scilab/modules/interpolation/help/ja_JP/interp2d.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
   2 <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="interp2d" xml:lang="ja">
   3     <refnamediv>
   4         <refname>interp2d</refname>
   5         <refpurpose>双3次スプライン (2d) 評価関数</refpurpose>
   6     </refnamediv>
   7     <refsynopsisdiv>
   8         <title>呼び出し手順</title>
   9         <synopsis>[zp[,dzpdx,dzpdy[,d2zpdxx,d2zpdxy,d2zpdyy]]]=interp2d(xp,yp,x,y,C [,out_mode])</synopsis>
  10     </refsynopsisdiv>
  11     <refsection>
  12         <title>パラメータ</title>
  13         <variablelist>
  14             <varlistentry>
  15                 <term>xp, yp</term>
  16                 <listitem>
  17                     <para>同じ大きさの実数行列または行列</para>
  18                 </listitem>
  19             </varlistentry>
  20             <varlistentry>
  21                 <term>x,y,C</term>
  22                 <listitem>
  23                     <para>
  24                         双3次スプラインまたはサブスプライン関数を定義する実数ベクトル
  25                         (以下<literal>s</literal>と呼びます)
  26                     </para>
  27                 </listitem>
  28             </varlistentry>
  29             <varlistentry>
  30                 <term>out_mode</term>
  31                 <listitem>
  32                     <para>[x(1),x(nx)]x[y(1),y(ny)]の外にある値の評価方法を定義する(オプションの)文字列</para>
  33                 </listitem>
  34             </varlistentry>
  35             <varlistentry>
  36                 <term>zp</term>
  37                 <listitem>
  38                     <para>
  39                         <literal>xp</literal> および
  40                         <literal>yp</literal>と同じ形式のベクトルまたは行列 ,
  41                         これらの点における<literal>s</literal>の要素毎の評価.
  42                     </para>
  43                 </listitem>
  44             </varlistentry>
  45             <varlistentry>
  46                 <term>dzpdx, dzpdy</term>
  47                 <listitem>
  48                     <para>
  49                         <literal>xp</literal> および <literal>yp</literal>と同じ形式のベクトル (または行列)
  50                         これらの点における<literal>s</literal>の要素毎の1次微分.
  51                     </para>
  52                 </listitem>
  53             </varlistentry>
  54             <varlistentry>
  55                 <term>d2zpdxx, d2zpdxy, d2zpdyy</term>
  56                 <listitem>
  57                     <para>
  58                         <literal>xp</literal> および <literal>yp</literal>と同じ形式の
  59                         ベクトル (または行列),
  60                         これらの点における<literal>s</literal>の要素毎の2次微分.
  61                     </para>
  62                 </listitem>
  63             </varlistentry>
  64         </variablelist>
  65     </refsection>
  66     <refsection>
  67         <title>説明</title>
  68         <para>
  69             双3次スプラインまたはサブスプライン関数を定義する
  70             3つのベクトル <literal>(x,y,C)</literal>
  71             (<link linkend="splin2d">splin2d</link>参照)を指定すると,
  72             この関数は, 次のように<emphasis>(xp(i),yp(i))</emphasis>における
  73             <emphasis>s</emphasis> (要すれば <emphasis>ds/dx,
  74                 ds/dy, d2s/dxx, d2s/dxy, d2s/dyy
  75             </emphasis>
  76             も)を評価します:
  77         </para>
  78         <informalequation>
  79             <mediaobject>
  80                 <imageobject>
  81                     <imagedata fileref="../mml/interp2_equation_1.mml"/>
  82                 </imageobject>
  83             </mediaobject>
  84         </informalequation>
  85         <para>
  86             <literal>out_mode</literal> パラメータは,
  87             捕外,すなわち<emphasis>(xp(i),yp(i))</emphasis>が
  88             [x(1),x(nx)]x[y(1),y(ny)]にない場合,
  89             の計算手法を定義します:
  90         </para>
  91         <variablelist>
  92             <varlistentry>
  93                 <term>"by_zero"</term>
  94                 <listitem>
  95                     <para>ゼロによる捕外が行われます</para>
  96                 </listitem>
  97             </varlistentry>
  98             <varlistentry>
  99                 <term>"by_nan"</term>
 100                 <listitem>
 101                     <para>Nanによる捕外</para>
 102                 </listitem>
 103             </varlistentry>
 104             <varlistentry>
 105                 <term>"C0"</term>
 106                 <listitem>
 107                     <para>捕外は以下のように定義されます :</para>
 108                     <programlisting role=""><![CDATA[
 109 s(x,y) = s(proj(x,y)) where proj(x,y) is nearest point
 110                       of [x(1),x(nx)]x[y(1),y(ny)] from (x,y)
 111  ]]></programlisting>
 112                 </listitem>
 113             </varlistentry>
 114             <varlistentry>
 115                 <term>"natural"</term>
 116                 <listitem>
 117                     <para>捕外は(x,y)から最も近い双三次パッチにより行われます.</para>
 118                 </listitem>
 119             </varlistentry>
 120             <varlistentry>
 121                 <term>"periodic"</term>
 122                 <listitem>
 123                     <para>
 124                         <literal>s</literal> は周期的に拡張されます.
 125                     </para>
 126                 </listitem>
 127             </varlistentry>
 128         </variablelist>
 129     </refsection>
 130     <refsection>
 131         <title>例</title>
 132         <programlisting role="example"><![CDATA[
 133 // see the examples of splin2d
 134
 135 // this example shows some different extrapolation features
 136 // interpolation of cos(x)cos(y)
 137 n = 7;  // a n x n interpolation grid
 138 x = linspace(0,2*%pi,n); y = x;
 139 z = cos(x')*cos(y);
 140 C = splin2d(x, y, z, "periodic");
 141
 142 // now evaluate on a bigger domain than [0,2pi]x [0,2pi]
 143 m = 80; // discretisation parameter of the evaluation grid
 144 xx = linspace(-0.5*%pi,2.5*%pi,m); yy = xx;
 145 [XX,YY] = ndgrid(xx,yy);
 146 zz1 = interp2d(XX,YY, x, y, C, "C0");
 147 zz2 = interp2d(XX,YY, x, y, C, "by_zero");
 148 zz3 = interp2d(XX,YY, x, y, C, "periodic");
 149 zz4 = interp2d(XX,YY, x, y, C, "natural");
 150 clf()
 151 subplot(2,2,1)
 152 plot3d(xx, yy, zz1, flag=[2 6 4])
 153 xtitle("extrapolation with the C0 outmode")
 154 subplot(2,2,2)
 155 plot3d(xx, yy, zz2, flag=[2 6 4])
 156 xtitle("extrapolation with the by_zero outmode")
 157 subplot(2,2,3)
 158 plot3d(xx, yy, zz3, flag=[2 6 4])
 159 xtitle("extrapolation with the periodic outmode")
 160 subplot(2,2,4)
 161 plot3d(xx, yy, zz4, flag=[2 6 4])
 162 xtitle("extrapolation with the natural outmode")
 163 show_window()
 164  ]]></programlisting>
 165     </refsection>
 166     <refsection role="see also">
 167         <title>参照</title>
 168         <simplelist type="inline">
 169             <member>
 170                 <link linkend="splin2d">splin2d</link>
 171             </member>
 172         </simplelist>
 173     </refsection>
 174 </refentry>