scilab/modules/differential_equations/help/ja_JP/daskr.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
   2
   3 <!--\r
   4  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab\r
   5  * Copyright (C) 2013 - Scilab Enterprises\r
   6  *\r
   7  * This file must be used under the terms of the CeCILL.\r
   8  * This source file is licensed as described in the file COPYING, which\r
   9  * you should have received as part of this distribution.\r
  10  * The terms are also available at\r
  11  * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt\r
  12  *\r
  13  -->
  14
  15 <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="daskr" xml:lang="ja">
  16
  17     <refnamediv>
  18
  19         <refname>daskr</refname>
  20
  21         <refpurpose>ゼロ交差を有するDAEソルバー</refpurpose>
  22
  23     </refnamediv>
  24
  25     <refsynopsisdiv>
  26
  27         <title>呼び出し手順</title>
  28
  29         <synopsis>[r, nn [, hd]] = daskr(x0, t0, t [, atol [, rtol]], res [, jac], ng, surf [, info [, psol] [, pjac]] [, hd])</synopsis>
  30
  31     </refsynopsisdiv>
  32
  33     <refsection>
  34
  35         <title>引数</title>
  36
  37         <variablelist>
  38
  39             <varlistentry>
  40
  41                 <term>x0</term>
  42
  43                 <listitem>
  44
  45                     <para>
  46
  47                         は <literal>y0</literal> (<literal>ydot0</literal> は
  48
  49                         ゼロを初期推定値として <literal>dassl</literal> により推定)
  50
  51                         または行列 <literal>[y0 ydot0]</literal>のどちらかです.
  52
  53                         <literal>g(t,y0,ydot0)</literal> はゼロに等しい必要があります.
  54
  55                         <literal>ydot0</literal> の推定値のみ既知の場合,
  56
  57                         <literal>info(7)=1</literal> を指定してください.
  58
  59                     </para>
  60
  61                     <variablelist>
  62
  63                         <varlistentry>
  64
  65                             <term>y0</term>
  66
  67                             <listitem>
  68
  69                                 <para>初期条件の実数列ベクトル.</para>
  70
  71                             </listitem>
  72
  73                         </varlistentry>
  74
  75                         <varlistentry>
  76
  77                             <term>ydot0</term>
  78
  79                             <listitem>
  80
  81                                 <para>
  82
  83                                     <literal>y</literal> at <literal>t0</literal> (推定値でも可)における<literal>y</literal>の時間微分の実数列ベクトル.
  84
  85                                 </para>
  86
  87                             </listitem>
  88
  89                         </varlistentry>
  90
  91                     </variablelist>
  92
  93                 </listitem>
  94
  95             </varlistentry>
  96
  97             <varlistentry>
  98
  99                 <term>t0</term>
 100
 101                 <listitem>
 102
 103                     <para>実数, 初期時間.</para>
 104
 105                 </listitem>
 106
 107             </varlistentry>
 108
 109             <varlistentry>
 110
 111                 <term>t</term>
 112
 113                 <listitem>
 114
 115                     <para>実数スカラーまたはベクトル.
 116
 117                         解を得る時刻を指定します.
 118
 119                         <literal>info(2)=1</literal>と指定することにより,
 120
 121                         dasslの各ステップ点で解を得ることができます.
 122
 123                     </para>
 124
 125                 </listitem>
 126
 127             </varlistentry>
 128
 129             <varlistentry>
 130
 131                 <term>nn</term>
 132
 133                 <listitem>
 134
 135                     <para>
 136
 137                         2個のエントリ <literal>[times num]</literal>を有するベクトル.
 138
 139                         <literal>times</literal> は面が交差する点における時間の値,
 140
 141                         <literal>num</literal> は交差する面の数です.
 142
 143                     </para>
 144
 145                 </listitem>
 146
 147             </varlistentry>
 148
 149             <varlistentry>
 150
 151                 <term>atol, rtol</term>
 152
 153                 <listitem>
 154
 155                     <para>
 156
 157                         <literal>y</literal>と同じ大きさの実数スカラーまたは列ベクトル.
 158
 159                         <literal>atol, rtol</literal> はそれぞれ解の絶対及び相対許容誤差を
 160
 161                         表します. この許容誤差は
 162
 163                         <literal>y</literal>の各要素について指定されます.
 164
 165                     </para>
 166
 167                 </listitem>
 168
 169             </varlistentry>
 170
 171             <varlistentry>
 172
 173                 <term>res</term>
 174
 175                 <listitem>
 176
 177                     <para>
 178
 179                         <link linkend="external">external</link> (関数またはリストまたは文字列).
 180
 181                         <literal>g(t,y,ydot)</literal>の値を計算します. 以下のようになります :
 182
 183                     </para>
 184
 185                     <itemizedlist>
 186
 187                         <listitem>
 188
 189                             <para>Scilab関数.</para>
 190
 191                             <para>呼び出し手順は以下とします
 192
 193                                 <literal>[r,ires]=res(t,y,ydot)</literal> かつ
 194
 195                                 <literal>res</literal> は残差
 196
 197                                 <literal>r=g(t,y,ydot)</literal> かつ エラーフラグ
 198
 199                                 <literal>ires</literal>を返すこと.
 200
 201                                 <literal>res</literal> は, <literal>r</literal>の計算に成功した場合は<literal>ires = 0</literal>,
 202
 203                                 残差が<literal>(t,y,ydot)</literal> において局所的に定義されないには
 204
 205                                 <literal>=-1</literal>, パラメータが許容範囲を逸脱している場合には <literal>=-2</literal>
 206
 207                                 となります.
 208
 209                             </para>
 210
 211                         </listitem>
 212
 213                         <listitem>
 214
 215                             <para>リスト.</para>
 216
 217                             <para>この形式により, t, y, ydot 以外のパラメータを関数に指定出来ます.
 218
 219                                 以下のような形式とする必要があります:
 220
 221                             </para>
 222
 223                             <programlisting role="no-scilab-exec"><![CDATA[\r
 224 list(res,x1,x2,...)\r
 225  ]]></programlisting>
 226
 227                             <para>ただし関数
 228
 229                                 <literal>res</literal> の呼び出し形式は以下とします
 230
 231                             </para>
 232
 233                             <programlisting role="no-scilab-exec"><![CDATA[\r
 234 r=res(t,y,ydot,x1,x2,...)\r
 235  ]]></programlisting>
 236
 237                             <para>
 238
 239                                 <literal>res</literal> は
 240
 241                                 <literal>(t,y,ydot,x1,x2,...)</literal>の関数として<literal>r=g(t,y,ydot)</literal>を返します.
 242
 243                             </para>
 244
 245                             <para>
 246                                 警告: この形式は<literal>関数</literal>に渡す別の引数が存在しない場合には
 247
 248                                 使用するべきではありません.
 249
 250                             </para>
 251
 252                         </listitem>
 253
 254                         <listitem>
 255
 256                             <para>文字列.</para>
 257
 258                             <para>ScilabにリンクされたCまたはFortranサブルーチンの名前を指定します.
 259
 260                             </para>
 261
 262                             <para>Cの場合, 呼び出し手順は次のようにします:</para>
 263
 264                             <programlisting role="no-scilab-exec"><![CDATA[\r
 265 void res(double *t, double y[], double yd[], double r[],\r
 266          int *ires, double rpar[], int ipar[])\r
 267  ]]></programlisting>
 268
 269                             <para>Fortranの場合, 以下としま:</para>
 270
 271                             <programlisting role="no-scilab-exec"><![CDATA[\r
 272 subroutine res(t,y,yd,r,ires,rpar,ipar)\r
 273 double precision t, y(*),yd(*),r(*),rpar(*)\r
 274 integer ires,ipar(*)\r
 275  ]]></programlisting>
 276
 277                             <para>
 278
 279                                 <literal>rpar</literal> および <literal>ipar</literal> 配列は存在する必要がありますが使用できません.
 280
 281                             </para>
 282
 283                         </listitem>
 284
 285                     </itemizedlist>
 286
 287                 </listitem>
 288
 289             </varlistentry>
 290
 291             <varlistentry>
 292
 293                 <term>jac</term>
 294
 295                 <listitem>
 296
 297                     <para>
 298
 299                         <link linkend="external">external</link> (関数またはリストまたは文字列). 指定した<literal>cj</literal>
 300
 301                         の値について, <literal>dg/dy + cj*dg/dydot</literal> の値を計算します.
 302
 303                     </para>
 304
 305                     <itemizedlist>
 306
 307                         <listitem>
 308
 309                             <para>Scilab関数.</para>
 310
 311                             <para>
 312                                 呼び出し手順は <literal>r=jac(t,y,ydot,cj)</literal> で,
 313
 314                                 <literal>jac</literal> 関数は
 315
 316                                 <literal>r=dg(t,y,ydot)/dy+cj*dg(t,y,ydot)/dydot</literal>を返す必要があります.
 317
 318                                 ただし,
 319
 320                                 <literal>cj</literal> は実数スカラーです.
 321
 322                             </para>
 323
 324                         </listitem>
 325
 326                         <listitem>
 327
 328                             <para>リスト.</para>
 329
 330                             <para>以下のように指定します</para>
 331
 332                             <programlisting role="no-scilab-exec"><![CDATA[\r
 333 list(jac,x1,x2,...)\r
 334  ]]></programlisting>
 335
 336                             <para>ただし関数
 337
 338                                 <literal>jac</literal> の呼び出し手順は以下のようになります
 339
 340                             </para>
 341
 342                             <programlisting role="no-scilab-exec"><![CDATA[\r
 343 r=jac(t,y,ydot,cj,x1,x2,...)\r
 344  ]]></programlisting>
 345
 346                             <para>
 347
 348                                 さらに<literal>jac</literal> は
 349
 350                                 <literal>(t,y,ydot,cj,x1,x2,...)</literal>の関数として<literal>dg/dy + cj*dg/dydot</literal> を返します.
 351
 352                             </para>
 353
 354                         </listitem>
 355
 356                         <listitem>
 357
 358                             <para>文字列.</para>
 359
 360                             <para>scilabにリンクされたCまたはFortran サブルーチンの名前を指定します
 361
 362                             </para>
 363
 364                             <para>Cの場合, 呼び出し手順は以下となります:</para>
 365
 366                             <programlisting role="no-scilab-exec"><![CDATA[\r
 367 void jac(double *t, double y[], double yd[], double pd[],\r
 368          double *cj, double rpar[], int ipar[])\r
 369  ]]></programlisting>
 370
 371                             <para>Fortranの場合は以下となります:</para>
 372
 373                             <programlisting role="no-scilab-exec"><![CDATA[\r
 374 subroutine jac(t,y,yd,pd,cj,rpar,ipar)\r
 375 double precision t, y(*),yd(*),pd(*),cj,rpar(*)\r
 376 integer ipar(*)\r
 377  ]]></programlisting>
 378
 379                         </listitem>
 380
 381                     </itemizedlist>
 382
 383                 </listitem>
 384
 385             </varlistentry>
 386
 387             <varlistentry>
 388
 389                 <term>surf</term>
 390
 391                 <listitem>
 392
 393                     <para>
 394
 395                         <link linkend="external">external</link> (関数またはリストまたは文字列).
 396
 397                         <literal>ng</literal>個の要素を有する列ベクトル <literal>surf(t,y)</literal> の値を計算します.
 398
 399                         各要素は局面を定義します.
 400
 401                         これは以下のように定義できます:
 402
 403                     </para>
 404
 405                     <itemizedlist>
 406
 407                         <listitem>
 408
 409                             <para>Scilab関数.</para>
 410
 411                             <para>呼び出し手順は
 412
 413                                 <literal>surf(t,y)</literal>とします
 414
 415                             </para>
 416
 417                         </listitem>
 418
 419                         <listitem>
 420
 421                             <para>リスト.</para>
 422
 423                             <para>以下のように定義します</para>
 424
 425                             <programlisting role="no-scilab-exec"><![CDATA[\r
 426 list(surf,x1,x2,...)\r
 427  ]]></programlisting>
 428
 429                             <para>ただし関数
 430
 431                                 <literal>surf</literal>の呼び出し手順は以下とします
 432
 433                             </para>
 434
 435                             <programlisting role="no-scilab-exec"><![CDATA[\r
 436 r=surf(t,y,x1,x2,...)\r
 437  ]]></programlisting>
 438
 439                         </listitem>
 440
 441                         <listitem>
 442
 443                             <para>文字列.</para>
 444
 445                             <para>ScilabにリンクされたC または Fortran サブルーチンの名前を指定します.
 446
 447                             </para>
 448
 449                             <para>Cの場合, 呼び出し手順は以下とします:</para>
 450
 451                             <programlisting role="no-scilab-exec"><![CDATA[\r
 452 void surf(int *ny, double *t, double y[], int *ng, double gout[])\r
 453  ]]></programlisting>
 454
 455                             <para>Fortranの場合,  以下とします:</para>
 456
 457                             <programlisting role="no-scilab-exec"><![CDATA[\r
 458 subroutine surf(ny,t,y,ng,gout)\r
 459 double precision t, y(*),gout(*)\r
 460 integer ny,ng\r
 461  ]]></programlisting>
 462
 463                         </listitem>
 464
 465                     </itemizedlist>
 466
 467                 </listitem>
 468
 469             </varlistentry>
 470
 471             <varlistentry>
 472
 473                 <term>info</term>
 474
 475                 <listitem>
 476
 477                     <para>
 478
 479                         <literal>14</literal> 個の要素を有するリスト. デフォルト値は
 480
 481                         <literal>list([],0,[],[],[],0,[],0,[],0,[],[],[],1)</literal>です.
 482
 483                     </para>
 484
 485                     <variablelist>
 486
 487                         <varlistentry>
 488
 489                             <term>info(1)</term>
 490
 491                             <listitem>
 492
 493                                 <para>
 494
 495                                     <literal>g</literal> を評価できる時刻の最大値を実数スカラーで指定します.
 496
 497                                     時間を制限しない場合は空の行列<literal>[]</literal>を指定します.
 498
 499                                 </para>
 500
 501                             </listitem>
 502
 503                         </varlistentry>
 504
 505                         <varlistentry>
 506
 507                             <term>info(2)</term>
 508
 509                             <listitem>
 510
 511                                 <para>
 512
 513                                     <literal>dassl</literal> が中間計算値を返すか(<literal>flag=1</literal>)
 514
 515                                     またはユーザが指定した時刻のみを返すか
 516
 517                                     (<literal>flag=0</literal>)を指定するフラグ.
 518
 519                                 </para>
 520
 521                             </listitem>
 522
 523                         </varlistentry>
 524
 525                         <varlistentry>
 526
 527                             <term>info(3)</term>
 528
 529                             <listitem>
 530
 531                                 <para>
 532
 533                                     <literal>2</literal> 要素のベクトルで,
 534
 535                                     <literal>jac</literal>; <literal>r(i - j + ml + mu + 1,j) =
 536
 537                                         "dg(i)/dy(j)+cj*dg(i)/dydot(j)"
 538
 539                                     </literal>
 540                                     で計算するバンド行列の定義域<literal>[ml,mu]</literal>を指定します.
 541
 542                                     <literal>info(3)=[]</literal>の場合, <literal>jac</literal> は通常の行列
 543
 544                                     を返します.
 545
 546                                     <literal>info(8)=1</literal>の場合, ダミーとして扱われます.
 547
 548                                 </para>
 549
 550                             </listitem>
 551
 552                         </varlistentry>
 553
 554                         <varlistentry>
 555
 556                             <term>info(4)</term>
 557
 558                             <listitem>
 559
 560                                 <para>最大ステップサイズを指定する実数スカラー値.
 561
 562                                     制限しない場合は <literal>info(4)=[]</literal>を指定します.
 563
 564                                 </para>
 565
 566                             </listitem>
 567
 568                         </varlistentry>
 569
 570                         <varlistentry>
 571
 572                             <term>info(5)</term>
 573
 574                             <listitem>
 575
 576                                 <para>初期ステップサイズを指定する実数スカラー値.
 577
 578                                     指定しない場合は <literal>info(5)=[]</literal>を指定します.
 579
 580                                 </para>
 581
 582                             </listitem>
 583
 584                         </varlistentry>
 585
 586                         <varlistentry>
 587
 588                             <term>info(6)</term>
 589
 590                             <listitem>
 591
 592                                 <para>
 593
 594                                     解が非負であることが既知な場合は <literal>info(6)=1</literal>,
 595
 596                                     それ以外は <literal>info(6)=0</literal> を指定します.
 597
 598                                 </para>
 599
 600                             </listitem>
 601
 602                         </varlistentry>
 603
 604                         <varlistentry>
 605
 606                             <term>info(7)</term>
 607
 608                             <listitem>
 609
 610                                 <para>
 611
 612                                     ydot0 が<literal>g(t0,y0,ydot0)=0</literal>のように指定された場合,
 613
 614                                     <literal>info(7)=[]</literal> と指定します.
 615
 616                                     それ以外の場合は <literal>info(7)=[+-1, ..., +-1]</literal>とします.
 617
 618                                     ここで,y(i)が微分変数の場合は<literal>info(7)(i)=1</literal>,
 619
 620                                     y(i)が代数変数(関数g(t,y,ydot)に微分値が陽に現れない)の場合は
 621
 622                                     <literal>info(7)(i)=-1</literal>とします.
 623
 624                                 </para>
 625
 626                             </listitem>
 627
 628                         </varlistentry>
 629
 630                         <varlistentry>
 631
 632                             <term>info(8)</term>
 633
 634                             <listitem>
 635
 636                                 <para>
 637
 638                                     直接法 / Krylov.
 639
 640                                     ソルバーでKrylov反復法を使用したい場合,<literal>info(8)=1</literal>と指定し,
 641
 642                                     <literal>psol</literal>にルーチンを指定します.
 643
 644                                     それ以外の場合(dasslの直接法)は<literal>info(8)=0</literal>を指定します.
 645
 646                                 </para>
 647
 648                             </listitem>
 649
 650                         </varlistentry>
 651
 652                         <varlistentry>
 653
 654                             <term>info(9)</term>
 655
 656                             <listitem>
 657
 658                                 <para>
 659
 660                                     Krylovパラメータ.
 661
 662                                     <literal>info(8)=0</literal>とした場合はダミー引数として処理されます.
 663
 664                                     それ以外の場合は
 665
 666                                     <literal>info(9)=[maxl kmp nrmax epli]</literal>を指定します, ただし:
 667
 668                                 </para>
 669
 670                                 <para>
 671
 672                                     - maxl = mSPIGMRアルゴリズムの最大反復回数 (デフォルト
 673
 674                                     <literal>min(5,neq)</literal>),
 675
 676                                 </para>
 677
 678                                 <para>
 679
 680                                     - kmp = SPIGMRアルゴリズムで直交化を行うベクトルの数
 681
 682                                     (デフォルト maxl),
 683
 684                                 </para>
 685
 686                                 <para>
 687
 688                                     - nrmax = 各非線形反復におけるSPIGMRアルゴリズムのリスタート最大数
 689
 690                                     (デフォルト <literal>5</literal>),
 691
 692                                 </para>
 693
 694                                 <para>
 695
 696                                     - epli = SPIGMRアルゴリズムの収束安定定数 (デフォルト <literal>0.05</literal>).
 697
 698                                 </para>
 699
 700                             </listitem>
 701
 702                         </varlistentry>
 703
 704                         <varlistentry>
 705
 706                             <term>info(10)</term>
 707
 708                             <listitem>
 709
 710                                 <para>
 711
 712                                     初期条件.
 713
 714                                     <literal>info(7)=[]</literal>の場合はダミーとして処理されます.
 715
 716                                     初期条件の計算直後にソルバーを停止させる場合は
 717
 718                                     <literal>info(10)=1</literal>と指定し,それ以外は
 719
 720                                     <literal>info(10)=0</literal>と指定します.
 721
 722                                 </para>
 723
 724                             </listitem>
 725
 726                         </varlistentry>
 727
 728                         <varlistentry>
 729
 730                             <term>info(11)</term>
 731
 732                             <listitem>
 733
 734                                 <para>
 735
 736                                     <literal>psol</literal>用のプリコンディショナ計算およびLU分解ルーチン.
 737
 738                                     <literal>info(8)=0</literal>の場合はダミーとして扱われます.
 739
 740                                     <link linkend="external">external</link> <literal>psol</literal>が特定の
 741
 742                                     ルーチンを使用する必要がある場合は,<literal>info(11)=1</literal>を指定し,
 743
 744                                     <literal>pjac</literal>ルーチンを指定します.
 745
 746                                     それ以外は<literal>info(11)=0</literal>とします.
 747
 748                                 </para>
 749
 750                             </listitem>
 751
 752                         </varlistentry>
 753
 754                         <varlistentry>
 755
 756                             <term>info(12)</term>
 757
 758                             <listitem>
 759
 760                                 <para>
 761
 762                                     全変数についてエラー制御をローカルに行いたい場合,
 763
 764                                     <literal>info(12)=[]</literal>を指定します. それ以外は,
 765
 766                                     <literal>info(12)=[+-1, ..., +-1]</literal>を指定します.
 767
 768                                     ただし, y(i)が微分変数の場合は  <literal>info(12)(i)=1</literal>,
 769
 770                                     y(i)が代数変数(微係数が関数g(t,y,ydot)に陽に現れない) の場合は
 771
 772                                     <literal>info(12)(i)=-1</literal>とします.
 773
 774                                 </para>
 775
 776                             </listitem>
 777
 778                         </varlistentry>
 779
 780                         <varlistentry>
 781
 782                             <term>info(13)</term>
 783
 784                             <listitem>
 785
 786                                 <para>
 787
 788                                     経験的なパラメータ.
 789
 790                                     <literal>info(7)=[]</literal>の場合はダミーとして扱われます.
 791
 792                                     それ以外の場合,
 793
 794                                     <literal>info(13)=[mxnit mxnj mxnh lsoff stptol epinit]</literal>を指定します,
 795
 796                                     ただし:
 797
 798                                 </para>
 799
 800                                 <para>
 801
 802                                     - mxnit = ヤコビアンまたはプリコンディショナ評価毎のニュートン反復の最大回数
 803
 804                                     (デフォルト:<literal>info(8)=0</literal>の場合は <literal>5</literal>,
 805
 806                                     それ以外は <literal>15</literal>),
 807
 808                                 </para>
 809
 810                                 <para>
 811
 812                                     - mxnj = ヤコビアンまたはプリコンディショナ評価の最大回数
 813
 814                                     (デフォルト:<literal>info(8)=0</literal>の場合は <literal>6</literal>,
 815
 816                                     それ以外は <literal>2</literal>),
 817
 818                                 </para>
 819
 820                                 <para>
 821
 822                                     - mxnh = info(7) &#8800; []　の場合に試行する人工的なステップサイズ
 823
 824                                     パラメータHの最大値
 825
 826                                     (デフォルト <literal>5</literal>),
 827
 828                                 </para>
 829
 830                                 <para>
 831
 832                                     - lsoff = ライン探索アルゴリズムをオフにするフラグ
 833
 834                                     (lsoff = 0 はライン探索有効を意味します, lsoff = 1 はオフを意味します)
 835
 836                                     (デフォルト: <literal>0</literal>),
 837
 838                                 </para>
 839
 840                                 <para>
 841
 842                                     - stptol = ライン探索アルゴリズムの最小スケール刻み (デフォルト: <literal>(丸め誤差単位)^(2/3)</literal>),
 843
 844                                 </para>
 845
 846                                 <para>
 847
 848                                     - epinit = ニュートン反復収束判定の振幅係数 (デフォルト <literal>0.01</literal>).
 849
 850                                 </para>
 851
 852                             </listitem>
 853
 854                         </varlistentry>
 855
 856                         <varlistentry>
 857
 858                             <term>info(14)</term>
 859
 860                             <listitem>
 861
 862                                 <para>
 863
 864                                     冗長性.
 865
 866                                     出力を最小化する場合は <literal>info(14)=1</literal>,
 867
 868                                     最大化する場合は <literal>info(14)=2</literal>, それ以外は
 869
 870                                     <literal>info(14)=0</literal>を指定します.
 871
 872                                 </para>
 873
 874                             </listitem>
 875
 876                         </varlistentry>
 877
 878                     </variablelist>
 879
 880                 </listitem>
 881
 882             </varlistentry>
 883
 884             <varlistentry>
 885
 886                 <term>psol</term>
 887
 888                 <listitem>
 889
 890                     <para>
 891
 892                         <link linkend="external">external</link> (関数またはリストまたは文字列).
 893
 894                         線形システム<literal>P*x = b</literal>を解きます.
 895
 896                         ただし, P はプリコンディショナで, ルーチン <literal>pjac</literal>
 897
 898                         が事前に計算して, wp 及び iwpに保存します.
 899
 900                     </para>
 901
 902                     <itemizedlist>
 903
 904                         <listitem>
 905
 906                             <para>Scilab関数.</para>
 907
 908                             <para>呼び出し手順は
 909
 910                                 <literal>[r, ier] = psol(wp, iwp, b)</literal> とします.
 911
 912                                 <literal>psol</literal> 関数はシステムの解<literal>r</literal>と
 913
 914                                 エラーフラグ<literal>ier</literal>を返す必要があります.
 915
 916                             </para>
 917
 918                         </listitem>
 919
 920                         <listitem>
 921
 922                             <para>リスト.</para>
 923
 924                             <para>以下のような形式とします</para>
 925
 926                             <programlisting role="no-scilab-exec"><![CDATA[\r
 927 list(psol,x1,x2,...)\r
 928  ]]></programlisting>
 929
 930                             <para>ただし, 関数
 931
 932                                 <literal>psol</literal>の呼び出し手順は以下とします
 933
 934                             </para>
 935
 936                             <programlisting role="no-scilab-exec"><![CDATA[\r
 937 psol(wp,iwp,b,x1,x2,...)\r
 938  ]]></programlisting>
 939
 940                             <para>
 941
 942                                 <literal>psol</literal> は <literal>r</literal>の解を返します.
 943
 944                             </para>
 945
 946                         </listitem>
 947
 948                         <listitem>
 949
 950                             <para>文字列.</para>
 951
 952                             <para>ScilabにリンクされたCまたはFortranサブルーチンの名前を指定します
 953
 954                             </para>
 955
 956                             <para>Cの場合,呼び出し手順は以下とします:</para>
 957
 958                             <programlisting role="no-scilab-exec"><![CDATA[\r
 959 void psol (int*neq, double*t, double*y, double*ydot, double*savr,\r
 960   double*wk, double*cj, double*wght, double*wp, int*iwp, double*b, double*eplin, int*ier, double*rpar, int*ipar)\r
 961  ]]></programlisting>
 962
 963                             ただし,配列 <literal>wp</literal> および <literal>iwp</literal> はプリコンディショナ
 964
 965                             <literal>P</literal>の行列要素を行圧縮形式で有します.
 966
 967                             <para>Fortranの場合は以下とします:</para>
 968
 969                             <programlisting role="no-scilab-exec"><![CDATA[\r
 970 subroutine psol (neq, t, y, ydot, savr, wk, cj, wght,\r
 971   wp, iwp, b, eplin, ier, rpar, ipar)\r
 972 double precision t,y(*),ydot(*),savr(*),wk(*),cj,wght(*),wp(*),\r
 973   b(*),eplin,rpar(*)\r
 974 integer neq,iwp(*),ier,ipar(*)\r
 975  ]]></programlisting>
 976
 977                         </listitem>
 978
 979                     </itemizedlist>
 980
 981                 </listitem>
 982
 983             </varlistentry>
 984
 985             <varlistentry>
 986
 987                 <term>pjac</term>
 988
 989                 <listitem>
 990
 991                     <para>
 992
 993                         <link linkend="external">external</link> (関数またはリストまたは文字列).
 994
 995                         指定したパラメータ<literal>cj</literal>について
 996
 997                         <literal>dg/dy + cj*dg/dydot</literal>を計算し,
 998
 999                         doubleおよびint配列にLU分解を行います.
1000
1001                     </para>
1002
1003                     <itemizedlist>
1004
1005                         <listitem>
1006
1007                             <para>Scilab関数.</para>
1008
1009                             <para>呼び出し手順は
1010
1011                                 <literal>[wp, iwp, ires] = pjac(neq, t, y, ydot, h, cj, rewt, savr)</literal>
1012
1013                                 となり, 結果として,
1014
1015                                 配列 wp および iwp には全てのプリコンディショナ情報が
1016
1017                                 圧縮スパース行形式で返されます.
1018
1019                             </para>
1020
1021                         </listitem>
1022
1023                         <listitem>
1024
1025                             <para>リスト.</para>
1026
1027                             <para>以下の形式とします</para>
1028
1029                             <programlisting role="no-scilab-exec"><![CDATA[\r
1030 list(pjac,x1,x2,...)\r
1031  ]]></programlisting>
1032
1033                             <para>ただし,関数
1034
1035                                 <literal>pjac</literal>の呼び出し手順は以下とします
1036
1037                             </para>
1038
1039                             <programlisting role="no-scilab-exec"><![CDATA[\r
1040 pjac(neq,t,y,ydot,h,cj,rewt,savr,x1,x2,...)\r
1041  ]]></programlisting>
1042
1043                             <para>
1044
1045                                 <literal>pjac</literal> は,
1046
1047                                 <literal>(neq,t,y,ydot,h,cj,rewt,savr,x1,x2,...)</literal>の関数として
1048
1049                                 分解した <literal>dg/dy + cj*dg/dydot</literal> を返します.
1050
1051                             </para>
1052
1053                         </listitem>
1054
1055                         <listitem>
1056
1057                             <para>文字列.</para>
1058
1059                             <para>ScilabにリンクされたCまたはFortran形式のサブルーチン名を指定します
1060
1061                             </para>
1062
1063                             <para>Cの場合,呼び出し手順は以下とします:</para>
1064
1065                             <programlisting role="no-scilab-exec"><![CDATA[\r
1066 void pjac (double*res, int*ires, int*neq, double*t, double*y, double*ydot, double*rewt, double*savr,\r
1067 double*wk, double*h, double*cj, double*wp, int*iwp, int*ier, double*rpar, int*ipar)\r
1068  ]]></programlisting>
1069
1070                             <para>Fortranの場合, 以下のとします:</para>
1071
1072                             <programlisting role="no-scilab-exec"><![CDATA[\r
1073 subroutine pjac (res, ires, neq, t, y, ydot, rewt, savr,\r
1074   wk, h, cj, wp, iwp, ier, rpar, ipar)\r
1075 double precision res(*), t, y(*), ydot(*), rewt(*), savr(*),\r
1076   wk(*), h, cj, wp(*), rpar(*)\r
1077 integer ires, neq, iwp(*), ier, ipar(*)\r
1078  ]]></programlisting>
1079
1080                         </listitem>
1081
1082                     </itemizedlist>
1083
1084                 </listitem>
1085
1086             </varlistentry>
1087
1088             <varlistentry>
1089
1090                 <term>hd</term>
1091
1092                 <listitem>
1093
1094                     <para>
1095
1096                         <literal>dassl</literal>コンテキストを保存し,積分を再開できるようにする実数ベクトル.
1097
1098                     </para>
1099
1100                 </listitem>
1101
1102             </varlistentry>
1103
1104             <varlistentry>
1105
1106                 <term>r</term>
1107
1108                 <listitem>
1109
1110                     <para>
1111
1112                         実数行列 .
1113
1114                         各列はベクトル<literal>[t;x(t);xdot(t)]</literal>で,
1115
1116                         <literal>t</literal> は解が計算される添字の時刻です.
1117
1118                     </para>
1119
1120                 </listitem>
1121
1122             </varlistentry>
1123
1124         </variablelist>
1125
1126     </refsection>
1127
1128     <refsection>
1129
1130         <title>説明</title>
1131
1132         <para>陰的微分方程式の解.</para>
1133
1134         <programlisting role="no-scilab-exec"><![CDATA[\r
1135 g(t,y,ydot) = 0\r
1136 y(t0) = y0  and   ydot(t0) = ydot0\r
1137  ]]></programlisting>
1138
1139         <para>
1140
1141             局面交差した時刻と面交差した数を<literal>nn</literal>に返します.
1142
1143         </para>
1144
1145         <para>詳細な例は SCI/modules/differential_equations/tests/unit_tests/daskr.tst にあります.</para>
1146
1147     </refsection>
1148
1149     <refsection>
1150
1151         <title>例</title>
1152
1153         <programlisting role="example"><![CDATA[\r
1154 // dy/dt = ((2*log(y)+8)/t -5)*y,  y(1) = 1,  1 <= t <=6\r
1155 // g1 = ((2*log(y)+8)/t - 5)*y\r
1156 // g2 = log(y) - 2.2491\r
1157 y0 = 1; t = 2:6; t0 = 1; y0d = 3;\r
1158 atol = 1.d-6; rtol = 0; ng = 2;\r
1159 \r
1160 deff('[delta,ires] = res1(t,y,ydot)','ires = 0; delta = ydot-((2*log(y)+8)/t-5)*y')\r
1161 deff('[rts] = gr1(t,y)','rts = [((2*log(y)+8)/t-5)*y; log(y)-2.2491]')\r
1162 \r
1163 [yy,nn] = daskr([y0,y0d],t0,t,atol,rtol,res1,ng,gr1);\r
1164 nn\r
1165 \r
1166 // nn = [2.4698972 2] を返します\r
1167  ]]></programlisting>
1168
1169     </refsection>
1170
1171     <refsection role="see also">
1172
1173         <title>参照</title>
1174
1175         <simplelist type="inline">
1176
1177             <member>
1178
1179                 <link linkend="ode">ode</link>
1180
1181             </member>
1182
1183             <member>
1184
1185                 <link linkend="dasrt">dasrt</link>
1186
1187             </member>
1188
1189             <member>
1190
1191                 <link linkend="dassl">dassl</link>
1192
1193             </member>
1194
1195             <member>
1196
1197                 <link linkend="impl">impl</link>
1198
1199             </member>
1200
1201             <member>
1202
1203                 <link linkend="fort">fort</link>
1204
1205             </member>
1206
1207             <member>
1208
1209                 <link linkend="link">link</link>
1210
1211             </member>
1212
1213             <member>
1214
1215                 <link linkend="external">external</link>
1216
1217             </member>
1218
1219         </simplelist>
1220
1221     </refsection>
1222
1223     <refsection>
1224
1225         <title>履歴</title>
1226
1227         <revhistory>
1228
1229             <revision>
1230
1231                 <revnumber>5.5.0</revnumber>
1232
1233                 <revdescription>daskr ソルバーが追加されました</revdescription>
1234
1235             </revision>
1236
1237         </revhistory>
1238
1239     </refsection>
1240
1241 </refentry>
1242