Actual source code: fischer.c

  1: #include <petsc/private/kspimpl.h>
  2: #include <petscblaslapack.h>

  4: typedef struct {
  5:   PetscInt         method; /* 1, 2 or 3 */
  6:   PetscInt         curl;   /* Current number of basis vectors */
  7:   PetscInt         maxl;   /* Maximum number of basis vectors */
  8:   PetscBool        monitor;
  9:   PetscScalar     *alpha;  /* */
 10:   Vec             *xtilde; /* Saved x vectors */
 11:   Vec             *btilde; /* Saved b vectors, methods 1 and 3 */
 12:   Vec              Ax;     /* method 2 */
 13:   Vec              guess;
 14:   PetscScalar     *corr;         /* correlation matrix in column-major format, method 3 */
 15:   PetscReal        tol;          /* tolerance for determining rank, method 3 */
 16:   Vec              last_b;       /* last b provided to FormGuess (not owned by this object), method 3 */
 17:   PetscObjectState last_b_state; /* state of last_b as of the last call to FormGuess, method 3 */
 18:   PetscScalar     *last_b_coefs; /* dot products of last_b and btilde, method 3 */
 19: } KSPGuessFischer;

 21: static PetscErrorCode KSPGuessReset_Fischer(KSPGuess guess)
 22: {
 23:   KSPGuessFischer *itg  = (KSPGuessFischer *)guess->data;
 24:   PetscLayout      Alay = NULL, vlay = NULL;
 25:   PetscBool        cong;

 27:   PetscFunctionBegin;
 28:   itg->curl = 0;
 29:   /* destroy vectors if the size of the linear system has changed */
 30:   if (guess->A) PetscCall(MatGetLayouts(guess->A, &Alay, NULL));
 31:   if (itg->xtilde) PetscCall(VecGetLayout(itg->xtilde[0], &vlay));
 32:   cong = PETSC_FALSE;
 33:   if (vlay && Alay) PetscCall(PetscLayoutCompare(Alay, vlay, &cong));
 34:   if (!cong) {
 35:     PetscCall(VecDestroyVecs(itg->maxl, &itg->btilde));
 36:     PetscCall(VecDestroyVecs(itg->maxl, &itg->xtilde));
 37:     PetscCall(VecDestroy(&itg->guess));
 38:     PetscCall(VecDestroy(&itg->Ax));
 39:   }
 40:   if (itg->corr) PetscCall(PetscMemzero(itg->corr, sizeof(*itg->corr) * itg->maxl * itg->maxl));
 41:   itg->last_b       = NULL;
 42:   itg->last_b_state = 0;
 43:   if (itg->last_b_coefs) PetscCall(PetscMemzero(itg->last_b_coefs, sizeof(*itg->last_b_coefs) * itg->maxl));
 44:   PetscFunctionReturn(PETSC_SUCCESS);
 45: }

 47: static PetscErrorCode KSPGuessSetUp_Fischer(KSPGuess guess)
 48: {
 49:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;

 51:   PetscFunctionBegin;
 52:   if (!itg->alpha) PetscCall(PetscMalloc1(itg->maxl, &itg->alpha));
 53:   if (!itg->xtilde) PetscCall(KSPCreateVecs(guess->ksp, itg->maxl, &itg->xtilde, 0, NULL));
 54:   if (!itg->btilde && (itg->method == 1 || itg->method == 3)) PetscCall(KSPCreateVecs(guess->ksp, itg->maxl, &itg->btilde, 0, NULL));
 55:   if (!itg->Ax && itg->method == 2) PetscCall(VecDuplicate(itg->xtilde[0], &itg->Ax));
 56:   if (!itg->guess && (itg->method == 1 || itg->method == 2)) PetscCall(VecDuplicate(itg->xtilde[0], &itg->guess));
 57:   if (!itg->corr && itg->method == 3) PetscCall(PetscCalloc1(itg->maxl * itg->maxl, &itg->corr));
 58:   if (!itg->last_b_coefs && itg->method == 3) PetscCall(PetscCalloc1(itg->maxl, &itg->last_b_coefs));
 59:   PetscFunctionReturn(PETSC_SUCCESS);
 60: }

 62: static PetscErrorCode KSPGuessDestroy_Fischer(KSPGuess guess)
 63: {
 64:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;

 66:   PetscFunctionBegin;
 67:   PetscCall(PetscFree(itg->alpha));
 68:   PetscCall(VecDestroyVecs(itg->maxl, &itg->btilde));
 69:   PetscCall(VecDestroyVecs(itg->maxl, &itg->xtilde));
 70:   PetscCall(VecDestroy(&itg->guess));
 71:   PetscCall(VecDestroy(&itg->Ax));
 72:   PetscCall(PetscFree(itg->corr));
 73:   PetscCall(PetscFree(itg->last_b_coefs));
 74:   PetscCall(PetscFree(itg));
 75:   PetscCall(PetscObjectComposeFunction((PetscObject)guess, "KSPGuessFischerSetModel_C", NULL));
 76:   PetscFunctionReturn(PETSC_SUCCESS);
 77: }

 79: /* Note: do not change the b right hand side as is done in the publication */
 80: static PetscErrorCode KSPGuessFormGuess_Fischer_1(KSPGuess guess, Vec b, Vec x)
 81: {
 82:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;
 83:   PetscInt         i;

 85:   PetscFunctionBegin;
 86:   PetscCall(VecSet(x, 0.0));
 87:   PetscCall(VecMDot(b, itg->curl, itg->btilde, itg->alpha));
 88:   if (itg->monitor) {
 89:     PetscCall(PetscPrintf(((PetscObject)guess)->comm, "KSPFischerGuess alphas ="));
 90:     for (i = 0; i < itg->curl; i++) PetscCall(PetscPrintf(((PetscObject)guess)->comm, " %g", (double)PetscAbsScalar(itg->alpha[i])));
 91:     PetscCall(PetscPrintf(((PetscObject)guess)->comm, "\n"));
 92:   }
 93:   PetscCall(VecMAXPY(x, itg->curl, itg->alpha, itg->xtilde));
 94:   PetscCall(VecCopy(x, itg->guess));
 95:   PetscFunctionReturn(PETSC_SUCCESS);
 96: }

 98: static PetscErrorCode KSPGuessUpdate_Fischer_1(KSPGuess guess, Vec b, Vec x)
 99: {
100:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;
101:   PetscReal        norm;
102:   int              curl = itg->curl, i;

104:   PetscFunctionBegin;
105:   if (curl == itg->maxl) {
106:     PetscCall(KSP_MatMult(guess->ksp, guess->A, x, itg->btilde[0]));
107:     /* PetscCall(VecCopy(b,itg->btilde[0])); */
108:     PetscCall(VecNormalize(itg->btilde[0], &norm));
109:     PetscCall(VecCopy(x, itg->xtilde[0]));
110:     PetscCall(VecScale(itg->xtilde[0], 1.0 / norm));
111:     itg->curl = 1;
112:   } else {
113:     if (!curl) {
114:       PetscCall(VecCopy(x, itg->xtilde[curl]));
115:     } else {
116:       PetscCall(VecWAXPY(itg->xtilde[curl], -1.0, itg->guess, x));
117:     }
118:     PetscCall(KSP_MatMult(guess->ksp, guess->A, itg->xtilde[curl], itg->btilde[curl]));
119:     PetscCall(VecMDot(itg->btilde[curl], curl, itg->btilde, itg->alpha));
120:     for (i = 0; i < curl; i++) itg->alpha[i] = -itg->alpha[i];
121:     PetscCall(VecMAXPY(itg->btilde[curl], curl, itg->alpha, itg->btilde));
122:     PetscCall(VecMAXPY(itg->xtilde[curl], curl, itg->alpha, itg->xtilde));
123:     PetscCall(VecNormalize(itg->btilde[curl], &norm));
124:     if (norm) {
125:       PetscCall(VecScale(itg->xtilde[curl], 1.0 / norm));
126:       itg->curl++;
127:     } else {
128:       PetscCall(PetscInfo(guess->ksp, "Not increasing dimension of Fischer space because new direction is identical to previous\n"));
129:     }
130:   }
131:   PetscFunctionReturn(PETSC_SUCCESS);
132: }

134: /*
135:   Given a basis generated already this computes a new guess x from the new right hand side b
136:   Figures out the components of b in each btilde direction and adds them to x
137:   Note: do not change the b right hand side as is done in the publication
138: */
139: static PetscErrorCode KSPGuessFormGuess_Fischer_2(KSPGuess guess, Vec b, Vec x)
140: {
141:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;
142:   PetscInt         i;

144:   PetscFunctionBegin;
145:   PetscCall(VecSet(x, 0.0));
146:   PetscCall(VecMDot(b, itg->curl, itg->xtilde, itg->alpha));
147:   if (itg->monitor) {
148:     PetscCall(PetscPrintf(((PetscObject)guess)->comm, "KSPFischerGuess alphas ="));
149:     for (i = 0; i < itg->curl; i++) PetscCall(PetscPrintf(((PetscObject)guess)->comm, " %g", (double)PetscAbsScalar(itg->alpha[i])));
150:     PetscCall(PetscPrintf(((PetscObject)guess)->comm, "\n"));
151:   }
152:   PetscCall(VecMAXPY(x, itg->curl, itg->alpha, itg->xtilde));
153:   PetscCall(VecCopy(x, itg->guess));
154:   PetscFunctionReturn(PETSC_SUCCESS);
155: }

157: static PetscErrorCode KSPGuessUpdate_Fischer_2(KSPGuess guess, Vec b, Vec x)
158: {
159:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;
160:   PetscScalar      norm;
161:   int              curl = itg->curl, i;

163:   PetscFunctionBegin;
164:   if (curl == itg->maxl) {
165:     PetscCall(KSP_MatMult(guess->ksp, guess->A, x, itg->Ax)); /* norm = sqrt(x'Ax) */
166:     PetscCall(VecDot(x, itg->Ax, &norm));
167:     PetscCall(VecCopy(x, itg->xtilde[0]));
168:     PetscCall(VecScale(itg->xtilde[0], 1.0 / PetscSqrtScalar(norm)));
169:     itg->curl = 1;
170:   } else {
171:     if (!curl) {
172:       PetscCall(VecCopy(x, itg->xtilde[curl]));
173:     } else {
174:       PetscCall(VecWAXPY(itg->xtilde[curl], -1.0, itg->guess, x));
175:     }
176:     PetscCall(KSP_MatMult(guess->ksp, guess->A, itg->xtilde[curl], itg->Ax));
177:     PetscCall(VecMDot(itg->Ax, curl, itg->xtilde, itg->alpha));
178:     for (i = 0; i < curl; i++) itg->alpha[i] = -itg->alpha[i];
179:     PetscCall(VecMAXPY(itg->xtilde[curl], curl, itg->alpha, itg->xtilde));

181:     PetscCall(KSP_MatMult(guess->ksp, guess->A, itg->xtilde[curl], itg->Ax)); /* norm = sqrt(xtilde[curl]'Axtilde[curl]) */
182:     PetscCall(VecDot(itg->xtilde[curl], itg->Ax, &norm));
183:     if (PetscAbsScalar(norm) != 0.0) {
184:       PetscCall(VecScale(itg->xtilde[curl], 1.0 / PetscSqrtScalar(norm)));
185:       itg->curl++;
186:     } else {
187:       PetscCall(PetscInfo(guess->ksp, "Not increasing dimension of Fischer space because new direction is identical to previous\n"));
188:     }
189:   }
190:   PetscFunctionReturn(PETSC_SUCCESS);
191: }

193: /*
194:   Rather than the standard algorithm implemented in 2, we treat the provided x and b vectors to be spanning sets (not necessarily linearly independent) and use them to compute a windowed correlation matrix. Since the correlation matrix may be singular we solve it with the pseudoinverse, provided by SYEV/HEEV.
195: */
196: static PetscErrorCode KSPGuessFormGuess_Fischer_3(KSPGuess guess, Vec b, Vec x)
197: {
198:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;
199:   PetscInt         i, j, m;
200:   PetscReal       *s_values;
201:   PetscScalar     *corr, *work, *scratch_vec, zero = 0.0, one = 1.0;
202:   PetscBLASInt     blas_m, blas_info, blas_rank = 0, blas_lwork, blas_one = 1;
203: #if defined(PETSC_USE_COMPLEX)
204:   PetscReal *rwork;
205: #endif

207:   /* project provided b onto space of stored btildes */
208:   PetscFunctionBegin;
209:   PetscCall(VecSet(x, 0.0));
210:   m           = itg->curl;
211:   itg->last_b = b;
212:   PetscCall(PetscObjectStateGet((PetscObject)b, &itg->last_b_state));
213:   if (m > 0) {
214:     PetscCall(PetscBLASIntCast(m, &blas_m));
215:     blas_lwork = (/* assume a block size of m */ blas_m + 2) * blas_m;
216: #if defined(PETSC_USE_COMPLEX)
217:     PetscCall(PetscCalloc5(m * m, &corr, m, &s_values, blas_lwork, &work, 3 * m - 2, &rwork, m, &scratch_vec));
218: #else
219:     PetscCall(PetscCalloc4(m * m, &corr, m, &s_values, blas_lwork, &work, m, &scratch_vec));
220: #endif
221:     PetscCall(VecMDot(b, itg->curl, itg->btilde, itg->last_b_coefs));
222:     for (j = 0; j < m; ++j) {
223:       for (i = 0; i < m; ++i) corr[m * j + i] = itg->corr[(itg->maxl) * j + i];
224:     }
225:     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
226:     PetscReal max_s_value = 0.0;
227: #if defined(PETSC_USE_COMPLEX)
228:     PetscCallBLAS("LAPACKheev", LAPACKheev_("V", "L", &blas_m, corr, &blas_m, s_values, work, &blas_lwork, rwork, &blas_info));
229: #else
230:     PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "L", &blas_m, corr, &blas_m, s_values, work, &blas_lwork, &blas_info));
231: #endif

233:     if (blas_info == 0) {
234:       /* make corr store singular vectors and s_values store singular values */
235:       for (j = 0; j < m; ++j) {
236:         if (s_values[j] < 0.0) {
237:           s_values[j] = PetscAbsReal(s_values[j]);
238:           for (i = 0; i < m; ++i) corr[m * j + i] *= -1.0;
239:         }
240:         max_s_value = PetscMax(max_s_value, s_values[j]);
241:       }

243:       /* manually apply the action of the pseudoinverse */
244:       PetscCallBLAS("BLASgemv", BLASgemv_("T", &blas_m, &blas_m, &one, corr, &blas_m, itg->last_b_coefs, &blas_one, &zero, scratch_vec, &blas_one));
245:       for (j = 0; j < m; ++j) {
246:         if (s_values[j] > itg->tol * max_s_value) {
247:           scratch_vec[j] /= s_values[j];
248:           blas_rank += 1;
249:         } else {
250:           scratch_vec[j] = 0.0;
251:         }
252:       }
253:       PetscCallBLAS("BLASgemv", BLASgemv_("N", &blas_m, &blas_m, &one, corr, &blas_m, scratch_vec, &blas_one, &zero, itg->alpha, &blas_one));

255:     } else {
256:       PetscCall(PetscInfo(guess, "Warning eigenvalue solver failed with error code %d - setting initial guess to zero\n", (int)blas_info));
257:       PetscCall(PetscMemzero(itg->alpha, sizeof(*itg->alpha) * itg->maxl));
258:     }
259:     PetscCall(PetscFPTrapPop());

261:     if (itg->monitor && blas_info == 0) {
262:       PetscCall(PetscPrintf(((PetscObject)guess)->comm, "KSPFischerGuess correlation rank = %d\n", (int)blas_rank));
263:       PetscCall(PetscPrintf(((PetscObject)guess)->comm, "KSPFischerGuess singular values = "));
264:       for (i = 0; i < itg->curl; i++) PetscCall(PetscPrintf(((PetscObject)guess)->comm, " %g", (double)s_values[i]));
265:       PetscCall(PetscPrintf(((PetscObject)guess)->comm, "\n"));

267:       PetscCall(PetscPrintf(((PetscObject)guess)->comm, "KSPFischerGuess alphas ="));
268:       for (i = 0; i < itg->curl; i++) PetscCall(PetscPrintf(((PetscObject)guess)->comm, " %g", (double)PetscAbsScalar(itg->alpha[i])));
269:       PetscCall(PetscPrintf(((PetscObject)guess)->comm, "\n"));
270:     }
271:     /* Form the initial guess by using b's projection coefficients with the xs */
272:     PetscCall(VecMAXPY(x, itg->curl, itg->alpha, itg->xtilde));
273: #if defined(PETSC_USE_COMPLEX)
274:     PetscCall(PetscFree5(corr, s_values, work, rwork, scratch_vec));
275: #else
276:     PetscCall(PetscFree4(corr, s_values, work, scratch_vec));
277: #endif
278:   }
279:   PetscFunctionReturn(PETSC_SUCCESS);
280: }

282: static PetscErrorCode KSPGuessUpdate_Fischer_3(KSPGuess guess, Vec b, Vec x)
283: {
284:   KSPGuessFischer *itg    = (KSPGuessFischer *)guess->data;
285:   PetscBool        rotate = itg->curl == itg->maxl ? PETSC_TRUE : PETSC_FALSE;
286:   PetscInt         i, j;
287:   PetscObjectState b_state;
288:   PetscScalar     *last_column;
289:   Vec              oldest;

291:   PetscFunctionBegin;
292:   if (rotate) {
293:     /* we have the maximum number of vectors so rotate: oldest vector is at index 0 */
294:     oldest = itg->xtilde[0];
295:     for (i = 1; i < itg->curl; ++i) itg->xtilde[i - 1] = itg->xtilde[i];
296:     itg->xtilde[itg->curl - 1] = oldest;
297:     PetscCall(VecCopy(x, itg->xtilde[itg->curl - 1]));

299:     oldest = itg->btilde[0];
300:     for (i = 1; i < itg->curl; ++i) itg->btilde[i - 1] = itg->btilde[i];
301:     itg->btilde[itg->curl - 1] = oldest;
302:     PetscCall(VecCopy(b, itg->btilde[itg->curl - 1]));
303:     /* shift correlation matrix up and left */
304:     for (j = 1; j < itg->maxl; ++j) {
305:       for (i = 1; i < itg->maxl; ++i) itg->corr[(j - 1) * itg->maxl + i - 1] = itg->corr[j * itg->maxl + i];
306:     }
307:   } else {
308:     /* append new vectors */
309:     PetscCall(VecCopy(x, itg->xtilde[itg->curl]));
310:     PetscCall(VecCopy(b, itg->btilde[itg->curl]));
311:     itg->curl++;
312:   }

314:   /*
315:       Populate new column of the correlation matrix and then copy it into the
316:       row. itg->maxl is the allocated length per column: itg->curl is the actual
317:       column length.
318:       If possible reuse the dot products from FormGuess
319:   */
320:   last_column = itg->corr + (itg->curl - 1) * itg->maxl;
321:   PetscCall(PetscObjectStateGet((PetscObject)b, &b_state));
322:   if (b_state == itg->last_b_state && b == itg->last_b) {
323:     if (rotate) {
324:       for (i = 1; i < itg->maxl; ++i) itg->last_b_coefs[i - 1] = itg->last_b_coefs[i];
325:     }
326:     PetscCall(VecDot(b, b, &itg->last_b_coefs[itg->curl - 1]));
327:     PetscCall(PetscArraycpy(last_column, itg->last_b_coefs, itg->curl));
328:   } else {
329:     PetscCall(VecMDot(b, itg->curl, itg->btilde, last_column));
330:   }
331:   for (i = 0; i < itg->curl; ++i) itg->corr[i * itg->maxl + itg->curl - 1] = last_column[i];
332:   PetscFunctionReturn(PETSC_SUCCESS);
333: }

335: static PetscErrorCode KSPGuessSetFromOptions_Fischer(KSPGuess guess)
336: {
337:   KSPGuessFischer *ITG  = (KSPGuessFischer *)guess->data;
338:   PetscInt         nmax = 2, model[2];
339:   PetscBool        flg;

341:   PetscFunctionBegin;
342:   model[0] = ITG->method;
343:   model[1] = ITG->maxl;
344:   PetscOptionsBegin(PetscObjectComm((PetscObject)guess), ((PetscObject)guess)->prefix, "Fischer guess options", "KSPGuess");
345:   PetscCall(PetscOptionsIntArray("-ksp_guess_fischer_model", "Model type and dimension of basis", "KSPGuessFischerSetModel", model, &nmax, &flg));
346:   if (flg) PetscCall(KSPGuessFischerSetModel(guess, model[0], model[1]));
347:   PetscCall(PetscOptionsReal("-ksp_guess_fischer_tol", "Tolerance to determine rank via ratio of singular values", "KSPGuessSetTolerance", ITG->tol, &ITG->tol, NULL));
348:   PetscCall(PetscOptionsBool("-ksp_guess_fischer_monitor", "Monitor the guess", NULL, ITG->monitor, &ITG->monitor, NULL));
349:   PetscOptionsEnd();
350:   PetscFunctionReturn(PETSC_SUCCESS);
351: }

353: static PetscErrorCode KSPGuessSetTolerance_Fischer(KSPGuess guess, PetscReal tol)
354: {
355:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;

357:   PetscFunctionBegin;
358:   itg->tol = tol;
359:   PetscFunctionReturn(PETSC_SUCCESS);
360: }

362: static PetscErrorCode KSPGuessView_Fischer(KSPGuess guess, PetscViewer viewer)
363: {
364:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;
365:   PetscBool        isascii;

367:   PetscFunctionBegin;
368:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
369:   if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer, "Model %" PetscInt_FMT ", size %" PetscInt_FMT "\n", itg->method, itg->maxl));
370:   PetscFunctionReturn(PETSC_SUCCESS);
371: }

373: /*@
374:   KSPGuessFischerSetModel - Set the Paul Fischer algorithm or its variants to compute the initial guess for a `KSPSolve()`

376:   Logically Collective

378:   Input Parameters:
379: + guess - the initial guess context
380: . model - use model 1, model 2, model 3, or any other number to turn it off
381: - size  - size of subspace used to generate initial guess

383:   Options Database Key:
384: . -ksp_guess_fischer_model <model,size> - uses the Fischer initial guess generator for repeated linear solves

386:   Level: advanced

388: .seealso: [](ch_ksp), `KSPGuess`, `KSPGuessCreate()`, `KSPSetUseFischerGuess()`, `KSPSetGuess()`, `KSPGetGuess()`, `KSP`
389: @*/
390: PetscErrorCode KSPGuessFischerSetModel(KSPGuess guess, PetscInt model, PetscInt size)
391: {
392:   PetscFunctionBegin;
395:   PetscTryMethod(guess, "KSPGuessFischerSetModel_C", (KSPGuess, PetscInt, PetscInt), (guess, model, size));
396:   PetscFunctionReturn(PETSC_SUCCESS);
397: }

399: static PetscErrorCode KSPGuessFischerSetModel_Fischer(KSPGuess guess, PetscInt model, PetscInt size)
400: {
401:   KSPGuessFischer *itg = (KSPGuessFischer *)guess->data;

403:   PetscFunctionBegin;
404:   if (model == 1) {
405:     guess->ops->update    = KSPGuessUpdate_Fischer_1;
406:     guess->ops->formguess = KSPGuessFormGuess_Fischer_1;
407:   } else if (model == 2) {
408:     guess->ops->update    = KSPGuessUpdate_Fischer_2;
409:     guess->ops->formguess = KSPGuessFormGuess_Fischer_2;
410:   } else if (model == 3) {
411:     guess->ops->update    = KSPGuessUpdate_Fischer_3;
412:     guess->ops->formguess = KSPGuessFormGuess_Fischer_3;
413:   } else {
414:     guess->ops->update    = NULL;
415:     guess->ops->formguess = NULL;
416:     itg->method           = 0;
417:     PetscFunctionReturn(PETSC_SUCCESS);
418:   }
419:   if (size != itg->maxl) {
420:     PetscCall(PetscFree(itg->alpha));
421:     PetscCall(VecDestroyVecs(itg->maxl, &itg->btilde));
422:     PetscCall(VecDestroyVecs(itg->maxl, &itg->xtilde));
423:     PetscCall(VecDestroy(&itg->guess));
424:     PetscCall(VecDestroy(&itg->Ax));
425:   }
426:   itg->method = model;
427:   itg->maxl   = size;
428:   PetscFunctionReturn(PETSC_SUCCESS);
429: }

431: /*MC
432:     KSPGUESSFISCHER - Implements Paul Fischer's initial guess algorithms {cite}`fischer1998projection`
433:     and a non-orthogonalizing variant for situations where a linear system is solved repeatedly

435:     Level: intermediate

437:     Notes:
438:     The algorithm is different from Fischer's paper because we do not CHANGE the right hand side of the new
439:     problem and solve the problem with an initial guess of zero, rather we solve the original problem
440:     with a nonzero initial guess (this is done so that the linear solver convergence tests are based on
441:     the original RHS). We use the $xtilde = x - xguess$ as the new direction so that it is not
442:     mostly orthogonal to the previous solutions.

444:     These are not intended to be used directly, they are called by `KSPSolve()` automatically with the command
445:     line options `-ksp_guess_type fischer` `-ksp_guess_fischer_model <int,int>` or programmatically with
446: .vb
447:     KSPGetGuess(ksp,&guess);
448:     KSPGuessSetType(guess,KSPGUESSFISCHER);
449:     KSPGuessFischerSetModel(guess,model,basis);
450:     KSPGuessSetTolerance(guess,PETSC_MACHINE_EPSILON);
451: .ve
452:     The default tolerance (which is only used in Method 3) is 32*`PETSC_MACHINE_EPSILON`. This value was chosen
453:     empirically by trying a range of tolerances and picking the one that lowered the solver iteration count the most
454:     with five vectors.

456:     Method 2 is only for positive definite matrices, since it uses the energy norm.

458:     Method 3 is not in the original paper. It is the same as the first two methods except that it
459:     does not orthogonalize the input vectors or use A at all. This choice is faster but provides a
460:     less effective initial guess for large (about 10) numbers of stored vectors.

462:     Developer Note:
463:     The option `-ksp_fischer_guess <int,int>` is still available for backward compatibility

465: .seealso: [](ch_ksp), `KSPGuess`, `KSPGuessType`, `KSP`
466: M*/

468: PetscErrorCode KSPGuessCreate_Fischer(KSPGuess guess)
469: {
470:   KSPGuessFischer *fischer;

472:   PetscFunctionBegin;
473:   PetscCall(PetscNew(&fischer));
474:   fischer->method = 1; /* defaults to method 1 */
475:   fischer->maxl   = 10;
476:   fischer->tol    = 32.0 * PETSC_MACHINE_EPSILON;
477:   guess->data     = fischer;

479:   guess->ops->setfromoptions = KSPGuessSetFromOptions_Fischer;
480:   guess->ops->destroy        = KSPGuessDestroy_Fischer;
481:   guess->ops->settolerance   = KSPGuessSetTolerance_Fischer;
482:   guess->ops->setup          = KSPGuessSetUp_Fischer;
483:   guess->ops->view           = KSPGuessView_Fischer;
484:   guess->ops->reset          = KSPGuessReset_Fischer;
485:   guess->ops->update         = KSPGuessUpdate_Fischer_1;
486:   guess->ops->formguess      = KSPGuessFormGuess_Fischer_1;

488:   PetscCall(PetscObjectComposeFunction((PetscObject)guess, "KSPGuessFischerSetModel_C", KSPGuessFischerSetModel_Fischer));
489:   PetscFunctionReturn(PETSC_SUCCESS);
490: }