Elementary function: move ndgrid to the right place after 6ad9efdc
[scilab.git] / scilab / modules / elementary_functions / help / pt_BR / elementarymatrices / ndgrid.xml
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>
+