Actual source code: mffd.c

  1: #include <../src/mat/impls/shell/shell.h>
  2: #include <../src/mat/impls/mffd/mffdimpl.h>

  4: PetscFunctionList MatMFFDList              = NULL;
  5: PetscBool         MatMFFDRegisterAllCalled = PETSC_FALSE;

  7: PetscClassId  MATMFFD_CLASSID;
  8: PetscLogEvent MATMFFD_Mult;

 10: static PetscBool MatMFFDPackageInitialized = PETSC_FALSE;

 12: /*@C
 13:   MatMFFDFinalizePackage - This function destroys everything in the MATMFFD` package. It is
 14:   called from `PetscFinalize()`.

 16:   Level: developer

 18: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `PetscFinalize()`, `MatCreateMFFD()`, `MatCreateSNESMF()`
 19: @*/
 20: PetscErrorCode MatMFFDFinalizePackage(void)
 21: {
 22:   PetscFunctionBegin;
 23:   PetscCall(PetscFunctionListDestroy(&MatMFFDList));
 24:   MatMFFDPackageInitialized = PETSC_FALSE;
 25:   MatMFFDRegisterAllCalled  = PETSC_FALSE;
 26:   PetscFunctionReturn(PETSC_SUCCESS);
 27: }

 29: /*@C
 30:   MatMFFDInitializePackage - This function initializes everything in the MATMFFD` package. It is called
 31:   from `MatInitializePackage()`.

 33:   Level: developer

 35: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `PetscInitialize()`
 36: @*/
 37: PetscErrorCode MatMFFDInitializePackage(void)
 38: {
 39:   char      logList[256];
 40:   PetscBool opt, pkg;

 42:   PetscFunctionBegin;
 43:   if (MatMFFDPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
 44:   MatMFFDPackageInitialized = PETSC_TRUE;
 45:   /* Register Classes */
 46:   PetscCall(PetscClassIdRegister("MatMFFD", &MATMFFD_CLASSID));
 47:   /* Register Constructors */
 48:   PetscCall(MatMFFDRegisterAll());
 49:   /* Register Events */
 50:   PetscCall(PetscLogEventRegister("MatMult MF", MATMFFD_CLASSID, &MATMFFD_Mult));
 51:   /* Process Info */
 52:   {
 53:     PetscClassId classids[1];

 55:     classids[0] = MATMFFD_CLASSID;
 56:     PetscCall(PetscInfoProcessClass("matmffd", 1, classids));
 57:   }
 58:   /* Process summary exclusions */
 59:   PetscCall(PetscOptionsGetString(NULL, NULL, "-log_exclude", logList, sizeof(logList), &opt));
 60:   if (opt) {
 61:     PetscCall(PetscStrInList("matmffd", logList, ',', &pkg));
 62:     if (pkg) PetscCall(PetscLogEventExcludeClass(MATMFFD_CLASSID));
 63:   }
 64:   /* Register package finalizer */
 65:   PetscCall(PetscRegisterFinalize(MatMFFDFinalizePackage));
 66:   PetscFunctionReturn(PETSC_SUCCESS);
 67: }

 69: static PetscErrorCode MatMFFDSetType_MFFD(Mat mat, MatMFFDType ftype)
 70: {
 71:   MatMFFD   ctx;
 72:   PetscBool match;
 73:   PetscErrorCode (*r)(MatMFFD);

 75:   PetscFunctionBegin;
 77:   PetscAssertPointer(ftype, 2);
 78:   PetscCall(MatShellGetContext(mat, &ctx));

 80:   /* already set, so just return */
 81:   PetscCall(PetscObjectTypeCompare((PetscObject)ctx, ftype, &match));
 82:   if (match) PetscFunctionReturn(PETSC_SUCCESS);

 84:   /* destroy the old one if it exists */
 85:   PetscTryTypeMethod(ctx, destroy);

 87:   PetscCall(PetscFunctionListFind(MatMFFDList, ftype, &r));
 88:   PetscCheck(r, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown MatMFFD type %s given", ftype);
 89:   PetscCall((*r)(ctx));
 90:   PetscCall(PetscObjectChangeTypeName((PetscObject)ctx, ftype));
 91:   PetscFunctionReturn(PETSC_SUCCESS);
 92: }

 94: /*@
 95:   MatMFFDSetType - Sets the method that is used to compute the
 96:   differencing parameter for finite difference matrix-free formulations.

 98:   Input Parameters:
 99: + mat   - the "matrix-free" matrix created via `MatCreateSNESMF()`, or `MatCreateMFFD()`
100:           or `MatSetType`(mat,`MATMFFD`);
101: - ftype - the type requested, either `MATMFFD_WP` or `MATMFFD_DS`

103:   Level: advanced

105:   Note:
106:   For example, such routines can compute `h` for use in
107:   Jacobian-vector products of the form
108: .vb

110:                         F(x+ha) - F(x)
111:           F'(u)a  ~=  ----------------
112:                               h
113: .ve

115: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MATMFFD_WP`, `MATMFFD_DS`, `MatCreateSNESMF()`, `MatMFFDRegister()`, `MatMFFDSetFunction()`, `MatCreateMFFD()`
116: @*/
117: PetscErrorCode MatMFFDSetType(Mat mat, MatMFFDType ftype)
118: {
119:   PetscFunctionBegin;
121:   PetscAssertPointer(ftype, 2);
122:   PetscTryMethod(mat, "MatMFFDSetType_C", (Mat, MatMFFDType), (mat, ftype));
123:   PetscFunctionReturn(PETSC_SUCCESS);
124: }

126: static PetscErrorCode MatGetDiagonal_MFFD(Mat, Vec);

128: typedef PetscErrorCode (*FCN1)(void *, Vec); /* force argument to next function to not be extern C*/
129: static PetscErrorCode MatMFFDSetFunctioniBase_MFFD(Mat mat, FCN1 func)
130: {
131:   MatMFFD ctx;

133:   PetscFunctionBegin;
134:   PetscCall(MatShellGetContext(mat, &ctx));
135:   ctx->funcisetbase = func;
136:   PetscFunctionReturn(PETSC_SUCCESS);
137: }

139: typedef PetscErrorCode (*FCN2)(void *, PetscInt, Vec, PetscScalar *); /* force argument to next function to not be extern C*/
140: static PetscErrorCode MatMFFDSetFunctioni_MFFD(Mat mat, FCN2 funci)
141: {
142:   MatMFFD ctx;

144:   PetscFunctionBegin;
145:   PetscCall(MatShellGetContext(mat, &ctx));
146:   ctx->funci = funci;
147:   PetscCall(MatShellSetOperation(mat, MATOP_GET_DIAGONAL, (void (*)(void))MatGetDiagonal_MFFD));
148:   PetscFunctionReturn(PETSC_SUCCESS);
149: }

151: static PetscErrorCode MatMFFDGetH_MFFD(Mat mat, PetscScalar *h)
152: {
153:   MatMFFD ctx;

155:   PetscFunctionBegin;
156:   PetscCall(MatShellGetContext(mat, &ctx));
157:   *h = ctx->currenth;
158:   PetscFunctionReturn(PETSC_SUCCESS);
159: }

161: static PetscErrorCode MatMFFDResetHHistory_MFFD(Mat J)
162: {
163:   MatMFFD ctx;

165:   PetscFunctionBegin;
166:   PetscCall(MatShellGetContext(J, &ctx));
167:   ctx->ncurrenth = 0;
168:   PetscFunctionReturn(PETSC_SUCCESS);
169: }

171: /*@C
172:   MatMFFDRegister - Adds a method to the `MATMFFD` registry.

174:   Not Collective, No Fortran Support

176:   Input Parameters:
177: + sname    - name of a new user-defined compute-h module
178: - function - routine to create method context

180:   Level: developer

182:   Note:
183:   `MatMFFDRegister()` may be called multiple times to add several user-defined solvers.

185:   Example Usage:
186: .vb
187:    MatMFFDRegister("my_h", MyHCreate);
188: .ve

190:   Then, your solver can be chosen with the procedural interface via `MatMFFDSetType`(mfctx, "my_h")` or at runtime via the option
191:   `-mat_mffd_type my_h`

193: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDRegisterAll()`, `MatMFFDRegisterDestroy()`
194:  @*/
195: PetscErrorCode MatMFFDRegister(const char sname[], PetscErrorCode (*function)(MatMFFD))
196: {
197:   PetscFunctionBegin;
198:   PetscCall(MatInitializePackage());
199:   PetscCall(PetscFunctionListAdd(&MatMFFDList, sname, function));
200:   PetscFunctionReturn(PETSC_SUCCESS);
201: }

203: static PetscErrorCode MatDestroy_MFFD(Mat mat)
204: {
205:   MatMFFD ctx;

207:   PetscFunctionBegin;
208:   PetscCall(MatShellGetContext(mat, &ctx));
209:   PetscCall(VecDestroy(&ctx->w));
210:   PetscCall(VecDestroy(&ctx->current_u));
211:   if (ctx->current_f_allocated) PetscCall(VecDestroy(&ctx->current_f));
212:   PetscTryTypeMethod(ctx, destroy);
213:   PetscCall(PetscHeaderDestroy(&ctx));

215:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetBase_C", NULL));
216:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunctioniBase_C", NULL));
217:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunctioni_C", NULL));
218:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunction_C", NULL));
219:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunctionError_C", NULL));
220:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetCheckh_C", NULL));
221:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetPeriod_C", NULL));
222:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDResetHHistory_C", NULL));
223:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetHHistory_C", NULL));
224:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetType_C", NULL));
225:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDGetH_C", NULL));
226:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSNESMFSetReuseBase_C", NULL));
227:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSNESMFGetReuseBase_C", NULL));
228:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetContext_C", NULL));
229:   PetscFunctionReturn(PETSC_SUCCESS);
230: }

232: /*
233:    MatMFFDView_MFFD - Views matrix-free parameters.

235: */
236: static PetscErrorCode MatView_MFFD(Mat J, PetscViewer viewer)
237: {
238:   MatMFFD     ctx;
239:   PetscBool   iascii, viewbase, viewfunction;
240:   const char *prefix;

242:   PetscFunctionBegin;
243:   PetscCall(MatShellGetContext(J, &ctx));
244:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
245:   if (iascii) {
246:     PetscCall(PetscViewerASCIIPrintf(viewer, "Matrix-free approximation:\n"));
247:     PetscCall(PetscViewerASCIIPushTab(viewer));
248:     PetscCall(PetscViewerASCIIPrintf(viewer, "err=%g (relative error in function evaluation)\n", (double)ctx->error_rel));
249:     if (!((PetscObject)ctx)->type_name) {
250:       PetscCall(PetscViewerASCIIPrintf(viewer, "The compute h routine has not yet been set\n"));
251:     } else {
252:       PetscCall(PetscViewerASCIIPrintf(viewer, "Using %s compute h routine\n", ((PetscObject)ctx)->type_name));
253:     }
254: #if defined(PETSC_USE_COMPLEX)
255:     if (ctx->usecomplex) PetscCall(PetscViewerASCIIPrintf(viewer, "Using Lyness complex number trick to compute the matrix-vector product\n"));
256: #endif
257:     PetscTryTypeMethod(ctx, view, viewer);
258:     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)J, &prefix));

260:     PetscCall(PetscOptionsHasName(((PetscObject)J)->options, prefix, "-mat_mffd_view_base", &viewbase));
261:     if (viewbase) {
262:       PetscCall(PetscViewerASCIIPrintf(viewer, "Base:\n"));
263:       PetscCall(VecView(ctx->current_u, viewer));
264:     }
265:     PetscCall(PetscOptionsHasName(((PetscObject)J)->options, prefix, "-mat_mffd_view_function", &viewfunction));
266:     if (viewfunction) {
267:       PetscCall(PetscViewerASCIIPrintf(viewer, "Function:\n"));
268:       PetscCall(VecView(ctx->current_f, viewer));
269:     }
270:     PetscCall(PetscViewerASCIIPopTab(viewer));
271:   }
272:   PetscFunctionReturn(PETSC_SUCCESS);
273: }

275: /*
276:    MatAssemblyEnd_MFFD - Resets the ctx->ncurrenth to zero. This
277:    allows the user to indicate the beginning of a new linear solve by calling
278:    MatAssemblyXXX() on the matrix-free matrix. This then allows the
279:    MatCreateMFFD_WP() to properly compute ||U|| only the first time
280:    in the linear solver rather than every time.

282:    This function is referenced directly from MatAssemblyEnd_SNESMF(), which may be in a different shared library hence
283:    it must be labeled as PETSC_EXTERN
284: */
285: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J, MatAssemblyType mt)
286: {
287:   MatMFFD j;

289:   PetscFunctionBegin;
290:   PetscCall(MatShellGetContext(J, &j));
291:   PetscCall(MatMFFDResetHHistory(J));
292:   PetscFunctionReturn(PETSC_SUCCESS);
293: }

295: /*
296:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

298:         y ~= (F(u + ha) - F(u))/h,
299:   where F = nonlinear function, as set by SNESSetFunction()
300:         u = current iterate
301:         h = difference interval
302: */
303: static PetscErrorCode MatMult_MFFD(Mat mat, Vec a, Vec y)
304: {
305:   MatMFFD     ctx;
306:   PetscScalar h;
307:   Vec         w, U, F;
308:   PetscBool   zeroa;

310:   PetscFunctionBegin;
311:   PetscCall(MatShellGetContext(mat, &ctx));
312:   PetscCheck(ctx->current_u, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MatMFFDSetBase() has not been called, this is often caused by forgetting to call MatAssemblyBegin/End on the first Mat in the SNES compute function");
313:   /* We log matrix-free matrix-vector products separately, so that we can
314:      separate the performance monitoring from the cases that use conventional
315:      storage.  We may eventually modify event logging to associate events
316:      with particular objects, hence alleviating the more general problem. */
317:   PetscCall(PetscLogEventBegin(MATMFFD_Mult, a, y, 0, 0));

319:   w = ctx->w;
320:   U = ctx->current_u;
321:   F = ctx->current_f;
322:   /*
323:       Compute differencing parameter
324:   */
325:   if (!((PetscObject)ctx)->type_name) {
326:     PetscCall(MatMFFDSetType(mat, MATMFFD_WP));
327:     PetscCall(MatSetFromOptions(mat));
328:   }
329:   PetscUseTypeMethod(ctx, compute, U, a, &h, &zeroa);
330:   if (zeroa) {
331:     PetscCall(VecSet(y, 0.0));
332:     PetscCall(PetscLogEventEnd(MATMFFD_Mult, a, y, 0, 0));
333:     PetscFunctionReturn(PETSC_SUCCESS);
334:   }

336:   PetscCheck(!mat->erroriffailure || !PetscIsInfOrNanScalar(h), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Computed Nan differencing parameter h");
337:   if (ctx->checkh) PetscCall((*ctx->checkh)(ctx->checkhctx, U, a, &h));

339:   /* keep a record of the current differencing parameter h */
340:   ctx->currenth = h;
341: #if defined(PETSC_USE_COMPLEX)
342:   PetscCall(PetscInfo(mat, "Current differencing parameter: %g + %g i\n", (double)PetscRealPart(h), (double)PetscImaginaryPart(h)));
343: #else
344:   PetscCall(PetscInfo(mat, "Current differencing parameter: %15.12e\n", (double)PetscRealPart(h)));
345: #endif
346:   if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) ctx->historyh[ctx->ncurrenth] = h;
347:   ctx->ncurrenth++;

349: #if defined(PETSC_USE_COMPLEX)
350:   if (ctx->usecomplex) h = PETSC_i * h;
351: #endif

353:   /* w = u + ha */
354:   PetscCall(VecWAXPY(w, h, a, U));

356:   /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
357:   if (ctx->ncurrenth == 1 && ctx->current_f_allocated) PetscCall((*ctx->func)(ctx->funcctx, U, F));
358:   PetscCall((*ctx->func)(ctx->funcctx, w, y));

360: #if defined(PETSC_USE_COMPLEX)
361:   if (ctx->usecomplex) {
362:     PetscCall(VecImaginaryPart(y));
363:     h = PetscImaginaryPart(h);
364:   } else {
365:     PetscCall(VecAXPY(y, -1.0, F));
366:   }
367: #else
368:   PetscCall(VecAXPY(y, -1.0, F));
369: #endif
370:   PetscCall(VecScale(y, 1.0 / h));
371:   if (mat->nullsp) PetscCall(MatNullSpaceRemove(mat->nullsp, y));

373:   PetscCall(PetscLogEventEnd(MATMFFD_Mult, a, y, 0, 0));
374:   PetscFunctionReturn(PETSC_SUCCESS);
375: }

377: /*
378:   MatGetDiagonal_MFFD - Gets the diagonal for a matrix-free matrix

380:         y ~= (F(u + ha) - F(u))/h,
381:   where F = nonlinear function, as set by SNESSetFunction()
382:         u = current iterate
383:         h = difference interval
384: */
385: static PetscErrorCode MatGetDiagonal_MFFD(Mat mat, Vec a)
386: {
387:   MatMFFD     ctx;
388:   PetscScalar h, *aa, *ww, v;
389:   PetscReal   epsilon = PETSC_SQRT_MACHINE_EPSILON, umin = 100.0 * PETSC_SQRT_MACHINE_EPSILON;
390:   Vec         w, U;
391:   PetscInt    i, rstart, rend;

393:   PetscFunctionBegin;
394:   PetscCall(MatShellGetContext(mat, &ctx));
395:   PetscCheck(ctx->func, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Requires calling MatMFFDSetFunction() first");
396:   PetscCheck(ctx->funci, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Requires calling MatMFFDSetFunctioni() first");
397:   w = ctx->w;
398:   U = ctx->current_u;
399:   PetscCall((*ctx->func)(ctx->funcctx, U, a));
400:   if (ctx->funcisetbase) PetscCall((*ctx->funcisetbase)(ctx->funcctx, U));
401:   PetscCall(VecCopy(U, w));

403:   PetscCall(VecGetOwnershipRange(a, &rstart, &rend));
404:   PetscCall(VecGetArray(a, &aa));
405:   for (i = rstart; i < rend; i++) {
406:     PetscCall(VecGetArray(w, &ww));
407:     h = ww[i - rstart];
408:     if (h == 0.0) h = 1.0;
409:     if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
410:     else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
411:     h *= epsilon;

413:     ww[i - rstart] += h;
414:     PetscCall(VecRestoreArray(w, &ww));
415:     PetscCall((*ctx->funci)(ctx->funcctx, i, w, &v));
416:     aa[i - rstart] = (v - aa[i - rstart]) / h;

418:     PetscCall(VecGetArray(w, &ww));
419:     ww[i - rstart] -= h;
420:     PetscCall(VecRestoreArray(w, &ww));
421:   }
422:   PetscCall(VecRestoreArray(a, &aa));
423:   PetscFunctionReturn(PETSC_SUCCESS);
424: }

426: PETSC_EXTERN PetscErrorCode MatMFFDSetBase_MFFD(Mat J, Vec U, Vec F)
427: {
428:   MatMFFD ctx;

430:   PetscFunctionBegin;
431:   PetscCall(MatShellGetContext(J, &ctx));
432:   PetscCall(MatMFFDResetHHistory(J));
433:   if (!ctx->current_u) {
434:     PetscCall(VecDuplicate(U, &ctx->current_u));
435:     PetscCall(VecLockReadPush(ctx->current_u));
436:   }
437:   PetscCall(VecLockReadPop(ctx->current_u));
438:   PetscCall(VecCopy(U, ctx->current_u));
439:   PetscCall(VecLockReadPush(ctx->current_u));
440:   if (F) {
441:     if (ctx->current_f_allocated) PetscCall(VecDestroy(&ctx->current_f));
442:     ctx->current_f           = F;
443:     ctx->current_f_allocated = PETSC_FALSE;
444:   } else if (!ctx->current_f_allocated) {
445:     PetscCall(MatCreateVecs(J, NULL, &ctx->current_f));
446:     ctx->current_f_allocated = PETSC_TRUE;
447:   }
448:   if (!ctx->w) PetscCall(VecDuplicate(ctx->current_u, &ctx->w));
449:   J->assembled = PETSC_TRUE;
450:   PetscFunctionReturn(PETSC_SUCCESS);
451: }

453: typedef PetscErrorCode (*FCN3)(void *, Vec, Vec, PetscScalar *); /* force argument to next function to not be extern C*/

455: static PetscErrorCode MatMFFDSetCheckh_MFFD(Mat J, FCN3 fun, void *ectx)
456: {
457:   MatMFFD ctx;

459:   PetscFunctionBegin;
460:   PetscCall(MatShellGetContext(J, &ctx));
461:   ctx->checkh    = fun;
462:   ctx->checkhctx = ectx;
463:   PetscFunctionReturn(PETSC_SUCCESS);
464: }

466: /*@
467:   MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all
468:   MATMFFD` options in the database.

470:   Collective

472:   Input Parameters:
473: + mat    - the `MATMFFD` context
474: - prefix - the prefix to prepend to all option names

476:   Note:
477:   A hyphen (-) must NOT be given at the beginning of the prefix name.
478:   The first character of all runtime options is AUTOMATICALLY the hyphen.

480:   Level: advanced

482: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatSetFromOptions()`, `MatCreateSNESMF()`, `MatCreateMFFD()`
483: @*/
484: PetscErrorCode MatMFFDSetOptionsPrefix(Mat mat, const char prefix[])
485: {
486:   MatMFFD mfctx;

488:   PetscFunctionBegin;
490:   PetscCall(MatShellGetContext(mat, &mfctx));
492:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mfctx, prefix));
493:   PetscFunctionReturn(PETSC_SUCCESS);
494: }

496: static PetscErrorCode MatSetFromOptions_MFFD(Mat mat, PetscOptionItems *PetscOptionsObject)
497: {
498:   MatMFFD   mfctx;
499:   PetscBool flg;
500:   char      ftype[256];

502:   PetscFunctionBegin;
503:   PetscCall(MatShellGetContext(mat, &mfctx));
505:   PetscObjectOptionsBegin((PetscObject)mfctx);
506:   PetscCall(PetscOptionsFList("-mat_mffd_type", "Matrix free type", "MatMFFDSetType", MatMFFDList, ((PetscObject)mfctx)->type_name, ftype, 256, &flg));
507:   if (flg) PetscCall(MatMFFDSetType(mat, ftype));

509:   PetscCall(PetscOptionsReal("-mat_mffd_err", "set sqrt relative error in function", "MatMFFDSetFunctionError", mfctx->error_rel, &mfctx->error_rel, NULL));
510:   PetscCall(PetscOptionsInt("-mat_mffd_period", "how often h is recomputed", "MatMFFDSetPeriod", mfctx->recomputeperiod, &mfctx->recomputeperiod, NULL));

512:   flg = PETSC_FALSE;
513:   PetscCall(PetscOptionsBool("-mat_mffd_check_positivity", "Insure that U + h*a is nonnegative", "MatMFFDSetCheckh", flg, &flg, NULL));
514:   if (flg) PetscCall(MatMFFDSetCheckh(mat, MatMFFDCheckPositivity, NULL));
515: #if defined(PETSC_USE_COMPLEX)
516:   PetscCall(PetscOptionsBool("-mat_mffd_complex", "Use Lyness complex number trick to compute the matrix-vector product", "None", mfctx->usecomplex, &mfctx->usecomplex, NULL));
517: #endif
518:   PetscTryTypeMethod(mfctx, setfromoptions, PetscOptionsObject);
519:   PetscOptionsEnd();
520:   PetscFunctionReturn(PETSC_SUCCESS);
521: }

523: static PetscErrorCode MatMFFDSetPeriod_MFFD(Mat mat, PetscInt period)
524: {
525:   MatMFFD ctx;

527:   PetscFunctionBegin;
528:   PetscCall(MatShellGetContext(mat, &ctx));
529:   ctx->recomputeperiod = period;
530:   PetscFunctionReturn(PETSC_SUCCESS);
531: }

533: static PetscErrorCode MatMFFDSetFunction_MFFD(Mat mat, PetscErrorCode (*func)(void *, Vec, Vec), void *funcctx)
534: {
535:   MatMFFD ctx;

537:   PetscFunctionBegin;
538:   PetscCall(MatShellGetContext(mat, &ctx));
539:   ctx->func    = func;
540:   ctx->funcctx = funcctx;
541:   PetscFunctionReturn(PETSC_SUCCESS);
542: }

544: static PetscErrorCode MatMFFDSetFunctionError_MFFD(Mat mat, PetscReal error)
545: {
546:   PetscFunctionBegin;
547:   if (error != (PetscReal)PETSC_DEFAULT) {
548:     MatMFFD ctx;

550:     PetscCall(MatShellGetContext(mat, &ctx));
551:     ctx->error_rel = error;
552:   }
553:   PetscFunctionReturn(PETSC_SUCCESS);
554: }

556: static PetscErrorCode MatMFFDSetHHistory_MFFD(Mat J, PetscScalar history[], PetscInt nhistory)
557: {
558:   MatMFFD ctx;

560:   PetscFunctionBegin;
561:   PetscCall(MatShellGetContext(J, &ctx));
562:   ctx->historyh    = history;
563:   ctx->maxcurrenth = nhistory;
564:   ctx->currenth    = 0.;
565:   PetscFunctionReturn(PETSC_SUCCESS);
566: }

568: /*MC
569:   MATMFFD - "mffd" - A matrix-free matrix type.

571:   Level: advanced

573:   Developer Notes:
574:   This is implemented on top of `MATSHELL` to get support for scaling and shifting without requiring duplicate code

576:   Users should not MatShell... operations on this class, there is some error checking for that incorrect usage

578: .seealso: [](ch_matrices), `Mat`, `MatCreateMFFD()`, `MatCreateSNESMF()`, `MatMFFDSetFunction()`, `MatMFFDSetType()`,
579:           `MatMFFDSetFunctionError()`, `MatMFFDDSSetUmin()`, `MatMFFDSetFunction()`
580:           `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `MatCreateSNESMF()`,
581:           `MatMFFDGetH()`,
582: M*/
583: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
584: {
585:   MatMFFD mfctx;

587:   PetscFunctionBegin;
588:   PetscCall(MatMFFDInitializePackage());

590:   PetscCall(PetscHeaderCreate(mfctx, MATMFFD_CLASSID, "MatMFFD", "Matrix-free Finite Differencing", "Mat", PetscObjectComm((PetscObject)A), NULL, NULL));

592:   mfctx->error_rel                = PETSC_SQRT_MACHINE_EPSILON;
593:   mfctx->recomputeperiod          = 1;
594:   mfctx->count                    = 0;
595:   mfctx->currenth                 = 0.0;
596:   mfctx->historyh                 = NULL;
597:   mfctx->ncurrenth                = 0;
598:   mfctx->maxcurrenth              = 0;
599:   ((PetscObject)mfctx)->type_name = NULL;

601:   /*
602:      Create the empty data structure to contain compute-h routines.
603:      These will be filled in below from the command line options or
604:      a later call with MatMFFDSetType() or if that is not called
605:      then it will default in the first use of MatMult_MFFD()
606:   */
607:   mfctx->ops->compute        = NULL;
608:   mfctx->ops->destroy        = NULL;
609:   mfctx->ops->view           = NULL;
610:   mfctx->ops->setfromoptions = NULL;
611:   mfctx->hctx                = NULL;

613:   mfctx->func    = NULL;
614:   mfctx->funcctx = NULL;
615:   mfctx->w       = NULL;
616:   mfctx->mat     = A;

618:   PetscCall(MatSetType(A, MATSHELL));
619:   PetscCall(MatShellSetContext(A, mfctx));
620:   PetscCall(MatShellSetOperation(A, MATOP_MULT, (void (*)(void))MatMult_MFFD));
621:   PetscCall(MatShellSetOperation(A, MATOP_DESTROY, (void (*)(void))MatDestroy_MFFD));
622:   PetscCall(MatShellSetOperation(A, MATOP_VIEW, (void (*)(void))MatView_MFFD));
623:   PetscCall(MatShellSetOperation(A, MATOP_ASSEMBLY_END, (void (*)(void))MatAssemblyEnd_MFFD));
624:   PetscCall(MatShellSetOperation(A, MATOP_SET_FROM_OPTIONS, (void (*)(void))MatSetFromOptions_MFFD));
625:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", MatShellSetContext_Immutable));
626:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContextDestroy_C", MatShellSetContextDestroy_Immutable));
627:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetManageScalingShifts_C", MatShellSetManageScalingShifts_Immutable));

629:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetBase_C", MatMFFDSetBase_MFFD));
630:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunctioniBase_C", MatMFFDSetFunctioniBase_MFFD));
631:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunctioni_C", MatMFFDSetFunctioni_MFFD));
632:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunction_C", MatMFFDSetFunction_MFFD));
633:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetCheckh_C", MatMFFDSetCheckh_MFFD));
634:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetPeriod_C", MatMFFDSetPeriod_MFFD));
635:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunctionError_C", MatMFFDSetFunctionError_MFFD));
636:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDResetHHistory_C", MatMFFDResetHHistory_MFFD));
637:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetHHistory_C", MatMFFDSetHHistory_MFFD));
638:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetType_C", MatMFFDSetType_MFFD));
639:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDGetH_C", MatMFFDGetH_MFFD));
640:   PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATMFFD));
641:   PetscFunctionReturn(PETSC_SUCCESS);
642: }

644: /*@
645:   MatCreateMFFD - Creates a matrix-free matrix of type `MATMFFD`. See also `MatCreateSNESMF()`

647:   Collective

649:   Input Parameters:
650: + comm - MPI communicator
651: . m    - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
652:            This value should be the same as the local size used in creating the
653:            y vector for the matrix-vector product y = Ax.
654: . n    - This value should be the same as the local size used in creating the
655:        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
656:        calculated if `N` is given) For square matrices `n` is almost always `m`.
657: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
658: - N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)

660:   Output Parameter:
661: . J - the matrix-free matrix

663:   Options Database Keys:
664: + -mat_mffd_type             - wp or ds (see `MATMFFD_WP` or `MATMFFD_DS`)
665: . -mat_mffd_err              - square root of estimated relative error in function evaluation
666: . -mat_mffd_period           - how often h is recomputed, defaults to 1, every time
667: . -mat_mffd_check_positivity - possibly decrease `h` until U + h*a has only positive values
668: . -mat_mffd_umin <umin>      - Sets umin (for default PETSc routine that computes h only)
669: - -mat_mffd_complex          - use the Lyness trick with complex numbers to compute the matrix-vector product instead of differencing
670:                        (requires real valued functions but that PETSc be configured for complex numbers)

672:   Level: advanced

674:   Notes:
675:   The matrix-free matrix context merely contains the function pointers
676:   and work space for performing finite difference approximations of
677:   Jacobian-vector products, F'(u)*a,

679:   The default code uses the following approach to compute h

681: .vb
682:      F'(u)*a = [F(u+h*a) - F(u)]/h where
683:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
684:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
685:  where
686:      error_rel = square root of relative error in function evaluation
687:      umin = minimum iterate parameter
688: .ve

690:   You can call `SNESSetJacobian()` with `MatMFFDComputeJacobian()` if you are using matrix and not a different
691:   preconditioner matrix

693:   The user can set the error_rel via `MatMFFDSetFunctionError()` and
694:   umin via `MatMFFDDSSetUmin()`.

696:   The user should call `MatDestroy()` when finished with the matrix-free
697:   matrix context.

699: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatDestroy()`, `MatMFFDSetFunctionError()`, `MatMFFDDSSetUmin()`, `MatMFFDSetFunction()`
700:           `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `MatCreateSNESMF()`,
701:           `MatMFFDGetH()`, `MatMFFDRegister()`, `MatMFFDComputeJacobian()`
702: @*/
703: PetscErrorCode MatCreateMFFD(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, Mat *J)
704: {
705:   PetscFunctionBegin;
706:   PetscCall(MatCreate(comm, J));
707:   PetscCall(MatSetSizes(*J, m, n, M, N));
708:   PetscCall(MatSetType(*J, MATMFFD));
709:   PetscCall(MatSetUp(*J));
710:   PetscFunctionReturn(PETSC_SUCCESS);
711: }

713: /*@
714:   MatMFFDGetH - Gets the last value that was used as the differencing for a `MATMFFD` matrix
715:   parameter.

717:   Not Collective

719:   Input Parameters:
720: . mat - the `MATMFFD` matrix

722:   Output Parameter:
723: . h - the differencing step size

725:   Level: advanced

727: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDSetHHistory()`, `MatCreateMFFD()`, `MatMFFDResetHHistory()`
728: @*/
729: PetscErrorCode MatMFFDGetH(Mat mat, PetscScalar *h)
730: {
731:   PetscFunctionBegin;
733:   PetscAssertPointer(h, 2);
734:   PetscUseMethod(mat, "MatMFFDGetH_C", (Mat, PetscScalar *), (mat, h));
735:   PetscFunctionReturn(PETSC_SUCCESS);
736: }

738: /*@C
739:   MatMFFDSetFunction - Sets the function used in applying the matrix-free `MATMFFD` matrix.

741:   Logically Collective

743:   Input Parameters:
744: + mat     - the matrix-free matrix `MATMFFD` created via `MatCreateSNESMF()` or `MatCreateMFFD()`
745: . func    - the function to use
746: - funcctx - optional function context passed to function

748:   Calling sequence of `func`:
749: + funcctx - user provided context
750: . x       - input vector
751: - f       - computed output function

753:   Level: advanced

755:   Notes:
756:   If you use this you MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` on the matrix-free
757:   matrix inside your compute Jacobian routine

759:   If this is not set then it will use the function set with `SNESSetFunction()` if `MatCreateSNESMF()` was used.

761: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatCreateMFFD()`,
762:           `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `SNESSetFunction()`
763: @*/
764: PetscErrorCode MatMFFDSetFunction(Mat mat, PetscErrorCode (*func)(void *funcctx, Vec x, Vec f), void *funcctx)
765: {
766:   PetscFunctionBegin;
768:   PetscTryMethod(mat, "MatMFFDSetFunction_C", (Mat, PetscErrorCode (*)(void *, Vec, Vec), void *), (mat, func, funcctx));
769:   PetscFunctionReturn(PETSC_SUCCESS);
770: }

772: /*@C
773:   MatMFFDSetFunctioni - Sets the function for a single component for a `MATMFFD` matrix

775:   Logically Collective

777:   Input Parameters:
778: + mat   - the matrix-free matrix `MATMFFD`
779: - funci - the function to use

781:   Level: advanced

783:   Notes:
784:   If you use this you MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` on the matrix-free
785:   matrix inside your compute Jacobian routine.

787:   This function is necessary to compute the diagonal of the matrix.
788:   funci must not contain any MPI call as it is called inside a loop on the local portion of the vector.

790: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `SNESetFunction()`, `MatGetDiagonal()`
791: @*/
792: PetscErrorCode MatMFFDSetFunctioni(Mat mat, PetscErrorCode (*funci)(void *, PetscInt, Vec, PetscScalar *))
793: {
794:   PetscFunctionBegin;
796:   PetscTryMethod(mat, "MatMFFDSetFunctioni_C", (Mat, PetscErrorCode (*)(void *, PetscInt, Vec, PetscScalar *)), (mat, funci));
797:   PetscFunctionReturn(PETSC_SUCCESS);
798: }

800: /*@C
801:   MatMFFDSetFunctioniBase - Sets the base vector for a single component function evaluation for a `MATMFFD` matrix

803:   Logically Collective

805:   Input Parameters:
806: + mat  - the `MATMFFD` matrix-free matrix
807: - func - the function to use

809:   Level: advanced

811:   Notes:
812:   If you use this you MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` on the matrix-free
813:   matrix inside your compute Jacobian routine.

815:   This function is necessary to compute the diagonal of the matrix, used for example with `PCJACOBI`

817: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatCreateMFFD()`,
818:           `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `SNESetFunction()`, `MatGetDiagonal()`
819: @*/
820: PetscErrorCode MatMFFDSetFunctioniBase(Mat mat, PetscErrorCode (*func)(void *, Vec))
821: {
822:   PetscFunctionBegin;
824:   PetscTryMethod(mat, "MatMFFDSetFunctioniBase_C", (Mat, PetscErrorCode (*)(void *, Vec)), (mat, func));
825:   PetscFunctionReturn(PETSC_SUCCESS);
826: }

828: /*@
829:   MatMFFDSetPeriod - Sets how often h is recomputed for a `MATMFFD` matrix, by default it is every time

831:   Logically Collective

833:   Input Parameters:
834: + mat    - the `MATMFFD` matrix-free matrix
835: - period - 1 for every time, 2 for every second etc

837:   Options Database Key:
838: . -mat_mffd_period <period> - Sets how often `h` is recomputed

840:   Level: advanced

842: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`,
843:           `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`
844: @*/
845: PetscErrorCode MatMFFDSetPeriod(Mat mat, PetscInt period)
846: {
847:   PetscFunctionBegin;
850:   PetscTryMethod(mat, "MatMFFDSetPeriod_C", (Mat, PetscInt), (mat, period));
851:   PetscFunctionReturn(PETSC_SUCCESS);
852: }

854: /*@
855:   MatMFFDSetFunctionError - Sets the error_rel for the approximation of matrix-vector products using finite differences with the `MATMFFD` matrix

857:   Logically Collective

859:   Input Parameters:
860: + mat   - the `MATMFFD` matrix-free matrix
861: - error - relative error (should be set to the square root of the relative error in the function evaluations)

863:   Options Database Key:
864: . -mat_mffd_err <error_rel> - Sets error_rel

866:   Level: advanced

868:   Note:
869:   The default matrix-free matrix-vector product routine computes
870: .vb
871:      F'(u)*a = [F(u+h*a) - F(u)]/h where
872:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
873:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
874: .ve

876: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatCreateMFFD()`,
877:           `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`
878: @*/
879: PetscErrorCode MatMFFDSetFunctionError(Mat mat, PetscReal error)
880: {
881:   PetscFunctionBegin;
884:   PetscTryMethod(mat, "MatMFFDSetFunctionError_C", (Mat, PetscReal), (mat, error));
885:   PetscFunctionReturn(PETSC_SUCCESS);
886: }

888: /*@
889:   MatMFFDSetHHistory - Sets an array to collect a history of the
890:   differencing values (h) computed for the matrix-free product `MATMFFD` matrix

892:   Logically Collective

894:   Input Parameters:
895: + J        - the `MATMFFD` matrix-free matrix
896: . history  - space to hold the history
897: - nhistory - number of entries in history, if more entries are generated than
898:               nhistory, then the later ones are discarded

900:   Level: advanced

902:   Note:
903:   Use `MatMFFDResetHHistory()` to reset the history counter and collect
904:   a new batch of differencing parameters, h.

906: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDGetH()`, `MatCreateSNESMF()`,
907:           `MatMFFDResetHHistory()`, `MatMFFDSetFunctionError()`
908: @*/
909: PetscErrorCode MatMFFDSetHHistory(Mat J, PetscScalar history[], PetscInt nhistory)
910: {
911:   PetscFunctionBegin;
913:   if (history) PetscAssertPointer(history, 2);
915:   PetscUseMethod(J, "MatMFFDSetHHistory_C", (Mat, PetscScalar[], PetscInt), (J, history, nhistory));
916:   PetscFunctionReturn(PETSC_SUCCESS);
917: }

919: /*@
920:   MatMFFDResetHHistory - Resets the counter to zero to begin
921:   collecting a new set of differencing histories for the `MATMFFD` matrix

923:   Logically Collective

925:   Input Parameter:
926: . J - the matrix-free matrix context

928:   Level: advanced

930:   Note:
931:   Use `MatMFFDSetHHistory()` to create the original history counter.

933: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDGetH()`, `MatCreateSNESMF()`,
934:           `MatMFFDSetHHistory()`, `MatMFFDSetFunctionError()`
935: @*/
936: PetscErrorCode MatMFFDResetHHistory(Mat J)
937: {
938:   PetscFunctionBegin;
940:   PetscTryMethod(J, "MatMFFDResetHHistory_C", (Mat), (J));
941:   PetscFunctionReturn(PETSC_SUCCESS);
942: }

944: /*@
945:   MatMFFDSetBase - Sets the vector `U` at which matrix vector products of the
946:   Jacobian are computed for the `MATMFFD` matrix

948:   Logically Collective

950:   Input Parameters:
951: + J - the `MATMFFD` matrix
952: . U - the vector
953: - F - (optional) vector that contains F(u) if it has been already computed

955:   Level: advanced

957:   Notes:
958:   This is rarely used directly

960:   If `F` is provided then it is not recomputed. Otherwise the function is evaluated at the base
961:   point during the first `MatMult()` after each call to `MatMFFDSetBase()`.

963: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMult()`
964: @*/
965: PetscErrorCode MatMFFDSetBase(Mat J, Vec U, Vec F)
966: {
967:   PetscFunctionBegin;
971:   PetscTryMethod(J, "MatMFFDSetBase_C", (Mat, Vec, Vec), (J, U, F));
972:   PetscFunctionReturn(PETSC_SUCCESS);
973: }

975: /*@C
976:   MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
977:   it to satisfy some criteria for the `MATMFFD` matrix

979:   Logically Collective

981:   Input Parameters:
982: + J   - the `MATMFFD` matrix
983: . fun - the function that checks `h`
984: - ctx - any context needed by the function

986:   Options Database Keys:
987: . -mat_mffd_check_positivity <bool> - Insure that U + h*a is non-negative

989:   Level: advanced

991:   Notes:
992:   For example, `MatMFFDCheckPositivity()` insures that all entries of U + h*a are non-negative

994:   The function you provide is called after the default `h` has been computed and allows you to
995:   modify it.

997: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDCheckPositivity()`
998: @*/
999: PetscErrorCode MatMFFDSetCheckh(Mat J, PetscErrorCode (*fun)(void *, Vec, Vec, PetscScalar *), void *ctx)
1000: {
1001:   PetscFunctionBegin;
1003:   PetscTryMethod(J, "MatMFFDSetCheckh_C", (Mat, PetscErrorCode (*)(void *, Vec, Vec, PetscScalar *), void *), (J, fun, ctx));
1004:   PetscFunctionReturn(PETSC_SUCCESS);
1005: }

1007: /*@
1008:   MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1009:   zero, decreases h until this is satisfied for a `MATMFFD` matrix

1011:   Logically Collective

1013:   Input Parameters:
1014: + U     - base vector that is added to
1015: . a     - vector that is added
1016: . h     - scaling factor on a
1017: - dummy - context variable (unused)

1019:   Options Database Keys:
1020: . -mat_mffd_check_positivity <bool> - Insure that U + h*a is nonnegative

1022:   Level: advanced

1024:   Note:
1025:   This is rarely used directly, rather it is passed as an argument to `MatMFFDSetCheckh()`

1027: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDSetCheckh()`
1028: @*/
1029: PetscErrorCode MatMFFDCheckPositivity(void *dummy, Vec U, Vec a, PetscScalar *h)
1030: {
1031:   PetscReal    val, minval;
1032:   PetscScalar *u_vec, *a_vec;
1033:   PetscInt     i, n;
1034:   MPI_Comm     comm;

1036:   PetscFunctionBegin;
1039:   PetscAssertPointer(h, 4);
1040:   PetscCall(PetscObjectGetComm((PetscObject)U, &comm));
1041:   PetscCall(VecGetArray(U, &u_vec));
1042:   PetscCall(VecGetArray(a, &a_vec));
1043:   PetscCall(VecGetLocalSize(U, &n));
1044:   minval = PetscAbsScalar(*h) * PetscRealConstant(1.01);
1045:   for (i = 0; i < n; i++) {
1046:     if (PetscRealPart(u_vec[i] + *h * a_vec[i]) <= 0.0) {
1047:       val = PetscAbsScalar(u_vec[i] / a_vec[i]);
1048:       if (val < minval) minval = val;
1049:     }
1050:   }
1051:   PetscCall(VecRestoreArray(U, &u_vec));
1052:   PetscCall(VecRestoreArray(a, &a_vec));
1053:   PetscCallMPI(MPIU_Allreduce(&minval, &val, 1, MPIU_REAL, MPIU_MIN, comm));
1054:   if (val <= PetscAbsScalar(*h)) {
1055:     val = 0.99 * val;
1056:     PetscCall(PetscInfo(U, "Scaling back h from %g to %g\n", (double)PetscRealPart(*h), (double)val));
1057:     if (PetscRealPart(*h) > 0.0) *h = val;
1058:     else *h = -val;
1059:   }
1060:   PetscFunctionReturn(PETSC_SUCCESS);
1061: }