s''(xp(i,j))
-yp3(i) = s'''(xp(i))   ou  yp3(i,j) = s'''(xp(i,j))
- ]]></programlisting>
+        <para>
+            <table align="center">
+            <tr align="center">
+                <td><emphasis>
+                        yp<subscript>i</subscript> = s(xp<subscript>i</subscript>)
+                           ou   
+                        yp<subscript>ij</subscript> = s(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp1<subscript>i</subscript> = s'(xp<subscript>i</subscript>)
+                           ou   
+                        yp1<subscript>ij</subscript> = s'(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp2<subscript>i</subscript> = s''(xp<subscript>i</subscript>)
+                           ou   
+                        yp2<subscript>ij</subscript> = s''(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            <tr align="center">
+                <td><emphasis>
+                        yp3<subscript>i</subscript> = s'''(xp<subscript>i</subscript>)
+                           ou   
+                        yp3<subscript>ij</subscript> = s'''(xp<subscript>ij</subscript>)
+                    </emphasis>
+                </td>
+            </tr>
+            </table>
+        </para>
         <para>
             O parâmetro <literal>out_mode</literal> ajusta a regra de avaliação
-            para extrapolação, i.e., para <literal>xp(i)</literal> fora de [x1,xn] :
+            para extrapolação, i.e., para <literal>xp(i)</literal> fora de
+            [x<subscript>1</subscript>, x<subscript>n</subscript>] :
         </para>
         <variablelist>
             <varlistentry>
@@ -91,42 +133,69 @@ yp3(i) = s'''(xp(i))   ou  yp3(i,j) = s'''(xp(i,j))
             <varlistentry>
                 <term>"C0"</term>
                 <listitem>
-                    <para>a extrapolação é definida como segue :</para>
-                    <programlisting role=""><![CDATA[
-s(x) = y1  para  x < x1
-s(x) = yn  para  x > xn
- ]]></programlisting>
+                    <para>a extrapolação é definida como segue :
+                        <table align="center">
+                        <tr align="center"><td><emphasis>
+                            xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                            yp<subscript>i</subscript> = y<subscript>1</subscript>
+                            </emphasis></td></tr>
+                        <tr align="center"><td><emphasis>
+                            xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                            yp<subscript>i</subscript> = y<subscript>n</subscript>
+                            </emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"natural"</term>
                 <listitem>
-                    <para>a extrapolação é definida como segue (p_i sendo o polinômio
-                        que define <literal>s</literal> em [x_i,x_{i+1}]) :
+                    <para>a extrapolação é definida como segue (p<subscript>i</subscript>(x) sendo
+                        o polinômio que define <literal>s</literal> em
+                        [x<subscript>i</subscript>, x<subscript>i+1</subscript>]) :
                     </para>
-                    <programlisting role=""><![CDATA[
-s(x) = p_1(x)      para  x < x1
-s(x) = p_{n-1}(x)  para  x > xn
- ]]></programlisting>
+                    <table align="center">
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = p<subscript>1</subscript>(xp<subscript>i</subscript>)
+                        </emphasis></td></tr>
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = p<subscript>n-1</subscript>(xp<subscript>i</subscript>)
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"linear"</term>
                 <listitem>
                     <para>a extrapolação é definida como segue :</para>
-                    <programlisting role=""><![CDATA[
-s(x) = y1 + s'(x1)(x-x1)  para  x < x1
-s(x) = yn + s'(xn)(x-xn)  para  x > xn
- ]]></programlisting>
+                    <table align="center">
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = y<subscript>1</subscript> +
+                            d<subscript>1</subscript>.(xp<subscript>i</subscript> - x<subscript>1</subscript>)
+                        </emphasis></td></tr>
+                    <tr align="center"><td><emphasis>
+                        xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
+                        yp<subscript>i</subscript> = y<subscript>n</subscript> +
+                            d<subscript>n</subscript>.(xp<subscript>i</subscript> - x<subscript>n</subscript>)
+                        </emphasis></td></tr>
+                    </table>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"periodic"</term>
                 <listitem>
                     <para>
-                        <literal>s</literal> é estendido por periodicidade.
+                        <literal>s</literal> é estendido por periodicidade :
                     </para>
-                </listitem>
+                    <table align="center">
+                    <tr><td><emphasis>
+                        yp<subscript>i</subscript> = s( x<subscript>1</subscript> + (xp<subscript>i</subscript> - x<subscript>1</subscript>) modulo (x<subscript>n</subscript>-x<subscript>1</subscript>) )
+                        </emphasis></td></tr>
+                    </table>
+               </listitem>
             </varlistentry>
         </variablelist>
     </refsection>
@@ -159,7 +228,33 @@ subplot(3,1,3)
 plot2d(xx, [yy2k yy2f])
 legends(["spline não é um nó","sub-spline rápido"], [1 2], "lr",%f)
 xtitle("interpolação por splines (segundas derivadas)")
-
+ ]]></programlisting>
+        <scilab:image>
+            a = -8; b = 8;
+            x = linspace(a,b,20)';
+            y = sinc(x);
+            dk = splin(x,y);  // not_a_knot
+            df = splin(x,y, "fast");
+            xx = linspace(a,b,800)';
+            [yyk, yy1k, yy2k] = interp(xx, x, y, dk);
+            [yyf, yy1f, yy2f] = interp(xx, x, y, df);
+            clf()
+            subplot(3,1,1)
+            plot2d(xx, [yyk yyf])
+            plot2d(x, y, style=-9)
+            legends(["not_a_knot spline","fast sub-spline","interpolation points"],...
+            [1 2 -9], "ur",%f)
+            xtitle("spline interpolation")
+            subplot(3,1,2)
+            plot2d(xx, [yy1k yy1f])
+            legends(["not_a_knot spline","fast sub-spline"], [1 2], "ur",%f)
+            xtitle("spline interpolation (derivatives)")
+            subplot(3,1,3)
+            plot2d(xx, [yy2k yy2f])
+            legends(["not_a_knot spline","fast sub-spline"], [1 2], "lr",%f)
+            xtitle("spline interpolation (second derivatives)")
+        </scilab:image>
+        <programlisting role="example"><![CDATA[
 // aqui está um exemplo mostrando as diferentes possibilidades de extrapolação
 x = linspace(0,1,11)';
 y = cosh(x-0.5);
@@ -173,6 +268,19 @@ clf()
 plot2d(xx,[yy0 yy1 yy2 yy3],style=2:5,frameflag=2,leg="C0@linear@natural@periodic")
 xtitle(" Modos diferentes de avaliar um spline fora de seu domínio")
  ]]></programlisting>
+        <scilab:image>
+            x = linspace(0,1,11)';
+            y = cosh(x-0.5);
+            d = splin(x,y);
+            xx = linspace(-0.5,1.5,401)';
+            yy0 = interp(xx,x,y,d,"C0");
+            yy1 = interp(xx,x,y,d,"linear");
+            yy2 = interp(xx,x,y,d,"natural");
+            yy3 = interp(xx,x,y,d,"periodic");
+            clf()
+            plot2d(xx,[yy0 yy1 yy2 yy3],style=2:5,frameflag=2,leg="C0@linear@natural@periodic")
+            xtitle(" different way to evaluate a spline outside its domain")
+        </scilab:image>
     </refsection>
     <refsection role="see also">
         <title>Ver Também</title>
index bd7aa75..d3b954f 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="pt">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="pt">
     <refnamediv>
         <refname>linear_interpn</refname>
         <refpurpose>interpolação linear n-dimensional</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>vp = linear_interpn(xp1,xp2,..,xpn, x1, ..., xn, v [,out_mode])</synopsis>
+        <synopsis>
+            vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v)
+            vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v, out_mode)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
                 ..., xn
             </literal>
             eos valores <literal>v</literal> de uma função (aqui
-            nomeada <emphasis>f</emphasis>) nos pontos do grid : 
+            nomeada <emphasis>f</emphasis>) nos pontos do grid :
+        </para>
+        <para>
+            <table align="center">
+            <tr><td>
+                    v(i<subscript>1</subscript>,
+                      i<subscript>2</subscript>,…,
+                      i<subscript>n</subscript>) =
+                      <emphasis>f</emphasis>(x1(i<subscript>1</subscript>),
+                                             x2(i<subscript>2</subscript>),…,
+                                             xn(i<subscript>n</subscript>))
+                </td>
+            </tr>
+            </table>
         </para>
-        <programlisting role=""><![CDATA[
-v(i1,i2,...,in) = f(x1(i1),x2(i2), ..., xn(in))
- ]]></programlisting>
         <para>
             esta função computa o interpolante linear de <emphasis>f</emphasis>
             do grid (chamado de s a partir daqui) nos pontos nos quais as coordenadas
@@ -74,20 +90,28 @@ v(i1,i2,...,in) = f(x1(i1),x2(i2), ..., xn(in))
             </literal>
             :
         </para>
-        <programlisting role=""><![CDATA[
-vp(i) = s(xp1(i),xp2(i), ..., xpn(i))
-
-or vp(i,j) = s(xp1(i,j),xp2(i,j), ..., xpn(i,j)) caso xpk sejam matrizes
- ]]></programlisting>
+        <para>
+            <table align="center">
+            <tr align="center">
+                <td>vp(i) = <emphasis>s</emphasis>(xp1(i), xp2(i), …, xpn(i))</td></tr>
+            <tr align="center"><td>or</td></tr>
+            <tr align="center">
+                <td>vp(i,j) = <emphasis>s</emphasis>(xp1(i,j), xp2(i,j), …, xpn(i,j))</td>
+            </tr>
+            </table>
+            caso xpk sejam matrizes.
+        </para>
         <para>
             O parâmetro <literal>out_mode</literal> ajusta a regra para
             extrapolação: se notarmos
             <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> , então
-            <literal>out_mode</literal> define a regra de avaliação quando: 
+            <literal>out_mode</literal> define a regra de avaliação quando:
+        </para>
+        <para>
+            <table align="center">
+            <tr><td>P(i) ∉ [x1(1), x1($)] × [x2(1), x2($)] × … × [xn(1), xn($)]</td></tr>
+            </table>
         </para>
-        <programlisting role=""><![CDATA[ 
-P(i) está fora de  [x1(1) x1($)] x [x2(1) x2($)] x ... x [xn(1) xn($)]
- ]]></programlisting>
         <para>As escolhas são: </para>
         <variablelist>
             <varlistentry>
@@ -106,8 +130,8 @@ P(i) está fora de  [x1(1) x1($)] x [x2(1) x2($)] x ... x [xn(1) xn($)]
                 <term>"C0"</term>
                 <listitem>
                     <para>a extrapolação é definida como segue: </para>
-                    <programlisting role=""><![CDATA[ 
-s(P) = s(proj(P)) onde  proj(P) é o ponto mais próximo de P 
+                    <programlisting role=""><![CDATA[
+s(P) = s(proj(P)) onde  proj(P) é o ponto mais próximo de P
                   localizado na fronteira do grid.
  ]]></programlisting>
                 </listitem>
@@ -132,7 +156,7 @@ s(P) = s(proj(P)) onde  proj(P) é o ponto mais próximo de P
     </refsection>
     <refsection>
         <title>Exemplos </title>
-        <programlisting role="example"><![CDATA[ 
+        <programlisting role="example"><![CDATA[
 // exemplo 1 : interpolação linear 1d
 x = linspace(0,2*%pi,11);
 y = sin(x);
index c207ebf..fe9a1fc 100644 (file)
@@ -1,5 +1,21 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lsq_splin" xml:lang="pt">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="lsq_splin" xml:lang="pt">
     <refnamediv>
         <refname>lsq_splin</refname>
         <refpurpose>ajuste ponderado por spline cúbico de mínimos
@@ -8,7 +24,10 @@
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>[y, d] = lsq_splin(xd, yd [, wd], x)</synopsis>
+        <synopsis>
+            [y, d] = lsq_splin(xd, yd, x)
+            [y, d] = lsq_splin(xd, yd, wd, x)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
             pontos de interrupção <emphasis>x1 &lt; x2 &lt; ... &lt; xn</emphasis>
             então, o spline resultante s é tal que:
         </para>
-        <programlisting role=""><![CDATA[
-_m_                               _m_
-\                           2     \                           2
-/   wd(k) (s(xd(k)) - yd(k))  <=  /   wd(k) (f(xd(k)) - yd(k))
----                               ---
-k=1                               k=1
- ]]></programlisting>
         <para>
-            para todo <emphasis>fem S</emphasis>, i.e., realiza o mínimo da
+            <latex style="display" fontsize="18" alt="∑_k=1→m wd(k).[s(xd(k))-yd(k)]² ⬅ ∑_k=1→m wd(k).[f(xd(k))-yd(k)]²">
+                \sum_{k=1}^m wd(k)\left(s(xd(k))-yd(k)\right)^2 \,\leftarrow\,
+                \sum_{k=1}^m wd(k)\left(f(xd(k))-yd(k)\right)^2
+            </latex>
+        </para>
+        <para>
+            para todo <emphasis>f em S</emphasis>, i.e., realiza o mínimo da
             soma de todos os erros quadrados sobre todas as funções de
             <emphasis>S</emphasis>.
         </para>
@@ -140,6 +158,12 @@ show_window()
         <title>Ver Também</title>
         <simplelist type="inline">
             <member>
+                <link linkend="backslash">backslash</link>
+            </member>
+            <member>
+                <link linkend="datafit">datafit</link>
+            </member>
+            <member>
                 <link linkend="interp">interp</link>
             </member>
             <member>
@@ -147,12 +171,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>Autores</title>
-        <simplelist type="vert">
-            <member>C. De Boor, A.H. Morris (código da biblioteca FORTRAN NSWC)
-            </member>
-            <member>B. Pincon (interface Scilab e ligeiras modificações)</member>
-        </simplelist>
-    </refsection>
 </refentry>
index 48b66ae..9de109c 100644 (file)
@@ -1,12 +1,32 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin" xml:lang="pt">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) F. N. Fritsch (rotina pchim.f Slatec é usada para interpolação monótona)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin" xml:lang="pt">
     <refnamediv>
         <refname>splin</refname>
         <refpurpose>interpolação por spline cúbico</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>d = splin(x, y [,spline_type [, der]])</synopsis>
+        <synopsis>
+            d = splin(x, y)
+            d = splin(x, y, spline_type)
+            d = splin(x, y, spline_type, der)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
@@ -65,9 +85,9 @@
             <literal>d</literal> é o vetor com as derivadas nos <literal>xi</literal>:
             <emphasis>s'(xi)=di</emphasis> (esta forma é chamada de forma de
             <emphasis>Hermite ou hermitiana</emphasis> ). A avaliação do spline em
-            alguns pontos deve ser feita pela função <link linkend="interp">interp</link>. Vários tipos de splines podem ser
-            computados selecionando o parâmetro <literal>spline_type</literal>
-            apropriado:
+            alguns pontos deve ser feita pela função <link linkend="interp">interp</link>.
+            Vários tipos de splines podem ser  computados selecionando o parâmetro
+            <literal>spline_type</literal> apropriado:
         </para>
         <variablelist>
             <varlistentry>
                     <para>este é o caso padrão, o spline cúbico é computado sob as
                         seguintes condições (considerando n pontos x1,...,xn):
                     </para>
-                    <programlisting role=""><![CDATA[
-s'''(x2-) = s'''(x2+)
-s'''(x{n-1}-) = s'''(x{n-1}+)
- ]]></programlisting>
+                    <para>
+                        <latex fontsize="18" alt="s′′′(x₂⁻)=s′′′(x₂⁺), s′′′(x{n-1}⁻)=s′′′(x{n-1}⁺)">
+                            s'''(x_2^-) = s'''(x_2^+) \\
+                            s'''(x_{n-1}^-) = s'''(x_{n-1}^+)
+                        </latex>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
@@ -89,20 +111,24 @@ s'''(x{n-1}-) = s'''(x{n-1}+)
                         extremidades do intervalo que devem ser fornecidas como último
                         argumento <literal>der</literal>:
                     </para>
-                    <programlisting role=""><![CDATA[
-s'(x1) = der(1)
-s'(xn) = der(2)
- ]]></programlisting>
+                    <para>
+                        <table align="center">
+                        <tr align="center"><td><emphasis>s'(x<subscript>1</subscript>) = der(1)</emphasis></td></tr>
+                        <tr align="center"><td><emphasis>s'(x<subscript>n</subscript>) = der(2)</emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>"natural"</term>
                 <listitem>
                     <para>o spline cúbico é computado sob as seguintes condições:</para>
-                    <programlisting role=""><![CDATA[
-s''(x1) = 0
-s''(xn) = 0
- ]]></programlisting>
+                    <para>
+                        <table align="center">
+                        <tr align="center"><td><emphasis>s''(x<subscript>1</subscript>) = 0</emphasis></td></tr>
+                        <tr align="center"><td><emphasis>s''(x<subscript>n</subscript>) = 0</emphasis></td></tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
@@ -113,10 +139,20 @@ s''(xn) = 0
                         deve verificar <emphasis>y1=yn</emphasis>) sob as seguintes
                         condições:
                     </para>
-                    <programlisting role=""><![CDATA[
-s'(x1) = s'(xn)
-s''(x1) = s''(xn)
- ]]></programlisting>
+                    <para>
+                        <table align="center">
+                        <tr align="center">
+                            <td>
+                            <emphasis>s'(x<subscript>1</subscript>) = s'(x<subscript>n</subscript>)</emphasis>
+                            </td>
+                        </tr>
+                        <tr align="center">
+                            <td>
+                            <emphasis>s''(x<subscript>1</subscript>) = s''(x<subscript>n</subscript>)</emphasis>
+                            </td>
+                        </tr>
+                        </table>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
@@ -128,10 +164,16 @@ s''(x1) = s''(xn)
                         para os <emphasis>di</emphasis> tais que s é monótono em cada
                         intervalo:
                     </para>
-                    <programlisting role=""><![CDATA[
-if y(i) <= y(i+1)  s é crescente em [x(i), x(i+1)]
-if y(i) >= y(i+1)  s é decrescente em [x(i), x(i+1)]
- ]]></programlisting>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                If y(i) ≤ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
+                            </listitem>
+                            <listitem>
+                                If y(i) ≥ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
+                            </listitem>
+                        </itemizedlist>
+                    </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
@@ -162,21 +204,25 @@ if y(i) >= y(i+1)  s é decrescente em [x(i), x(i+1)]
         <title>Observações </title>
         <para>De um ponto de vista de precisão, use essencialmente o tipo
             <emphasis role="bold">clamped</emphasis> se você conhece as derivadas nas
-            extremidades, de outro modo, use <emphasis role="bold">not_a_knot</emphasis>. Mas se a função subjacente aproximada é
-            periódica, use o tipo <emphasis role="bold">periodic</emphasis> Sob boas
-            suposições, estes tipos de spline têm um comportamento assintótico
-            <literal>O(h^4)</literal> do erro. Não use o tipo <emphasis role="bold">natural</emphasis> a não ser que a função subjacente possua
-            zero derivadas segundas nas extremidades.
+            extremidades, de outro modo, use <emphasis role="bold">not_a_knot</emphasis>.
+            Mas se a função subjacente aproximada é periódica, use o tipo
+            <emphasis role="bold">periodic</emphasis> Sob boas suposições, estes tipos de spline
+            têm um comportamento assintótico <literal>O(h^4)</literal> do erro.
+            Não use o tipo <emphasis role="bold">natural</emphasis> a não ser que a função
+            subjacente possua zero derivadas segundas nas extremidades.
         </para>
         <para>
-            Os tipos <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis> (ou <emphasis role="bold">fast_periodic</emphasis>) podem ser úteis e alguns caso, por
+            Os tipos <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis>
+            (ou <emphasis role="bold">fast_periodic</emphasis>) podem ser úteis e alguns caso, por
             exemplo, para limitar oscilações (estes tipos de sub-splines têm um
             comportamento assintótico <literal>O(h^3)</literal> do erro).
         </para>
         <para>
             Se <emphasis>n=2</emphasis> (e <literal>spline_type</literal> não é
             <emphasis role="bold">clamped</emphasis>) é usada interpolação linear. Se
-            <emphasis>n=3</emphasis> e <literal>spline_type</literal> é <emphasis role="bold">not_a_knot</emphasis>, então, um sub-spline tipo <emphasis role="bold">fast</emphasis> é computado, na verdade.
+            <emphasis>n=3</emphasis> e <literal>spline_type</literal> é
+            <emphasis role="bold">not_a_knot</emphasis>, então, um sub-spline tipo
+            <emphasis role="bold">fast</emphasis> é computado, na verdade.
         </para>
     </refsection>
     <refsection>
@@ -225,13 +271,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>Autores</title>
-        <simplelist type="vert">
-            <member>B. Pincon</member>
-            <member>F. N. Fritsch (rotina pchim.f Slatec é usada para interpolação
-                monótona)
-            </member>
-        </simplelist>
-    </refsection>
 </refentry>
index 75e229c..ead6854 100644 (file)
@@ -1,12 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin2d" xml:lang="pt">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin2d" xml:lang="pt">
     <refnamediv>
         <refname>splin2d</refname>
         <refpurpose>interpolação por spline bicúbico em grides 2d</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>C = splin2d(x, y, z, [,spline_type])</synopsis>
+        <synopsis>
+            C = splin2d(x, y, z)
+            C = splin2d(x, y, z, spline_type)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
             ,<emphasis>s</emphasis> é definido por
             :
         </para>
-        <programlisting role=""><![CDATA[
-             _4_   _4_
-             \     \                   k-1       l-1
-    s(x,y) = /     /    C (k,l) (x - xi)  (y - yj)
-             ---   ---   ij
-             k=1   l=1
- ]]></programlisting>
         <para>
-            A avaliação de s em alguns pontos deve ser feita pela função <link linkend="interp2d">interp2d</link> Vários tipos de splines podem ser
+            <latex style="display" fontsize="18"
+                   alt="s(x,y) = ∑_m=1→4 ∑_n=1→4 c_ij(m,n).(x-x_i)^{m-1}.(y-y_j)^{n-1}">
+                s(x,y)=\sum_{k=1}^4\sum_{l=1}^4 c_{ij}(k,l)\cdot(x-x_i)^{k-1}\cdot(y-y_j)^{l-1}
+            </latex>
+        </para>
+        <para>
+            A avaliação de s em alguns pontos deve ser feita pela função
+            <link linkend="interp2d">interp2d</link> Vários tipos de splines podem ser
             computados selecionando o parâmetro <literal>spline_type</literal>
             apropriado. O método usada para computar os splines (ou sub-spline)
             bicúbicos é o mesmo do antigo, i.e., computar em cada ponto do grid
     </refsection>
     <refsection>
         <title>Exemplos</title>
-        <programlisting role="example"><![CDATA[ 
+        <programlisting role="example"><![CDATA[
 // exemplo 1 : interpolação de cos(x)cos(y)
 n = 7;  // um grid regular com n x n pontos de interpolação
         // será usado
@@ -143,9 +149,11 @@ clf()
 plot3d(xx, yy, zz, flag=[2 4 4])
 [X,Y] = ndgrid(x,y);
 param3d1(X,Y,list(z,-9*ones(1,n)), flag=[0 0])
-str = msprintf(" com %d x %d pontos de interpolação. ermax = %g",n,n,emax) 
+str = msprintf(" com %d x %d pontos de interpolação. ermax = %g",n,n,emax)
 xtitle("Interpolação por spline de cos(x)cos(y)"+str)
-
+     ]]></programlisting>
+        <para/>
+        <programlisting role="example"><![CDATA[
 // exemplo 2 : diferentes funções de interpolação em dados aleatórios
 n = 6;
 x = linspace(0,1,n); y = x;
@@ -171,8 +179,9 @@ xtitle("natural")
 subplot(2,2,4)
 plot3d1(xp, yp, ZP4, flag=[2 2 4])
 xtitle("monotone")
-show_window()
-
+     ]]></programlisting>
+        <para/>
+        <programlisting role="example"><![CDATA[
 // exemplo 3 : spline not_a_knot e sub-spline monotone
 //             em uma função de degraus
 a = 0; b = 1; c = 0.25; d = 0.75;
@@ -196,7 +205,7 @@ xtitle("spline (not_a_knot)")
 subplot(1,2,2)
 plot3d1(xp, xp, zp2, flag=[-2 6 4])
 xtitle("subspline (monotone)")
- ]]></programlisting>
+     ]]></programlisting>
     </refsection>
     <refsection role="see also">
         <title>Ver Também</title>
index 0c718f1..7cbcaf5 100644 (file)
@@ -1,12 +1,31 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin3d" xml:lang="pt">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
+ * Copyright (C) B. Pincon (interface Scilab)
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
+          xml:id="splin3d" xml:lang="pt">
     <refnamediv>
         <refname>splin3d</refname>
         <refpurpose>interpolação spline em grides 3d</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>tl = splin3d(x, y, z, v, [order])</synopsis>
+        <synopsis>
+            tl = splin3d(x, y, z, v)
+            tl = splin3d(x, y, z, v, order)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
             é definido por <literal>tl</literal> que consiste em uma representação
             B-tensor-spline de <emphasis>s</emphasis>. A avaliação de s em alguns
             pontos deve ser feita pela função <link linkend="interp3d">interp3d</link>
-            (para computar s e suas derivadas primeiras) ou pela função <link linkend="bsplin3val">bsplin3val</link> (para computar uma derivada
+            (para computar s e suas derivadas primeiras) ou pela função
+            <link linkend="bsplin3val">bsplin3val</link> (para computar uma derivada
             arbitrária de s) . Vários tipos de splines podem ser computados
             selecionando a ordem dos splines em cada direção
             <literal>order=[kx,ky,kz]</literal>.
         </para>
-    </refsection>
-    <refsection>
-        <title>Observação</title>
-        <para>Esta função funciona sob as condições: </para>
-        <programlisting role=""><![CDATA[ 
-nx, ny, nz <= 3
-2 <= kx < nx
-2 <= ky < ny
-2 <= kz < nz
- ]]></programlisting>
-        <para>Há erro quando estas condições não são respeitadas. </para>
+        <para>
+            Observação : Esta função funciona sob as condições
+            <table align="center"  style="float:center">
+                <tr><td>nx, ny, nz ≥ 3</td></tr>
+                <tr><td>2 ≤ kx &lt; nx</td></tr>
+                <tr><td>2 ≤ ky &lt; ny</td></tr>
+                <tr><td>2 ≤ kz &lt; nz</td></tr>
+            </table>
+        </para>
+        <para>
+            Há erro quando estas condições não são respeitadas.
+        </para>
     </refsection>
     <refsection>
         <title>Exemplos</title>
@@ -92,12 +113,14 @@ vp_exact = f(xp,yp,zp);
 vp_interp = interp3d(xp,yp,zp, tl);
 er = max(abs(vp_exact - vp_interp))
 // tente agora com n=20 e veja o erro
-
+     ]]></programlisting>
+        <para/>
+        <programlisting role="example"><![CDATA[
 // exemplo 2 (veja a página de ajuda de linear_interpn que contém o
 //            mesmo exemplo com interpolação trilinear)
 // =============================================================================
 
-exec("SCI/modules/interpolation/demos/interp_demo.sci")
+exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
 func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
 deff("v=f(x,y,z)",func);
 n = 5;
@@ -110,27 +133,60 @@ m = 41;
 dir = ["z="  "z="  "z="  "x="  "y="];
 val = [ 0.1   0.5   0.9   0.5   0.5];
 ebox = [0 1 0 1 0 1];
-XF=[]; YF=[]; ZF=[]; VF=[];
+[XF, YF, ZF, VF] = ([], [], [], []);
 for i = 1:length(val)
-   [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m);
-   Vm = interp3d(Xm,Ym,Zm, tl);
-   [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
-   Vp = interp3d(Xp,Yp,Zp, tl);
-   [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
+    [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m);
+    Vm = interp3d(Xm,Ym,Zm, tl);
+    [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
+    XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
+    Vp = interp3d(Xp,Yp,Zp, tl);
+    [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
+    XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
 end
-nb_col = 128;
-vmin = min(VF); vmax = max(VF);
+
+clf
+[nb_col, vmin, vmax] = (128, min(VF), max(VF));
 color = dsearch(VF,linspace(vmin,vmax,nb_col+1));
 gcf().color_map = jetcolormap(nb_col);
-clf();
 gca().hiddencolor = gca().background;
 colorbar(vmin,vmax)
 plot3d(XF, YF, list(ZF,color), flag=[-1 6 4])
-xtitle("interpolação por spline 3d da função "+func)
-show_window()
- ]]></programlisting>
+title("interpolação por spline 3d da função "+func, "fontsize",3)
+     ]]></programlisting>
+        <scilab:image localized="true">
+            exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
+            func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
+            deff("v=f(x,y,z)",func);
+            n = 5;
+            x = linspace(0,1,n); y=x; z=x;
+            [X,Y,Z] = ndgrid(x,y,z);
+            V = f(X,Y,Z);
+            tl = splin3d(x,y,z,V);
+            // computando e exibindo o spline interpolante 3d em algumas fatias
+            m = 41;
+            dir = ["z="  "z="  "z="  "x="  "y="];
+            val = [ 0.1   0.5   0.9   0.5   0.5];
+            ebox = [0 1 0 1 0 1];
+            XF=[]; YF=[]; ZF=[]; VF=[];
+            for i = 1:length(val)
+               [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m);
+               Vm = interp3d(Xm,Ym,Zm, tl);
+               [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
+               XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
+               Vp = interp3d(Xp,Yp,Zp, tl);
+               [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
+               XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
+            end
+            nb_col = 128;
+            vmin = min(VF); vmax = max(VF);
+            color = dsearch(VF,linspace(vmin,vmax,nb_col+1));
+            gcf().color_map = jetcolormap(nb_col);
+            clf();
+            gca().hiddencolor = gca().background;
+            colorbar(vmin,vmax)
+            plot3d(XF, YF, list(ZF,color), flag=[-1 6 4])
+            xtitle("interpolação por spline 3d da função "+func)
+        </scilab:image>
     </refsection>
     <refsection role="see also">
         <title>Ver Também</title>
@@ -146,12 +202,4 @@ show_window()
             </member>
         </simplelist>
     </refsection>
-    <refsection>
-        <title>Autores</title>
-        <simplelist type="vert">
-            <member>R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
-            </member>
-            <member>B. Pincon (interface Scilab)</member>
-        </simplelist>
-    </refsection>
 </refentry>
index 7718202..c4c3b1f 100644 (file)
@@ -20,7 +20,7 @@
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>z = beta(x,y)</synopsis>
+        <synopsis>z = beta(x, y)</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
     <refsection>
         <title>Description</title>
         <para>Computes the complete beta function :</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/beta_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18" alt="B(x,y)=∫_0→1 t^{x-1}.(1-t)^{y-1} dt = Γ(x).Γ(y)/ Γ(x+y)">
+                B(x,y)=\int_0^1\!t^{x-1}\left(1-t\right)^{y-1}dt=\frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)}
+            </latex>
+        </para>
         <para>
             For small <literal>x</literal> and <literal>y</literal> (<literal>x+y ≤ 2</literal> elementwise),
             the algorithm uses the expression in function of the gamma function, else it
index 0d0d3c7..beddeb1 100644 (file)
             <literal>x</literal> the logarithmic derivative of the gamma function
             which corresponds also to the derivative of the gammaln function :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/dlgamma_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" alt="d(ln(Γ(x))/dx = dΓ(x)/dx . 1/Γ(x)">
+                \frac{d\,\ln\left(\Gamma(x)\right)}{dx}=\frac{d\Gamma(x)}{dx\,\Gamma(x)}
+            </latex>
+        </para>
         <para>
             <literal>x</literal> must be real. Also known as the psi
             function.
index 0865793..8fd0c46 100644 (file)
         </para>
         <para>
             <emphasis role="bold">gamma(u)</emphasis> computes
-            <latex style="display" fontsize="18" alt="Γ(u)= ∫_0→∞ t^{u-1}.exp(-t).dt">
-                \Gamma(u)=\int_0^\infty\! t^{u-1}e^{-t}\,dt
+            <latex style="display" fontsize="18" alt="Γ(x)= ∫_0→∞ t^{x-1}.exp(-t).dt">
+                \Gamma(x)=\int_0^\infty\! t^{x-1}e^{-t}\,dt
             </latex>
         </para>
+        <para>and generalizes the factorial function for real numbers
+            (<literal>gamma(u+1) = u*gamma(u)</literal>).
+        </para>
         <refsect3>
             <title>Incomplete normalized integrals</title>
             <para>
index 2859019..3278aae 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"  xml:id="legendre" xml:lang="en">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org"  xml:id="legendre" xml:lang="en">
     <refnamediv>
         <refname>legendre</refname>
         <refpurpose>associated Legendre functions</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>y = legendre(n,m,x [,normflag])</synopsis>
+        <synopsis>
+            y = legendre(n, m, x)
+            y = legendre(n, m, x, normflag)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
             function Pnm(x) at all the elements of <literal>x</literal>. The
             definition used is :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/legendre_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18" alt="Pn|m(x)=(-1)^m.(1-x^2)^{m/2}.d^m[Pn(x)]/dx^m">
+                P_n^m(x)=(-1)^m\cdot(1-x^2)^{m/2}\cdot\frac{d^mP_n(x)}{dx^m}
+            </latex>
+        </para>
         <para>
             where <literal>Pn</literal> is the Legendre polynomial of degree
             <literal>n</literal>. So <literal>legendre(n,0,x)</literal> evaluates the
         <para>When the normflag is equal to "norm" you get a normalized version
             (without the <literal>(-1)^m</literal> factor), precisely :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/legendre_equation2.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18"
+                   alt="Pn|m(x,norm)=sqrt[(2n+1)/2 .(n-m)!/(n+m)!].(1-x^2)^{m/2}.d^m[Pn(x)]/dx^m">
+                P_n^m(x,norm)=\sqrt{\frac{2n+1}{2}\frac{(n-m)!}{(n+m)!}}\cdot(1-x^2)^{m/2}\cdot\frac{d^mP_n(x)}{dx^m}
+            </latex>
+        </para>
         <para>which is useful to compute spherical harmonic functions (see Example
             3):
         </para>
index d3dae9d..2694006 100644 (file)
             <literal>dlgamma(x)</literal> calcule la dérivée de la fonction
             gammaln pour chaque composante de <literal>x</literal>.
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/dlgamma_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" alt="d(ln(Γ(x))/dx = dΓ(x)/dx . 1/Γ(x)">
+                \frac{d\,\ln\left(\Gamma(x)\right)}{dx}=\frac{d\Gamma(x)}{dx\,\Gamma(x)}
+            </latex>
+        </para>
         <para>
             <literal>x</literal> doit être réel. Cette fonction est aussi connue
             sous le nom de fonction psi
index bc82f8c..75cbdeb 100644 (file)
     <refsection>
         <title>説明</title>
         <para>完全ベータ関数を計算します :</para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/beta_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18" alt="B(x,y)=∫_0→1 t^{x-1}.(1-t)^{y-1} dt = Γ(x).Γ(y)/ Γ(x+y)">
+                B(x,y)=\int_0^1\!t^{x-1}\left(1-t\right)^{y-1}dt=\frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)}
+            </latex>
+        </para>
         <para>
             <literal>x</literal> および<literal>y</literal>が小さい場合,
             このアルゴリズムは,関数内でガンマ関数の式を使用します.
index e170d93..923c686 100644 (file)
             の全ての要素について,ガンマ関数の対数微分を計算します.
             この値はgammaln関数の微分に一致します:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/dlgamma_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" alt="d(ln(Γ(x))/dx = dΓ(x)/dx . 1/Γ(x)">
+                \frac{d\,\ln\left(\Gamma(x)\right)}{dx}=\frac{d\Gamma(x)}{dx\,\Gamma(x)}
+            </latex>
+        </para>
         <para>
             <literal>x</literal> は実数である必要があります.
             psi 関数としても知られています.
diff --git a/scilab/modules/special_functions/help/ja_JP/gamma.xml b/scilab/modules/special_functions/help/ja_JP/gamma.xml
new file mode 100644 (file)
index 0000000..87e6852
--- /dev/null
@@ -0,0 +1,128 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ *
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"  xml:id="gamma" xml:lang="ja">
+    <refnamediv>
+        <refname>gamma</refname>
+        <refpurpose>ガンマ関数.</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>呼び出し手順</title>
+        <synopsis>y = gamma(x)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>引数</title>
+        <variablelist>
+            <varlistentry>
+                <term>x</term>
+                <listitem>
+                    <para>
+                       scalar, vector, matrix, or hypermatrix of real numbers.
+                    </para>
+                    <note>
+                      <literal>gamma</literal> can be overloaded for complex numbers or
+                      of lists, tlists or mlists.
+                    </note>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>y</term>
+                <listitem>
+                    <para>(xと同じ大きさの)実数ベクトルまたは行列.</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>説明</title>
+        <para>
+            <literal>gamma(x)</literal> は,
+            <literal>x</literal>の全要素についてガンマ関数を計算します.
+            ガンマ関数は以下のように定義されます:
+        </para>
+        <para>
+            <latex style="display" fontsize="18" alt="Γ(x)= ∫_0→∞ t^{x-1}.exp(-t).dt">
+                \Gamma(x)=\int_0^\infty\! t^{x-1}e^{-t}\,dt
+            </latex>
+        </para>
+        <para>そして,階乗関数を実数に一般化します.
+            (<literal>gamma(u+1) = u*gamma(u)</literal>).
+        </para>
+    </refsection>
+    <refsection>
+        <title>例</title>
+        <programlisting role="example"><![CDATA[
+// 簡単な例
+gamma(0.5)
+gamma(6)-prod(1:5)
+ ]]></programlisting>
+        <programlisting role="example"><![CDATA[
+// [a,b]のガンマ関数のグラフ
+a = -3; b = 5;
+x = linspace(a,b,40000);
+y = gamma(x);
+clf()
+plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10])
+xtitle("The gamma function on ["+string(a)+","+string(b)+"]")
+show_window()
+ ]]></programlisting>
+        <scilab:image>
+            a = -3; b = 5;
+            x = linspace(a,b,40000)';
+            y = gamma(x);
+            plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10])
+            xtitle("The gamma function on ["+string(a)+","+string(b)+"]")
+        </scilab:image>
+    </refsection>
+    <refsection role="see also">
+        <title>参照</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="gammaln">gammaln</link>
+            </member>
+            <member>
+                <link linkend="dlgamma">dlgamma</link>
+            </member>
+            <member>
+                <link linkend="factorial">factorial</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>履歴</title>
+        <revhistory>
+            <revision>
+                <revnumber>5.4.0</revnumber>
+                <revremark>
+                    list, mlist, tlistおよびハイパー行列型のオーバーロードが
+                    可能となりました.
+                </revremark>
+            </revision>
+            <revision>
+              <revnumber>6.0.2</revnumber>
+              <revremark>
+                <itemizedlist>
+                  <listitem>
+                    The input can now be an hypermatrix.
+                  </listitem>
+                  <listitem>
+                    <literal>gamma</literal> can now be overloaded for complex numbers.
+                  </listitem>
+                </itemizedlist>
+              </revremark>
+            </revision>
+        </revhistory>
+    </refsection>
+</refentry>
index 438d5cd..16842ec 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="legendre" xml:lang="ja">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="legendre" xml:lang="ja">
     <refnamediv>
         <refname>legendre</refname>
         <refpurpose>随伴ルジャンドル関数</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>y = legendre(n,m,x [,normflag])</synopsis>
+        <synopsis>
+            y = legendre(n, m, x)
+            y = legendre(n, m, x, normflag)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>パラメータ</title>
             随伴ルジャンドル関数Pnm(x)を計算します.
             使用される定義を以下に示します:
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/legendre_equation1.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18" alt="Pn|m(x)=(-1)^m.(1-x^2)^{m/2}.d^m[Pn(x)]/dx^m">
+                P_n^m(x)=(-1)^m\cdot(1-x^2)^{m/2}\cdot\frac{d^mP_n(x)}{dx^m}
+            </latex>
+        </para>
         <para>
             ただし,<literal>Pn</literal>は<literal>n</literal>次の
             ルジャンドル多項式です.
             (<literal>(-1)^m</literal>係数を付けずに)
             正規化された出力が得られます :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../mml/legendre_equation2.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" fontsize="18"
+                   alt="Pn|m(x,norm)=sqrt[(2n+1)/2 .(n-m)!/(n+m)!].(1-x^2)^{m/2}.d^m[Pn(x)]/dx^m">
+                P_n^m(x,norm)=\sqrt{\frac{2n+1}{2}\frac{(n-m)!}{(n+m)!}}\cdot(1-x^2)^{m/2}\cdot\frac{d^mP_n(x)}{dx^m}
+            </latex>
+        </para>
         <para>これは,球面調和関数を計算する際に有用です(例3参照):</para>
         <para>効率化のため,
             最初の2つの引数の一つをベクトルとすることができ,
diff --git a/scilab/modules/special_functions/help/mml/beta_equation1.mml b/scilab/modules/special_functions/help/mml/beta_equation1.mml
deleted file mode 100644 (file)
index 5317044..0000000
+++ /dev/null
@@ -1,94 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mi>B</math:mi>
-   <math:mrow>
-    <math:mrow>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mrow>
-       <math:mi>x</math:mi>
-       <math:mi>,</math:mi>
-       <math:mi>y</math:mi>
-      </math:mrow>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-     <math:mo math:stretchy="false">=</math:mo>
-     <math:mrow>
-      <math:mrow>
-       <math:mrow>
-        <math:munderover>
-         <math:mo math:stretchy="false">∫</math:mo>
-         <math:mn>0</math:mn>
-         <math:mn>1</math:mn>
-        </math:munderover>
-        <math:msup>
-         <math:mi>t</math:mi>
-         <math:mrow>
-          <math:mi>x</math:mi>
-          <math:mo math:stretchy="false">−</math:mo>
-          <math:mn>1</math:mn>
-         </math:mrow>
-        </math:msup>
-       </math:mrow>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:msup>
-        <math:mrow>
-         <math:mo math:stretchy="false">(</math:mo>
-         <math:mrow>
-          <math:mn>1</math:mn>
-          <math:mo math:stretchy="false">−</math:mo>
-          <math:mi>t</math:mi>
-         </math:mrow>
-         <math:mo math:stretchy="false">)</math:mo>
-        </math:mrow>
-        <math:mrow>
-         <math:mi>y</math:mi>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:mn>1</math:mn>
-        </math:mrow>
-       </math:msup>
-      </math:mrow>
-      <math:mo math:stretchy="false">⋅</math:mo>
-      <math:mi math:fontstyle="italic">dt</math:mi>
-     </math:mrow>
-    </math:mrow>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mfrac>
-     <math:mrow>
-      <math:mo math:stretchy="false">Γ</math:mo>
-      <math:mrow>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mo math:stretchy="false">⋅</math:mo>
-       <math:mo math:stretchy="false">Γ</math:mo>
-      </math:mrow>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mi>y</math:mi>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-     <math:mrow>
-      <math:mo math:stretchy="false">Γ</math:mo>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">+</math:mo>
-        <math:mi>y</math:mi>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-    </math:mfrac>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">B(x,y) = int from 0 to 1 t^{x-1} cdot (1-t)^{y-1} cdot dt = {{%GAMMA(x) cdot %GAMMA(y)} over {%GAMMA(x + y)}}</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/special_functions/help/mml/dlgamma_equation1.mml b/scilab/modules/special_functions/help/mml/dlgamma_equation1.mml
deleted file mode 100644 (file)
index 5b70cb3..0000000
+++ /dev/null
@@ -1,58 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mfrac>
-    <math:mn>1</math:mn>
-    <math:mrow>
-     <math:mo math:stretchy="false">Γ</math:mo>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mi>x</math:mi>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-    </math:mrow>
-   </math:mfrac>
-   <math:mrow>
-    <math:mfrac>
-     <math:mrow>
-      <math:mi>d</math:mi>
-      <math:mo math:stretchy="false">Γ</math:mo>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mi>x</math:mi>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-     </math:mrow>
-     <math:mi math:fontstyle="italic">dx</math:mi>
-    </math:mfrac>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mfrac>
-     <math:mi>d</math:mi>
-     <math:mi math:fontstyle="italic">dx</math:mi>
-    </math:mfrac>
-   </math:mrow>
-   <math:mrow>
-    <math:mo math:stretchy="false">(</math:mo>
-    <math:mrow>
-     <math:mi>ln</math:mi>
-     <math:mrow>
-      <math:mo math:stretchy="false">(</math:mo>
-      <math:mrow>
-       <math:mo math:stretchy="false">Γ</math:mo>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mi>x</math:mi>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-      </math:mrow>
-      <math:mo math:stretchy="false">)</math:mo>
-     </math:mrow>
-    </math:mrow>
-    <math:mo math:stretchy="false">)</math:mo>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">{1 over {%GAMMA(x)}}{{d %GAMMA(x)} over {dx}} = {d over dx} (ln(%GAMMA(x)))</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/special_functions/help/mml/legendre_equation1.mml b/scilab/modules/special_functions/help/mml/legendre_equation1.mml
deleted file mode 100644 (file)
index 50c88a1..0000000
+++ /dev/null
@@ -1,77 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:msubsup>
-    <math:mi>P</math:mi>
-    <math:mi>n</math:mi>
-    <math:mi>m</math:mi>
-   </math:msubsup>
-   <math:mrow>
-    <math:mrow>
-     <math:mo math:stretchy="false">(</math:mo>
-     <math:mi>x</math:mi>
-     <math:mo math:stretchy="false">)</math:mo>
-    </math:mrow>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mrow>
-     <math:mrow>
-      <math:msup>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:mn>1</math:mn>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mi>m</math:mi>
-      </math:msup>
-      <math:mo math:stretchy="false">⋅</math:mo>
-      <math:msup>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mn>1</math:mn>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:msup>
-          <math:mi>x</math:mi>
-          <math:mn>2</math:mn>
-         </math:msup>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mrow>
-        <math:mi>m</math:mi>
-        <math:mo math:stretchy="false">/</math:mo>
-        <math:mn>2</math:mn>
-       </math:mrow>
-      </math:msup>
-     </math:mrow>
-     <math:mo math:stretchy="false">⋅</math:mo>
-     <math:mfrac>
-      <math:msup>
-       <math:mi>d</math:mi>
-       <math:mi>m</math:mi>
-      </math:msup>
-      <math:msup>
-       <math:mi math:fontstyle="italic">dx</math:mi>
-       <math:mi>m</math:mi>
-      </math:msup>
-     </math:mfrac>
-    </math:mrow>
-   </math:mrow>
-   <math:msub>
-    <math:mi>P</math:mi>
-    <math:mi>n</math:mi>
-   </math:msub>
-   <math:mrow>
-    <math:mo math:stretchy="false">(</math:mo>
-    <math:mi>x</math:mi>
-    <math:mo math:stretchy="false">)</math:mo>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">P_n^m(x) = (-1)^m cdot (1-x^2)^{m/2} cdot {d^m over dx^m}P_n(x)</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
diff --git a/scilab/modules/special_functions/help/mml/legendre_equation2.mml b/scilab/modules/special_functions/help/mml/legendre_equation2.mml
deleted file mode 100644 (file)
index 8ce2da5..0000000
+++ /dev/null
@@ -1,113 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:msubsup>
-    <math:mi>P</math:mi>
-    <math:mi>n</math:mi>
-    <math:mi>m</math:mi>
-   </math:msubsup>
-   <math:mrow>
-    <math:mrow>
-     <math:mo math:stretchy="false">(</math:mo>
-     <math:mrow>
-      <math:mi>x</math:mi>
-      <math:mi>,</math:mi>
-      <math:mtext>norm</math:mtext>
-     </math:mrow>
-     <math:mo math:stretchy="false">)</math:mo>
-    </math:mrow>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mrow>
-     <math:mrow>
-      <math:msqrt>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mfrac>
-          <math:mrow>
-           <math:mn>2n</math:mn>
-           <math:mo math:stretchy="false">+</math:mo>
-           <math:mn>1</math:mn>
-          </math:mrow>
-          <math:mn>2</math:mn>
-         </math:mfrac>
-         <math:mo math:stretchy="false">⋅</math:mo>
-         <math:mfrac>
-          <math:mrow>
-           <math:mrow>
-            <math:mo math:stretchy="false">(</math:mo>
-            <math:mrow>
-             <math:mi>n</math:mi>
-             <math:mo math:stretchy="false">−</math:mo>
-             <math:mi>m</math:mi>
-            </math:mrow>
-            <math:mo math:stretchy="false">)</math:mo>
-           </math:mrow>
-           <math:mi>!</math:mi>
-          </math:mrow>
-          <math:mrow>
-           <math:mrow>
-            <math:mo math:stretchy="false">(</math:mo>
-            <math:mrow>
-             <math:mi>n</math:mi>
-             <math:mo math:stretchy="false">+</math:mo>
-             <math:mi>m</math:mi>
-            </math:mrow>
-            <math:mo math:stretchy="false">)</math:mo>
-           </math:mrow>
-           <math:mi>!</math:mi>
-          </math:mrow>
-         </math:mfrac>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-      </math:msqrt>
-      <math:mo math:stretchy="false">⋅</math:mo>
-      <math:msup>
-       <math:mrow>
-        <math:mo math:stretchy="false">(</math:mo>
-        <math:mrow>
-         <math:mn>1</math:mn>
-         <math:mo math:stretchy="false">−</math:mo>
-         <math:msup>
-          <math:mi>x</math:mi>
-          <math:mn>2</math:mn>
-         </math:msup>
-        </math:mrow>
-        <math:mo math:stretchy="false">)</math:mo>
-       </math:mrow>
-       <math:mrow>
-        <math:mi>m</math:mi>
-        <math:mo math:stretchy="false">/</math:mo>
-        <math:mn>2</math:mn>
-       </math:mrow>
-      </math:msup>
-     </math:mrow>
-     <math:mo math:stretchy="false">⋅</math:mo>
-     <math:mfrac>
-      <math:msup>
-       <math:mi>d</math:mi>
-       <math:mi>m</math:mi>
-      </math:msup>
-      <math:msup>
-       <math:mi math:fontstyle="italic">dx</math:mi>
-       <math:mi>m</math:mi>
-      </math:msup>
-     </math:mfrac>
-    </math:mrow>
-   </math:mrow>
-   <math:msub>
-    <math:mi>P</math:mi>
-    <math:mi>n</math:mi>
-   </math:msub>
-   <math:mrow>
-    <math:mo math:stretchy="false">(</math:mo>
-    <math:mi>x</math:mi>
-    <math:mo math:stretchy="false">)</math:mo>
-   </math:mrow>
-  </math:mrow>
-  <math:annotation math:encoding="StarMath 5.0">P_n^m(x,&quot;norm&quot;) = {sqrt({{2n+1} over {2}} cdot {{(n-m)!} over {(n+m)!}})} cdot (1-x^2)^{m/2} cdot {d^m over dx^m}P_n(x)</math:annotation>
- </math:semantics>
-</math:math>
\ No newline at end of file
index fb4e013..8ba8c93 100644 (file)
     <refsection>
         <title>Descrição</title>
         <para>Computa a função beta completa : </para>
-        <programlisting role=""><![CDATA[
-               /1
-               |   x-1     y-1        gamma(x) gamma(y)
-  beta(x,y) =  |  t   (1-t)    dt  =  ----------------
-               /0                        gamma(x+y)
- ]]></programlisting>
+        <para>
+            <latex style="display" fontsize="18" alt="B(x,y)=∫_0→1 t^{x-1}.(1-t)^{y-1} dt = Γ(x).Γ(y)/ Γ(x+y)">
+                B(x,y)=\int_0^1\!t^{x-1}\left(1-t\right)^{y-1}dt=\frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)}
+            </latex>
+        </para>
         <para>
             Para <literal>x</literal> e <literal>y</literal> pequenos, o
             algoritmo usa a expressão em função da função gama, de outro modo, ele
index a4a142b..a8a8fa1 100644 (file)
             <literal>x</literal> a derivada logarítmica da função gama (gamma), que
             corresponde também à derivada da função ln(gama) (gammaln):
         </para>
-        <programlisting role=""><![CDATA[
-d/dx (gamma(x)) / gamma(x) = d/dx (ln gamma(x))
- ]]></programlisting>
+        <para>
+            <latex style="display" alt="d(ln(Γ(x))/dx = dΓ(x)/dx . 1/Γ(x)">
+                \frac{d\,\ln\left(\Gamma(x)\right)}{dx}=\frac{d\Gamma(x)}{dx\,\Gamma(x)}
+            </latex>
+        </para>
         <para>
             <literal>x</literal> deve ser real. Também é conhecida como a função
             psi.
diff --git a/scilab/modules/special_functions/help/pt_BR/gamma.xml b/scilab/modules/special_functions/help/pt_BR/gamma.xml
new file mode 100644 (file)
index 0000000..04b09a5
--- /dev/null
@@ -0,0 +1,117 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ *
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="gamma" xml:lang="pt">
+    <refnamediv>
+        <refname>gamma</refname>
+        <refpurpose>função gama </refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Seqüência de Chamamento</title>
+        <synopsis>y = gamma(x)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Parâmetros</title>
+        <variablelist>
+            <varlistentry>
+                <term>x</term>
+                <listitem>
+                    <para>
+                       scalar, vector, matrix, or hypermatrix of real numbers.
+                    </para>
+                    <note>
+                      <literal>gamma</literal> can be overloaded for complex numbers or
+                      of lists, tlists or mlists.
+                    </note>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>y</term>
+                <listitem>
+                    <para>vetor ou matriz de reais ou complexos de mesmo tamanho que
+                        x
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Descrição</title>
+        <para>
+            <literal>gamma(x)</literal> avalia a função gama em todos os
+            elementos de <literal>x</literal>. A função gama é defininda por :
+        </para>
+        <para>
+            <latex style="display" fontsize="18" alt="Γ(x)= ∫_0→∞ t^{x-1}.exp(-t).dt">
+                \Gamma(x)=\int_0^\infty\! t^{x-1}e^{-t}\,dt
+            </latex>
+        </para>
+        <para>e generaliza a função fatorial para os números reais
+            (<literal>gamma(u+1) = u*gamma(u)</literal>).
+        </para>
+    </refsection>
+    <refsection>
+        <title>Exemplos</title>
+        <programlisting role="example"><![CDATA[
+// exemplos simples
+gamma(0.5)
+gamma(6)-prod(1:5)
+
+// o gráfico da função gama em [a,b]
+a = -3; b = 5;
+x = linspace(a,b,40000);
+y = gamma(x);
+clf()
+plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10])
+xtitle("A função gama em  ["+string(a)+","+string(b)+"]")
+show_window() ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>Ver Também</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="gammaln">gammaln</link>
+            </member>
+            <member>
+                <link linkend="dlgamma">dlgamma</link>
+            </member>
+            <member>
+                <link linkend="factorial">factorial</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>Histórico</title>
+        <revhistory>
+            <revision>
+                <revnumber>5.4.0</revnumber>
+                <revremark>Overloading allowed for list, mlist, tlist and hypermatrix types.</revremark>
+            </revision>
+            <revision>
+              <revnumber>6.0.2</revnumber>
+              <revremark>
+                <itemizedlist>
+                  <listitem>
+                    The input can now be an hypermatrix.
+                  </listitem>
+                  <listitem>
+                    <literal>gamma</literal> can now be overloaded for complex numbers.
+                  </listitem>
+                </itemizedlist>
+              </revremark>
+            </revision>
+        </revhistory>
+    </refsection>
+</refentry>
index 9c42be0..d22ea43 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="legendre" xml:lang="pt">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="legendre" xml:lang="pt">
     <refnamediv>
         <refname>legendre</refname>
         <refpurpose>funções associadas de Legendre</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Seqüência de Chamamento</title>
-        <synopsis>y = legendre(n,m,x [,normflag])</synopsis>
+        <synopsis>
+            y = legendre(n, m, x)
+            y = legendre(n, m, x, normflag)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Parâmetros</title>
         <para>
             Quando <literal>n</literal> e <literal>m</literal> são escalares,
             <literal>legendre(n,m,x)</literal> avalia a função de Legendre associada
-            Pnm(x) em todos os elementos de <literal>x</literal>. A definição usada é
-            :
+            Pnm(x) em todos os elementos de <literal>x</literal>. A definição usada é :
+        </para>
+        <para>
+            <latex style="display" fontsize="18" alt="Pn|m(x)=(-1)^m.(1-x^2)^{m/2}.d^m[Pn(x)]/dx^m">
+                P_n^m(x)=(-1)^m\cdot(1-x^2)^{m/2}\cdot\frac{d^mP_n(x)}{dx^m}
+            </latex>
         </para>
-        <programlisting role=""><![CDATA[
-                            m
-             m        m/2  d
-Pnm(x) = (-1)  (1-x^2)    --- Pn(x)
-                            m
-                          dx
- ]]></programlisting>
         <para>
             onde <literal>Pn</literal> é o polinômio de Legendre de grau
             <literal>n</literal>. Então, <literal>legendre(n,0,x)</literal> avalia o
@@ -82,13 +85,12 @@ Pnm(x) = (-1)  (1-x^2)    --- Pn(x)
         <para>Quando normflag é igual a "norm" o resultado é uma versão
             normalizada (sem o fator <literal>(-1)^m</literal> ), precisamente :
         </para>
-        <programlisting role=""><![CDATA[
-                   _____________                m
-                  /(2n+1)(n-m)!          m/2   d
-Pnm(x,"norm") =  /--------------  (1-x^2)     --- Pn(x)
-               \/     2  (n+m)!                 m
-                                              dx
- ]]></programlisting>
+        <para>
+            <latex style="display" fontsize="18"
+                   alt="Pn|m(x,norm)=sqrt[(2n+1)/2 .(n-m)!/(n+m)!].(1-x^2)^{m/2}.d^m[Pn(x)]/dx^m">
+                P_n^m(x,norm)=\sqrt{\frac{2n+1}{2}\frac{(n-m)!}{(n+m)!}}\cdot(1-x^2)^{m/2}\cdot\frac{d^mP_n(x)}{dx^m}
+            </latex>
+        </para>
         <para>que é útil para computar funções harmônicas esféricas (ver exemplo
             3):
         </para>
index 58ddbae..d15d2bd 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="binomial" xml:lang="en">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="binomial" xml:lang="en">
     <refnamediv>
         <refname>binomial</refname>
         <refpurpose>binomial distribution probabilities</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>pr=binomial(p,n)</synopsis>
+        <synopsis>pr = binomial(p, n)</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
             random variable following the B(n,p) distribution, and numerically
             :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../../mml/binomial_equation_1_en_US.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" alt="pr(k+1) = p^k (1-p)^(n-k) n!/[k!(n-k)!]">
+                pr(k+1)=\left(\frac{n!}{k!\,(n-k)!}\right)\,p^k\,(1-p)^{n-k}
+            </latex>
+        </para>
     </refsection>
     <refsection>
         <title>Examples</title>
index 05d37b1..4ea5559 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="binomial" xml:lang="ja">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="binomial" xml:lang="ja">
     <refnamediv>
         <refname>binomial</refname>
         <refpurpose>2項分布確率</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>呼び出し手順</title>
-        <synopsis>pr=binomial(p,n)</synopsis>
+        <synopsis>pr = binomial(p, n)</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>パラメータ</title>
             <literal>pr(k+1) = probability(X=k)</literal>で,
             数値的には以下のようになります :
         </para>
-        <informalequation>
-            <mediaobject>
-                <imageobject>
-                    <imagedata align="center" fileref="../../mml/binomial_equation_1_en_US.mml"/>
-                </imageobject>
-            </mediaobject>
-        </informalequation>
+        <para>
+            <latex style="display" alt="pr(k+1) = p^k (1-p)^(n-k) n!/[k!(n-k)!]">
+                pr(k+1)=\left(\frac{n!}{k!\,(n-k)!}\right)\,p^k\,(1-p)^{n-k}
+            </latex>
+        </para>
     </refsection>
     <refsection>
         <title>例</title>
diff --git a/scilab/modules/statistics/help/mml/binomial_equation_1_en_US.mml b/scilab/modules/statistics/help/mml/binomial_equation_1_en_US.mml
deleted file mode 100644 (file)
index 3ec3380..0000000
+++ /dev/null
@@ -1,95 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
-<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
- <math:semantics>
-  <math:mrow>
-   <math:mi math:fontstyle="italic">pr</math:mi>
-   <math:mrow>
-    <math:mrow>
-     <math:mo math:stretchy="false">(</math:mo>
-     <math:mrow>
-      <math:mi>k</math:mi>
-      <math:mo math:stretchy="false">+</math:mo>
-      <math:mn>1</math:mn>
-     </math:mrow>
-     <math:mo math:stretchy="false">)</math:mo>
-    </math:mrow>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mrow>
-     <math:mrow>
-      <math:mfenced math:open="" math:close="">
-       <math:mtable>
-        <math:mtr>
-         <math:mi>n</math:mi>
-        </math:mtr>
-        <math:mtr>
-         <math:mi>k</math:mi>
-        </math:mtr>
-       </math:mtable>
-      </math:mfenced>
-      <math:mo math:stretchy="false">⋅</math:mo>
-      <math:msup>
-       <math:mi>p</math:mi>
-       <math:mi>k</math:mi>
-      </math:msup>
-     </math:mrow>
-     <math:mo math:stretchy="false">⋅</math:mo>
-     <math:msup>
-      <math:mrow>
-       <math:mo math:stretchy="false">(</math:mo>
-       <math:mrow>
-        <math:mn>1</math:mn>
-        <math:mo math:stretchy="false">−</math:mo>
-        <math:mi>p</math:mi>
-       </math:mrow>
-       <math:mo math:stretchy="false">)</math:mo>
-      </math:mrow>
-      <math:mrow>
-       <math:mi>n</math:mi>
-       <math:mo math:stretchy="false">−</math:mo>
-       <math:mi>k</math:mi>
-      </math:mrow>
-     </math:msup>
-    </math:mrow>
-   </math:mrow>
-   <math:mtext> with </math:mtext>
-   <math:mrow>
-    <math:mfenced math:open="" math:close="">
-     <math:mtable>
-      <math:mtr>
-       <math:mi>n</math:mi>
-      </math:mtr>
-      <math:mtr>
-       <math:mi>k</math:mi>
-      </math:mtr>
-     </math:mtable>
-    </math:mfenced>
-    <math:mo math:stretchy="false">=</math:mo>
-    <math:mfrac>
-     <math:mrow>
-      <math:mi>n</math:mi>