Actual source code: mffd.c
2: #include <petsc/private/matimpl.h>
3: #include <../src/mat/impls/mffd/mffdimpl.h>
5: PetscFunctionList MatMFFDList = NULL;
6: PetscBool MatMFFDRegisterAllCalled = PETSC_FALSE;
8: PetscClassId MATMFFD_CLASSID;
9: PetscLogEvent MATMFFD_Mult;
11: 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;
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, PETSC_COMM_SELF, 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: /*@C
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;
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
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: Sample usage:
186: .vb
187: MatMFFDRegister("my_h", MyHCreate);
188: .ve
190: Then, your solver can be chosen with the procedural interface via
191: $ `MatMFFDSetType`(mfctx, "my_h")
192: or at runtime via the option
193: $ -mat_mffd_type my_h
195: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDRegisterAll()`, `MatMFFDRegisterDestroy()`
196: @*/
197: PetscErrorCode MatMFFDRegister(const char sname[], PetscErrorCode (*function)(MatMFFD))
198: {
199: PetscFunctionBegin;
200: PetscCall(MatInitializePackage());
201: PetscCall(PetscFunctionListAdd(&MatMFFDList, sname, function));
202: PetscFunctionReturn(PETSC_SUCCESS);
203: }
205: static PetscErrorCode MatDestroy_MFFD(Mat mat)
206: {
207: MatMFFD ctx;
209: PetscFunctionBegin;
210: PetscCall(MatShellGetContext(mat, &ctx));
211: PetscCall(VecDestroy(&ctx->w));
212: PetscCall(VecDestroy(&ctx->current_u));
213: if (ctx->current_f_allocated) PetscCall(VecDestroy(&ctx->current_f));
214: PetscTryTypeMethod(ctx, destroy);
215: PetscCall(PetscHeaderDestroy(&ctx));
217: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetBase_C", NULL));
218: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunctioniBase_C", NULL));
219: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunctioni_C", NULL));
220: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunction_C", NULL));
221: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetFunctionError_C", NULL));
222: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetCheckh_C", NULL));
223: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetPeriod_C", NULL));
224: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDResetHHistory_C", NULL));
225: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetHHistory_C", NULL));
226: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDSetType_C", NULL));
227: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMFFDGetH_C", NULL));
228: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSNESMFSetReuseBase_C", NULL));
229: PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSNESMFGetReuseBase_C", NULL));
230: PetscFunctionReturn(PETSC_SUCCESS);
231: }
233: /*
234: MatMFFDView_MFFD - Views matrix-free parameters.
236: */
237: static PetscErrorCode MatView_MFFD(Mat J, PetscViewer viewer)
238: {
239: MatMFFD ctx;
240: PetscBool iascii, viewbase, viewfunction;
241: const char *prefix;
243: PetscFunctionBegin;
244: PetscCall(MatShellGetContext(J, &ctx));
245: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
246: if (iascii) {
247: PetscCall(PetscViewerASCIIPrintf(viewer, "Matrix-free approximation:\n"));
248: PetscCall(PetscViewerASCIIPushTab(viewer));
249: PetscCall(PetscViewerASCIIPrintf(viewer, "err=%g (relative error in function evaluation)\n", (double)ctx->error_rel));
250: if (!((PetscObject)ctx)->type_name) {
251: PetscCall(PetscViewerASCIIPrintf(viewer, "The compute h routine has not yet been set\n"));
252: } else {
253: PetscCall(PetscViewerASCIIPrintf(viewer, "Using %s compute h routine\n", ((PetscObject)ctx)->type_name));
254: }
255: #if defined(PETSC_USE_COMPLEX)
256: if (ctx->usecomplex) PetscCall(PetscViewerASCIIPrintf(viewer, "Using Lyness complex number trick to compute the matrix-vector product\n"));
257: #endif
258: PetscTryTypeMethod(ctx, view, viewer);
259: PetscCall(PetscObjectGetOptionsPrefix((PetscObject)J, &prefix));
261: PetscCall(PetscOptionsHasName(((PetscObject)J)->options, prefix, "-mat_mffd_view_base", &viewbase));
262: if (viewbase) {
263: PetscCall(PetscViewerASCIIPrintf(viewer, "Base:\n"));
264: PetscCall(VecView(ctx->current_u, viewer));
265: }
266: PetscCall(PetscOptionsHasName(((PetscObject)J)->options, prefix, "-mat_mffd_view_function", &viewfunction));
267: if (viewfunction) {
268: PetscCall(PetscViewerASCIIPrintf(viewer, "Function:\n"));
269: PetscCall(VecView(ctx->current_f, viewer));
270: }
271: PetscCall(PetscViewerASCIIPopTab(viewer));
272: }
273: PetscFunctionReturn(PETSC_SUCCESS);
274: }
276: /*
277: MatAssemblyEnd_MFFD - Resets the ctx->ncurrenth to zero. This
278: allows the user to indicate the beginning of a new linear solve by calling
279: MatAssemblyXXX() on the matrix free matrix. This then allows the
280: MatCreateMFFD_WP() to properly compute ||U|| only the first time
281: in the linear solver rather than every time.
283: This function is referenced directly from MatAssemblyEnd_SNESMF(), which may be in a different shared library hence
284: it must be labeled as PETSC_EXTERN
285: */
286: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J, MatAssemblyType mt)
287: {
288: MatMFFD j;
290: PetscFunctionBegin;
291: PetscCall(MatShellGetContext(J, &j));
292: PetscCall(MatMFFDResetHHistory(J));
293: PetscFunctionReturn(PETSC_SUCCESS);
294: }
296: /*
297: MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:
299: y ~= (F(u + ha) - F(u))/h,
300: where F = nonlinear function, as set by SNESSetFunction()
301: u = current iterate
302: h = difference interval
303: */
304: static PetscErrorCode MatMult_MFFD(Mat mat, Vec a, Vec y)
305: {
306: MatMFFD ctx;
307: PetscScalar h;
308: Vec w, U, F;
309: PetscBool zeroa;
311: PetscFunctionBegin;
312: PetscCall(MatShellGetContext(mat, &ctx));
313: PetscCheck(ctx->current_u, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MatMFFDSetBase() has not been called, this is often caused by forgetting to call \n\t\tMatAssemblyBegin/End on the first Mat in the SNES compute function");
314: /* We log matrix-free matrix-vector products separately, so that we can
315: separate the performance monitoring from the cases that use conventional
316: storage. We may eventually modify event logging to associate events
317: with particular objects, hence alleviating the more general problem. */
318: PetscCall(PetscLogEventBegin(MATMFFD_Mult, a, y, 0, 0));
320: w = ctx->w;
321: U = ctx->current_u;
322: F = ctx->current_f;
323: /*
324: Compute differencing parameter
325: */
326: if (!((PetscObject)ctx)->type_name) {
327: PetscCall(MatMFFDSetType(mat, MATMFFD_WP));
328: PetscCall(MatSetFromOptions(mat));
329: }
330: PetscUseTypeMethod(ctx, compute, U, a, &h, &zeroa);
331: if (zeroa) {
332: PetscCall(VecSet(y, 0.0));
333: PetscCall(PetscLogEventEnd(MATMFFD_Mult, a, y, 0, 0));
334: PetscFunctionReturn(PETSC_SUCCESS);
335: }
337: PetscCheck(!mat->erroriffailure || !PetscIsInfOrNanScalar(h), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Computed Nan differencing parameter h");
338: if (ctx->checkh) PetscCall((*ctx->checkh)(ctx->checkhctx, U, a, &h));
340: /* keep a record of the current differencing parameter h */
341: ctx->currenth = h;
342: #if defined(PETSC_USE_COMPLEX)
343: PetscCall(PetscInfo(mat, "Current differencing parameter: %g + %g i\n", (double)PetscRealPart(h), (double)PetscImaginaryPart(h)));
344: #else
345: PetscCall(PetscInfo(mat, "Current differencing parameter: %15.12e\n", (double)PetscRealPart(h)));
346: #endif
347: if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) ctx->historyh[ctx->ncurrenth] = h;
348: ctx->ncurrenth++;
350: #if defined(PETSC_USE_COMPLEX)
351: if (ctx->usecomplex) h = PETSC_i * h;
352: #endif
354: /* w = u + ha */
355: PetscCall(VecWAXPY(w, h, a, U));
357: /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
358: if (ctx->ncurrenth == 1 && ctx->current_f_allocated) PetscCall((*ctx->func)(ctx->funcctx, U, F));
359: PetscCall((*ctx->func)(ctx->funcctx, w, y));
361: #if defined(PETSC_USE_COMPLEX)
362: if (ctx->usecomplex) {
363: PetscCall(VecImaginaryPart(y));
364: h = PetscImaginaryPart(h);
365: } else {
366: PetscCall(VecAXPY(y, -1.0, F));
367: }
368: #else
369: PetscCall(VecAXPY(y, -1.0, F));
370: #endif
371: PetscCall(VecScale(y, 1.0 / h));
372: if (mat->nullsp) PetscCall(MatNullSpaceRemove(mat->nullsp, y));
374: PetscCall(PetscLogEventEnd(MATMFFD_Mult, a, y, 0, 0));
375: PetscFunctionReturn(PETSC_SUCCESS);
376: }
378: /*
379: MatGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix
381: y ~= (F(u + ha) - F(u))/h,
382: where F = nonlinear function, as set by SNESSetFunction()
383: u = current iterate
384: h = difference interval
385: */
386: PetscErrorCode MatGetDiagonal_MFFD(Mat mat, Vec a)
387: {
388: MatMFFD ctx;
389: PetscScalar h, *aa, *ww, v;
390: PetscReal epsilon = PETSC_SQRT_MACHINE_EPSILON, umin = 100.0 * PETSC_SQRT_MACHINE_EPSILON;
391: Vec w, U;
392: PetscInt i, rstart, rend;
394: PetscFunctionBegin;
395: PetscCall(MatShellGetContext(mat, &ctx));
396: PetscCheck(ctx->func, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Requires calling MatMFFDSetFunction() first");
397: PetscCheck(ctx->funci, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Requires calling MatMFFDSetFunctioni() first");
398: w = ctx->w;
399: U = ctx->current_u;
400: PetscCall((*ctx->func)(ctx->funcctx, U, a));
401: if (ctx->funcisetbase) PetscCall((*ctx->funcisetbase)(ctx->funcctx, U));
402: PetscCall(VecCopy(U, w));
404: PetscCall(VecGetOwnershipRange(a, &rstart, &rend));
405: PetscCall(VecGetArray(a, &aa));
406: for (i = rstart; i < rend; i++) {
407: PetscCall(VecGetArray(w, &ww));
408: h = ww[i - rstart];
409: if (h == 0.0) h = 1.0;
410: if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
411: else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
412: h *= epsilon;
414: ww[i - rstart] += h;
415: PetscCall(VecRestoreArray(w, &ww));
416: PetscCall((*ctx->funci)(ctx->funcctx, i, w, &v));
417: aa[i - rstart] = (v - aa[i - rstart]) / h;
419: PetscCall(VecGetArray(w, &ww));
420: ww[i - rstart] -= h;
421: PetscCall(VecRestoreArray(w, &ww));
422: }
423: PetscCall(VecRestoreArray(a, &aa));
424: PetscFunctionReturn(PETSC_SUCCESS);
425: }
427: PETSC_EXTERN PetscErrorCode MatMFFDSetBase_MFFD(Mat J, Vec U, Vec F)
428: {
429: MatMFFD ctx;
431: PetscFunctionBegin;
432: PetscCall(MatShellGetContext(J, &ctx));
433: PetscCall(MatMFFDResetHHistory(J));
434: if (!ctx->current_u) {
435: PetscCall(VecDuplicate(U, &ctx->current_u));
436: PetscCall(VecLockReadPush(ctx->current_u));
437: }
438: PetscCall(VecLockReadPop(ctx->current_u));
439: PetscCall(VecCopy(U, ctx->current_u));
440: PetscCall(VecLockReadPush(ctx->current_u));
441: if (F) {
442: if (ctx->current_f_allocated) PetscCall(VecDestroy(&ctx->current_f));
443: ctx->current_f = F;
444: ctx->current_f_allocated = PETSC_FALSE;
445: } else if (!ctx->current_f_allocated) {
446: PetscCall(MatCreateVecs(J, NULL, &ctx->current_f));
447: ctx->current_f_allocated = PETSC_TRUE;
448: }
449: if (!ctx->w) PetscCall(VecDuplicate(ctx->current_u, &ctx->w));
450: J->assembled = PETSC_TRUE;
451: PetscFunctionReturn(PETSC_SUCCESS);
452: }
454: typedef PetscErrorCode (*FCN3)(void *, Vec, Vec, PetscScalar *); /* force argument to next function to not be extern C*/
456: static PetscErrorCode MatMFFDSetCheckh_MFFD(Mat J, FCN3 fun, void *ectx)
457: {
458: MatMFFD ctx;
460: PetscFunctionBegin;
461: PetscCall(MatShellGetContext(J, &ctx));
462: ctx->checkh = fun;
463: ctx->checkhctx = ectx;
464: PetscFunctionReturn(PETSC_SUCCESS);
465: }
467: /*@C
468: MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all
469: MATMFFD` options in the database.
471: Collective
473: Input Parameters:
474: + A - the `MATMFFD` context
475: - prefix - the prefix to prepend to all option names
477: Note:
478: A hyphen (-) must NOT be given at the beginning of the prefix name.
479: The first character of all runtime options is AUTOMATICALLY the hyphen.
481: Level: advanced
483: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatSetFromOptions()`, `MatCreateSNESMF()`, `MatCreateMFFD()`
484: @*/
485: PetscErrorCode MatMFFDSetOptionsPrefix(Mat mat, const char prefix[])
486: {
487: MatMFFD mfctx;
489: PetscFunctionBegin;
491: PetscCall(MatShellGetContext(mat, &mfctx));
493: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mfctx, prefix));
494: PetscFunctionReturn(PETSC_SUCCESS);
495: }
497: static PetscErrorCode MatSetFromOptions_MFFD(Mat mat, PetscOptionItems *PetscOptionsObject)
498: {
499: MatMFFD mfctx;
500: PetscBool flg;
501: char ftype[256];
503: PetscFunctionBegin;
504: PetscCall(MatShellGetContext(mat, &mfctx));
506: PetscObjectOptionsBegin((PetscObject)mfctx);
507: PetscCall(PetscOptionsFList("-mat_mffd_type", "Matrix free type", "MatMFFDSetType", MatMFFDList, ((PetscObject)mfctx)->type_name, ftype, 256, &flg));
508: if (flg) PetscCall(MatMFFDSetType(mat, ftype));
510: PetscCall(PetscOptionsReal("-mat_mffd_err", "set sqrt relative error in function", "MatMFFDSetFunctionError", mfctx->error_rel, &mfctx->error_rel, NULL));
511: PetscCall(PetscOptionsInt("-mat_mffd_period", "how often h is recomputed", "MatMFFDSetPeriod", mfctx->recomputeperiod, &mfctx->recomputeperiod, NULL));
513: flg = PETSC_FALSE;
514: PetscCall(PetscOptionsBool("-mat_mffd_check_positivity", "Insure that U + h*a is nonnegative", "MatMFFDSetCheckh", flg, &flg, NULL));
515: if (flg) PetscCall(MatMFFDSetCheckh(mat, MatMFFDCheckPositivity, NULL));
516: #if defined(PETSC_USE_COMPLEX)
517: PetscCall(PetscOptionsBool("-mat_mffd_complex", "Use Lyness complex number trick to compute the matrix-vector product", "None", mfctx->usecomplex, &mfctx->usecomplex, NULL));
518: #endif
519: PetscTryTypeMethod(mfctx, setfromoptions, PetscOptionsObject);
520: PetscOptionsEnd();
521: PetscFunctionReturn(PETSC_SUCCESS);
522: }
524: static PetscErrorCode MatMFFDSetPeriod_MFFD(Mat mat, PetscInt period)
525: {
526: MatMFFD ctx;
528: PetscFunctionBegin;
529: PetscCall(MatShellGetContext(mat, &ctx));
530: ctx->recomputeperiod = period;
531: PetscFunctionReturn(PETSC_SUCCESS);
532: }
534: static PetscErrorCode MatMFFDSetFunction_MFFD(Mat mat, PetscErrorCode (*func)(void *, Vec, Vec), void *funcctx)
535: {
536: MatMFFD ctx;
538: PetscFunctionBegin;
539: PetscCall(MatShellGetContext(mat, &ctx));
540: ctx->func = func;
541: ctx->funcctx = funcctx;
542: PetscFunctionReturn(PETSC_SUCCESS);
543: }
545: static PetscErrorCode MatMFFDSetFunctionError_MFFD(Mat mat, PetscReal error)
546: {
547: PetscFunctionBegin;
548: if (error != (PetscReal)PETSC_DEFAULT) {
549: MatMFFD ctx;
551: PetscCall(MatShellGetContext(mat, &ctx));
552: ctx->error_rel = error;
553: }
554: PetscFunctionReturn(PETSC_SUCCESS);
555: }
557: PetscErrorCode MatMFFDSetHHistory_MFFD(Mat J, PetscScalar history[], PetscInt nhistory)
558: {
559: MatMFFD ctx;
561: PetscFunctionBegin;
562: PetscCall(MatShellGetContext(J, &ctx));
563: ctx->historyh = history;
564: ctx->maxcurrenth = nhistory;
565: ctx->currenth = 0.;
566: PetscFunctionReturn(PETSC_SUCCESS);
567: }
569: /*MC
570: MATMFFD - "mffd" - A matrix free matrix type.
572: Level: advanced
574: Developers Note:
575: This is implemented on top of `MATSHELL` to get support for scaling and shifting without requiring duplicate code
577: .seealso: [](ch_matrices), `Mat`, `MatCreateMFFD()`, `MatCreateSNESMF()`, `MatMFFDSetFunction()`, `MatMFFDSetType()`,
578: `MatMFFDSetFunctionError()`, `MatMFFDDSSetUmin()`, `MatMFFDSetFunction()`
579: `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `MatCreateSNESMF()`,
580: `MatMFFDGetH()`,
581: M*/
582: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
583: {
584: MatMFFD mfctx;
586: PetscFunctionBegin;
587: PetscCall(MatMFFDInitializePackage());
589: PetscCall(PetscHeaderCreate(mfctx, MATMFFD_CLASSID, "MatMFFD", "Matrix-free Finite Differencing", "Mat", PetscObjectComm((PetscObject)A), NULL, NULL));
591: mfctx->error_rel = PETSC_SQRT_MACHINE_EPSILON;
592: mfctx->recomputeperiod = 1;
593: mfctx->count = 0;
594: mfctx->currenth = 0.0;
595: mfctx->historyh = NULL;
596: mfctx->ncurrenth = 0;
597: mfctx->maxcurrenth = 0;
598: ((PetscObject)mfctx)->type_name = NULL;
600: /*
601: Create the empty data structure to contain compute-h routines.
602: These will be filled in below from the command line options or
603: a later call with MatMFFDSetType() or if that is not called
604: then it will default in the first use of MatMult_MFFD()
605: */
606: mfctx->ops->compute = NULL;
607: mfctx->ops->destroy = NULL;
608: mfctx->ops->view = NULL;
609: mfctx->ops->setfromoptions = NULL;
610: mfctx->hctx = NULL;
612: mfctx->func = NULL;
613: mfctx->funcctx = NULL;
614: mfctx->w = NULL;
615: mfctx->mat = A;
617: PetscCall(MatSetType(A, MATSHELL));
618: PetscCall(MatShellSetContext(A, mfctx));
619: PetscCall(MatShellSetOperation(A, MATOP_MULT, (void (*)(void))MatMult_MFFD));
620: PetscCall(MatShellSetOperation(A, MATOP_DESTROY, (void (*)(void))MatDestroy_MFFD));
621: PetscCall(MatShellSetOperation(A, MATOP_VIEW, (void (*)(void))MatView_MFFD));
622: PetscCall(MatShellSetOperation(A, MATOP_ASSEMBLY_END, (void (*)(void))MatAssemblyEnd_MFFD));
623: PetscCall(MatShellSetOperation(A, MATOP_SET_FROM_OPTIONS, (void (*)(void))MatSetFromOptions_MFFD));
625: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetBase_C", MatMFFDSetBase_MFFD));
626: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunctioniBase_C", MatMFFDSetFunctioniBase_MFFD));
627: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunctioni_C", MatMFFDSetFunctioni_MFFD));
628: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunction_C", MatMFFDSetFunction_MFFD));
629: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetCheckh_C", MatMFFDSetCheckh_MFFD));
630: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetPeriod_C", MatMFFDSetPeriod_MFFD));
631: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetFunctionError_C", MatMFFDSetFunctionError_MFFD));
632: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDResetHHistory_C", MatMFFDResetHHistory_MFFD));
633: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetHHistory_C", MatMFFDSetHHistory_MFFD));
634: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDSetType_C", MatMFFDSetType_MFFD));
635: PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMFFDGetH_C", MatMFFDGetH_MFFD));
636: PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATMFFD));
637: PetscFunctionReturn(PETSC_SUCCESS);
638: }
640: /*@
641: MatCreateMFFD - Creates a matrix-free matrix of type `MATMFFD`. See also `MatCreateSNESMF()`
643: Collective
645: Input Parameters:
646: + comm - MPI communicator
647: . m - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
648: This value should be the same as the local size used in creating the
649: y vector for the matrix-vector product y = Ax.
650: . n - This value should be the same as the local size used in creating the
651: x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
652: calculated if `N` is given) For square matrices `n` is almost always `m`.
653: . M - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
654: - N - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
656: Output Parameter:
657: . J - the matrix-free matrix
659: Options Database Keys:
660: + -mat_mffd_type - wp or ds (see `MATMFFD_WP` or `MATMFFD_DS`)
661: . -mat_mffd_err - square root of estimated relative error in function evaluation
662: . -mat_mffd_period - how often h is recomputed, defaults to 1, every time
663: . -mat_mffd_check_positivity - possibly decrease `h` until U + h*a has only positive values
664: . -mat_mffd_umin <umin> - Sets umin (for default PETSc routine that computes h only)
665: - -mat_mffd_complex - use the Lyness trick with complex numbers to compute the matrix-vector product instead of differencing
666: (requires real valued functions but that PETSc be configured for complex numbers)
668: Level: advanced
670: Notes:
671: The matrix-free matrix context merely contains the function pointers
672: and work space for performing finite difference approximations of
673: Jacobian-vector products, F'(u)*a,
675: The default code uses the following approach to compute h
677: .vb
678: F'(u)*a = [F(u+h*a) - F(u)]/h where
679: h = error_rel*u'a/||a||^2 if |u'a| > umin*||a||_{1}
680: = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2 otherwise
681: where
682: error_rel = square root of relative error in function evaluation
683: umin = minimum iterate parameter
684: .ve
686: You can call `SNESSetJacobian()` with `MatMFFDComputeJacobian()` if you are using matrix and not a different
687: preconditioner matrix
689: The user can set the error_rel via `MatMFFDSetFunctionError()` and
690: umin via `MatMFFDDSSetUmin()`.
692: The user should call `MatDestroy()` when finished with the matrix-free
693: matrix context.
695: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatDestroy()`, `MatMFFDSetFunctionError()`, `MatMFFDDSSetUmin()`, `MatMFFDSetFunction()`
696: `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `MatCreateSNESMF()`,
697: `MatMFFDGetH()`, `MatMFFDRegister()`, `MatMFFDComputeJacobian()`
698: @*/
699: PetscErrorCode MatCreateMFFD(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, Mat *J)
700: {
701: PetscFunctionBegin;
702: PetscCall(MatCreate(comm, J));
703: PetscCall(MatSetSizes(*J, m, n, M, N));
704: PetscCall(MatSetType(*J, MATMFFD));
705: PetscCall(MatSetUp(*J));
706: PetscFunctionReturn(PETSC_SUCCESS);
707: }
709: /*@
710: MatMFFDGetH - Gets the last value that was used as the differencing for a `MATMFFD` matrix
711: parameter.
713: Not Collective
715: Input Parameters:
716: . mat - the `MATMFFD` matrix
718: Output Parameter:
719: . h - the differencing step size
721: Level: advanced
723: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDSetHHistory()`, `MatCreateMFFD()`, `MATMFFD`, `MatMFFDResetHHistory()`
724: @*/
725: PetscErrorCode MatMFFDGetH(Mat mat, PetscScalar *h)
726: {
727: PetscFunctionBegin;
730: PetscUseMethod(mat, "MatMFFDGetH_C", (Mat, PetscScalar *), (mat, h));
731: PetscFunctionReturn(PETSC_SUCCESS);
732: }
734: /*@C
735: MatMFFDSetFunction - Sets the function used in applying the matrix free `MATMFFD` matrix.
737: Logically Collective
739: Input Parameters:
740: + mat - the matrix free matrix `MATMFFD` created via `MatCreateSNESMF()` or `MatCreateMFFD()`
741: . func - the function to use
742: - funcctx - optional function context passed to function
744: Calling Sequence of `func`:
745: $ PetscErrorCode func(void *funcctx, Vec x, Vec f)
746: + funcctx - user provided context
747: . x - input vector
748: - f - computed output function
750: Level: advanced
752: Notes:
753: If you use this you MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` on the matrix free
754: matrix inside your compute Jacobian routine
756: If this is not set then it will use the function set with `SNESSetFunction()` if `MatCreateSNESMF()` was used.
758: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatCreateMFFD()`, `MATMFFD`,
759: `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `SNESetFunction()`
760: @*/
761: PetscErrorCode MatMFFDSetFunction(Mat mat, PetscErrorCode (*func)(void *, Vec, Vec), void *funcctx)
762: {
763: PetscFunctionBegin;
765: PetscTryMethod(mat, "MatMFFDSetFunction_C", (Mat, PetscErrorCode(*)(void *, Vec, Vec), void *), (mat, func, funcctx));
766: PetscFunctionReturn(PETSC_SUCCESS);
767: }
769: /*@C
770: MatMFFDSetFunctioni - Sets the function for a single component for a `MATMFFD` matrix
772: Logically Collective
774: Input Parameters:
775: + mat - the matrix free matrix `MATMFFD`
776: - funci - the function to use
778: Level: advanced
780: Notes:
781: If you use this you MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` on the matrix free
782: matrix inside your compute Jacobian routine.
784: This function is necessary to compute the diagonal of the matrix.
785: funci must not contain any MPI call as it is called inside a loop on the local portion of the vector.
787: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `SNESetFunction()`, `MatGetDiagonal()`
788: @*/
789: PetscErrorCode MatMFFDSetFunctioni(Mat mat, PetscErrorCode (*funci)(void *, PetscInt, Vec, PetscScalar *))
790: {
791: PetscFunctionBegin;
793: PetscTryMethod(mat, "MatMFFDSetFunctioni_C", (Mat, PetscErrorCode(*)(void *, PetscInt, Vec, PetscScalar *)), (mat, funci));
794: PetscFunctionReturn(PETSC_SUCCESS);
795: }
797: /*@C
798: MatMFFDSetFunctioniBase - Sets the base vector for a single component function evaluation for a `MATMFFD` matrix
800: Logically Collective
802: Input Parameters:
803: + mat - the `MATMFFD` matrix free matrix
804: - func - the function to use
806: Level: advanced
808: Notes:
809: If you use this you MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` on the matrix free
810: matrix inside your compute Jacobian routine.
812: This function is necessary to compute the diagonal of the matrix, used for example with `PCJACOBI`
814: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatCreateMFFD()`, `MATMFFD`
815: `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`, `SNESetFunction()`, `MatGetDiagonal()`
816: @*/
817: PetscErrorCode MatMFFDSetFunctioniBase(Mat mat, PetscErrorCode (*func)(void *, Vec))
818: {
819: PetscFunctionBegin;
821: PetscTryMethod(mat, "MatMFFDSetFunctioniBase_C", (Mat, PetscErrorCode(*)(void *, Vec)), (mat, func));
822: PetscFunctionReturn(PETSC_SUCCESS);
823: }
825: /*@
826: MatMFFDSetPeriod - Sets how often h is recomputed for a `MATMFFD` matrix, by default it is every time
828: Logically Collective
830: Input Parameters:
831: + mat - the `MATMFFD` matrix free matrix
832: - period - 1 for every time, 2 for every second etc
834: Options Database Key:
835: . -mat_mffd_period <period> - Sets how often `h` is recomputed
837: Level: advanced
839: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`,
840: `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`
841: @*/
842: PetscErrorCode MatMFFDSetPeriod(Mat mat, PetscInt period)
843: {
844: PetscFunctionBegin;
847: PetscTryMethod(mat, "MatMFFDSetPeriod_C", (Mat, PetscInt), (mat, period));
848: PetscFunctionReturn(PETSC_SUCCESS);
849: }
851: /*@
852: MatMFFDSetFunctionError - Sets the error_rel for the approximation of matrix-vector products using finite differences with the `MATMFFD` matrix
854: Logically Collective
856: Input Parameters:
857: + mat - the `MATMFFD` matrix free matrix
858: - error_rel - relative error (should be set to the square root of the relative error in the function evaluations)
860: Options Database Key:
861: . -mat_mffd_err <error_rel> - Sets error_rel
863: Level: advanced
865: Note:
866: The default matrix-free matrix-vector product routine computes
867: .vb
868: F'(u)*a = [F(u+h*a) - F(u)]/h where
869: h = error_rel*u'a/||a||^2 if |u'a| > umin*||a||_{1}
870: = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2 else
871: .ve
873: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatCreateSNESMF()`, `MatMFFDGetH()`, `MatCreateMFFD()`, `MATMFFD`
874: `MatMFFDSetHHistory()`, `MatMFFDResetHHistory()`
875: @*/
876: PetscErrorCode MatMFFDSetFunctionError(Mat mat, PetscReal error)
877: {
878: PetscFunctionBegin;
881: PetscTryMethod(mat, "MatMFFDSetFunctionError_C", (Mat, PetscReal), (mat, error));
882: PetscFunctionReturn(PETSC_SUCCESS);
883: }
885: /*@
886: MatMFFDSetHHistory - Sets an array to collect a history of the
887: differencing values (h) computed for the matrix-free product `MATMFFD` matrix
889: Logically Collective
891: Input Parameters:
892: + J - the `MATMFFD` matrix-free matrix
893: . history - space to hold the history
894: - nhistory - number of entries in history, if more entries are generated than
895: nhistory, then the later ones are discarded
897: Level: advanced
899: Note:
900: Use `MatMFFDResetHHistory()` to reset the history counter and collect
901: a new batch of differencing parameters, h.
903: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDGetH()`, `MatCreateSNESMF()`,
904: `MatMFFDResetHHistory()`, `MatMFFDSetFunctionError()`
905: @*/
906: PetscErrorCode MatMFFDSetHHistory(Mat J, PetscScalar history[], PetscInt nhistory)
907: {
908: PetscFunctionBegin;
912: PetscUseMethod(J, "MatMFFDSetHHistory_C", (Mat, PetscScalar[], PetscInt), (J, history, nhistory));
913: PetscFunctionReturn(PETSC_SUCCESS);
914: }
916: /*@
917: MatMFFDResetHHistory - Resets the counter to zero to begin
918: collecting a new set of differencing histories for the `MATMFFD` matrix
920: Logically Collective
922: Input Parameter:
923: . J - the matrix-free matrix context
925: Level: advanced
927: Note:
928: Use `MatMFFDSetHHistory()` to create the original history counter.
930: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDGetH()`, `MatCreateSNESMF()`,
931: `MatMFFDSetHHistory()`, `MatMFFDSetFunctionError()`
932: @*/
933: PetscErrorCode MatMFFDResetHHistory(Mat J)
934: {
935: PetscFunctionBegin;
937: PetscTryMethod(J, "MatMFFDResetHHistory_C", (Mat), (J));
938: PetscFunctionReturn(PETSC_SUCCESS);
939: }
941: /*@
942: MatMFFDSetBase - Sets the vector `U` at which matrix vector products of the
943: Jacobian are computed for the `MATMFFD` matrix
945: Logically Collective
947: Input Parameters:
948: + J - the `MATMFFD` matrix
949: . U - the vector
950: - F - (optional) vector that contains F(u) if it has been already computed
952: Level: advanced
954: Notes:
955: This is rarely used directly
957: If `F` is provided then it is not recomputed. Otherwise the function is evaluated at the base
958: point during the first `MatMult()` after each call to `MatMFFDSetBase()`.
960: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMult()`, `MatMFFDSetBase()`
961: @*/
962: PetscErrorCode MatMFFDSetBase(Mat J, Vec U, Vec F)
963: {
964: PetscFunctionBegin;
968: PetscTryMethod(J, "MatMFFDSetBase_C", (Mat, Vec, Vec), (J, U, F));
969: PetscFunctionReturn(PETSC_SUCCESS);
970: }
972: /*@C
973: MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
974: it to satisfy some criteria for the `MATMFFD` matrix
976: Logically Collective
978: Input Parameters:
979: + J - the `MATMFFD` matrix
980: . fun - the function that checks `h`
981: - ctx - any context needed by the function
983: Options Database Keys:
984: . -mat_mffd_check_positivity <bool> - Insure that U + h*a is non-negative
986: Level: advanced
988: Notes:
989: For example, `MatMFFDCheckPositivity()` insures that all entries of U + h*a are non-negative
991: The function you provide is called after the default `h` has been computed and allows you to
992: modify it.
994: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDCheckPositivity()`
995: @*/
996: PetscErrorCode MatMFFDSetCheckh(Mat J, PetscErrorCode (*fun)(void *, Vec, Vec, PetscScalar *), void *ctx)
997: {
998: PetscFunctionBegin;
1000: PetscTryMethod(J, "MatMFFDSetCheckh_C", (Mat, PetscErrorCode(*)(void *, Vec, Vec, PetscScalar *), void *), (J, fun, ctx));
1001: PetscFunctionReturn(PETSC_SUCCESS);
1002: }
1004: /*@
1005: MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1006: zero, decreases h until this is satisfied for a `MATMFFD` matrix
1008: Logically Collective
1010: Input Parameters:
1011: + U - base vector that is added to
1012: . a - vector that is added
1013: . h - scaling factor on a
1014: - dummy - context variable (unused)
1016: Options Database Keys:
1017: . -mat_mffd_check_positivity <bool> - Insure that U + h*a is nonnegative
1019: Level: advanced
1021: Note:
1022: This is rarely used directly, rather it is passed as an argument to `MatMFFDSetCheckh()`
1024: .seealso: [](ch_matrices), `Mat`, `MATMFFD`, `MatMFFDSetCheckh()`
1025: @*/
1026: PetscErrorCode MatMFFDCheckPositivity(void *dummy, Vec U, Vec a, PetscScalar *h)
1027: {
1028: PetscReal val, minval;
1029: PetscScalar *u_vec, *a_vec;
1030: PetscInt i, n;
1031: MPI_Comm comm;
1033: PetscFunctionBegin;
1037: PetscCall(PetscObjectGetComm((PetscObject)U, &comm));
1038: PetscCall(VecGetArray(U, &u_vec));
1039: PetscCall(VecGetArray(a, &a_vec));
1040: PetscCall(VecGetLocalSize(U, &n));
1041: minval = PetscAbsScalar(*h) * PetscRealConstant(1.01);
1042: for (i = 0; i < n; i++) {
1043: if (PetscRealPart(u_vec[i] + *h * a_vec[i]) <= 0.0) {
1044: val = PetscAbsScalar(u_vec[i] / a_vec[i]);
1045: if (val < minval) minval = val;
1046: }
1047: }
1048: PetscCall(VecRestoreArray(U, &u_vec));
1049: PetscCall(VecRestoreArray(a, &a_vec));
1050: PetscCall(MPIU_Allreduce(&minval, &val, 1, MPIU_REAL, MPIU_MIN, comm));
1051: if (val <= PetscAbsScalar(*h)) {
1052: PetscCall(PetscInfo(U, "Scaling back h from %g to %g\n", (double)PetscRealPart(*h), (double)(.99 * val)));
1053: if (PetscRealPart(*h) > 0.0) *h = 0.99 * val;
1054: else *h = -0.99 * val;
1055: }
1056: PetscFunctionReturn(PETSC_SUCCESS);
1057: }