95575bdbfc5c6f481d5c699cba798d5136de7e92
[scilab.git] / 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 xselect()
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>