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  • 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

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modules/interpolation/help/en_US/eval_cshep2d.xml
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<?xml version="1.0" encoding="UTF-8"?>
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:id="eval_cshep2d" xml:lang="en">
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  <refnamediv>
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    <refname>eval_cshep2d</refname>
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    <refpurpose>bidimensional cubic shepard interpolation
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      evaluation
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    </refpurpose>
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  </refnamediv>
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  <refsynopsisdiv>
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    <title>Calling Sequence</title>
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    <synopsis>[zp [,dzpdx, dzpdy [,d2zpdxx,d2zpdxy,d2zpdyy]]] = eval_cshep2d(xp, yp, tl_coef)</synopsis>
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  </refsynopsisdiv>
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  <refsection>
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    <title>Arguments</title>
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    <variablelist>
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      <varlistentry>
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        <term>xp, yp</term>
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        <listitem>
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          <para>two real vectors (or matrices) of the same size</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>tl_coef</term>
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        <listitem>
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          <para>a tlist scilab structure (of type cshep2d) defining a cubic
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            Shepard interpolation function (named <literal>S</literal> in the
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            following)
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          </para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>zp</term>
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        <listitem>
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          <para>
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            vector (or matrix) of the same size than <literal>xp</literal>
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            and <literal>yp</literal>, evaluation of the interpolant
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            <literal>S</literal> at these points
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          </para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>dzpdx,dzpdy</term>
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        <listitem>
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          <para>vectors (or matrices) of the same size than
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            <literal>xp</literal> and <literal>yp</literal>, evaluation of the
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            first derivatives of <literal>S</literal> at these points
47
 
          </para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>d2zpdxx,d2zpdxy,d2zpdyy</term>
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        <listitem>
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          <para>vectors (or matrices) of the same size than
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            <literal>xp</literal> and <literal>yp</literal>, evaluation of the
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            second derivatives of <literal>S</literal> at these points
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          </para>
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        </listitem>
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      </varlistentry>
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    </variablelist>
60
 
  </refsection>
61
 
  <refsection>
62
 
    <title>Description</title>
63
 
    <para>This is the evaluation routine for cubic Shepard interpolation
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      function computed with <link linkend="cshep2d">cshep2d</link>, that is
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      :
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    </para>
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    <informalequation>
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      <mediaobject>
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        <imageobject>
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          <imagedata align="center" fileref="../mml/eval_cshep2d_equation1.mml"/>
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        </imageobject>
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      </mediaobject>
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    </informalequation>
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  </refsection>
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  <refsection>
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    <title>Remark</title>
77
 
    <para>
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      The interpolant <emphasis>S</emphasis> is C2 (twice continuously
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      differentiable) but is also extended by zero for
80
 
      <emphasis>(x,y)</emphasis> far enough the interpolation points. This leads
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      to a discontinuity in a region far outside the interpolation points, and
82
 
      so, is not cumbersome in practice (in a general manner, evaluation outside
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      interpolation points (i.e. extrapolation) leads to very inacurate
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      results).
85
 
    </para>
86
 
  </refsection>
87
 
  <refsection>
88
 
    <title>Examples</title>
89
 
    <programlisting role="example"><![CDATA[ 
 
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    <refnamediv>
 
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        <refname>eval_cshep2d</refname>
 
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        <refpurpose>bidimensional cubic shepard interpolation
 
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            evaluation
 
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        </refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
10
        <title>Calling Sequence</title>
 
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        <synopsis>[zp [,dzpdx, dzpdy [,d2zpdxx,d2zpdxy,d2zpdyy]]] = eval_cshep2d(xp, yp, tl_coef)</synopsis>
 
12
    </refsynopsisdiv>
 
13
    <refsection>
 
14
        <title>Arguments</title>
 
15
        <variablelist>
 
16
            <varlistentry>
 
17
                <term>xp, yp</term>
 
18
                <listitem>
 
19
                    <para>two real vectors (or matrices) of the same size</para>
 
20
                </listitem>
 
21
            </varlistentry>
 
22
            <varlistentry>
 
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                <term>tl_coef</term>
 
24
                <listitem>
 
25
                    <para>a tlist scilab structure (of type cshep2d) defining a cubic
 
26
                        Shepard interpolation function (named <literal>S</literal> in the
 
27
                        following)
 
28
                    </para>
 
29
                </listitem>
 
30
            </varlistentry>
 
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            <varlistentry>
 
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                <term>zp</term>
 
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                <listitem>
 
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                    <para>
 
35
                        vector (or matrix) of the same size than <literal>xp</literal>
 
36
                        and <literal>yp</literal>, evaluation of the interpolant
 
37
                        <literal>S</literal> at these points
 
38
                    </para>
 
39
                </listitem>
 
40
            </varlistentry>
 
41
            <varlistentry>
 
42
                <term>dzpdx,dzpdy</term>
 
43
                <listitem>
 
44
                    <para>vectors (or matrices) of the same size than
 
45
                        <literal>xp</literal> and <literal>yp</literal>, evaluation of the
 
46
                        first derivatives of <literal>S</literal> at these points
 
47
                    </para>
 
48
                </listitem>
 
49
            </varlistentry>
 
50
            <varlistentry>
 
51
                <term>d2zpdxx,d2zpdxy,d2zpdyy</term>
 
52
                <listitem>
 
53
                    <para>vectors (or matrices) of the same size than
 
54
                        <literal>xp</literal> and <literal>yp</literal>, evaluation of the
 
55
                        second derivatives of <literal>S</literal> at these points
 
56
                    </para>
 
57
                </listitem>
 
58
            </varlistentry>
 
59
        </variablelist>
 
60
    </refsection>
 
61
    <refsection>
 
62
        <title>Description</title>
 
63
        <para>This is the evaluation routine for cubic Shepard interpolation
 
64
            function computed with <link linkend="cshep2d">cshep2d</link>, that is
 
65
            :
 
66
        </para>
 
67
        <informalequation>
 
68
            <mediaobject>
 
69
                <imageobject>
 
70
                    <imagedata align="center" fileref="../mml/eval_cshep2d_equation1.mml"/>
 
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                </imageobject>
 
72
            </mediaobject>
 
73
        </informalequation>
 
74
    </refsection>
 
75
    <refsection>
 
76
        <title>Remark</title>
 
77
        <para>
 
78
            The interpolant <emphasis>S</emphasis> is C2 (twice continuously
 
79
            differentiable) but is also extended by zero for
 
80
            <emphasis>(x,y)</emphasis> far enough the interpolation points. This leads
 
81
            to a discontinuity in a region far outside the interpolation points, and
 
82
            so, is not cumbersome in practice (in a general manner, evaluation outside
 
83
            interpolation points (i.e. extrapolation) leads to very inacurate
 
84
            results).
 
85
        </para>
 
86
    </refsection>
 
87
    <refsection>
 
88
        <title>Examples</title>
 
89
        <programlisting role="example"><![CDATA[ 
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// see example section of cshep2d
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// this example shows the behavior far from the interpolation points ...
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legends(["extrapolation region","interpolation region"],[2 3],1)
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show_window()
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 ]]></programlisting>
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  </refsection>
116
 
  <refsection role="see also">
117
 
    <title>See Also</title>
118
 
    <simplelist type="inline">
119
 
      <member>
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        <link linkend="cshep2d">cshep2d</link>
121
 
      </member>
122
 
    </simplelist>
123
 
  </refsection>
124
 
  <refsection>
125
 
    <title>History</title>
126
 
    <revhistory>
127
 
      <revision>
128
 
        <revnumber>5.4.0</revnumber>
129
 
        <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
130
 
      </revision>
131
 
    </revhistory>
132
 
  </refsection>
 
115
    </refsection>
 
116
    <refsection role="see also">
 
117
        <title>See Also</title>
 
118
        <simplelist type="inline">
 
119
            <member>
 
120
                <link linkend="cshep2d">cshep2d</link>
 
121
            </member>
 
122
        </simplelist>
 
123
    </refsection>
 
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    <refsection>
 
125
        <title>History</title>
 
126
        <revhistory>
 
127
            <revision>
 
128
                <revnumber>5.4.0</revnumber>
 
129
                <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
 
130
            </revision>
 
131
        </revhistory>
 
132
    </refsection>
133
133
</refentry>