Actual source code: fdmatrix.c

  1: /*
  2:    This is where the abstract matrix operations are defined that are
  3:   used for finite difference computations of Jacobians using coloring.
  4: */

 6:  #include src/mat/matimpl.h

  8: /* Logging support */
  9: PetscCookie MAT_FDCOLORING_COOKIE = 0;

 13: PetscErrorCode MatFDColoringSetF(MatFDColoring fd,Vec F)
 14: {
 16:   fd->F = F;
 17:   return(0);
 18: }

 22: static PetscErrorCode MatFDColoringView_Draw_Zoom(PetscDraw draw,void *Aa)
 23: {
 24:   MatFDColoring  fd = (MatFDColoring)Aa;
 26:   PetscInt       i,j;
 27:   PetscReal      x,y;


 31:   /* loop over colors  */
 32:   for (i=0; i<fd->ncolors; i++) {
 33:     for (j=0; j<fd->nrows[i]; j++) {
 34:       y = fd->M - fd->rows[i][j] - fd->rstart;
 35:       x = fd->columnsforrow[i][j];
 36:       PetscDrawRectangle(draw,x,y,x+1,y+1,i+1,i+1,i+1,i+1);
 37:     }
 38:   }
 39:   return(0);
 40: }

 44: static PetscErrorCode MatFDColoringView_Draw(MatFDColoring fd,PetscViewer viewer)
 45: {
 47:   PetscTruth     isnull;
 48:   PetscDraw      draw;
 49:   PetscReal      xr,yr,xl,yl,h,w;

 52:   PetscViewerDrawGetDraw(viewer,0,&draw);
 53:   PetscDrawIsNull(draw,&isnull); if (isnull) return(0);

 55:   PetscObjectCompose((PetscObject)fd,"Zoomviewer",(PetscObject)viewer);

 57:   xr  = fd->N; yr = fd->M; h = yr/10.0; w = xr/10.0;
 58:   xr += w;     yr += h;    xl = -w;     yl = -h;
 59:   PetscDrawSetCoordinates(draw,xl,yl,xr,yr);
 60:   PetscDrawZoom(draw,MatFDColoringView_Draw_Zoom,fd);
 61:   PetscObjectCompose((PetscObject)fd,"Zoomviewer",PETSC_NULL);
 62:   return(0);
 63: }

 67: /*@C
 68:    MatFDColoringView - Views a finite difference coloring context.

 70:    Collective on MatFDColoring

 72:    Input  Parameters:
 73: +  c - the coloring context
 74: -  viewer - visualization context

 76:    Level: intermediate

 78:    Notes:
 79:    The available visualization contexts include
 80: +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
 81: .     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
 82:         output where only the first processor opens
 83:         the file.  All other processors send their 
 84:         data to the first processor to print. 
 85: -     PETSC_VIEWER_DRAW_WORLD - graphical display of nonzero structure

 87:    Notes:
 88:      Since PETSc uses only a small number of basic colors (currently 33), if the coloring
 89:    involves more than 33 then some seemingly identical colors are displayed making it look
 90:    like an illegal coloring. This is just a graphical artifact.

 92: .seealso: MatFDColoringCreate()

 94: .keywords: Mat, finite differences, coloring, view
 95: @*/
 96: PetscErrorCode MatFDColoringView(MatFDColoring c,PetscViewer viewer)
 97: {
 98:   PetscErrorCode    ierr;
 99:   PetscInt          i,j;
100:   PetscTruth        isdraw,iascii;
101:   PetscViewerFormat format;

105:   if (!viewer) viewer = PETSC_VIEWER_STDOUT_(c->comm);

109:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);
110:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
111:   if (isdraw) {
112:     MatFDColoringView_Draw(c,viewer);
113:   } else if (iascii) {
114:     PetscViewerASCIIPrintf(viewer,"MatFDColoring Object:\n");
115:     PetscViewerASCIIPrintf(viewer,"  Error tolerance=%g\n",c->error_rel);
116:     PetscViewerASCIIPrintf(viewer,"  Umin=%g\n",c->umin);
117:     PetscViewerASCIIPrintf(viewer,"  Number of colors=%D\n",c->ncolors);

119:     PetscViewerGetFormat(viewer,&format);
120:     if (format != PETSC_VIEWER_ASCII_INFO) {
121:       for (i=0; i<c->ncolors; i++) {
122:         PetscViewerASCIIPrintf(viewer,"  Information for color %D\n",i);
123:         PetscViewerASCIIPrintf(viewer,"    Number of columns %D\n",c->ncolumns[i]);
124:         for (j=0; j<c->ncolumns[i]; j++) {
125:           PetscViewerASCIIPrintf(viewer,"      %D\n",c->columns[i][j]);
126:         }
127:         PetscViewerASCIIPrintf(viewer,"    Number of rows %D\n",c->nrows[i]);
128:         for (j=0; j<c->nrows[i]; j++) {
129:           PetscViewerASCIIPrintf(viewer,"      %D %D \n",c->rows[i][j],c->columnsforrow[i][j]);
130:         }
131:       }
132:     }
133:     PetscViewerFlush(viewer);
134:   } else {
135:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for MatFDColoring",((PetscObject)viewer)->type_name);
136:   }
137:   return(0);
138: }

142: /*@
143:    MatFDColoringSetParameters - Sets the parameters for the sparse approximation of
144:    a Jacobian matrix using finite differences.

146:    Collective on MatFDColoring

148:    The Jacobian is estimated with the differencing approximation
149: .vb
150:        F'(u)_{:,i} = [F(u+h*dx_{i}) - F(u)]/h where
151:        h = error_rel*u[i]                 if  abs(u[i]) > umin
152:          = +/- error_rel*umin             otherwise, with +/- determined by the sign of u[i]
153:        dx_{i} = (0, ... 1, .... 0)
154: .ve

156:    Input Parameters:
157: +  coloring - the coloring context
158: .  error_rel - relative error
159: -  umin - minimum allowable u-value magnitude

161:    Level: advanced

163: .keywords: Mat, finite differences, coloring, set, parameters

165: .seealso: MatFDColoringCreate()
166: @*/
167: PetscErrorCode MatFDColoringSetParameters(MatFDColoring matfd,PetscReal error,PetscReal umin)
168: {

172:   if (error != PETSC_DEFAULT) matfd->error_rel = error;
173:   if (umin != PETSC_DEFAULT)  matfd->umin      = umin;
174:   return(0);
175: }

179: /*@
180:    MatFDColoringSetFrequency - Sets the frequency for computing new Jacobian
181:    matrices. 

183:    Collective on MatFDColoring

185:    Input Parameters:
186: +  coloring - the coloring context
187: -  freq - frequency (default is 1)

189:    Options Database Keys:
190: .  -mat_fd_coloring_freq <freq>  - Sets coloring frequency

192:    Level: advanced

194:    Notes:
195:    Using a modified Newton strategy, where the Jacobian remains fixed for several
196:    iterations, can be cost effective in terms of overall nonlinear solution 
197:    efficiency.  This parameter indicates that a new Jacobian will be computed every
198:    <freq> nonlinear iterations.  

200: .keywords: Mat, finite differences, coloring, set, frequency

202: .seealso: MatFDColoringCreate(), MatFDColoringGetFrequency(), MatFDColoringSetRecompute()
203: @*/
204: PetscErrorCode MatFDColoringSetFrequency(MatFDColoring matfd,PetscInt freq)
205: {

209:   matfd->freq = freq;
210:   return(0);
211: }

215: /*@
216:    MatFDColoringGetFrequency - Gets the frequency for computing new Jacobian
217:    matrices. 

219:    Not Collective

221:    Input Parameters:
222: .  coloring - the coloring context

224:    Output Parameters:
225: .  freq - frequency (default is 1)

227:    Options Database Keys:
228: .  -mat_fd_coloring_freq <freq> - Sets coloring frequency

230:    Level: advanced

232:    Notes:
233:    Using a modified Newton strategy, where the Jacobian remains fixed for several
234:    iterations, can be cost effective in terms of overall nonlinear solution 
235:    efficiency.  This parameter indicates that a new Jacobian will be computed every
236:    <freq> nonlinear iterations.  

238: .keywords: Mat, finite differences, coloring, get, frequency

240: .seealso: MatFDColoringSetFrequency()
241: @*/
242: PetscErrorCode MatFDColoringGetFrequency(MatFDColoring matfd,PetscInt *freq)
243: {
246:   *freq = matfd->freq;
247:   return(0);
248: }

252: /*@C
253:    MatFDColoringSetFunction - Sets the function to use for computing the Jacobian.

255:    Collective on MatFDColoring

257:    Input Parameters:
258: +  coloring - the coloring context
259: .  f - the function
260: -  fctx - the optional user-defined function context

262:    Level: intermediate

264:    Notes:
265:     In Fortran you must call MatFDColoringSetFunctionSNES() for a coloring object to 
266:   be used with the SNES solvers and MatFDColoringSetFunctionTS() if it is to be used
267:   with the TS solvers.

269: .keywords: Mat, Jacobian, finite differences, set, function
270: @*/
271: PetscErrorCode MatFDColoringSetFunction(MatFDColoring matfd,PetscErrorCode (*f)(void),void *fctx)
272: {
275:   matfd->f    = f;
276:   matfd->fctx = fctx;
277:   return(0);
278: }

282: /*@
283:    MatFDColoringSetFromOptions - Sets coloring finite difference parameters from 
284:    the options database.

286:    Collective on MatFDColoring

288:    The Jacobian, F'(u), is estimated with the differencing approximation
289: .vb
290:        F'(u)_{:,i} = [F(u+h*dx_{i}) - F(u)]/h where
291:        h = error_rel*u[i]                 if  abs(u[i]) > umin
292:          = +/- error_rel*umin             otherwise, with +/- determined by the sign of u[i]
293:        dx_{i} = (0, ... 1, .... 0)
294: .ve

296:    Input Parameter:
297: .  coloring - the coloring context

299:    Options Database Keys:
300: +  -mat_fd_coloring_err <err> - Sets <err> (square root
301:            of relative error in the function)
302: .  -mat_fd_coloring_umin <umin> - Sets umin, the minimum allowable u-value magnitude
303: .  -mat_fd_coloring_freq <freq> - Sets frequency of computing a new Jacobian
304: .  -mat_fd_coloring_view - Activates basic viewing
305: .  -mat_fd_coloring_view_info - Activates viewing info
306: -  -mat_fd_coloring_view_draw - Activates drawing

308:     Level: intermediate

310: .keywords: Mat, finite differences, parameters

312: .seealso: MatFDColoringCreate(), MatFDColoringView(), MatFDColoringSetParameters()

314: @*/
315: PetscErrorCode MatFDColoringSetFromOptions(MatFDColoring matfd)
316: {


322:   PetscOptionsBegin(matfd->comm,matfd->prefix,"Jacobian computation via finite differences option","MatFD");
323:     PetscOptionsReal("-mat_fd_coloring_err","Square root of relative error in function","MatFDColoringSetParameters",matfd->error_rel,&matfd->error_rel,0);
324:     PetscOptionsReal("-mat_fd_coloring_umin","Minimum allowable u magnitude","MatFDColoringSetParameters",matfd->umin,&matfd->umin,0);
325:     PetscOptionsInt("-mat_fd_coloring_freq","How often Jacobian is recomputed","MatFDColoringSetFrequency",matfd->freq,&matfd->freq,0);
326:     /* not used here; but so they are presented in the GUI */
327:     PetscOptionsName("-mat_fd_coloring_view","Print entire datastructure used for Jacobian","None",0);
328:     PetscOptionsName("-mat_fd_coloring_view_info","Print number of colors etc for Jacobian","None",0);
329:     PetscOptionsName("-mat_fd_coloring_view_draw","Plot nonzero structure ofJacobian","None",0);
330:   PetscOptionsEnd();
331:   return(0);
332: }

336: PetscErrorCode MatFDColoringView_Private(MatFDColoring fd)
337: {
339:   PetscTruth     flg;

342:   PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_view",&flg);
343:   if (flg) {
344:     MatFDColoringView(fd,PETSC_VIEWER_STDOUT_(fd->comm));
345:   }
346:   PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_view_info",&flg);
347:   if (flg) {
348:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_(fd->comm),PETSC_VIEWER_ASCII_INFO);
349:     MatFDColoringView(fd,PETSC_VIEWER_STDOUT_(fd->comm));
350:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_(fd->comm));
351:   }
352:   PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_view_draw",&flg);
353:   if (flg) {
354:     MatFDColoringView(fd,PETSC_VIEWER_DRAW_(fd->comm));
355:     PetscViewerFlush(PETSC_VIEWER_DRAW_(fd->comm));
356:   }
357:   return(0);
358: }

362: /*@C
363:    MatFDColoringCreate - Creates a matrix coloring context for finite difference 
364:    computation of Jacobians.

366:    Collective on Mat

368:    Input Parameters:
369: +  mat - the matrix containing the nonzero structure of the Jacobian
370: -  iscoloring - the coloring of the matrix

372:     Output Parameter:
373: .   color - the new coloring context
374:    
375:     Level: intermediate

377: .seealso: MatFDColoringDestroy(),SNESDefaultComputeJacobianColor(), ISColoringCreate(),
378:           MatFDColoringSetFunction(), MatFDColoringSetFromOptions(), MatFDColoringApply(),
379:           MatFDColoringSetFrequency(), MatFDColoringSetRecompute(), MatFDColoringView(),
380:           MatFDColoringSetParameters()
381: @*/
382: PetscErrorCode MatFDColoringCreate(Mat mat,ISColoring iscoloring,MatFDColoring *color)
383: {
384:   MatFDColoring  c;
385:   MPI_Comm       comm;
387:   PetscInt       M,N;

390:   PetscLogEventBegin(MAT_FDColoringCreate,mat,0,0,0);
391:   MatGetSize(mat,&M,&N);
392:   if (M != N) SETERRQ(PETSC_ERR_SUP,"Only for square matrices");

394:   PetscObjectGetComm((PetscObject)mat,&comm);
395:   PetscHeaderCreate(c,_p_MatFDColoring,int,MAT_FDCOLORING_COOKIE,0,"MatFDColoring",comm,MatFDColoringDestroy,MatFDColoringView);
396:   PetscLogObjectCreate(c);

398:   if (mat->ops->fdcoloringcreate) {
399:     (*mat->ops->fdcoloringcreate)(mat,iscoloring,c);
400:   } else {
401:     SETERRQ(PETSC_ERR_SUP,"Code not yet written for this matrix type");
402:   }

404:   c->error_rel         = PETSC_SQRT_MACHINE_EPSILON;
405:   c->umin              = 100.0*PETSC_SQRT_MACHINE_EPSILON;
406:   c->freq              = 1;
407:   c->usersetsrecompute = PETSC_FALSE;
408:   c->recompute         = PETSC_FALSE;
409:   c->currentcolor      = -1;

411:   *color = c;
412:   PetscLogEventEnd(MAT_FDColoringCreate,mat,0,0,0);
413:   return(0);
414: }

418: /*@C
419:     MatFDColoringDestroy - Destroys a matrix coloring context that was created
420:     via MatFDColoringCreate().

422:     Collective on MatFDColoring

424:     Input Parameter:
425: .   c - coloring context

427:     Level: intermediate

429: .seealso: MatFDColoringCreate()
430: @*/
431: PetscErrorCode MatFDColoringDestroy(MatFDColoring c)
432: {
434:   PetscInt       i;

437:   if (--c->refct > 0) return(0);

439:   for (i=0; i<c->ncolors; i++) {
440:     if (c->columns[i])         {PetscFree(c->columns[i]);}
441:     if (c->rows[i])            {PetscFree(c->rows[i]);}
442:     if (c->columnsforrow[i])   {PetscFree(c->columnsforrow[i]);}
443:     if (c->vscaleforrow && c->vscaleforrow[i]) {PetscFree(c->vscaleforrow[i]);}
444:   }
445:   PetscFree(c->ncolumns);
446:   PetscFree(c->columns);
447:   PetscFree(c->nrows);
448:   PetscFree(c->rows);
449:   PetscFree(c->columnsforrow);
450:   if (c->vscaleforrow) {PetscFree(c->vscaleforrow);}
451:   if (c->vscale)       {VecDestroy(c->vscale);}
452:   if (c->w1) {
453:     VecDestroy(c->w1);
454:     VecDestroy(c->w2);
455:     VecDestroy(c->w3);
456:   }
457:   PetscLogObjectDestroy(c);
458:   PetscHeaderDestroy(c);
459:   return(0);
460: }

464: /*@C
465:     MatFDColoringGetPerturbedColumns - Returns the indices of the columns that
466:       that are currently being perturbed.

468:     Not Collective

470:     Input Parameters:
471: .   coloring - coloring context created with MatFDColoringCreate()

473:     Output Parameters:
474: +   n - the number of local columns being perturbed
475: -   cols - the column indices, in global numbering

477:    Level: intermediate

479: .seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView(), MatFDColoringApply()

481: .keywords: coloring, Jacobian, finite differences
482: @*/
483: EXTERN PetscErrorCode MatFDColoringGetPerturbedColumns(MatFDColoring coloring,PetscInt *n,PetscInt *cols[])
484: {
486:   if (coloring->currentcolor >= 0) {
487:     *n    = coloring->ncolumns[coloring->currentcolor];
488:     *cols = coloring->columns[coloring->currentcolor];
489:   } else {
490:     *n = 0;
491:   }
492:   return(0);
493: }

497: /*@
498:     MatFDColoringApply - Given a matrix for which a MatFDColoring context 
499:     has been created, computes the Jacobian for a function via finite differences.

501:     Collective on MatFDColoring

503:     Input Parameters:
504: +   mat - location to store Jacobian
505: .   coloring - coloring context created with MatFDColoringCreate()
506: .   x1 - location at which Jacobian is to be computed
507: -   sctx - optional context required by function (actually a SNES context)

509:     Options Database Keys:
510: +    -mat_fd_coloring_freq <freq> - Sets coloring frequency
511: .    -mat_fd_coloring_view - Activates basic viewing or coloring
512: .    -mat_fd_coloring_view_draw - Activates drawing of coloring
513: -    -mat_fd_coloring_view_info - Activates viewing of coloring info

515:     Level: intermediate

517: .seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView()

519: .keywords: coloring, Jacobian, finite differences
520: @*/
521: PetscErrorCode MatFDColoringApply(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
522: {
523:   PetscErrorCode (*f)(void*,Vec,Vec,void*) = (PetscErrorCode (*)(void*,Vec,Vec,void *))coloring->f;
525:   PetscInt       k,N,start,end,l,row,col,srow,**vscaleforrow,m1,m2;
526:   PetscScalar    dx,mone = -1.0,*y,*xx,*w3_array;
527:   PetscScalar    *vscale_array;
528:   PetscReal      epsilon = coloring->error_rel,umin = coloring->umin;
529:   Vec            w1,w2,w3;
530:   void           *fctx = coloring->fctx;
531:   PetscTruth     flg;



539:   if (coloring->usersetsrecompute) {
540:     if (!coloring->recompute) {
541:       *flag = SAME_PRECONDITIONER;
542:       PetscLogInfo(J,"MatFDColoringApply:Skipping Jacobian, since user called MatFDColorSetRecompute()\n");
543:       return(0);
544:     } else {
545:       coloring->recompute = PETSC_FALSE;
546:     }
547:   }

549:   PetscLogEventBegin(MAT_FDColoringApply,coloring,J,x1,0);
550:   if (J->ops->fdcoloringapply) {
551:     (*J->ops->fdcoloringapply)(J,coloring,x1,flag,sctx);
552:   } else {

554:     if (!coloring->w1) {
555:       VecDuplicate(x1,&coloring->w1);
556:       PetscLogObjectParent(coloring,coloring->w1);
557:       VecDuplicate(x1,&coloring->w2);
558:       PetscLogObjectParent(coloring,coloring->w2);
559:       VecDuplicate(x1,&coloring->w3);
560:       PetscLogObjectParent(coloring,coloring->w3);
561:     }
562:     w1 = coloring->w1; w2 = coloring->w2; w3 = coloring->w3;

564:     MatSetUnfactored(J);
565:     PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_dont_rezero",&flg);
566:     if (flg) {
567:       PetscLogInfo(coloring,"MatFDColoringApply: Not calling MatZeroEntries()\n");
568:     } else {
569:       PetscTruth assembled;
570:       MatAssembled(J,&assembled);
571:       if (assembled) {
572:         MatZeroEntries(J);
573:       }
574:     }

576:     VecGetOwnershipRange(x1,&start,&end);
577:     VecGetSize(x1,&N);
578: 
579:     /*
580:       This is a horrible, horrible, hack. See DMMGComputeJacobian_Multigrid() it inproperly sets
581:       coloring->F for the coarser grids from the finest
582:     */
583:     if (coloring->F) {
584:       VecGetLocalSize(coloring->F,&m1);
585:       VecGetLocalSize(w1,&m2);
586:       if (m1 != m2) {
587:         coloring->F = 0;
588:       }
589:     }

591:     if (coloring->F) {
592:       w1          = coloring->F; /* use already computed value of function */
593:       coloring->F = 0;
594:     } else {
595:       PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);
596:       (*f)(sctx,x1,w1,fctx);
597:       PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);
598:     }

600:     /* 
601:        Compute all the scale factors and share with other processors
602:     */
603:     VecGetArray(x1,&xx);xx = xx - start;
604:     VecGetArray(coloring->vscale,&vscale_array);vscale_array = vscale_array - start;
605:     for (k=0; k<coloring->ncolors; k++) {
606:       /*
607:         Loop over each column associated with color adding the 
608:         perturbation to the vector w3.
609:       */
610:       for (l=0; l<coloring->ncolumns[k]; l++) {
611:         col = coloring->columns[k][l];    /* column of the matrix we are probing for */
612:         dx  = xx[col];
613:         if (dx == 0.0) dx = 1.0;
614: #if !defined(PETSC_USE_COMPLEX)
615:         if (dx < umin && dx >= 0.0)      dx = umin;
616:         else if (dx < 0.0 && dx > -umin) dx = -umin;
617: #else
618:         if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
619:         else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
620: #endif
621:         dx                *= epsilon;
622:         vscale_array[col] = 1.0/dx;
623:       }
624:     }
625:     vscale_array = vscale_array + start;VecRestoreArray(coloring->vscale,&vscale_array);
626:     VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);
627:     VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);

629:     /*  VecView(coloring->vscale,PETSC_VIEWER_STDOUT_WORLD);
630:         VecView(x1,PETSC_VIEWER_STDOUT_WORLD);*/

632:     if (coloring->vscaleforrow) vscaleforrow = coloring->vscaleforrow;
633:     else                        vscaleforrow = coloring->columnsforrow;

635:     VecGetArray(coloring->vscale,&vscale_array);
636:     /*
637:       Loop over each color
638:     */
639:     for (k=0; k<coloring->ncolors; k++) {
640:       coloring->currentcolor = k;
641:       VecCopy(x1,w3);
642:       VecGetArray(w3,&w3_array);w3_array = w3_array - start;
643:       /*
644:         Loop over each column associated with color adding the 
645:         perturbation to the vector w3.
646:       */
647:       for (l=0; l<coloring->ncolumns[k]; l++) {
648:         col = coloring->columns[k][l];    /* column of the matrix we are probing for */
649:         dx  = xx[col];
650:         if (dx == 0.0) dx = 1.0;
651: #if !defined(PETSC_USE_COMPLEX)
652:         if (dx < umin && dx >= 0.0)      dx = umin;
653:         else if (dx < 0.0 && dx > -umin) dx = -umin;
654: #else
655:         if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
656:         else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
657: #endif
658:         dx            *= epsilon;
659:         if (!PetscAbsScalar(dx)) SETERRQ(PETSC_ERR_PLIB,"Computed 0 differencing parameter");
660:         w3_array[col] += dx;
661:       }
662:       w3_array = w3_array + start; VecRestoreArray(w3,&w3_array);

664:       /*
665:         Evaluate function at x1 + dx (here dx is a vector of perturbations)
666:       */

668:       PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);
669:       (*f)(sctx,w3,w2,fctx);
670:       PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);
671:       VecAXPY(&mone,w1,w2);

673:       /*
674:         Loop over rows of vector, putting results into Jacobian matrix
675:       */
676:       VecGetArray(w2,&y);
677:       for (l=0; l<coloring->nrows[k]; l++) {
678:         row    = coloring->rows[k][l];
679:         col    = coloring->columnsforrow[k][l];
680:         y[row] *= vscale_array[vscaleforrow[k][l]];
681:         srow   = row + start;
682:         MatSetValues(J,1,&srow,1,&col,y+row,INSERT_VALUES);
683:       }
684:       VecRestoreArray(w2,&y);
685:     }
686:     coloring->currentcolor = -1;
687:     VecRestoreArray(coloring->vscale,&vscale_array);
688:     xx = xx + start; VecRestoreArray(x1,&xx);
689:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
690:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
691:   }
692:   PetscLogEventEnd(MAT_FDColoringApply,coloring,J,x1,0);

694:   PetscOptionsHasName(PETSC_NULL,"-mat_null_space_test",&flg);
695:   if (flg) {
696:     MatNullSpaceTest(J->nullsp,J);
697:   }
698:   MatFDColoringView_Private(coloring);

700:   return(0);
701: }

705: /*@
706:     MatFDColoringApplyTS - Given a matrix for which a MatFDColoring context 
707:     has been created, computes the Jacobian for a function via finite differences.

709:    Collective on Mat, MatFDColoring, and Vec

711:     Input Parameters:
712: +   mat - location to store Jacobian
713: .   coloring - coloring context created with MatFDColoringCreate()
714: .   x1 - location at which Jacobian is to be computed
715: -   sctx - optional context required by function (actually a SNES context)

717:    Options Database Keys:
718: .  -mat_fd_coloring_freq <freq> - Sets coloring frequency

720:    Level: intermediate

722: .seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView()

724: .keywords: coloring, Jacobian, finite differences
725: @*/
726: PetscErrorCode MatFDColoringApplyTS(Mat J,MatFDColoring coloring,PetscReal t,Vec x1,MatStructure *flag,void *sctx)
727: {
728:   PetscErrorCode (*f)(void*,PetscReal,Vec,Vec,void*)=(PetscErrorCode (*)(void*,PetscReal,Vec,Vec,void *))coloring->f;
730:   PetscInt       k,N,start,end,l,row,col,srow,**vscaleforrow;
731:   PetscScalar    dx,mone = -1.0,*y,*xx,*w3_array;
732:   PetscScalar    *vscale_array;
733:   PetscReal      epsilon = coloring->error_rel,umin = coloring->umin;
734:   Vec            w1,w2,w3;
735:   void           *fctx = coloring->fctx;
736:   PetscTruth     flg;


743:   PetscLogEventBegin(MAT_FDColoringApply,coloring,J,x1,0);
744:   if (!coloring->w1) {
745:     VecDuplicate(x1,&coloring->w1);
746:     PetscLogObjectParent(coloring,coloring->w1);
747:     VecDuplicate(x1,&coloring->w2);
748:     PetscLogObjectParent(coloring,coloring->w2);
749:     VecDuplicate(x1,&coloring->w3);
750:     PetscLogObjectParent(coloring,coloring->w3);
751:   }
752:   w1 = coloring->w1; w2 = coloring->w2; w3 = coloring->w3;

754:   MatSetUnfactored(J);
755:   PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_dont_rezero",&flg);
756:   if (flg) {
757:     PetscLogInfo(coloring,"MatFDColoringApply: Not calling MatZeroEntries()\n");
758:   } else {
759:     PetscTruth assembled;
760:     MatAssembled(J,&assembled);
761:     if (assembled) {
762:       MatZeroEntries(J);
763:     }
764:   }

766:   VecGetOwnershipRange(x1,&start,&end);
767:   VecGetSize(x1,&N);
768:   PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);
769:   (*f)(sctx,t,x1,w1,fctx);
770:   PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);

772:   /* 
773:       Compute all the scale factors and share with other processors
774:   */
775:   VecGetArray(x1,&xx);xx = xx - start;
776:   VecGetArray(coloring->vscale,&vscale_array);vscale_array = vscale_array - start;
777:   for (k=0; k<coloring->ncolors; k++) {
778:     /*
779:        Loop over each column associated with color adding the 
780:        perturbation to the vector w3.
781:     */
782:     for (l=0; l<coloring->ncolumns[k]; l++) {
783:       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
784:       dx  = xx[col];
785:       if (dx == 0.0) dx = 1.0;
786: #if !defined(PETSC_USE_COMPLEX)
787:       if (dx < umin && dx >= 0.0)      dx = umin;
788:       else if (dx < 0.0 && dx > -umin) dx = -umin;
789: #else
790:       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
791:       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
792: #endif
793:       dx                *= epsilon;
794:       vscale_array[col] = 1.0/dx;
795:     }
796:   }
797:   vscale_array = vscale_array - start;VecRestoreArray(coloring->vscale,&vscale_array);
798:   VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);
799:   VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);

801:   if (coloring->vscaleforrow) vscaleforrow = coloring->vscaleforrow;
802:   else                        vscaleforrow = coloring->columnsforrow;

804:   VecGetArray(coloring->vscale,&vscale_array);
805:   /*
806:       Loop over each color
807:   */
808:   for (k=0; k<coloring->ncolors; k++) {
809:     VecCopy(x1,w3);
810:     VecGetArray(w3,&w3_array);w3_array = w3_array - start;
811:     /*
812:        Loop over each column associated with color adding the 
813:        perturbation to the vector w3.
814:     */
815:     for (l=0; l<coloring->ncolumns[k]; l++) {
816:       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
817:       dx  = xx[col];
818:       if (dx == 0.0) dx = 1.0;
819: #if !defined(PETSC_USE_COMPLEX)
820:       if (dx < umin && dx >= 0.0)      dx = umin;
821:       else if (dx < 0.0 && dx > -umin) dx = -umin;
822: #else
823:       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
824:       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
825: #endif
826:       dx            *= epsilon;
827:       w3_array[col] += dx;
828:     }
829:     w3_array = w3_array + start; VecRestoreArray(w3,&w3_array);

831:     /*
832:        Evaluate function at x1 + dx (here dx is a vector of perturbations)
833:     */
834:     PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);
835:     (*f)(sctx,t,w3,w2,fctx);
836:     PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);
837:     VecAXPY(&mone,w1,w2);

839:     /*
840:        Loop over rows of vector, putting results into Jacobian matrix
841:     */
842:     VecGetArray(w2,&y);
843:     for (l=0; l<coloring->nrows[k]; l++) {
844:       row    = coloring->rows[k][l];
845:       col    = coloring->columnsforrow[k][l];
846:       y[row] *= vscale_array[vscaleforrow[k][l]];
847:       srow   = row + start;
848:       MatSetValues(J,1,&srow,1,&col,y+row,INSERT_VALUES);
849:     }
850:     VecRestoreArray(w2,&y);
851:   }
852:   VecRestoreArray(coloring->vscale,&vscale_array);
853:   xx    = xx + start; VecRestoreArray(x1,&xx);
854:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
855:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
856:   PetscLogEventEnd(MAT_FDColoringApply,coloring,J,x1,0);
857:   return(0);
858: }


863: /*@C
864:    MatFDColoringSetRecompute - Indicates that the next time a Jacobian preconditioner
865:      is needed it sholuld be recomputed. Once this is called and the new Jacobian is computed
866:      no additional Jacobian's will be computed (the same one will be used) until this is
867:      called again.

869:    Collective on MatFDColoring

871:    Input  Parameters:
872: .  c - the coloring context

874:    Level: intermediate

876:    Notes: The MatFDColoringSetFrequency() is ignored once this is called

878: .seealso: MatFDColoringCreate(), MatFDColoringSetFrequency()

880: .keywords: Mat, finite differences, coloring
881: @*/
882: PetscErrorCode MatFDColoringSetRecompute(MatFDColoring c)
883: {
886:   c->usersetsrecompute = PETSC_TRUE;
887:   c->recompute         = PETSC_TRUE;
888:   return(0);
889: }