Elementary function: move ndgrid to the right place after 6ad9efdc 30/17830/3
Clément DAVID [Mon, 29 Feb 2016 17:02:38 +0000 (18:02 +0100)]
Change-Id: I17c3cf3e86c29520d5d4805fbb05c83c76dad9b9

scilab/modules/elementary_functions/help/en_US/elementarymatrices/ndgrid.xml
scilab/modules/elementary_functions/help/en_US/ndgrid.xml [deleted file]
scilab/modules/elementary_functions/help/fr_FR/elementarymatrices/ndgrid.xml [new file with mode: 0644]
scilab/modules/elementary_functions/help/fr_FR/ndgrid.xml [deleted file]
scilab/modules/elementary_functions/help/ja_JP/elementarymatrices/ndgrid.xml
scilab/modules/elementary_functions/help/ja_JP/ndgrid.xml [deleted file]
scilab/modules/elementary_functions/help/pt_BR/elementarymatrices/ndgrid.xml
scilab/modules/elementary_functions/help/pt_BR/ndgrid.xml [deleted file]
scilab/modules/elementary_functions/help/ru_RU/elementarymatrices/ndgrid.xml

index 17de745..a0ecee4 100644 (file)
 <?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="ndgrid" xml:lang="en">
+    
     <refnamediv>
+        
         <refname>ndgrid</refname>
-        <refpurpose>arrays for multidimensional function evaluation on
-            grid
+        
+        <refpurpose>build matrices or N-D arrays by replicating some template vectors
+            
         </refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>Calling Sequence</title>
+        
         <synopsis>[X, Y] = ndgrid(x,y)
+            
             [X, Y, Z] = ndgrid(x,y,z)
+            
             [X, Y, Z, T] = ndgrid(x,y,z,t)
+            
             [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
+            
         </synopsis>
+        
     </refsynopsisdiv>
-    <refsection>
+    
+    <refsection role="arguments">
+        
         <title>Arguments</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>x, y, z, ...</term>
+                
                 <listitem>
-                    <para>vectors</para>
+                    
+                    <para>vectors of any data types. They may have distinct data types.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>X, Y, Z, ...</term>
+                
                 <listitem>
-                    <para>matrices in case of 2 input arguments, or else
-                        hypermatrices
+                    
+                    <para>matrices in case of 2 input arguments, or hypermatrices otherwise.
+                        
+                        They all have the same sizes: size(X,"*") rows, size(Y,"*") columns, 
+                        
+                        size(Z,"*") layers, etc. 
+                        
+                        They have the datatypes of respective input vectors:
+                        
+                        <literal>typeof(X)==typeof(x)</literal>, 
+                        
+                        <literal>typeof(Y)==typeof(y)</literal>, etc.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
-    <refsection>
+    
+    <refsection role="description">
+        
         <title>Description</title>
-        <para>This is an utility routine useful to create arrays for function
-            evaluation on 2, 3, ..., n dimensional grids. For instance in 2d, a grid
-            is defined by two vectors, <literal>x</literal> and <literal> y</literal>
-            of length nx and ny, and you want to evaluate a function (says
-            <emphasis>f</emphasis>) on all the grid points, that is on all the points
-            of coordinates <emphasis>(x(i),y(j))</emphasis> with
-            <emphasis>i=1,..,nx</emphasis> and <emphasis>j=1,..,ny</emphasis>. In this
-            case, this function can compute the two matrices <literal>X,Y</literal> of
-            size <emphasis>nx x ny</emphasis> such that :
+        
+        <para>
+            The first application of <function>ndgrid</function> is to build
+            
+            a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3,
+            
+            or more sets
+            
+            <literal>x</literal>, <literal> y</literal>, etc.. of  
+            
+            "template" coordinates sampled along each direction/dimension of the
+            
+            space that you want to mesh.
+            
         </para>
-        <programlisting role="no-scilab-exec"><![CDATA[ 
-X(i,j) = x(i)   for all i in [1,nx]
-Y(i,j) = y(j)       and j in [1,ny]
- ]]></programlisting>
+        
         <para>
-            and the evaluation may be done with <literal>Z=f(X,Y)</literal> (at
-            the condition that you have coded <literal>f</literal> for evaluation on
-            vector arguments, which is done (in general) by using the element-wise
-            operators <literal>.*</literal>, <literal>./</literal> and
-            <literal>.^</literal> in place of <literal>*</literal>,
-            <literal>/</literal> and <literal>^</literal>).
+            Hence, the matrix or hypermatrix <literal>X</literal> is made
+            
+            by replicating the vector <literal>x</literal> as all its columns ; 
+            
+            the matrix or hypermatrix <literal>Y</literal> is made
+            
+            by replicating the vector <literal>y</literal> as all its rows ;
+            
+            <literal>Z</literal> is made of replicating the vector 
+            
+            <literal>z</literal> along all its local thicknesses (3rd dimension); 
+            
+            etc
+            
         </para>
+        
+        <screen>
+            
+            <![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])\r
+ X  = \r
+   1.   1.   1.   1.\r
+   3.   3.   3.   3.\r
+   4.   4.   4.   4.\r
+\r
+   Y  = \r
+   0.   2.   4.   6.\r
+   0.   2.   4.   6.\r
+   0.   2.   4.   6.\r
+]]>
+        </screen>
+        
+        <para>  
+            
+            Then, the coordinates of the node(i,j) in the 2D space 
+            
+            will be
+            
+            simply <literal>[x(i), y(j)]</literal> now given by
+            
+            <literal>[X(i,j), Y(i,j)]</literal>. As well, the coordinates of a
+            
+            <literal>node(i,j,k)</literal> of a 3D grid will be 
+            
+            <literal>[x(i), y(j), z(k)]</literal> now given by 
+            
+            <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.
+            
+        </para>
+        
         <para>
-            In the 3d case, considering 3 vectors <literal>x,y,z</literal> of
-            length nx, ny and nz, <literal>X,Y,Z</literal> are 3 hypermatrices of size
-            <emphasis>nx x ny x nz</emphasis> such that :
+            
+            This replication scheme can be generalized to any number of dimensions,
+            
+            as well to any type of uniform data. Let's for instance consider 2
+            
+            attributes:
+            
+            <orderedlist>
+                
+                <listitem>The first is a number, to be chosen from the vector say
+                    
+                    <literal>n = [ 3 7 ]</literal>
+                    
+                </listitem>
+                
+                <listitem>The second is a letter, to be chosen from the vector 
+                    
+                    say <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>
+                    
+                </listitem>
+                
+            </orderedlist>
+            
+            Then we want to build the set of all {n,c} possible pairs. It will
+            
+            just be the 2D grid:
+            
         </para>
-        <programlisting role="no-scilab-exec"><![CDATA[ 
-X(i,j,k) = x(i)  
-Y(i,j,k) = y(j)   for all (i,j,k) in [1,nx]x[1,ny]x[1,nz]
-Z(i,j,k) = z(k)
- ]]></programlisting>
+        
+        <screen>
+            
+            <![CDATA[--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"])\r
+ C  = \r
+!a  e  i  o  u  y  !\r
+!a  e  i  o  u  y  !\r
+\r
+ N  = \r
+   3.   3.   3.   3.   3.   3.\r
+   7.   7.   7.   7.   7.   7.\r
+]]>
+        </screen>
+        
+        <para>Then, the object(i,j) will have the properties 
+            
+            <literal>{n(i) c(j)}</literal> that now can be addressed with
+            
+            <literal>{N(i,j) C(i,j)}</literal>.
+            
+            This kind of grid may be useful to initialize an array of structures.
+            
+        </para>
+        
         <para>
-            In the general case of m input arguments <literal>x1, x2, ..,
-                xm
-            </literal>
-            ,then the m output arguments <literal>X1, X2, ..,
-                Xm
-            </literal>
-            are hypermatrices of size <emphasis>nx1 x nx2 x ... x
-                nxm
-            </emphasis>
-            and :
+            Following examples show how to use <varname>X, Y, Z</varname> in
+            
+            most frequent applications.
+            
         </para>
-        <programlisting role="no-scilab-exec"><![CDATA[ 
-Xj(i1,i2,...,ij,...,im) = xj(ij)   
-for all (i1,i2,...,im) in [1,nx1]x[1,nx2]x...x[1,nxm]  
- ]]></programlisting>
+         
+        
     </refsection>
-    <refsection>
+    
+    <refsection role="examples">
+        
         <title>Examples</title>
-        <programlisting role="example"><![CDATA[  
-// create a simple 2d grid
-nx = 40; ny = 40;
-x = linspace(-1,1,nx);
-y = linspace(-1,1,ny);
-[X,Y] = ndgrid(x,y);
-
-// compute a function on the grid and plot it
-//deff("z=f(x,y)","z=128*x.^2 .*(1-x).^2 .*y.^2 .*(1-y).^2");
-deff("z=f(x,y)","z=x.^2 + y.^3")
-Z = f(X,Y);
-clf()
-plot3d(x,y,Z, flag=[2 6 4]); show_window()
+        
+        <para>
+            <emphasis role="bold">Example #1:</emphasis> 
+        </para>
+        
+        <programlisting role="example"><![CDATA[  \r
+// Create a simple 2d grid\r
+x = linspace(-10,2,40);\r
+y = linspace(-5,5,40);\r
+[X,Y] = ndgrid(x,y);\r
+\r
+// Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y)\r
+Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
+clf()\r
+plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
  ]]></programlisting>
+        
         <scilab:image>
-            nx = 40; ny = 40;
-            x = linspace(-1,1,nx);
-            y = linspace(-1,1,ny);
+            
+            x = linspace(-10,2,40);
+            
+            y = linspace(-5,5,40);
+            
             [X,Y] = ndgrid(x,y);
-            deff("z=f(x,y)","z=x.^2 + y.^3")
-            Z = f(X,Y);
-            plot3d(x,y,Z, flag=[2 6 4]);
+            
+            Z = X - 3*X.*sin(X).*cos(Y-4) ;
+            
+            clf()
+            
+            plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
+            
         </scilab:image>
-        <programlisting role="example"><![CDATA[  
-// create a simple 3d grid
-nx = 10; ny = 6; nz = 4;
-x = linspace(0,2,nx);
-y = linspace(0,1,ny);
-z = linspace(0,0.5,nz);
-[X,Y,Z] = ndgrid(x,y,z);
-
-// try to display this 3d grid ...
-XF=[]; YF=[]; ZF=[];
-
-for k=1:nz
-   [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
-end
-
-for j=1:ny
-   [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
-                     matrix(Y(:,j,:),[nx,nz]),...
-                     matrix(Z(:,j,:),[nx,nz]));
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
-end
-
-clf()
-plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
-xtitle("A 3d grid !"); show_window()
+        
+        <para>
+            <emphasis role="bold">Example #2:</emphasis> 
+        </para>
+        
+        <programlisting role="example"><![CDATA[  \r
+// Create a simple 3d grid\r
+nx = 10; ny = 6; nz = 4;\r
+x = linspace(0,2,nx);\r
+y = linspace(0,1,ny);\r
+z = linspace(0,0.5,nz);\r
+[X,Y,Z] = ndgrid(x,y,z);\r
+\r
+// Try to display this 3d grid ...\r
+XF=[]; YF=[]; ZF=[];\r
+\r
+for k=1:nz\r
+   [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
+   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
+end\r
+\r
+for j=1:ny\r
+   [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
+                     matrix(Y(:,j,:),[nx,nz]),...\r
+                     matrix(Z(:,j,:),[nx,nz]));\r
+   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
+end\r
+\r
+clf()\r
+plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61,leg="X@Y@Z")\r
+xtitle("A 3d grid !"); show_window()\r
  ]]></programlisting>
+        
         <scilab:image>
+            
             nx = 10; ny = 6; nz = 4;
+            
             x = linspace(0,2,nx);
+            
             y = linspace(0,1,ny);
+            
             z = linspace(0,0.5,nz);
+            
             [X,Y,Z] = ndgrid(x,y,z);
             
+            
+            
             XF=[]; YF=[]; ZF=[];
             
+            
+            
             for k=1:nz
+            
             [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
+            
             XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+            
             end
             
+            
+            
             for j=1:ny
+            
             [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
+            
             matrix(Y(:,j,:),[nx,nz]),...
+            
             matrix(Z(:,j,:),[nx,nz]));
+            
             XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+            
             end
-            plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
+            
+            plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
+            
             xtitle("A 3d grid !"); 
+            
         </scilab:image>
+        
+        
+        
+        <para>
+            <emphasis role="bold">Example #3: Creates a table of digrams:</emphasis> 
+        </para>
+        
+        <programlisting role="example"><![CDATA[  \r
+[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
+c1+c2\r
+ ]]></programlisting>
+        
+        <screen>
+            
+            <![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
+ c2  = \r
+!a  b  c  d  e  f  g  h  !\r
+!a  b  c  d  e  f  g  h  !\r
+!a  b  c  d  e  f  g  h  !\r
+\r
+ c1  = \r
+!a  a  a  a  a  a  a  a  !\r
+!b  b  b  b  b  b  b  b  !\r
+!c  c  c  c  c  c  c  c  !\r
+\r
+--> c1+c2\r
+ ans  =\r
+!aa  ab  ac  ad  ae  af  ag  ah  !\r
+!ba  bb  bc  bd  be  bf  bg  bh  !\r
+!ca  cb  cc  cd  ce  cf  cg  ch  !\r
+]]>
+        </screen>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>See Also</title>
+        
         <simplelist type="inline">
+            
+            <member>
+                
+                <link linkend="meshgrid">meshgrid</link>
+                
+            </member>
+            
             <member>
+                
                 <link linkend="kron">kron</link>
+                
             </member>
+            
+            <member>
+                
+                <link linkend="feval">feval</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="eval3d">eval3d</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="nf3d">nf3d</link>
+                
+            </member>
+            
         </simplelist>
+        
     </refsection>
+    
+    <refsection role="history">
+        
+        <title>History</title>
+        
+        <revhistory>
+            
+            <revision>
+                
+                <revnumber>6.0</revnumber>
+                
+                <revdescription>Extension to all homogeneous datatypes ([], 
+                    
+                    booleans, encoded integers, polynomials, rationals, strings). 
+                    
+                    Revision of the help page.
+                    
+                </revdescription>
+                
+            </revision>
+            
+        </revhistory>
+        
+    </refsection>
+    
 </refentry>
+
diff --git a/scilab/modules/elementary_functions/help/en_US/ndgrid.xml b/scilab/modules/elementary_functions/help/en_US/ndgrid.xml
deleted file mode 100644 (file)
index ae8e5e2..0000000
+++ /dev/null
@@ -1,241 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>\r
-<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="ndgrid" xml:lang="en">\r
-    <refnamediv>\r
-        <refname>ndgrid</refname>\r
-        <refpurpose>build matrices or N-D arrays by replicating some template vectors\r
-        </refpurpose>\r
-    </refnamediv>\r
-    <refsynopsisdiv>\r
-        <title>Calling Sequence</title>\r
-        <synopsis>[X, Y] = ndgrid(x,y)\r
-            [X, Y, Z] = ndgrid(x,y,z)\r
-            [X, Y, Z, T] = ndgrid(x,y,z,t)\r
-            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)\r
-        </synopsis>\r
-    </refsynopsisdiv>\r
-    <refsection role="arguments">\r
-        <title>Arguments</title>\r
-        <variablelist>\r
-            <varlistentry>\r
-                <term>x, y, z, ...</term>\r
-                <listitem>\r
-                    <para>vectors of any data types. They may have distinct data types.</para>\r
-                </listitem>\r
-            </varlistentry>\r
-            <varlistentry>\r
-                <term>X, Y, Z, ...</term>\r
-                <listitem>\r
-                    <para>matrices in case of 2 input arguments, or hypermatrices otherwise.\r
-                    They all have the same sizes: size(X,"*") rows, size(Y,"*") columns, \r
-                        size(Z,"*") layers, etc. \r
-                        They have the datatypes of respective input vectors:\r
-                        <literal>typeof(X)==typeof(x)</literal>, \r
-                        <literal>typeof(Y)==typeof(y)</literal>, etc.\r
-                    </para>\r
-                </listitem>\r
-            </varlistentry>\r
-        </variablelist>\r
-    </refsection>\r
-    <refsection role="description">\r
-        <title>Description</title>\r
-        <para>The first application of <function>ndgrid</function> is to build\r
-            a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3,\r
-            or more sets\r
-            <literal>x</literal>, <literal> y</literal>, etc.. of  \r
-            "template" coordinates sampled along each direction/dimension of the\r
-            space that you want to mesh.\r
-        </para>\r
-        <para>Hence, the matrix or hypermatrix <literal>X</literal> is made\r
-            by replicating the vector <literal>x</literal> as all its columns ; \r
-            the matrix or hypermatrix <literal>Y</literal> is made\r
-            by replicating the vector <literal>y</literal> as all its rows ;\r
-            <literal>Z</literal> is made of replicating the vector \r
-            <literal>z</literal> along all its local thicknesses (3rd dimension); \r
-            etc\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])\r
- X  = \r
-   1.   1.   1.   1.\r
-   3.   3.   3.   3.\r
-   4.   4.   4.   4.\r
-\r
-   Y  = \r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-]]></screen>\r
-        <para>  \r
-            Then, the coordinates of the node(i,j) in the 2D space \r
-            will be\r
-            simply <literal>[x(i), y(j)]</literal> now given by\r
-            <literal>[X(i,j), Y(i,j)]</literal>. As well, the coordinates of a\r
-            <literal>node(i,j,k)</literal> of a 3D grid will be \r
-            <literal>[x(i), y(j), z(k)]</literal> now given by \r
-            <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.\r
-        </para>\r
-        <para>\r
-            This replication scheme can be generalized to any number of dimensions,\r
-            as well to any type of uniform data. Let's for instance consider 2\r
-            attributes:\r
-            <orderedlist>\r
-                <listitem>The first is a number, to be chosen from the vector say\r
-                <literal>n = [ 3 7 ]</literal>\r
-                </listitem>\r
-                <listitem>The second is a letter, to be chosen from the vector \r
-                say <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>\r
-                </listitem>\r
-            </orderedlist>\r
-            Then we want to build the set of all {n,c} possible pairs. It will\r
-            just be the 2D grid:\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"])\r
- C  = \r
-!a  e  i  o  u  y  !\r
-!a  e  i  o  u  y  !\r
-\r
- N  = \r
-   3.   3.   3.   3.   3.   3.\r
-   7.   7.   7.   7.   7.   7.\r
-]]></screen>\r
-        <para>Then, the object(i,j) will have the properties \r
-        <literal>{n(i) c(j)}</literal> that now can be addressed with\r
-        <literal>{N(i,j) C(i,j)}</literal>.\r
-        This kind of grid may be useful to initialize an array of structures.\r
-        </para>\r
-        <para>Following examples show how to use <varname>X, Y, Z</varname> in\r
-        most frequent applications.\r
-        </para> \r
-    </refsection>\r
-    <refsection role="examples">\r
-        <title>Examples</title>\r
-        <para><emphasis role="bold">Example #1:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-// Create a simple 2d grid\r
-x = linspace(-10,2,40);\r
-y = linspace(-5,5,40);\r
-[X,Y] = ndgrid(x,y);\r
-\r
-// Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y)\r
-Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-clf()\r
-plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
- ]]></programlisting>\r
-        <scilab:image>\r
-        x = linspace(-10,2,40);\r
-        y = linspace(-5,5,40);\r
-        [X,Y] = ndgrid(x,y);\r
-        Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-        clf()\r
-        plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
-        </scilab:image>\r
-        <para><emphasis role="bold">Example #2:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-// Create a simple 3d grid\r
-nx = 10; ny = 6; nz = 4;\r
-x = linspace(0,2,nx);\r
-y = linspace(0,1,ny);\r
-z = linspace(0,0.5,nz);\r
-[X,Y,Z] = ndgrid(x,y,z);\r
-\r
-// Try to display this 3d grid ...\r
-XF=[]; YF=[]; ZF=[];\r
-\r
-for k=1:nz\r
-   [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-\r
-for j=1:ny\r
-   [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-                     matrix(Y(:,j,:),[nx,nz]),...\r
-                     matrix(Z(:,j,:),[nx,nz]));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-\r
-clf()\r
-plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61,leg="X@Y@Z")\r
-xtitle("A 3d grid !"); show_window()\r
- ]]></programlisting>\r
-        <scilab:image>\r
-            nx = 10; ny = 6; nz = 4;\r
-            x = linspace(0,2,nx);\r
-            y = linspace(0,1,ny);\r
-            z = linspace(0,0.5,nz);\r
-            [X,Y,Z] = ndgrid(x,y,z);\r
-            \r
-            XF=[]; YF=[]; ZF=[];\r
-            \r
-            for k=1:nz\r
-            [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            \r
-            for j=1:ny\r
-            [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-            matrix(Y(:,j,:),[nx,nz]),...\r
-            matrix(Z(:,j,:),[nx,nz]));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")\r
-            xtitle("A 3d grid !"); \r
-        </scilab:image>\r
-\r
-        <para><emphasis role="bold">Example #3: Creates a table of digrams:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
-c1+c2\r
- ]]></programlisting>\r
-    <screen>\r
-<![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
- c2  = \r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-\r
- c1  = \r
-!a  a  a  a  a  a  a  a  !\r
-!b  b  b  b  b  b  b  b  !\r
-!c  c  c  c  c  c  c  c  !\r
-\r
---> c1+c2\r
- ans  =\r
-!aa  ab  ac  ad  ae  af  ag  ah  !\r
-!ba  bb  bc  bd  be  bf  bg  bh  !\r
-!ca  cb  cc  cd  ce  cf  cg  ch  !\r
-]]></screen>\r
-    </refsection>\r
-    <refsection role="see also">\r
-        <title>See Also</title>\r
-        <simplelist type="inline">\r
-            <member>\r
-                <link linkend="meshgrid">meshgrid</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="kron">kron</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="feval">feval</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="eval3d">eval3d</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="nf3d">nf3d</link>\r
-            </member>\r
-        </simplelist>\r
-    </refsection>\r
-    <refsection role="history">\r
-        <title>History</title>\r
-        <revhistory>\r
-            <revision>\r
-                <revnumber>6.0</revnumber>\r
-                <revdescription>Extension to all homogeneous datatypes ([], \r
-                booleans, encoded integers, polynomials, rationals, strings). \r
-                Revision of the help page.\r
-                </revdescription>\r
-            </revision>\r
-        </revhistory>\r
-    </refsection>\r
-</refentry>\r
diff --git a/scilab/modules/elementary_functions/help/fr_FR/elementarymatrices/ndgrid.xml b/scilab/modules/elementary_functions/help/fr_FR/elementarymatrices/ndgrid.xml
new file mode 100644 (file)
index 0000000..a8da8da
--- /dev/null
@@ -0,0 +1,459 @@
+<?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="ndgrid" xml:lang="fr">
+    
+    <refnamediv>
+        
+        <refname>ndgrid</refname>
+        
+        <refpurpose>construit des matrices ou hypermatrices en répliquant des vecteurs
+            
+        </refpurpose>
+        
+    </refnamediv>
+    
+    <refsynopsisdiv>
+        
+        <title>Séquences d'appel</title>
+        
+        <synopsis>[X, Y] = ndgrid(x,y)
+            
+            [X, Y, Z] = ndgrid(x,y,z)
+            
+            [X, Y, Z, T] = ndgrid(x,y,z,t)
+            
+            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
+            
+        </synopsis>
+        
+    </refsynopsisdiv>
+    
+    <refsection role="arguments">
+        
+        <title>Paramètres</title>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>x, y, z, ...</term>
+                
+                <listitem>
+                    
+                    <para>vecteurs de types simples quelconques possiblement
+                        
+                        distincts (booléens,
+                        
+                        entiers encodés, décimaux, complexes, polynômes, rationnels,
+                        
+                        textes).
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>X, Y, Z, ...</term>
+                
+                <listitem>
+                    
+                    <para>Matrices (si seulement 2 vecteurs d'entrée),
+                        
+                        ou hypermatrices, toutes de tailles identiques :
+                       size(x,"*") lignes, size(y,"*") colonnes,
+                        
+                        size(z,"*") feuilles, etc.
+                  </para>
+                  <para>Par ailleurs,
+                        <varname>X</varname> a le type de <varname>x</varname>;
+                        
+                        <varname>Y</varname> a le type de <varname>y</varname>;
+                        
+                        etc.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+    </refsection>
+    
+    <refsection role="description">
+        
+        <title>Description</title>
+        
+        <para>
+            La première application de <function>ndgrid</function> consiste à
+            
+            construire une grille multidimensionnelle de noeuds échantillonnant
+            
+            l'espace 2D ou 3D ou N-D, à partir de 2, 3 ou N vecteurs
+            
+            <literal>x</literal>, <literal> y</literal>, etc.. indiquant
+            
+            l'échantillonage de chaque direction de l'espace.
+            
+        </para>
+        
+        <para>Pour ce faire,
+            
+            <itemizedlist>
+                
+                <listitem>la matrice ou l'hypermatrice <literal>X</literal>
+                
+                est construite en répliquant le vecteur  <literal>x</literal>
+                
+                dans toutes ses colonnes ;
+                
+            </listitem>
+             
+            
+            <listitem>
+                la matrice ou l'hypermatrice <literal>Y</literal>
+                
+                est construite en répliquant le vecteur  <literal>y</literal>
+                
+                dans toutes ses lignes ;
+                
+            </listitem>
+             
+            
+            <listitem>
+                la matrice ou l'hypermatrice <literal>Z</literal>
+                
+                est construite en répliquant le vecteur  <literal>z</literal>
+                
+                en épaisseur pour tous les points (x,y) ;
+                
+                etc.
+                
+            </listitem>
+            
+        </itemizedlist>
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])
+ X  =
+   1.   1.   1.   1.
+   3.   3.   3.   3.
+   4.   4.   4.   4.
+
+   Y  =
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+]]>
+    </screen>
+    
+    <para>
+        
+        Les coordonnées du noeud node(i,j) dans l'espace 2D seront alors
+        
+        simplement <literal>[x(i), y(j)]</literal> maintenant données par
+        
+        <literal>[X(i,j), Y(i,j)]</literal>. De même, les coordonnées du noeud
+        
+        <literal>node(i,j,k)</literal> dans une grille 3D seront
+        
+        <literal>[x(i), y(j), z(k)]</literal> données par
+        
+        <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.
+        
+    </para>
+    
+    <para>Ce schéma de construction par réplication peut être utilisé
+        
+        pour construire une grille à un nombre N quelconque de dimensions.
+        
+        Par ailleurs, il est indépendant de la nature des vecteurs de base répliqués
+        
+        et peut donc être utilisé pour tous les types de données uniformes.
+        
+        A titre d'exemple, considérons un ensemble d'objets ayant tous 2 attributs :
+        
+        <orderedlist>
+            
+            <listitem>
+                Le premier est un nombre <literal>n</literal>,
+                
+                avec 2 valeurs possibles, par exemple: <literal>n = [ 3 7 ]</literal>
+                
+            </listitem>
+            
+            <listitem>Le second est une lettre, avec 6 choix possibles,
+                
+                par exemple: <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>
+                
+            </listitem>
+            
+        </orderedlist>
+        
+        Nous souhaitons maintenant générer l'ensemble complet des
+        
+        objets {n,c} possibles. Il s'agit juste d'une grille 2D
+        
+        d'<literal>objets</literal> :
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])
+ X  =
+   1.   1.   1.   1.
+   3.   3.   3.   3.
+   4.   4.   4.   4.
+
+   Y  =
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+]]>
+    </screen>
+    
+    <para>De là, l'objet(i,j) aura les attributs
+        
+        <literal>{n(i) c(j)}</literal> que l'on pourra maintenant désigner par
+        
+        <literal>{N(i,j) C(i,j)}</literal>.
+        
+        Ce type de grille pourra être utilisée pour initialiser un tableau
+        
+        2D de structures ayant 2 champs <literal>n</literal> et <literal>c</literal>.
+        
+    </para>
+    
+    <para>Les exemples suivants montrent comment utiliser les matrices ou
+        
+        hypermatrices <varname>X, Y, Z</varname> produites, pour des applications
+        
+        usuelles.
+        
+    </para>
+     
+    
+</refsection>
+
+<refsection role="examples">
+    
+    <title>Exemples</title>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Exemple #1:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
+// Créons une grille de points {X,Y}
+x = linspace(-10,2,40);
+y = linspace(-5,5,40);
+[X,Y] = ndgrid(x,y); // x et y sont répliqués pour créer la grille
+
+// Calculons des ordonnées Z(X,Y) et traçons Z(X,Y) :
+Z = X - 3*X.*sin(X).*cos(Y-4) ;
+clf()
+plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
+ ]]></programlisting>
+    
+    <scilab:image>
+        
+        x = linspace(-10,2,40);
+        
+        y = linspace(-5,5,40);
+        
+        [X,Y] = ndgrid(x,y);
+        
+        Z = X - 3*X.*sin(X).*cos(Y-4) ;
+        
+        clf()
+        
+        plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
+        
+    </scilab:image>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Exemple #2:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
+// Créons une grille en 3 dimensions
+nx = 10; ny = 6; nz = 4;
+x = linspace(0,2,nx);
+y = linspace(0,1,ny);
+z = linspace(0,0.5,nz);
+[X,Y,Z] = ndgrid(x,y,z);
+
+// Nous choisissons ici une représentation cartésienne, mais l'on pourrait
+// aussi travailler en coordonnées cylindriques, sphériques, ou autres.
+// Transformons les coordonnées pour plot3d() :
+XF=[]; YF=[]; ZF=[];
+
+for k=1:nz
+   [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
+   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+end
+
+for j=1:ny
+   [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
+                     matrix(Y(:,j,:),[nx,nz]),...
+                     matrix(Z(:,j,:),[nx,nz]));
+   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+end
+
+// Affichage :
+clf()
+plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
+xtitle("A 3d grid !"); show_window()
+ ]]></programlisting>
+    
+    <scilab:image>
+        
+        nx = 10; ny = 6; nz = 4;
+        
+        x = linspace(0,2,nx);
+        
+        y = linspace(0,1,ny);
+        
+        z = linspace(0,0.5,nz);
+        
+        [X,Y,Z] = ndgrid(x,y,z);
+        
+        
+        
+        XF=[]; YF=[]; ZF=[];
+        
+        
+        
+        for k=1:nz
+        
+        [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        
+        
+        for j=1:ny
+        
+        [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
+        
+        matrix(Y(:,j,:),[nx,nz]),...
+        
+        matrix(Z(:,j,:),[nx,nz]));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
+        
+        xtitle("A 3d grid !");
+        
+    </scilab:image>
+    
+    <para>
+        <emphasis role="bold">Exemple #3: création d'une table de digrammes</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
+[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+c1+c2
+ ]]></programlisting>
+    
+    <screen>
+        
+        <![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+ c2  =
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+
+ c1  =
+!a  a  a  a  a  a  a  a  !
+!b  b  b  b  b  b  b  b  !
+!c  c  c  c  c  c  c  c  !
+
+--> c1+c2
+ ans  =
+!aa  ab  ac  ad  ae  af  ag  ah  !
+!ba  bb  bc  bd  be  bf  bg  bh  !
+!ca  cb  cc  cd  ce  cf  cg  ch  !
+]]>
+    </screen>
+    
+</refsection>
+
+<refsection role="see also">
+    
+    <title>Voir aussi</title>
+    
+    <simplelist type="inline">
+        
+        <member>
+            
+            <link linkend="meshgrid">meshgrid</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="kron">kron</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="feval">feval</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="eval3d">eval3d</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="nf3d">nf3d</link>
+            
+        </member>
+        
+    </simplelist>
+    
+</refsection>
+
+<refsection role="history">
+    
+    <title>Historique</title>
+    
+    <revhistory>
+        
+        <revision>
+            
+            <revnumber>6.0</revnumber>
+            
+            <revdescription>Extension à tous les types de données uniformes ([], booleans, encoded integers, polynomials, rationals, strings). Révision de la page d'aide.
+                
+            </revdescription>
+            
+        </revision>
+        
+    </revhistory>
+    
+</refsection>
+
+</refentry>
+
diff --git a/scilab/modules/elementary_functions/help/fr_FR/ndgrid.xml b/scilab/modules/elementary_functions/help/fr_FR/ndgrid.xml
deleted file mode 100644 (file)
index a689b2d..0000000
+++ /dev/null
@@ -1,259 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>\r
-<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="ndgrid" xml:lang="fr">\r
-    <refnamediv>\r
-        <refname>ndgrid</refname>\r
-        <refpurpose>construit des matrices ou hypermatrices en répliquant des vecteurs\r
-        </refpurpose>\r
-    </refnamediv>\r
-    <refsynopsisdiv>\r
-        <title>Séquences d'appel</title>\r
-        <synopsis>[X, Y] = ndgrid(x,y)\r
-            [X, Y, Z] = ndgrid(x,y,z)\r
-            [X, Y, Z, T] = ndgrid(x,y,z,t)\r
-            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)\r
-        </synopsis>\r
-    </refsynopsisdiv>\r
-    <refsection role="arguments">\r
-        <title>Paramètres</title>\r
-        <variablelist>\r
-            <varlistentry>\r
-                <term>x, y, z, ...</term>\r
-                <listitem>\r
-                    <para>vecteurs de types simples quelconques possiblement\r
-                    distincts (booléens, \r
-                    entiers encodés, décimaux, complexes, polynômes, rationnels,\r
-                    textes).</para>\r
-                </listitem>\r
-            </varlistentry>\r
-            <varlistentry>\r
-                <term>X, Y, Z, ...</term>\r
-                <listitem>\r
-                    <para>Matrices (si seulement 2 vecteurs d'entrée),\r
-                    ou hypermatrices avec autant de dimensions qu'il y a de \r
-                    vecteurs d'entrée <literal>x1, x2, ..., xn</literal>.\r
-                    <varname>X</varname> a le type de <varname>x</varname> ; \r
-                    <varname>Y</varname> a le type de <varname>y</varname> ; \r
-                    etc. \r
-                    </para>\r
-                </listitem>\r
-            </varlistentry>\r
-        </variablelist>\r
-    </refsection>\r
-    <refsection role="description">\r
-        <title>Description</title>\r
-        <para>La première application de <function>ndgrid</function> consiste à\r
-            construire une grille multidimensionnelle de noeuds échantillonnant\r
-            l'espace 2D ou 3D ou N-D, à partir de 2, 3 ou N vecteurs \r
-            <literal>x</literal>, <literal> y</literal>, etc.. indiquant \r
-            l'échantillonage de chaque direction de l'espace.\r
-        </para>\r
-        <para>Pour ce faire, \r
-            <itemizedlist>\r
-                <listitem></listitem>la matrice ou l'hypermatrice <literal>X</literal> \r
-                est construite en répliquant le vecteur  <literal>x</literal> \r
-                dans toutes ses colonnes ;\r
-                </listitem> \r
-                <listitem>la matrice ou l'hypermatrice <literal>Y</literal> \r
-                est construite en répliquant le vecteur  <literal>y</literal> \r
-                dans toutes ses lignes ;\r
-                </listitem> \r
-                <listitem>la matrice ou l'hypermatrice <literal>Z</literal> \r
-                est construite en répliquant le vecteur  <literal>z</literal> \r
-                en épaisseur pour tous les points (x,y) ; \r
-                etc.\r
-                </listitem>\r
-            </itemizedlist>\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])\r
- X  = \r
-   1.   1.   1.   1.\r
-   3.   3.   3.   3.\r
-   4.   4.   4.   4.\r
-\r
-   Y  = \r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-]]></screen>\r
-        <para>\r
-            Les coordonnées du noeud node(i,j) dans l'espace 2D seront alors \r
-            simplement <literal>[x(i), y(j)]</literal> maintenant données par\r
-            <literal>[X(i,j), Y(i,j)]</literal>. De même, les coordonnées du noeud\r
-            <literal>node(i,j,k)</literal> dans une grille 3D seront\r
-            <literal>[x(i), y(j), z(k)]</literal> données par\r
-            <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.\r
-        </para>\r
-        <para>Ce schéma de construction par réplication peut être utilisé\r
-        pour construire une grille à un nombre N quelconque de dimensions.\r
-        Par ailleurs, il est indépendant de la nature des vecteurs de base répliqués\r
-        et peut donc être utilisé pour tous les types de données uniformes.\r
-        A titre d'exemple, considérons un ensemble d'objets ayant tous 2 attributs :\r
-            <orderedlist>\r
-                <listitem>Le premier est un nombre <literal>n</literal>, \r
-                avec 2 valeurs possibles, par exemple: <literal>n = [ 3 7 ]</literal>\r
-                </listitem>\r
-                <listitem>Le second est une lettre, avec 6 choix possibles, \r
-                par exemple: <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>\r
-                </listitem>\r
-            </orderedlist>\r
-            Nous souhaitons maintenant générer l'ensemble complet des \r
-            objets {n,c} possibles. Il s'agit juste d'une grille 2D \r
-            d'<literal>objets</literal> :\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])\r
- X  = \r
-   1.   1.   1.   1.\r
-   3.   3.   3.   3.\r
-   4.   4.   4.   4.\r
-\r
-   Y  = \r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-]]></screen>\r
-        <para>De là, l'objet(i,j) aura les attributs\r
-        <literal>{n(i) c(j)}</literal> que l'on pourra maintenant désigner par \r
-        <literal>{N(i,j) C(i,j)}</literal>.\r
-        Ce type de grille pourra être utilisée pour initialiser un tableau \r
-        2D de structures ayant 2 champs <literal>n</literal> et <literal>c</literal>.\r
-        </para>\r
-        <para>Les exemples suivants montrent comment utiliser les matrices ou\r
-        hypermatrices <varname>X, Y, Z</varname> produites, pour des applications\r
-        usuelles.\r
-        </para> \r
-    </refsection>\r
-    <refsection role="examples">\r
-        <title>Exemples</title>\r
-\r
-        <para><emphasis role="bold">Exemple #1:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-// Créons une grille de points {X,Y}\r
-x = linspace(-10,2,40);\r
-y = linspace(-5,5,40);\r
-[X,Y] = ndgrid(x,y); // x et y sont répliqués pour créer la grille\r
-\r
-// Calculons des ordonnées Z(X,Y) et traçons Z(X,Y) :\r
-Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-clf()\r
-plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
- ]]></programlisting>\r
-        <scilab:image>\r
-            x = linspace(-10,2,40);\r
-            y = linspace(-5,5,40);\r
-            [X,Y] = ndgrid(x,y);\r
-            Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-            clf()\r
-            plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
-        </scilab:image>\r
-\r
-        <para><emphasis role="bold">Exemple #2:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-// Créons une grille en 3 dimensions\r
-nx = 10; ny = 6; nz = 4;\r
-x = linspace(0,2,nx);\r
-y = linspace(0,1,ny);\r
-z = linspace(0,0.5,nz);\r
-[X,Y,Z] = ndgrid(x,y,z);\r
-\r
-// Nous choisissons ici une représentation cartésienne, mais l'on pourrait\r
-// aussi travailler en coordonnées cylindriques, sphériques, ou autres. \r
-// Transformons les coordonnées pour plot3d() :\r
-XF=[]; YF=[]; ZF=[];\r
-\r
-for k=1:nz\r
-   [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-\r
-for j=1:ny\r
-   [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-                     matrix(Y(:,j,:),[nx,nz]),...\r
-                     matrix(Z(:,j,:),[nx,nz]));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-\r
-// Affichage :\r
-clf()\r
-plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")\r
-xtitle("A 3d grid !"); show_window()\r
- ]]></programlisting>\r
-        <scilab:image>\r
-            nx = 10; ny = 6; nz = 4;\r
-            x = linspace(0,2,nx);\r
-            y = linspace(0,1,ny);\r
-            z = linspace(0,0.5,nz);\r
-            [X,Y,Z] = ndgrid(x,y,z);\r
-            \r
-            XF=[]; YF=[]; ZF=[];\r
-            \r
-            for k=1:nz\r
-            [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            \r
-            for j=1:ny\r
-            [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-            matrix(Y(:,j,:),[nx,nz]),...\r
-            matrix(Z(:,j,:),[nx,nz]));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")\r
-            xtitle("A 3d grid !"); \r
-        </scilab:image>\r
-        <para><emphasis role="bold">Exemple #3: création d'une table de digrammes</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
-c1+c2\r
- ]]></programlisting>\r
-    <screen>\r
-<![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
- c2  = \r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-\r
- c1  = \r
-!a  a  a  a  a  a  a  a  !\r
-!b  b  b  b  b  b  b  b  !\r
-!c  c  c  c  c  c  c  c  !\r
-\r
---> c1+c2\r
- ans  =\r
-!aa  ab  ac  ad  ae  af  ag  ah  !\r
-!ba  bb  bc  bd  be  bf  bg  bh  !\r
-!ca  cb  cc  cd  ce  cf  cg  ch  !\r
-]]></screen>\r
-    </refsection>\r
-    <refsection role="see also">\r
-        <title>Voir aussi</title>\r
-        <simplelist type="inline">\r
-            <member>\r
-                <link linkend="meshgrid">meshgrid</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="kron">kron</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="feval">feval</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="eval3d">eval3d</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="nf3d">nf3d</link>\r
-            </member>\r
-        </simplelist>\r
-    </refsection>\r
-    <refsection role="history">\r
-        <title>Historique</title>\r
-        <revhistory>\r
-            <revision>\r
-                <revnumber>6.0</revnumber>\r
-                <revdescription>Extension à tous les types de données uniformes ([], booleans, encoded integers, polynomials, rationals, strings). Révision de la page d'aide.\r
-                </revdescription>\r
-            </revision>\r
-        </revhistory>\r
-    </refsection>\r
-</refentry>\r
index 11b79d3..1d5fc05 100644 (file)
 <?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="ndgrid" xml:lang="ja">
+
+<refnamediv>
     
-    <refnamediv>
-        
-        <refname>ndgrid</refname>
-        
-        <refpurpose>
-            
-            多次元関数評価用グリッドの配列
-            
-        </refpurpose>
+    <refname>ndgrid</refname>
+    
+    <refpurpose>与えられたベクトルを複製することによって、行列またはN次元配列を作成
         
-    </refnamediv>
+    </refpurpose>
     
-    <refsynopsisdiv>
+</refnamediv>
+
+<refsynopsisdiv>
+    
+    <title>呼び出し手順</title>
+    
+    <synopsis>[X, Y] = ndgrid(x,y)
         
-        <title>呼び出し手順</title>
+        [X, Y, Z] = ndgrid(x,y,z)
         
-        <synopsis>[X, Y] = ndgrid(x,y)
-            
-            [X, Y, Z] = ndgrid(x,y,z)
-            
-            [X, Y, Z, T] = ndgrid(x,y,z,t)
-            
-            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
-            
-        </synopsis>
+        [X, Y, Z, T] = ndgrid(x,y,z,t)
         
-    </refsynopsisdiv>
-    
-    <refsection>
+        [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
         
-        <title>引数</title>
+    </synopsis>
+    
+</refsynopsisdiv>
+
+<refsection role="arguments">
+    
+    <title>引数</title>
+    
+    <variablelist>
         
-        <variablelist>
+        <varlistentry>
             
-            <varlistentry>
-                
-                <term>x, y, z, ...</term>
-                
-                <listitem>
-                    
-                    <para>ベクトル</para>
-                    
-                </listitem>
-                
-            </varlistentry>
+            <term>x, y, z, ...</term>
             
-            <varlistentry>
+            <listitem>
                 
-                <term>X, Y, Z, ...</term>
+                <para>vectors of any data types. They may have distinct data types.</para>
                 
+            </listitem>
+            
+        </varlistentry>
+        
+        <varlistentry>
+            
+            <term>X, Y, Z, ...</term>
+            
                 <listitem>
-                    
-                    <para>
+                    <para>Matrices in case of 2 input arguments, or hypermatrices otherwise.
                         
-                        入力引数が2個の場合は行列,
+                        They all have the same sizes: size(x,"*") rows, size(y,"*") columns,
                         
-                        それ以外の場合はハイパー行列
+                        size(z,"*") layers, etc.
+                  </para>
+                  <para>
+                        
+                        They have the datatypes of respective input vectors:
+                        
+                        <literal>typeof(X)==typeof(x)</literal>,
+                        
+                        <literal>typeof(Y)==typeof(y)</literal>, etc.
                         
                     </para>
                     
                 </listitem>
-                
-            </varlistentry>
-            
-        </variablelist>
+        </varlistentry>
         
-    </refsection>
+    </variablelist>
+    
+</refsection>
+
+<refsection role="description">
+    
+    <title>説明</title>
     
-    <refsection>
+    <para>
+        The first application of <function>ndgrid</function> is to build
         
-        <title>説明</title>
+        a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3,
         
-        <para>
-            
-            この関数はユーティリティルーチンで,
-            
-            2, 3, ..., n次元のグリッド上で関数の評価を行う
-            
-            ための配列を作成する際に便利です.
-            
-            例えば, 2次元の場合, グリッドは
-            
-            長さ nx および nyの
-            
-            2つのベクトル
-            
-            <literal>x</literal> および <literal> y</literal>
-            
-            で定義され,
-            
-            <emphasis>i=1,..,nx</emphasis> および <emphasis>j=1,..,ny</emphasis>
-            
-            として,座標<emphasis>(x(i),y(j))</emphasis>となります.
-            
-            そのグリッド上で (例えば<emphasis>f</emphasis>のような)関数の評価を
-            
-            行うことになります.
-            
-            この場合,この関数は,以下のような大きさ<emphasis>nx x ny</emphasis>の
-            
-            2つの行列<literal>X,Y</literal>を計算します :
-            
-        </para>
+        or more sets
         
-        <programlisting role="no-scilab-exec"><![CDATA[ 
-X(i,j) = x(i)   for all i in [1,nx]
-Y(i,j) = y(j)       and j in [1,ny]
- ]]></programlisting>
+        <literal>x</literal>, <literal> y</literal>, etc.. of
         
-        <para>
-            
-            評価は,<literal>Z=f(X,Y)</literal>で行うことができます.
-            
-            (ベクトル引数で<literal>f</literal>を評価するようコードが
-            
-            作成されている場合,
-            
-            <literal>*</literal>,
-            
-            <literal>/</literal> および <literal>^</literal>の部分に
-            
-            要素毎の演算 <literal>.*</literal>, <literal>./</literal> および
-            
-            <literal>.^</literal>を使用することにより,(一般に)動作します..
-            
-        </para>
+        "template" coordinates sampled along each direction/dimension of the
         
-        <para>
-            
-            3次元の場合, 長さ nx, ny および nzの3個のベクトル<literal>x,y,z</literal>
-            
-            を指定し,
-            
-            <literal>X,Y,Z</literal>は以下のように大きさ
-            
-            <emphasis>nx x ny x nz</emphasis>のハイパー行列となります :
-            
-        </para>
+        space that you want to mesh.
         
-        <programlisting role="no-scilab-exec"><![CDATA[ 
-X(i,j,k) = x(i)  
-Y(i,j,k) = y(j)   for all (i,j,k) in [1,nx]x[1,ny]x[1,nz]
-Z(i,j,k) = z(k)
- ]]></programlisting>
+    </para>
+    
+    <para>
+        Hence, the matrix or hypermatrix <literal>X</literal> is made
+        
+        by replicating the vector <literal>x</literal> as all its columns;
+        
+        the matrix or hypermatrix <literal>Y</literal> is made
+        
+        by replicating the vector <literal>y</literal> as all its rows;
         
-        <para>
+        <literal>Z</literal> is made of replicating the vector
+        
+        <literal>z</literal> along all its local thicknesses (3rd dimension);
+        
+        etc
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])
+ X  =
+   1.   1.   1.   1.
+   3.   3.   3.   3.
+   4.   4.   4.   4.
+
+   Y  =
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+]]>
+    </screen>
+    
+    <para>
+        
+        Then, the coordinates of the node(i,j) in the 2D space
+        
+        will be
+        
+        simply <literal>[x(i), y(j)]</literal> equal to
+        
+        <literal>[X(i,j), Y(i,j)]</literal>. As well, the coordinates of a
+        
+        <literal>node(i,j,k)</literal> of a 3D grid will be
+        
+        <literal>[x(i), y(j), z(k)]</literal> equal to
+        
+        <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.
+        
+    </para>
+    
+    <para>
+        
+        This replication scheme can be generalized to any number of dimensions,
+        
+        as well to any type of uniform data. Let's for instance consider 2
+        
+        attributes:
+        
+        <orderedlist>
             
-            一般的な場合, m 個の入力引数<literal>x1, x2, ..,
+            <listitem>The first is a number, to be chosen from the vector say
                 
-                xm
+                <literal>n = [ 3 7 ]</literal>
                 
-            </literal>
-            
-            ,それから m個の出力引数
+            </listitem>
             
-            <literal>X1, X2, .., Xm</literal> は以下のような
-            
-            大きさ <emphasis>nx1 x nx2 x ... x
+            <listitem>The second is a letter, to be chosen from the vector
                 
-                nxm
+                say <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>
                 
-            </emphasis>
-            
-            のハイパー行列となります :
+            </listitem>
             
-        </para>
+        </orderedlist>
         
-        <programlisting role="no-scilab-exec"><![CDATA[ 
-Xj(i1,i2,...,ij,...,im) = xj(ij)   
-for all (i1,i2,...,im) in [1,nx1]x[1,nx2]x...x[1,nxm]  
- ]]></programlisting>
+        Then we want to build the set of all {n,c} possible pairs. It will
+        
+        just be the 2D grid:
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"])
+ C  = 
+!a  e  i  o  u  y  !
+!a  e  i  o  u  y  !
+
+ N  = 
+   3.   3.   3.   3.   3.   3.
+   7.   7.   7.   7.   7.   7.
+]]>
+    </screen>
+    
+    <para>Then, the object(i,j) will have the properties
+        
+        <literal>{n(i) c(j)}</literal> that now can be addressed with
+        
+        <literal>{N(i,j) C(i,j)}</literal>.
         
-    </refsection>
+        This kind of grid may be useful to initialize an array of structures.
+        
+    </para>
     
-    <refsection>
+    <para>
+        Following examples show how to use <varname>X, Y, Z</varname> in
         
-        <title>例</title>
+        most frequent applications.
         
-        <programlisting role="example"><![CDATA[  
-// 簡単な2次元グリッドを作
-nx = 40; ny = 40;
-x = linspace(-1,1,nx);
-y = linspace(-1,1,ny);
+    </para>
+     
+    
+</refsection>
+
+<refsection role="examples">
+    
+    <title>例</title>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #1:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
+// Create a simple 2d grid
+x = linspace(-10,2,40);
+y = linspace(-5,5,40);
 [X,Y] = ndgrid(x,y);
-// グリッド上で関数を計算してプロット
-//deff("z=f(x,y)","z=128*x.^2 .*(1-x).^2 .*y.^2 .*(1-y).^2");
-deff("z=f(x,y)","z=x.^2 + y.^3")
-Z = f(X,Y);
+
+// Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y)
+Z = X - 3*X.*sin(X).*cos(Y-4) ;
 clf()
-plot3d(x,y,Z, flag=[2 6 4]); show_window()
+plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
  ]]></programlisting>
+    
+    <scilab:image>
         
-        <scilab:image>
-            
-            nx = 40; ny = 40;
-            
-            x = linspace(-1,1,nx);
-            
-            y = linspace(-1,1,ny);
-            
-            [X,Y] = ndgrid(x,y);
-            
-            deff("z=f(x,y)","z=x.^2 + y.^3")
-            
-            Z = f(X,Y);
-            
-            plot3d(x,y,Z, flag=[2 6 4]);
-            
-        </scilab:image>
+        x = linspace(-10,2,40);
+        
+        y = linspace(-5,5,40);
+        
+        [X,Y] = ndgrid(x,y);
+        
+        Z = X - 3*X.*sin(X).*cos(Y-4) ;
         
-        <programlisting role="example"><![CDATA[
+        clf()
+        
+        plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
+        
+    </scilab:image>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #2:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
 // 簡単な3次元グリッドを作成
 nx = 10; ny = 6; nz = 4;
 x = linspace(0,2,nx);
@@ -232,73 +270,140 @@ for j=1:ny
    XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
 end
 clf()
-plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
+plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
 xtitle("A 3d grid !"); show_window()
  ]]></programlisting>
+    
+    <scilab:image>
         
-        <scilab:image>
-            
-            nx = 10; ny = 6; nz = 4;
-            
-            x = linspace(0,2,nx);
-            
-            y = linspace(0,1,ny);
-            
-            z = linspace(0,0.5,nz);
-            
-            [X,Y,Z] = ndgrid(x,y,z);
-            
-            
-            
-            XF=[]; YF=[]; ZF=[];
-            
-            
-            
-            for k=1:nz
-            
-            [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
-            
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
-            
-            end
-            
+        nx = 10; ny = 6; nz = 4;
+        
+        x = linspace(0,2,nx);
+        
+        y = linspace(0,1,ny);
+        
+        z = linspace(0,0.5,nz);
+        
+        [X,Y,Z] = ndgrid(x,y,z);
+        
+        XF=[]; YF=[]; ZF=[];
+        
+        for k=1:nz
+        
+        [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        for j=1:ny
+        
+        [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
+        
+        matrix(Y(:,j,:),[nx,nz]),...
+        
+        matrix(Z(:,j,:),[nx,nz]));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
+        
+        xtitle("A 3d grid !");
+        
+    </scilab:image>
+    
+    <para>
+        <emphasis role="bold">Example #3: Create a table of digrams:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
+[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+c1+c2
+ ]]></programlisting>
+    
+    <screen>
+        
+        <![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+ c2  =
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+
+ c1  =
+!a  a  a  a  a  a  a  a  !
+!b  b  b  b  b  b  b  b  !
+!c  c  c  c  c  c  c  c  !
+
+--> c1+c2
+ ans  =
+!aa  ab  ac  ad  ae  af  ag  ah  !
+!ba  bb  bc  bd  be  bf  bg  bh  !
+!ca  cb  cc  cd  ce  cf  cg  ch  !
+]]>
+    </screen>
+    
+</refsection>
+
+<refsection role="see also">
+    
+    <title>参照</title>
+    
+    <simplelist type="inline">
+        
+        <member>
             
+            <link linkend="meshgrid">meshgrid</link>
             
-            for j=1:ny
+        </member>
+        
+        <member>
             
-            [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
+            <link linkend="kron">kron</link>
             
-            matrix(Y(:,j,:),[nx,nz]),...
+        </member>
+        
+        <member>
             
-            matrix(Z(:,j,:),[nx,nz]));
+            <link linkend="feval">feval</link>
             
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        </member>
+        
+        <member>
             
-            end
+            <link linkend="eval3d">eval3d</link>
             
-            plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
+        </member>
+        
+        <member>
             
-            xtitle("A 3d grid !"); 
+            <link linkend="nf3d">nf3d</link>
             
-        </scilab:image>
+        </member>
         
-    </refsection>
+    </simplelist>
     
-    <refsection role="see also">
-        
-        <title>参照</title>
+</refsection>
+
+<refsection role="history">
+    
+    <title>履歴</title>
+    
+    <revhistory>
         
-        <simplelist type="inline">
+        <revision>
             
-            <member>
-                
-                <link linkend="kron">kron</link>
+            <revnumber>6.0</revnumber>
+            
+            <revdescription>Extension to all homogeneous datatypes ([], booleans, encoded integers, polynomials, rationals, strings). Revision of the help page.
                 
-            </member>
+            </revdescription>
             
-        </simplelist>
+        </revision>
         
-    </refsection>
+    </revhistory>
     
-</refentry>
+</refsection>
 
+</refentry>
diff --git a/scilab/modules/elementary_functions/help/ja_JP/ndgrid.xml b/scilab/modules/elementary_functions/help/ja_JP/ndgrid.xml
deleted file mode 100644 (file)
index d7d432a..0000000
+++ /dev/null
@@ -1,230 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>\r
-<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="ndgrid" xml:lang="ja">\r
-    <refnamediv>\r
-        <refname>ndgrid</refname>\r
-        <refpurpose>与えられたベクトルを複製することによって、行列またはN次元配列を作成\r
-        </refpurpose>\r
-    </refnamediv>\r
-    <refsynopsisdiv>\r
-        <title>呼び出し手順</title>\r
-        <synopsis>[X, Y] = ndgrid(x,y)\r
-            [X, Y, Z] = ndgrid(x,y,z)\r
-            [X, Y, Z, T] = ndgrid(x,y,z,t)\r
-            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)\r
-        </synopsis>\r
-    </refsynopsisdiv>\r
-    <refsection role="arguments">\r
-        <title>引数</title>\r
-        <variablelist>\r
-            <varlistentry>\r
-                <term>x, y, z, ...</term>\r
-                <listitem>\r
-                    <para>vectors of any data types. They may have distinct data types.</para>\r
-                </listitem>\r
-            </varlistentry>\r
-            <varlistentry>\r
-                <term>X, Y, Z, ...</term>\r
-                <listitem>\r
-                    <para>\r
-                        入力引数が2個の場合は行列,\r
-                        それ以外の場合はハイパー行列\r
-                    </para>\r
-                </listitem>\r
-            </varlistentry>\r
-        </variablelist>\r
-    </refsection>\r
-    <refsection role="description">\r
-        <title>説明</title>\r
-        <para>The first application of <function>ndgrid</function> is to build\r
-            a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3,\r
-            or more sets\r
-            <literal>x</literal>, <literal> y</literal>, etc.. of  \r
-            "template" coordinates sampled along each direction/dimension of the\r
-            space that you want to mesh.\r
-        </para>\r
-        <para>Hence, the matrix or hypermatrix <literal>X</literal> is made\r
-            by replicating the vector <literal>x</literal> as all its columns ; \r
-            the matrix or hypermatrix <literal>Y</literal> is made\r
-            by replicating the vector <literal>y</literal> as all its rows ;\r
-            <literal>Z</literal> is made of replicating the vector \r
-            <literal>z</literal> along all its local thicknesses (3rd dimension); \r
-            etc\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])\r
- X  = \r
-   1.   1.   1.   1.\r
-   3.   3.   3.   3.\r
-   4.   4.   4.   4.\r
-\r
-   Y  = \r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-]]></screen>\r
-        <para>  \r
-            Then, the coordinates of the node(i,j) in the 2D space \r
-            will be\r
-            simply <literal>[x(i), y(j)]</literal> equal to \r
-            <literal>[X(i,j), Y(i,j)]</literal>. As well, the coordinates of a\r
-            <literal>node(i,j,k)</literal> of a 3D grid will be \r
-            <literal>[x(i), y(j), z(k)]</literal> equal to \r
-            <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.\r
-        </para>\r
-        <para>\r
-            This replication scheme can be generalized to any number of dimensions,\r
-            as well to any type of uniform data. Let's for instance consider 2\r
-            attributes:\r
-            <orderedlist>\r
-                <listitem>The first is a number, to be chosen from the vector say\r
-                <literal>n = [ 3 7 ]</literal>\r
-                </listitem>\r
-                <listitem>The second is a letter, to be chosen from the vector \r
-                say <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>\r
-                </listitem>\r
-            </orderedlist>\r
-            Then we want to build the set of all {n,c} possible pairs. It will\r
-            just be the 2D grid:\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"])\r
- C  = \r
-!a  e  i  o  u  y  !\r
-!a  e  i  o  u  y  !\r
-\r
- N  = \r
-   3.   3.   3.   3.   3.   3.\r
-   7.   7.   7.   7.   7.   7.\r
-]]></screen>\r
-        <para>Then, the object(i,j) will have the properties \r
-        <literal>{n(i) c(j)}</literal> that now can be addressed with\r
-        <literal>{N(i,j) C(i,j)}</literal>.\r
-        This kind of grid may be useful to initialize an array of structures.\r
-        </para>\r
-        <para>Following examples show how to use <varname>X, Y, Z</varname> in\r
-        most frequent applications.\r
-        </para> \r
-    </refsection>\r
-    <refsection role="examples">\r
-        <title>例</title>\r
-\r
-        <para><emphasis role="bold">Example #1:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[\r
-// Create a simple 2d grid\r
-x = linspace(-10,2,40);\r
-y = linspace(-5,5,40);\r
-[X,Y] = ndgrid(x,y);\r
-\r
-// Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y)\r
-Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-clf()\r
-plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
- ]]></programlisting>\r
-        <scilab:image>\r
-        x = linspace(-10,2,40);\r
-        y = linspace(-5,5,40);\r
-        [X,Y] = ndgrid(x,y);\r
-        Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-        clf()\r
-        plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
-        </scilab:image>\r
-\r
-        <para><emphasis role="bold">Example #2:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[\r
-// 簡単な3次元グリッドを作成\r
-nx = 10; ny = 6; nz = 4;\r
-x = linspace(0,2,nx);\r
-y = linspace(0,1,ny);\r
-z = linspace(0,0.5,nz);\r
-[X,Y,Z] = ndgrid(x,y,z);\r
-// 3次元グリッドを表示する ...\r
-XF=[]; YF=[]; ZF=[];\r
-for k=1:nz\r
-   [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-for j=1:ny\r
-   [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-                     matrix(Y(:,j,:),[nx,nz]),...\r
-                     matrix(Z(:,j,:),[nx,nz]));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-clf()\r
-plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")\r
-xtitle("A 3d grid !"); show_window()\r
- ]]></programlisting>\r
-        <scilab:image>\r
-            nx = 10; ny = 6; nz = 4;\r
-            x = linspace(0,2,nx);\r
-            y = linspace(0,1,ny);\r
-            z = linspace(0,0.5,nz);\r
-            [X,Y,Z] = ndgrid(x,y,z);\r
-            XF=[]; YF=[]; ZF=[];\r
-            for k=1:nz\r
-            [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            for j=1:ny\r
-            [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-            matrix(Y(:,j,:),[nx,nz]),...\r
-            matrix(Z(:,j,:),[nx,nz]));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")\r
-            xtitle("A 3d grid !");\r
-        </scilab:image>\r
-        <para><emphasis role="bold">Example #3: Create a table of digrams:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
-c1+c2\r
- ]]></programlisting>\r
-    <screen>\r
-<![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
- c2  = \r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-\r
- c1  = \r
-!a  a  a  a  a  a  a  a  !\r
-!b  b  b  b  b  b  b  b  !\r
-!c  c  c  c  c  c  c  c  !\r
-\r
---> c1+c2\r
- ans  =\r
-!aa  ab  ac  ad  ae  af  ag  ah  !\r
-!ba  bb  bc  bd  be  bf  bg  bh  !\r
-!ca  cb  cc  cd  ce  cf  cg  ch  !\r
-]]></screen>\r
-        </refsection>\r
-    <refsection role="see also">\r
-        <title>参照</title>\r
-        <simplelist type="inline">\r
-            <member>\r
-                <link linkend="meshgrid">meshgrid</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="kron">kron</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="feval">feval</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="eval3d">eval3d</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="nf3d">nf3d</link>\r
-            </member>\r
-        </simplelist>\r
-    </refsection>\r
-    <refsection role="history">\r
-        <title>履歴</title>\r
-        <revhistory>\r
-            <revision>\r
-                <revnumber>6.0</revnumber>\r
-                <revdescription>Extension to all homogeneous datatypes ([], booleans, encoded integers, polynomials, rationals, strings). Revision of the help page.\r
-                </revdescription>\r
-            </revision>\r
-        </revhistory>\r
-    </refsection>\r
-</refentry>
\ No newline at end of file
index 7d233df..5fa06e8 100644 (file)
-<?xml version="1.0" encoding="ISO-8859-1"?>
-<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="ndgrid" xml:lang="en">
-    <refnamediv>
-        <refname>ndgrid</refname>
-        <refpurpose>Arrays para avaliação de função multidimensional em
-            grid
-        </refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Seqüência de Chamamento</title>
-        <synopsis>[X, Y] = ndgrid(x,y)
-            [X, Y, Z] = ndgrid(x,y,z)
-            [X, Y, Z, T] = ndgrid(x,y,z,t)
-            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Parâmetros</title>
-        <variablelist>
-            <varlistentry>
-                <term>x, y, z, ...</term>
-                <listitem>
-                    <para>vetores </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>X, Y, Z, ...</term>
+<?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="ndgrid" xml:lang="pt">
+
+<refnamediv>
+    
+    <refname>ndgrid</refname>
+    
+    <refpurpose>constrói matrizes ou matrizes N-D, replicando alguns vetores dadas
+        
+    </refpurpose>
+    
+</refnamediv>
+
+<refsynopsisdiv>
+    
+    <title>Seqüência de Chamamento</title>
+    
+    <synopsis>[X, Y] = ndgrid(x,y)
+        
+        [X, Y, Z] = ndgrid(x,y,z)
+        
+        [X, Y, Z, T] = ndgrid(x,y,z,t)
+        
+        [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
+        
+    </synopsis>
+    
+</refsynopsisdiv>
+
+<refsection role="arguments">
+    
+    <title>Parâmetros</title>
+    
+    <variablelist>
+        
+        <varlistentry>
+            
+            <term>x, y, z, ...</term>
+            
+            <listitem>
+                
+                <para>vetores de quaisquer tipos de dados.
+                    
+                    Eles podem ter tipos de dados distintos.
+                </para>
+                
+            </listitem>
+            
+        </varlistentry>
+        
+        <varlistentry>
+            
+            <term>X, Y, Z, ...</term>
+            
                 <listitem>
-                    <para>matrizes, no caso de 2 argumentos de entrada, ou hipermatrizes
-                        em outro caso 
+                    
+                    <para>matrices in case of 2 input arguments, or hypermatrices otherwise.
+                        
+                        They all have the same sizes: size(x,"*") rows, size(x,"*") columns,
+                        
+                        size(z,"*") layers, etc.
+                        
+                        They have the datatypes of respective input vectors:
+                        
+                        <literal>typeof(X)==typeof(x)</literal>,
+                        
+                        <literal>typeof(Y)==typeof(y)</literal>, etc.
+                        
                     </para>
+                    
                 </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Descrição</title>
-        <para>Esta rotina utilitária é útil para criar arrays para a avaliação da
-            função em grids 2, 3, ..., n dimensionais. Por exemplo, em 2d, um grid é
-            definido por dois vetores, <literal>x</literal> e <literal> y</literal> de
-            comprimento nx e ny, e se deseja avaliar uma função (dita f) em todos os
-            pontos do grid, isto é, em todos os pontos de coordenadas (x(i),y(j)) com
-            i=1,..,nx e j=1,..,ny . Neste caso, esta função pode computar as duas
-            matrizes <literal>X,Y</literal> de tamanho nx x ny tais que : 
-        </para>
-        <programlisting role=""><![CDATA[ 
-      X(i,j) = x(i)   para todo i em [1,nx]
-      Y(i,j) = y(j)       e j em [1,ny]
- ]]></programlisting>
-        <para>
-            e a avaliação pode ser feita com <literal>Z=f(X,Y)</literal> (sob a
-            condição de que <literal>f</literal> foi codificada para a avaliação em
-            argumentos de vetor, que é feito (em geral) usando os operadores elemento
-            a elemento <literal>.*</literal>, <literal>./</literal> and
-            <literal>.^</literal> no lugar de <literal>*</literal>,
-            <literal>/</literal> e <literal>^</literal>).
-        </para>
-        <para>
-            No caso 3d, considerando 3 vetores <literal>x,y,z</literal> de
-            comprimentos nx, ny e nz, <literal>X,Y,Z</literal> são 3 hipermatrizes de
-            tamanho nx x ny x nz tais que : 
-        </para>
-        <programlisting role=""><![CDATA[ 
-      X(i,j,k) = x(i)  
-      Y(i,j,k) = y(j)   para todo (i,j,k) in [1,nx]x[1,ny]x[1,nz]
-      Z(i,j,k) = z(k)
- ]]></programlisting>
-        <para>
-            No caso geral de m argumentos de entrada <literal>x1, x2, ..,
-                xm
-            </literal>
-            ,os m argumentos de saída <literal>X1, X2, .., Xm</literal>
-            são hipermatrizes de tamanho <emphasis>nx1 x nx2 x ... x nxm</emphasis> e
-            :
-        </para>
-        <programlisting role=""><![CDATA[ 
-    Xj(i1,i2,...,ij,...,im) = xj(ij)   
-    for all (i1,i2,...,im) in [1,nx1]x[1,nx2]x...x[1,nxm]  
- ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>Exemplos </title>
-        <programlisting role="example"><![CDATA[ 
-// criando um grid 2d simples
-nx = 40; ny = 40;
-x = linspace(-1,1,nx);
-y = linspace(-1,1,ny);
+            
+        </varlistentry>
+        
+    </variablelist>
+    
+</refsection>
+
+<refsection role="description">
+    
+    <title>Descrição</title>
+    
+    <para>
+        The first application of <function>ndgrid</function> is to build
+        
+        a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3,
+        
+        or more sets
+        
+        <literal>x</literal>, <literal> y</literal>, etc.. of
+        
+        "template" coordinates sampled along each direction/dimension of the
+        
+        space that you want to mesh.
+        
+    </para>
+    
+    <para>
+        Hence, the matrix or hypermatrix <literal>X</literal> is made
+        
+        by replicating the vector <literal>x</literal> as all its columns;
+        
+        the matrix or hypermatrix <literal>Y</literal> is made
+        
+        by replicating the vector <literal>y</literal> as all its rows;
+        
+        <literal>Z</literal> is made of replicating the vector
+        
+        <literal>z</literal> along all its local thicknesses (3rd dimension);
+        
+        etc
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])
+ X  =
+   1.   1.   1.   1.
+   3.   3.   3.   3.
+   4.   4.   4.   4.
+
+   Y  =
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+]]>
+    </screen>
+    
+    <para>
+        
+        Then, the coordinates of the node(i,j) in the 2D space
+        
+        will be
+        
+        simply <literal>[x(i), y(j)]</literal> equal to
+        
+        <literal>[X(i,j), Y(i,j)]</literal>. As well, the coordinates of a
+        
+        <literal>node(i,j,k)</literal> of a 3D grid will be
+        
+        <literal>[x(i), y(j), z(k)]</literal> equal to
+        
+        <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.
+        
+    </para>
+    
+    <para>
+        
+        This replication scheme can be generalized to any number of dimensions,
+        
+        as well to any type of uniform data. Let's for instance consider 2
+        
+        attributes:
+        
+        <orderedlist>
+            
+            <listitem>The first is a number, to be chosen from the vector say
+                
+                <literal>n = [ 3 7 ]</literal>
+                
+            </listitem>
+            
+            <listitem>The second is a letter, to be chosen from the vector
+                
+                say <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>
+                
+            </listitem>
+            
+        </orderedlist>
+        
+        Then we want to build the set of all {n,c} possible pairs. It will
+        
+        just be the 2D grid:
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"])
+ C  =
+!a  e  i  o  u  y  !
+!a  e  i  o  u  y  !
+
+ N  =
+   3.   3.   3.   3.   3.   3.
+   7.   7.   7.   7.   7.   7.
+]]>
+    </screen>
+    
+    <para>Then, the object(i,j) will have the properties
+        
+        <literal>{n(i) c(j)}</literal> that now can be addressed with
+        
+        <literal>{N(i,j) C(i,j)}</literal>.
+        
+        This kind of grid may be useful to initialize an array of structures.
+        
+    </para>
+    
+    <para>
+        Following examples show how to use <varname>X, Y, Z</varname> in
+        
+        most frequent applications.
+        
+    </para>
+     
+    
+</refsection>
+
+<refsection role="examples">
+    
+    <title>Exemplos </title>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #1:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
+// Criando um grid 2d simples
+x = linspace(-10,2,40);
+y = linspace(-5,5,40);
 [X,Y] = ndgrid(x,y);
-// computando uma função no grid e plotando
-//deff("z=f(x,y)","z=128*x.^2 .*(1-x).^2 .*y.^2 .*(1-y).^2");
-deff("z=f(x,y)","z=x.^2 + y.^3")
-Z = f(X,Y);
+
+// Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y)
+Z = X - 3*X.*sin(X).*cos(Y-4) ;
 clf()
-plot3d(x,y,Z, flag=[2 6 4]); show_window()
+plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
  ]]></programlisting>
-        <scilab:image>
-            nx = 40; ny = 40;
-            x = linspace(-1,1,nx);
-            y = linspace(-1,1,ny);
-            [X,Y] = ndgrid(x,y);
-            deff("z=f(x,y)","z=x.^2 + y.^3")
-            Z = f(X,Y);
-            plot3d(x,y,Z, flag=[2 6 4]);
-        </scilab:image>
-        <programlisting role="example"><![CDATA[ 
+    
+    <scilab:image>
+        
+        x = linspace(-10,2,40);
+        
+        y = linspace(-5,5,40);
+        
+        [X,Y] = ndgrid(x,y);
+        
+        Z = X - 3*X.*sin(X).*cos(Y-4) ;
+        
+        clf()
+        
+        plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
+        
+    </scilab:image>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #2:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
 // criando um grid 3d simples
 nx = 10; ny = 6; nz = 4;
 x = linspace(0,2,nx);
@@ -122,39 +273,152 @@ for j=1:ny
    XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
 end
 clf()
-plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
+plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
 xtitle("A 3d grid !"); show_window()
- ]]></programlisting>
-        <scilab:image>
-            nx = 10; ny = 6; nz = 4;
-            x = linspace(0,2,nx);
-            y = linspace(0,1,ny);
-            z = linspace(0,0.5,nz);
-            [X,Y,Z] = ndgrid(x,y,z);
-            
-            XF=[]; YF=[]; ZF=[];
-            
-            for k=1:nz
-            [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
-            end
-            
-            for j=1:ny
-            [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
-            matrix(Y(:,j,:),[nx,nz]),...
-            matrix(Z(:,j,:),[nx,nz]));
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
-            end
-            plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
-            xtitle("A 3d grid !"); 
-        </scilab:image>
-    </refsection>
-    <refsection role="see also">
-        <title>Ver Também</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="kron">kron</link>
-            </member>
-        </simplelist>
-    </refsection>
+ ]]>    </programlisting>
+    
+    <scilab:image>
+        
+        nx = 10; ny = 6; nz = 4;
+        
+        x = linspace(0,2,nx);
+        
+        y = linspace(0,1,ny);
+        
+        z = linspace(0,0.5,nz);
+        
+        [X,Y,Z] = ndgrid(x,y,z);
+        
+        
+        
+        XF=[]; YF=[]; ZF=[];
+        
+        
+        
+        for k=1:nz
+        
+        [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        
+        
+        for j=1:ny
+        
+        [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...
+        
+        matrix(Y(:,j,:),[nx,nz]),...
+        
+        matrix(Z(:,j,:),[nx,nz]));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
+        
+        xtitle("A 3d grid !");
+        
+    </scilab:image>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #3: Create a table of digrams:</emphasis>
+    </para>
+    
+    <programlisting role="example"><![CDATA[
+[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+c1+c2
+ ]]>    </programlisting>
+    
+    <screen>
+        
+        <![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+ c2  =
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+
+ c1  =
+!a  a  a  a  a  a  a  a  !
+!b  b  b  b  b  b  b  b  !
+!c  c  c  c  c  c  c  c  !
+
+--> c1+c2
+ ans  =
+!aa  ab  ac  ad  ae  af  ag  ah  !
+!ba  bb  bc  bd  be  bf  bg  bh  !
+!ca  cb  cc  cd  ce  cf  cg  ch  !
+]]>
+    </screen>
+    
+    
+    
+</refsection>
+
+<refsection role="see also">
+    
+    <title>Ver Também</title>
+    
+    <simplelist type="inline">
+        
+        <member>
+            
+            <link linkend="meshgrid">meshgrid</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="kron">kron</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="feval">feval</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="eval3d">eval3d</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="nf3d">nf3d</link>
+            
+        </member>
+        
+    </simplelist>
+    
+</refsection>
+
+<refsection role="history">
+    
+    <title>Histórico</title>
+    
+    <revhistory>
+        
+        <revision>
+            
+            <revnumber>6.0</revnumber>
+            
+            <revdescription>Extension to all homogeneous datatypes ([], booleans, encoded integers,
+              polynomials, rationals, strings). Revision of the help page.
+                
+            </revdescription>
+            
+        </revision>
+        
+    </revhistory>
+    
+</refsection>
+
 </refentry>
+
diff --git a/scilab/modules/elementary_functions/help/pt_BR/ndgrid.xml b/scilab/modules/elementary_functions/help/pt_BR/ndgrid.xml
deleted file mode 100644 (file)
index 8bbc340..0000000
+++ /dev/null
@@ -1,235 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>\r
-<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="ndgrid" xml:lang="pt">\r
-    <refnamediv>\r
-        <refname>ndgrid</refname>\r
-        <refpurpose>constrói matrizes ou matrizes N-D, replicando alguns vetores dadas\r
-        </refpurpose>\r
-    </refnamediv>\r
-    <refsynopsisdiv>\r
-        <title>Seqüência de Chamamento</title>\r
-        <synopsis>[X, Y] = ndgrid(x,y)\r
-            [X, Y, Z] = ndgrid(x,y,z)\r
-            [X, Y, Z, T] = ndgrid(x,y,z,t)\r
-            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)\r
-        </synopsis>\r
-    </refsynopsisdiv>\r
-    <refsection role="arguments">\r
-        <title>Parâmetros</title>\r
-        <variablelist>\r
-            <varlistentry>\r
-                <term>x, y, z, ...</term>\r
-                <listitem>\r
-                    <para>vetores de quaisquer tipos de dados. \r
-                    Eles podem ter tipos de dados distintos.</para>\r
-                </listitem>\r
-            </varlistentry>\r
-            <varlistentry>\r
-                <term>X, Y, Z, ...</term>\r
-                <listitem>\r
-                    <para>matrizes, no caso de 2 argumentos de entrada, ou hipermatrizes\r
-                        em outro caso \r
-                    </para>\r
-                </listitem>\r
-            </varlistentry>\r
-        </variablelist>\r
-    </refsection>\r
-    <refsection role="description">\r
-        <title>Descrição</title>\r
-        <para>The first application of <function>ndgrid</function> is to build\r
-            a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3,\r
-            or more sets\r
-            <literal>x</literal>, <literal> y</literal>, etc.. of  \r
-            "template" coordinates sampled along each direction/dimension of the\r
-            space that you want to mesh.\r
-        </para>\r
-        <para>Hence, the matrix or hypermatrix <literal>X</literal> is made\r
-            by replicating the vector <literal>x</literal> as all its columns ; \r
-            the matrix or hypermatrix <literal>Y</literal> is made\r
-            by replicating the vector <literal>y</literal> as all its rows ;\r
-            <literal>Z</literal> is made of replicating the vector \r
-            <literal>z</literal> along all its local thicknesses (3rd dimension); \r
-            etc\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])\r
- X  = \r
-   1.   1.   1.   1.\r
-   3.   3.   3.   3.\r
-   4.   4.   4.   4.\r
-\r
-   Y  = \r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-   0.   2.   4.   6.\r
-]]></screen>\r
-        <para>  \r
-            Then, the coordinates of the node(i,j) in the 2D space \r
-            will be\r
-            simply <literal>[x(i), y(j)]</literal> equal to \r
-            <literal>[X(i,j), Y(i,j)]</literal>. As well, the coordinates of a\r
-            <literal>node(i,j,k)</literal> of a 3D grid will be \r
-            <literal>[x(i), y(j), z(k)]</literal> equal to \r
-            <literal>[X(i,j,k), Y(i,j,k), Z(i,j,k)]</literal>.\r
-        </para>\r
-        <para>\r
-            This replication scheme can be generalized to any number of dimensions,\r
-            as well to any type of uniform data. Let's for instance consider 2\r
-            attributes:\r
-            <orderedlist>\r
-                <listitem>The first is a number, to be chosen from the vector say\r
-                <literal>n = [ 3 7 ]</literal>\r
-                </listitem>\r
-                <listitem>The second is a letter, to be chosen from the vector \r
-                say <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>\r
-                </listitem>\r
-            </orderedlist>\r
-            Then we want to build the set of all {n,c} possible pairs. It will\r
-            just be the 2D grid:\r
-        </para>\r
-        <screen>\r
-<![CDATA[--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"])\r
- C  = \r
-!a  e  i  o  u  y  !\r
-!a  e  i  o  u  y  !\r
-\r
- N  = \r
-   3.   3.   3.   3.   3.   3.\r
-   7.   7.   7.   7.   7.   7.\r
-]]></screen>\r
-        <para>Then, the object(i,j) will have the properties \r
-        <literal>{n(i) c(j)}</literal> that now can be addressed with\r
-        <literal>{N(i,j) C(i,j)}</literal>.\r
-        This kind of grid may be useful to initialize an array of structures.\r
-        </para>\r
-        <para>Following examples show how to use <varname>X, Y, Z</varname> in\r
-        most frequent applications.\r
-        </para> \r
-    </refsection>\r
-    <refsection role="examples">\r
-        <title>Exemplos </title>\r
-        \r
-        <para><emphasis role="bold">Example #1:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[ \r
-// Criando um grid 2d simples\r
-x = linspace(-10,2,40);\r
-y = linspace(-5,5,40);\r
-[X,Y] = ndgrid(x,y);\r
-\r
-// Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y)\r
-Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-clf()\r
-plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
- ]]></programlisting>\r
-        <scilab:image>\r
-        x = linspace(-10,2,40);\r
-        y = linspace(-5,5,40);\r
-        [X,Y] = ndgrid(x,y);\r
-        Z = X - 3*X.*sin(X).*cos(Y-4) ;\r
-        clf()\r
-        plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()\r
-        </scilab:image>\r
-        \r
-        <para><emphasis role="bold">Example #2:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[ \r
-// criando um grid 3d simples\r
-nx = 10; ny = 6; nz = 4;\r
-x = linspace(0,2,nx);\r
-y = linspace(0,1,ny);\r
-z = linspace(0,0.5,nz);\r
-[X,Y,Z] = ndgrid(x,y,z);\r
-// tente exibir este grid 3d...\r
-XF=[]; YF=[]; ZF=[];\r
-for k=1:nz\r
-   [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-for j=1:ny\r
-   [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-                     matrix(Y(:,j,:),[nx,nz]),...\r
-                     matrix(Z(:,j,:),[nx,nz]));\r
-   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-end\r
-clf()\r
-plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")\r
-xtitle("A 3d grid !"); show_window()\r
- ]]>    </programlisting>\r
-        <scilab:image>\r
-            nx = 10; ny = 6; nz = 4;\r
-            x = linspace(0,2,nx);\r
-            y = linspace(0,1,ny);\r
-            z = linspace(0,0.5,nz);\r
-            [X,Y,Z] = ndgrid(x,y,z);\r
-            \r
-            XF=[]; YF=[]; ZF=[];\r
-            \r
-            for k=1:nz\r
-            [xf,yf,zf] = nf3d(X(:,:,k),Y(:,:,k),Z(:,:,k));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            \r
-            for j=1:ny\r
-            [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),...\r
-            matrix(Y(:,j,:),[nx,nz]),...\r
-            matrix(Z(:,j,:),[nx,nz]));\r
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];\r
-            end\r
-            plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")\r
-            xtitle("A 3d grid !"); \r
-        </scilab:image>\r
-\r
-        <para><emphasis role="bold">Example #3: Create a table of digrams:</emphasis> </para>\r
-        <programlisting role="example"><![CDATA[  \r
-[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
-c1+c2\r
- ]]>    </programlisting>\r
-        <screen>\r
-<![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])\r
- c2  = \r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-!a  b  c  d  e  f  g  h  !\r
-\r
- c1  = \r
-!a  a  a  a  a  a  a  a  !\r
-!b  b  b  b  b  b  b  b  !\r
-!c  c  c  c  c  c  c  c  !\r
-\r
---> c1+c2\r
- ans  =\r
-!aa  ab  ac  ad  ae  af  ag  ah  !\r
-!ba  bb  bc  bd  be  bf  bg  bh  !\r
-!ca  cb  cc  cd  ce  cf  cg  ch  !\r
-]]></screen>\r
-\r
-        </refsection>\r
-    <refsection role="see also">\r
-        <title>Ver Também</title>\r
-        <simplelist type="inline">\r
-            <member>\r
-                <link linkend="meshgrid">meshgrid</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="kron">kron</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="feval">feval</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="eval3d">eval3d</link>\r
-            </member>\r
-            <member>\r
-                <link linkend="nf3d">nf3d</link>\r
-            </member>\r
-        </simplelist>\r
-    </refsection>\r
-    <refsection role="history">\r
-        <title>Histórico</title>\r
-        <revhistory>\r
-            <revision>\r
-                <revnumber>6.0</revnumber>\r
-                <revdescription>Extension to all homogeneous datatypes ([], booleans, encoded integers, polynomials, rationals, strings). Revision of the help page.\r
-                </revdescription>\r
-            </revision>\r
-        </revhistory>\r
-    </refsection>\r
-</refentry>\r
index e70ecbe..58039fb 100644 (file)
 <?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="ndgrid" xml:lang="ru">
-    <refnamediv>
-        <refname>ndgrid</refname>
-        <refpurpose>
-            массивы для многомерного вычисления функций по координатной сетке
-        </refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Последовательность вызова</title>
-        <synopsis>
-            X, Y] = ndgrid(x,y)
-            [X, Y, Z] = ndgrid(x,y,z)
-            [X, Y, Z, T] = ndgrid(x,y,z,t)
-            [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Аргументы</title>
-        <variablelist>
-            <varlistentry>
-                <term>x, y, z, ...</term>
-                <listitem>
-                    <para>векторы</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>X, Y, Z, ...</term>
+
+<refnamediv>
+    
+    <refname>ndgrid</refname>
+    
+    <refpurpose>строит матриц или N-мерные массивы путем репликации данных векторов
+        
+    </refpurpose>
+    
+</refnamediv>
+
+<refsynopsisdiv>
+    
+    <title>Последовательность вызова</title>
+    
+    <synopsis>
+        
+        X, Y] = ndgrid(x,y)
+        
+        [X, Y, Z] = ndgrid(x,y,z)
+        
+        [X, Y, Z, T] = ndgrid(x,y,z,t)
+        
+        [X1, X2, ..., Xm] = ndgrid(x1,x2,...,xm)
+        
+    </synopsis>
+    
+</refsynopsisdiv>
+
+<refsection role="arguments">
+    
+    <title>Аргументы</title>
+    
+    <variablelist>
+        
+        <varlistentry>
+            
+            <term>x, y, z, ...</term>
+            
+            <listitem>
+                
+                <para>векторы любых типов данных. Они могут иметь различные типы данных.</para>
+                
+            </listitem>
+            
+        </varlistentry>
+        
+        <varlistentry>
+            
+            <term>X, Y, Z, ...</term>
+            
                 <listitem>
-                    <para>
-                        в случае двух входных аргументов - матрицы, в противном случае - гиперматрицы
+                    
+                    <para>Matrices in case of 2 input arguments, or hypermatrices otherwise.
+                        
+                        They all have the same sizes: size(x,"*") rows, size(y,"*") columns, 
+                        
+                        size(z,"*") layers, etc.
+                  </para>
+                  <para>
+                        
+                        They have the datatypes of respective input vectors:
+                        
+                        <literal>typeof(X)==typeof(x)</literal>, 
+                        
+                        <literal>typeof(Y)==typeof(y)</literal>, etc.
+                        
                     </para>
+                    
                 </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Описание</title>
-        <para>
-            Эта служебная программа полезна для создания массивов для вычисления функций по 2-х, 3-х, ... , n-мерной координатной сетке. Например, в двухмерная координатная сетка определяется двумя векторами, <literal>x</literal> и <literal>y</literal> длиной <literal>nx</literal> и <literal>ny</literal> и вы хотите вычислить функцию (скажем, <emphasis>f</emphasis>) во всех точках координатной сетки, то есть во всех точках с координатами <emphasis>(x(i),y(j))</emphasis>, где <emphasis>i=1,..,nx</emphasis> и <emphasis>j=1,..,ny</emphasis>. В этом случае данная функция может вычислить две матрицы <literal>X,Y</literal> размером <emphasis>nx x ny</emphasis> такие, что:
-        </para>
-        <screen><![CDATA[ 
-X(i,j) = x(i)  для всех i в [1,nx]
-Y(i,j) = y(j)         и j в [1,ny]
- ]]></screen>
-        <para>
-            и вычисление может быть сделано с <literal>Z=f(X,Y)</literal> (при условии, что вы написали код функции <literal>f</literal> для работы с векторными аргументами, что делается (вообще) с помощью поэлементных операторов <literal>.*</literal>, <literal>./</literal> и <literal>.^</literal> вместо <literal>*</literal>,    <literal>/</literal> и <literal>^</literal>).
-        </para>
-        <para>
-            В трёхмерном случае, рассматриваются три вектора <literal>x, y, z</literal> длиной <literal>nx</literal>, <literal>ny</literal> и <literal>nz</literal>.  <literal>X, Y, Z</literal> являются тремя гиперматрицами размерами <emphasis>nx x ny x nz</emphasis> такими, что:
-        </para>
-        <screen><![CDATA[ 
-X(i,j,k) = x(i)  
-Y(i,j,k) = y(j)   для всех (i,j,k) в [1,nx] x [1,ny] x [1,nz]
-Z(i,j,k) = z(k)
- ]]></screen>
-        <para>
-            В общем случае <literal>m</literal> входных аргументов <literal>x1, x2, ... , xm</literal>, тогда <literal>m</literal> выходных аргументов <literal>X1, X2, ... ,   Xm</literal> являются гиперматрицами размерами <emphasis>nx1 x nx2 x ... x    nxm</emphasis> и:
-        </para>
-        <screen><![CDATA[ 
-Xj(i1,i2,...,ij,...,im) = xj(ij)   
-для всех (i1,i2,...,im) в [1,nx1] x [1,nx2] x ... x [1,nxm]  
- ]]></screen>
-    </refsection>
-    <refsection>
-        <title>Примеры</title>
-        <programlisting role="example"><![CDATA[  
+            
+        </varlistentry>
+        
+    </variablelist>
+    
+</refsection>
+
+<refsection role="description">
+    
+    <title>Описание</title>
+    
+    <para>
+        The first application of <function>ndgrid</function> is to build
+        
+        a grid of nodes meshing the 2D or 3D or N-D space according to 2, 3,
+        
+        or more sets
+        
+        <literal>x</literal>, <literal> y</literal>, etc.. of  
+        
+        "template" coordinates sampled along each direction/dimension of the
+        
+        space that you want to mesh.
+        
+    </para>
+    
+    <para>
+        Hence, the matrix or hypermatrix <literal>X</literal> is made
+        
+        by replicating the vector <literal>x</literal> as all its columns; 
+        
+        the matrix or hypermatrix <literal>Y</literal> is made
+        
+        by replicating the vector <literal>y</literal> as all its rows;
+        
+        <literal>Z</literal> is made of replicating the vector 
+        
+        <literal>z</literal> along all its local thicknesses (3rd dimension); 
+        
+        etc
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [X, Y] = ndgrid([1 3 4], [0 2 4 6])
+ X  = 
+   1.   1.   1.   1.
+   3.   3.   3.   3.
+   4.   4.   4.   4.
+
+   Y  = 
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+   0.   2.   4.   6.
+]]>
+    </screen>
+    
+    <para>
+        
+        This replication scheme can be generalized to any number of dimensions,
+        
+        as well to any type of uniform data. Let's for instance consider 2
+        
+        attributes:
+        
+        <orderedlist>
+            
+            <listitem>The first is a number, to be chosen from the vector say
+                
+                <literal>n = [ 3 7 ]</literal>
+                
+            </listitem>
+            
+            <listitem>The second is a letter, to be chosen from the vector 
+                
+                say <literal>c = ["a" "e" "i" "o" "u" "y"]</literal>
+                
+            </listitem>
+            
+        </orderedlist>
+        
+        Then we want to build the set of all {n,c} possible pairs. It will
+        
+        just be the 2D grid:
+        
+    </para>
+    
+    <screen>
+        
+        <![CDATA[--> [N, C] = ndgrid([3 7],["a" "e" "i" "o" "u" "y"])
+ C  = 
+!a  e  i  o  u  y  !
+!a  e  i  o  u  y  !
+
+ N  = 
+   3.   3.   3.   3.   3.   3.
+   7.   7.   7.   7.   7.   7.
+]]>
+    </screen>
+    
+    <para>Then, the object(i,j) will have the properties 
+        
+        <literal>{n(i) c(j)}</literal> that now can be addressed with
+        
+        <literal>{N(i,j) C(i,j)}</literal>.
+        
+        This kind of grid may be useful to initialize an array of structures.
+        
+    </para>
+    
+    <para>
+        Following examples show how to use <varname>X, Y, Z</varname> in
+        
+        most frequent applications.
+        
+    </para>
+     
+    
+</refsection>
+
+<refsection role="examples">
+    
+    <title>Примеры</title>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #1:</emphasis> 
+    </para>
+    
+    <programlisting role="example"><![CDATA[  
 // создание простой двухмерной координатной сетки
-nx = 40; ny = 40;
-x = linspace(-1,1,nx);
-y = linspace(-1,1,ny);
+x = linspace(-10,2,40);
+y = linspace(-5,5,40);
 [X,Y] = ndgrid(x,y);
-// вычисление функции в координатной сетке и построение её на графике
-deff("z=f(x,y)","z=x.^2 + y.^3")
-Z = f(X,Y);
+
+// Compute ordinates Z(X,Y) on the {X, Y} grid and plot Z(X,Y)
+Z = X - 3*X.*sin(X).*cos(Y-4) ;
 clf()
-plot3d(x,y,Z, flag=[2 6 4]); show_window()
- ]]></programlisting>
-        <scilab:image>
-            nx = 40; ny = 40;
-            x = linspace(-1,1,nx);
-            y = linspace(-1,1,ny);
-            [X,Y] = ndgrid(x,y);
-            deff("z=f(x,y)","z=x.^2 + y.^3")
-            Z = f(X,Y);
-            plot3d(x,y,Z, flag=[2 6 4]);
-        </scilab:image>
-        <programlisting role="example"><![CDATA[  
+plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
+ ]]>    </programlisting>
+    
+    <scilab:image>
+        
+        x = linspace(-10,2,40);
+        
+        y = linspace(-5,5,40);
+        
+        [X,Y] = ndgrid(x,y);
+        
+        Z = X - 3*X.*sin(X).*cos(Y-4) ;
+        
+        clf()
+        
+        plot3d(x,y,Z, flag=[color("green") 2 4], alpha=7, theta=60); show_window()
+        
+    </scilab:image>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #2:</emphasis> 
+    </para>
+    
+    <programlisting role="example"><![CDATA[  
 // создание простой трёхмерной координатной сетки
 nx = 10; ny = 6; nz = 4;
 x = linspace(0,2,nx);
@@ -110,42 +260,157 @@ for j=1:ny
 end
  
 clf()
-plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
+plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
 xtitle("Трёхмерная сетка!"); show_window()
  ]]></programlisting>
-        <scilab:image localized="true">
-            nx = 10; ny = 6; nz = 4;
-            x = linspace(0,2,nx);
-            y = linspace(0,1,ny);
-            z = linspace(0,0.5,nz);
-            [X,Y,Z] = ndgrid(x,y,z);
-            
-            XF=[]; YF=[]; ZF=[];
-            
-            for k=1:nz
-            [xf,yf,zf] = nf3d(X(:,:,k), Y(:,:,k), Z(:,:,k));
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
-            end
-            
-            for j=1:ny
-            [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),..
-            matrix(Y(:,j,:),[nx,nz]),..
-            matrix(Z(:,j,:),[nx,nz]));
-            XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
-            end
-            
-            clf()
-            plot3d(XF,YF,ZF, flag=[0 6 3], leg="X@Y@Z")
-            xtitle("Трёхмерная сетка!"); show_window()
-            
-        </scilab:image>
-    </refsection>
-    <refsection role="see also">
-        <title>Смотрите также</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="kron">kron</link>
-            </member>
-        </simplelist>
-    </refsection>
+    
+    <scilab:image localized="true">
+        
+        nx = 10; ny = 6; nz = 4;
+        
+        x = linspace(0,2,nx);
+        
+        y = linspace(0,1,ny);
+        
+        z = linspace(0,0.5,nz);
+        
+        [X,Y,Z] = ndgrid(x,y,z);
+        
+        
+        
+        XF=[]; YF=[]; ZF=[];
+        
+        
+        
+        for k=1:nz
+        
+        [xf,yf,zf] = nf3d(X(:,:,k), Y(:,:,k), Z(:,:,k));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        
+        
+        for j=1:ny
+        
+        [xf,yf,zf] = nf3d(matrix(X(:,j,:),[nx,nz]),..
+        
+        matrix(Y(:,j,:),[nx,nz]),..
+        
+        matrix(Z(:,j,:),[nx,nz]));
+        
+        XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf];
+        
+        end
+        
+        
+        
+        clf()
+        
+        plot3d(XF,YF,ZF, flag=[0 6 3], 66, 61, leg="X@Y@Z")
+        
+        xtitle("Трёхмерная сетка!"); show_window()
+        
+        
+        
+    </scilab:image>
+    
+    
+    
+    <para>
+        <emphasis role="bold">Example #3: Create a table of digrams:</emphasis> 
+    </para>
+    
+    <programlisting role="example"><![CDATA[  
+[c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+c1+c2
+ ]]>    </programlisting>
+    
+    <screen>
+        
+        <![CDATA[--> [c1, c2] = ndgrid(["a" "b" "c"], ["a" "b" "c" "d" "e" "f" "g" "h"])
+ c2  = 
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+!a  b  c  d  e  f  g  h  !
+
+ c1  = 
+!a  a  a  a  a  a  a  a  !
+!b  b  b  b  b  b  b  b  !
+!c  c  c  c  c  c  c  c  !
+
+--> c1+c2
+ ans  =
+!aa  ab  ac  ad  ae  af  ag  ah  !
+!ba  bb  bc  bd  be  bf  bg  bh  !
+!ca  cb  cc  cd  ce  cf  cg  ch  !
+]]>
+    </screen>
+    
+    
+    
+</refsection>
+
+<refsection role="see also">
+    
+    <title>Смотрите также</title>
+    
+    <simplelist type="inline">
+        
+        <member>
+            
+            <link linkend="meshgrid">meshgrid</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="kron">kron</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="feval">feval</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="eval3d">eval3d</link>
+            
+        </member>
+        
+        <member>
+            
+            <link linkend="nf3d">nf3d</link>
+            
+        </member>
+        
+    </simplelist>
+    
+</refsection>
+
+<refsection role="history">
+    
+    <title>История</title>
+    
+    <revhistory>
+        
+        <revision>
+            
+            <revnumber>6.0</revnumber>
+            
+            <revdescription>Extension to all homogeneous datatypes ([], booleans, encoded integers, polynomials, rationals, strings). Revision of the help page.
+                
+            </revdescription>
+            
+        </revision>
+        
+    </revhistory>
+    
+</refsection>
+
 </refentry>
+