scilab/modules/interpolation/help/ja_JP/linear_interpn.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="linear_interpn" xml:lang="ja">
   3     <refnamediv>
   4         <refname>linear_interpn</refname>
   5         <refpurpose>n 次元線形補間</refpurpose>
   6     </refnamediv>
   7     <refsynopsisdiv>
   8         <title>呼び出し手順</title>
   9         <synopsis>vp = linear_interpn(xp1,xp2,..,xpn, x1, ..., xn, v [,out_mode])</synopsis>
  10     </refsynopsisdiv>
  11     <refsection>
  12         <title>パラメータ</title>
  13         <variablelist>
  14             <varlistentry>
  15                 <term>xp1, xp2, .., xpn</term>
  16                 <listitem>
  17                     <para>同じ大きさの実数ベクトル (または行列)</para>
  18                 </listitem>
  19             </varlistentry>
  20             <varlistentry>
  21                 <term>x1 ,x2, ..., xn</term>
  22                 <listitem>
  23                     <para>
  24                         n次元の補間グリッドを定義する
  25                         (最低でも2つの要素を有する)単調増加の行ベクトル
  26                     </para>
  27                 </listitem>
  28             </varlistentry>
  29             <varlistentry>
  30                 <term>v</term>
  31                 <listitem>
  32                     <para>ベクトル ( n=1の場合), 行列 (n=2の場合) またはハイパー行列 ( n
  33                         &gt; 2の場合) で,
  34                         グリッド点における補間関数の基準値を指定します.
  35                     </para>
  36                 </listitem>
  37             </varlistentry>
  38             <varlistentry>
  39                 <term>out_mode</term>
  40                 <listitem>
  41                     <para>(オプションの) 文字列で,
  42                         グリッド外の評価方法(捕外)を定義します.
  43                     </para>
  44                 </listitem>
  45             </varlistentry>
  46             <varlistentry>
  47                 <term>vp</term>
  48                 <listitem>
  49                     <para>
  50                         <literal>xp1, ...,
  51                             xpn
  52                         </literal>
  53                         と同じ大きさのベクトルまたは行列
  54                     </para>
  55                 </listitem>
  56             </varlistentry>
  57         </variablelist>
  58     </refsection>
  59     <refsection>
  60         <title>説明</title>
  61         <para>
  62             n個のベクトル<literal>x1 ,x2,..., xn</literal>で定義された n次元グリッド
  63             とそのグリッドにおける関数(例えば <emphasis>f</emphasis>)の値を次のように指定すると:
  64         </para>
  65         <informalequation>
  66             <mediaobject>
  67                 <imageobject>
  68                     <imagedata align="center" fileref="../mml/linear_interpn_equation1.mml"/>
  69                 </imageobject>
  70             </mediaobject>
  71         </informalequation>
  72         <para>
  73             この関数は, ベクトル<literal>xp1, xp2, ..., xpn</literal>(または行列)により定義された座標にある
  74             (以下 <emphasis>s</emphasis> と呼ぶ)グリッドから次のように
  75             <emphasis>f</emphasis>の線形補間を計算します:
  76         </para>
  77         <informalequation>
  78             <mediaobject>
  79                 <imageobject>
  80                     <imagedata align="center" fileref="../mml/linear_interpn_equation2.mml"/>
  81                 </imageobject>
  82             </mediaobject>
  83         </informalequation>
  84         <para>
  85             <literal>out_mode</literal> パラメータは捕外の評価規則を設定します:
  86             <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> とすると,
  87             <literal>out_mode</literal> は次の場合に評価規則を定義します:
  88         </para>
  89         <informalequation>
  90             <mediaobject>
  91                 <imageobject>
  92                     <imagedata align="center" fileref="../mml/linear_interpn_equation3.mml"/>
  93                 </imageobject>
  94             </mediaobject>
  95         </informalequation>
  96         <para>その他の選択肢は以下があります:</para>
  97         <variablelist>
  98             <varlistentry>
  99                 <term>"by_zero"</term>
 100                 <listitem>
 101                     <para>ゼロによる捕外が行われますa</para>
 102                 </listitem>
 103             </varlistentry>
 104             <varlistentry>
 105                 <term>"by_nan"</term>
 106                 <listitem>
 107                     <para>Nanによる捕外</para>
 108                 </listitem>
 109             </varlistentry>
 110             <varlistentry>
 111                 <term>"C0"</term>
 112                 <listitem>
 113                     <para>捕外が以下のように定義されます:</para>
 114                     <programlisting role=""><![CDATA[
 115 s(P) = s(proj(P)) where proj(P) is nearest point from P
 116                   located on the grid boundary.
 117  ]]></programlisting>
 118                 </listitem>
 119             </varlistentry>
 120             <varlistentry>
 121                 <term>"natural"</term>
 122                 <listitem>
 123                     <para>捕外はその点に最も近いn線形パッチにより行われます.
 124                     </para>
 125                 </listitem>
 126             </varlistentry>
 127             <varlistentry>
 128                 <term>"periodic"</term>
 129                 <listitem>
 130                     <para>
 131                         <literal>s</literal> は周期的に拡張されます.
 132                     </para>
 133                 </listitem>
 134             </varlistentry>
 135         </variablelist>
 136     </refsection>
 137     <refsection>
 138         <title>例</title>
 139         <programlisting role="example"><![CDATA[
 140 // example 1 : 1d linear interpolation
 141 x = linspace(0,2*%pi,11);
 142 y = sin(x);
 143 xx = linspace(-2*%pi,4*%pi,400)';
 144 yy = linear_interpn(xx, x, y, "periodic");
 145 clf()
 146 plot2d(xx,yy,style=2)
 147 plot2d(x,y,style=-9, strf="000")
 148 xtitle("linear interpolation of sin(x) with 11 interpolation points")
 149
 150 // example 2 : bilinear interpolation
 151 n = 8;
 152 x = linspace(0,2*%pi,n); y = x;
 153 z = 2*sin(x')*sin(y);
 154 xx = linspace(0,2*%pi, 40);
 155 [xp,yp] = ndgrid(xx,xx);
 156 zp = linear_interpn(xp,yp, x, y, z);
 157 clf()
 158 plot3d(xx, xx, zp, flag=[2 6 4])
 159 [xg,yg] = ndgrid(x,x);
 160 param3d1(xg,yg, list(z,-9*ones(1,n)), flag=[0 0])
 161 xtitle("Bilinear interpolation of 2sin(x)sin(y)")
 162 legends("interpolation points",-9,1)
 163 show_window()
 164
 165 // example 3 : bilinear interpolation and experimentation
 166 //             with all the outmode features
 167 nx = 20; ny = 30;
 168 x = linspace(0,1,nx);
 169 y = linspace(0,2, ny);
 170 [X,Y] = ndgrid(x,y);
 171 z = 0.4*cos(2*%pi*X).*cos(%pi*Y);
 172 nxp = 60 ; nyp = 120;
 173 xp = linspace(-0.5,1.5, nxp);
 174 yp = linspace(-0.5,2.5, nyp);
 175 [XP,YP] = ndgrid(xp,yp);
 176 zp1 = linear_interpn(XP, YP, x, y, z, "natural");
 177 zp2 = linear_interpn(XP, YP, x, y, z, "periodic");
 178 zp3 = linear_interpn(XP, YP, x, y, z, "C0");
 179 zp4 = linear_interpn(XP, YP, x, y, z, "by_zero");
 180 zp5 = linear_interpn(XP, YP, x, y, z, "by_nan");
 181 clf()
 182 subplot(2,3,1)
 183 plot3d(x, y, z, leg="x@y@z", flag = [2 4 4])
 184 xtitle("initial function 0.4 cos(2 pi x) cos(pi y)")
 185 subplot(2,3,2)
 186 plot3d(xp, yp, zp1, leg="x@y@z", flag = [2 4 4])
 187 xtitle("Natural")
 188 subplot(2,3,3)
 189 plot3d(xp, yp, zp2, leg="x@y@z", flag = [2 4 4])
 190 xtitle("Periodic")
 191 subplot(2,3,4)
 192 plot3d(xp, yp, zp3, leg="x@y@z", flag = [2 4 4])
 193 xtitle("C0")
 194 subplot(2,3,5)
 195 plot3d(xp, yp, zp4, leg="x@y@z", flag = [2 4 4])
 196 xtitle("by_zero")
 197 subplot(2,3,6)
 198 plot3d(xp, yp, zp5, leg="x@y@z", flag = [2 4 4])
 199 xtitle("by_nan")
 200 show_window()
 201
 202 // example 4 : trilinear interpolation (see splin3d help
 203 //             page which have the same example with
 204 //             tricubic spline interpolation)
 205 exec("SCI/modules/interpolation/demos/interp_demo.sci")
 206 func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
 207 deff("v=f(x,y,z)",func);
 208 n = 5;
 209 x = linspace(0,1,n); y=x; z=x;
 210 [X,Y,Z] = ndgrid(x,y,z);
 211 V = f(X,Y,Z);
 212 // compute (and display) the linear interpolant on some slices
 213 m = 41;
 214 dir = ["z="  "z="  "z="  "x="  "y="];
 215 val = [ 0.1   0.5   0.9   0.5   0.5];
 216 ebox = [0 1 0 1 0 1];
 217
 218 XF=[]; YF=[]; ZF=[]; VF=[];
 219 for i = 1:length(val)
 220   [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m);
 221   Vm = linear_interpn(Xm,Ym,Zm, x, y, z, V);
 222   [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
 223   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
 224   Vp =  linear_interpn(Xp,Yp,Zp, x, y, z, V);
 225   [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
 226   XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
 227 end
 228 nb_col = 128;
 229 vmin = min(VF); vmax = max(VF);
 230 color = dsearch(VF,linspace(vmin,vmax,nb_col+1));
 231 xset("colormap",jetcolormap(nb_col));
 232 clf()
 233 xset("hidden3d",xget("background"))
 234 colorbar(vmin,vmax)
 235 plot3d(XF, YF, list(ZF,color), flag=[-1 6 4])
 236 xtitle("tri-linear interpolation of "+func)
 237 show_window()
 238  ]]></programlisting>
 239     </refsection>
 240     <refsection role="see also">
 241         <title>参照</title>
 242         <simplelist type="inline">
 243             <member>
 244                 <link linkend="interpln">interpln</link>
 245             </member>
 246             <member>
 247                 <link linkend="splin">splin</link>
 248             </member>
 249             <member>
 250                 <link linkend="splin2d">splin2d</link>
 251             </member>
 252             <member>
 253                 <link linkend="splin3d">splin3d</link>
 254             </member>
 255         </simplelist>
 256     </refsection>
 257 </refentry>