scilab/modules/signal_processing/help/ja_JP/correlation_convolution/corr.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
   2
   3 <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" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="corr">
   4
   5     <refnamediv>
   6
   7         <refname>corr</refname>
   8
   9         <refpurpose>相関 , 共分散</refpurpose>
  10
  11     </refnamediv>
  12
  13     <refsynopsisdiv>
  14
  15         <title>呼び出し手順</title>
  16
  17         <synopsis>[cov,Mean]=corr(x,[y],nlags)
  18
  19             [cov,Mean]=corr('fft',xmacro,[ymacro],n,sect)
  20
  21
  22
  23             [w,xu]=corr('updt',x1,[y1],w0)
  24
  25             [w,xu]=corr('updt',x2,[y2],w,xu)
  26
  27             ...
  28
  29             [wk]=corr('updt',xk,[yk],w,xu)
  30
  31         </synopsis>
  32
  33     </refsynopsisdiv>
  34
  35     <refsection>
  36
  37         <title>引数</title>
  38
  39         <variablelist>
  40
  41             <varlistentry>
  42
  43                 <term>x</term>
  44
  45                 <listitem>
  46
  47                     <para>実数ベクトル</para>
  48
  49                 </listitem>
  50
  51             </varlistentry>
  52
  53             <varlistentry>
  54
  55                 <term>y</term>
  56
  57                 <listitem>
  58
  59                     <para>実数ベクトル, デフォルト値 x.</para>
  60
  61                 </listitem>
  62
  63             </varlistentry>
  64
  65             <varlistentry>
  66
  67                 <term>nlags</term>
  68
  69                 <listitem>
  70
  71                     <para>i整数, 指定した相関係数の数.</para>
  72
  73                 </listitem>
  74
  75             </varlistentry>
  76
  77             <varlistentry>
  78
  79                 <term>xmacro</term>
  80
  81                 <listitem>
  82
  83                     <para>scilab 外部ルーチン (下記参照).</para>
  84
  85                 </listitem>
  86
  87             </varlistentry>
  88
  89             <varlistentry>
  90
  91                 <term>ymacro</term>
  92
  93                 <listitem>
  94
  95                     <para>scilab 外部ルーチン (下記参照), デフォルト値: xmacro</para>
  96
  97                 </listitem>
  98
  99             </varlistentry>
 100
 101             <varlistentry>
 102
 103                 <term>n</term>
 104
 105                 <listitem>
 106
 107                     <para>整数, シーケンス全体の大きさ (下記参照).</para>
 108
 109                 </listitem>
 110
 111             </varlistentry>
 112
 113             <varlistentry>
 114
 115                 <term>sect</term>
 116
 117                 <listitem>
 118
 119                     <para>シーケンスのセクションの大きさ (下記参照).</para>
 120
 121                 </listitem>
 122
 123             </varlistentry>
 124
 125             <varlistentry>
 126
 127                 <term>xi</term>
 128
 129                 <listitem>
 130
 131                     <para>実数ベクトル</para>
 132
 133                 </listitem>
 134
 135             </varlistentry>
 136
 137             <varlistentry>
 138
 139                 <term>yi</term>
 140
 141                 <listitem>
 142
 143                     <para>実数ベクトル,デフォルト値: xi.</para>
 144
 145                 </listitem>
 146
 147             </varlistentry>
 148
 149             <varlistentry>
 150
 151                 <term>cov</term>
 152
 153                 <listitem>
 154
 155                     <para>実数ベクトル, 相関係数</para>
 156
 157                 </listitem>
 158
 159             </varlistentry>
 160
 161             <varlistentry>
 162
 163                 <term>Mean</term>
 164
 165                 <listitem>
 166
 167                     <para>実数または実数ベクトル,  x (および y)の平均</para>
 168
 169                 </listitem>
 170
 171             </varlistentry>
 172
 173         </variablelist>
 174
 175     </refsection>
 176
 177     <refsection>
 178
 179         <title>説明</title>
 180
 181         <para>
 182
 183             以下を計算します.
 184
 185         </para>
 186
 187         <programlisting role=""><![CDATA[
 188          n - m
 189          ====
 190          \                                       1
 191 cov(m) =  >   (x(k) - xmean) (y(m+k) - ymean) * ---
 192          /                                       n
 193          ====
 194          k = 1
 195  ]]></programlisting>
 196
 197         <para>
 198
 199             ただし,   m=0,..,<literal>nlag-1</literal> で,2つのベクトルは
 200
 201             <literal>x=[x(1),..,x(n)]</literal>,
 202
 203             <literal>y=[y(1),..,y(n)]</literal>です.
 204
 205         </para>
 206
 207         <para>
 208
 209             シーケンス x および y が異なる場合, corr(x,y,...)はcorr(y,x,...)
 210
 211             と異なることに注意してください.
 212
 213         </para>
 214
 215         <variablelist>
 216
 217             <varlistentry>
 218
 219                 <term>短いシーケンス</term>
 220
 221                 <listitem>
 222
 223                     <para>
 224
 225                         <literal>[cov,Mean]=corr(x,[y],nlags)</literal> は,
 226
 227                         最初の nlags 個の相関係数および Mean = <literal>mean(x)</literal>
 228
 229                         (<literal>y</literal> が引数として指定された場合,<literal>[x,y]</literal> の平均)
 230
 231                         を返します.
 232
 233                         シーケンス  <literal>x</literal> (または <literal>y</literal>) は実数,
 234
 235                         <literal>x</literal>と<literal>y</literal>は同じ次元 n と仮定されます.
 236
 237                     </para>
 238
 239                 </listitem>
 240
 241             </varlistentry>
 242
 243             <varlistentry>
 244
 245                 <term>長いシーケンス</term>
 246
 247                 <listitem>
 248
 249                     <para>
 250
 251                         <literal>[cov,Mean]=corr('fft',xmacro,[ymacro],n,sect)</literal>
 252
 253                         ここで,<literal>xmacro</literal> は以下のどちらかです
 254
 255                     </para>
 256
 257                     <itemizedlist>
 258
 259                         <listitem>
 260
 261                             <para>
 262
 263                                 <literal>[xx]=xmacro(sect,istart)</literal> という型の関数で,
 264
 265                                 <literal>istart</literal> から
 266
 267                                 <literal>istart+sect-1</literal>までの添字を有するシーケンスの
 268
 269                                 一部を含む
 270
 271                                 <literal>nsect</literal>次のベクトル<literal>xx</literal>を返します.
 272
 273                             </para>
 274
 275                         </listitem>
 276
 277                         <listitem>
 278
 279                             <para>
 280
 281                                 FortranサブルーチンまたはCプロシージャで,
 282
 283                                 同じ計算を行ないます(例えば,<literal>dgetx</literal>の
 284
 285                                 ソースコードを参照ください).
 286
 287                                 <literal>n</literal> = シーケンスの総数.
 288
 289                                 <literal>sect</literal> = シーケンスのセクションの大きさ.
 290
 291                                 <literal>sect</literal> は 2の累乗とする必要があります.
 292
 293                                 <literal>cov</literal> は
 294
 295                                 <literal>sect</literal>次です.
 296
 297                                 計算は FFT により行われます.
 298
 299                             </para>
 300
 301                         </listitem>
 302
 303                     </itemizedlist>
 304
 305                 </listitem>
 306
 307             </varlistentry>
 308
 309             <varlistentry>
 310
 311                 <term>更新法</term>
 312
 313                 <listitem>
 314
 315                     <programlisting role=""><![CDATA[
 316 [w,xu]=corr('updt',x1,[y1],w0)
 317 [w,xu]=corr('updt',x2,[y2],w,xu)
 318  ...
 319 wk=corr('updt',xk,[yk],w,xu)
 320  ]]></programlisting>
 321
 322                     <para>
 323
 324                         この呼び出し手順では,計算結果が<literal>corr</literal>をコールする度に
 325
 326                         更新されます.
 327
 328                     </para>
 329
 330                     <programlisting role=""><![CDATA[
 331 w0 = 0*ones(1,2*nlags);
 332 nlags = power of 2.
 333  ]]></programlisting>
 334
 335                     <para>
 336
 337                         <literal>x1,x2,...</literal> は,
 338
 339                         <literal>x=[x1,x2,...]</literal>で,<literal>xi</literal>の大きさが
 340
 341                         2の累乗となるような<literal>x</literal> の一部です.
 342
 343                         <literal>nlags</literal>個の係数を得るには,
 344
 345                         最後の fft を <literal>c=fft(w,1)/n</literal>;
 346
 347                         <literal>cov=c(1nlags)</literal>を実行する必要があります
 348
 349                         (<literal>n</literal> は <literal>x (y)</literal>の大きさ).
 350
 351                         注意:
 352
 353                         この呼び出し手順は <literal>xmean = ymean = 0</literal> を仮定します.
 354
 355                     </para>
 356
 357                 </listitem>
 358
 359             </varlistentry>
 360
 361         </variablelist>
 362
 363     </refsection>
 364
 365     <refsection>
 366
 367         <title>例</title>
 368
 369         <programlisting role="example"><![CDATA[
 370 x=%pi/10:%pi/10:102.4*%pi;
 371 rand('seed');rand('normal');
 372 y=[.8*sin(x)+.8*sin(2*x)+rand(x);.8*sin(x)+.8*sin(1.99*x)+rand(x)];
 373 c=[];
 374 for j=1:2,for k=1:2,c=[c;corr(y(k,:),y(j,:),64)];end;end;
 375 c=matrix(c,2,128);cov=[];
 376 for j=1:64,cov=[cov;c(:,(j-1)*2+1:2*j)];end;
 377 rand('unif')
 378
 379 rand('normal');x=rand(1,256);y=-x;
 380 deff('[z]=xx(inc,is)','z=x(is:is+inc-1)');
 381 deff('[z]=yy(inc,is)','z=y(is:is+inc-1)');
 382 [c,mxy]=corr(x,y,32);
 383 x=x-mxy(1)*ones(x);y=y-mxy(2)*ones(y);  //centring
 384 c1=corr(x,y,32);c2=corr(x,32);
 385 norm(c1+c2,1)
 386 [c3,m3]=corr('fft',xx,yy,256,32);
 387 norm(c1-c3,1)
 388 [c4,m4]=corr('fft',xx,256,32);
 389 norm(m3,1),norm(m4,1)
 390 norm(c3-c1,1),norm(c4-c2,1)
 391 x1=x(1:128);x2=x(129:256);
 392 y1=y(1:128);y2=y(129:256);
 393 w0=0*ones(1:64);   //32 coeffs
 394 [w1,xu]=corr('u',x1,y1,w0);w2=corr('u',x2,y2,w1,xu);
 395 zz=real(fft(w2,1))/256;c5=zz(1:32);
 396 norm(c5-c1,1)
 397 [w1,xu]=corr('u',x1,w0);w2=corr('u',x2,w1,xu);
 398 zz=real(fft(w2,1))/256;c6=zz(1:32);
 399 norm(c6-c2,1)
 400 rand('unif')
 401
 402 // Fortran または C 外部ルーチンのテスト
 403 //
 404 deff('[y]=xmacro(sec,ist)','y=sin(ist:(ist+sec-1))');
 405 x=xmacro(100,1);
 406 [cc1,mm1]=corr(x,2^3);
 407 [cc,mm]=corr('fft',xmacro,100,2^3);
 408 [cc2,mm2]=corr('fft','corexx',100,2^3);
 409 [max(abs(cc-cc1)),max(abs(mm-mm1)),max(abs(cc-cc2)),max(abs(mm-mm2))]
 410
 411 deff('[y]=ymacro(sec,ist)','y=cos(ist:(ist+sec-1))');
 412 y=ymacro(100,1);
 413 [cc1,mm1]=corr(x,y,2^3);
 414 [cc,mm]=corr('fft',xmacro,ymacro,100,2^3);
 415 [cc2,mm2]=corr('fft','corexx','corexy',100,2^3);
 416 [max(abs(cc-cc1)),max(abs(mm-mm1)),max(abs(cc-cc2)),max(abs(mm-mm2))]
 417  ]]></programlisting>
 418
 419     </refsection>
 420
 421     <refsection role="see also">
 422
 423         <title>参照</title>
 424
 425         <simplelist type="inline">
 426
 427             <member>
 428
 429                 <link linkend="fft">fft</link>
 430
 431             </member>
 432
 433         </simplelist>
 434
 435     </refsection>
 436
 437 </refentry>
 438