← Back to branch summary

~ubuntu-branches/ubuntu/raring/scilab/raring-proposed

« back to all changes in this revision

Viewing changes to modules/linear_algebra/help/en_US/range.xml

  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

Show diffs side-by-side

added added

removed removed

Lines of Context:
modules/linear_algebra/help/en_US/range.xml
1
 
<?xml version="1.0" encoding="UTF-8"?>
2
 
<!--
3
 
 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4
 
 * Copyright (C) 2008 - INRIA
5
 
 * 
6
 
 * This file must be used under the terms of the CeCILL.
7
 
 * This source file is licensed as described in the file COPYING, which
8
 
 * you should have received as part of this distribution.  The terms
9
 
 * are also available at    
10
 
 * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
11
 
 *
12
 
 -->
13
 
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="range">
14
 
  <refnamediv>
15
 
    <refname>range</refname>
16
 
    <refpurpose> range (span) of A^k</refpurpose>
17
 
  </refnamediv>
18
 
  <refsynopsisdiv>
19
 
    <title>Calling Sequence</title>
20
 
    <synopsis>[X,dim]=range(A,k)</synopsis>
21
 
  </refsynopsisdiv>
22
 
  <refsection>
23
 
    <title>Arguments</title>
24
 
    <variablelist>
25
 
      <varlistentry>
26
 
        <term>A</term>
27
 
        <listitem>
28
 
          <para>real square matrix</para>
29
 
        </listitem>
30
 
      </varlistentry>
31
 
      <varlistentry>
32
 
        <term>k</term>
33
 
        <listitem>
34
 
          <para>integer</para>
35
 
        </listitem>
36
 
      </varlistentry>
37
 
      <varlistentry>
38
 
        <term>X</term>
39
 
        <listitem>
40
 
          <para>orthonormal real matrix</para>
41
 
        </listitem>
42
 
      </varlistentry>
43
 
      <varlistentry>
44
 
        <term>dim</term>
45
 
        <listitem>
46
 
          <para>integer (dimension of subspace)</para>
47
 
        </listitem>
48
 
      </varlistentry>
49
 
    </variablelist>
50
 
  </refsection>
51
 
  <refsection>
52
 
    <title>Description</title>
53
 
    <para>
54
 
      Computation of Range <literal>A^k</literal> ; the first dim rows of <literal>X</literal> span the
55
 
      range of <literal>A^k</literal>. The last rows of <literal>X</literal> span the
56
 
      orthogonal complement of the range. <literal>X*X'</literal> is the Identity matrix
57
 
    </para>
58
 
  </refsection>
59
 
  <refsection>
60
 
    <title>Examples</title>
61
 
    <programlisting role="example"><![CDATA[ 
62
 
A=rand(4,2)*rand(2,4);   // 4 column vectors, 2 independent.
63
 
[X,dim]=range(A,1);dim   // compute the range
64
 
 
65
 
y1=A*rand(4,1);          //a vector which is in the range of A
66
 
y2=rand(4,1);            //a vector which is not  in the range of A
67
 
norm(X(dim+1:$,:)*y1)    //the last entries are zeros, y1 is in the range of A
68
 
norm(X(dim+1:$,:)*y2)    //the last entries are not zeros
69
 
 
70
 
I=X(1:dim,:)'            //I is a basis of the range
71
 
coeffs=X(1:dim,:)*y1     // components of y1 relative to the I basis
72
 
 
73
 
norm(I*coeffs-y1)        //check
74
 
 ]]></programlisting>
75
 
  </refsection>
76
 
  <refsection role="see also">
77
 
    <title>See Also</title>
78
 
    <simplelist type="inline">
79
 
      <member>
80
 
        <link linkend="fullrfk">fullrfk</link>
81
 
      </member>
82
 
      <member>
83
 
        <link linkend="rowcomp">rowcomp</link>
84
 
      </member>
85
 
    </simplelist>
86
 
  </refsection>
87
 
  <refsection>
88
 
    <title>Used Functions</title>
89
 
    <para>
90
 
      The <literal>range</literal> function is based on the <link linkend="rowcomp">rowcomp</link> function
91
 
      which uses the <link linkend="svd">svd</link> decomposition.
92
 
    </para>
93
 
  </refsection>
94
 
</refentry>