Actual source code: pod.c
1: #include <petsc/private/kspimpl.h>
2: #include <petsc/private/matimpl.h>
3: #include <petscblaslapack.h>
4: static PetscBool cited = PETSC_FALSE;
5: static const char citation[] = "@phdthesis{zampini2010non,\n"
6: " title={Non-overlapping Domain Decomposition Methods for Cardiac Reaction-Diffusion Models and Applications},\n"
7: " author={Zampini, S},\n"
8: " year={2010},\n"
9: " school={PhD thesis, Universita degli Studi di Milano}\n"
10: "}\n";
12: typedef struct {
13: PetscInt maxn; /* maximum number of snapshots */
14: PetscInt n; /* number of active snapshots */
15: PetscInt curr; /* current tip of snapshots set */
16: Vec *xsnap; /* snapshots */
17: Vec *bsnap; /* rhs snapshots */
18: Vec *work; /* parallel work vectors */
19: PetscScalar *dots_iallreduce;
20: MPI_Request req_iallreduce;
21: PetscInt ndots_iallreduce; /* if we have iallreduce we can hide the VecMDot communications */
22: PetscReal tol; /* relative tolerance to retain eigenvalues */
23: PetscBool Aspd; /* if true, uses the SPD operator as inner product */
24: PetscScalar *corr; /* correlation matrix */
25: PetscReal *eigs; /* eigenvalues */
26: PetscScalar *eigv; /* eigenvectors */
27: PetscBLASInt nen; /* dimension of lower dimensional system */
28: PetscInt st; /* first eigenvector of correlation matrix to be retained */
29: PetscBLASInt *iwork; /* integer work vector */
30: PetscScalar *yhay; /* Y^H * A * Y */
31: PetscScalar *low; /* lower dimensional linear system */
32: #if PetscDefined(USE_COMPLEX)
33: PetscReal *rwork;
34: #endif
35: PetscBLASInt lwork;
36: PetscScalar *swork;
37: PetscBool monitor;
38: } KSPGuessPOD;
40: static PetscErrorCode KSPGuessReset_POD(KSPGuess guess)
41: {
42: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
43: PetscLayout Alay = NULL, vlay = NULL;
44: PetscBool cong;
46: PetscFunctionBegin;
47: pod->nen = 0;
48: pod->n = 0;
49: pod->curr = 0;
50: /* need to wait for completion of outstanding requests */
51: if (pod->ndots_iallreduce) PetscCallMPI(MPI_Wait(&pod->req_iallreduce, MPI_STATUS_IGNORE));
52: pod->ndots_iallreduce = 0;
53: /* destroy vectors if the size of the linear system has changed */
54: if (guess->A) PetscCall(MatGetLayouts(guess->A, &Alay, NULL));
55: if (pod->xsnap) PetscCall(VecGetLayout(pod->xsnap[0], &vlay));
56: cong = PETSC_FALSE;
57: if (vlay && Alay) PetscCall(PetscLayoutCompare(Alay, vlay, &cong));
58: if (!cong) {
59: PetscCall(VecDestroyVecs(pod->maxn, &pod->xsnap));
60: PetscCall(VecDestroyVecs(pod->maxn, &pod->bsnap));
61: PetscCall(VecDestroyVecs(1, &pod->work));
62: }
63: PetscFunctionReturn(PETSC_SUCCESS);
64: }
66: static PetscErrorCode KSPGuessSetUp_POD(KSPGuess guess)
67: {
68: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
70: PetscFunctionBegin;
71: if (!pod->corr) {
72: PetscScalar sdummy;
73: PetscReal rdummy = 0;
74: PetscBLASInt bN, idummy = 0;
76: PetscCall(PetscCalloc6(pod->maxn * pod->maxn, &pod->corr, pod->maxn, &pod->eigs, pod->maxn * pod->maxn, &pod->eigv, 6 * pod->maxn, &pod->iwork, pod->maxn * pod->maxn, &pod->yhay, pod->maxn * pod->maxn, &pod->low));
77: #if PetscDefined(USE_COMPLEX)
78: PetscCall(PetscMalloc1(7 * pod->maxn, &pod->rwork));
79: #endif
80: #if PetscDefined(HAVE_MPI_NONBLOCKING_COLLECTIVES)
81: PetscCall(PetscMalloc1(3 * pod->maxn, &pod->dots_iallreduce));
82: #endif
83: pod->lwork = -1;
84: PetscCall(PetscBLASIntCast(pod->maxn, &bN));
85: #if !PetscDefined(USE_COMPLEX)
86: PetscCallLAPACKInfo("LAPACKsyevx", LAPACKsyevx_("V", "A", "L", &bN, pod->corr, &bN, &rdummy, &rdummy, &idummy, &idummy, &rdummy, &idummy, pod->eigs, pod->eigv, &bN, &sdummy, &pod->lwork, pod->iwork, pod->iwork + 5 * bN, &info));
87: #else
88: PetscCallLAPACKInfo("LAPACKsyevx", LAPACKsyevx_("V", "A", "L", &bN, pod->corr, &bN, &rdummy, &rdummy, &idummy, &idummy, &rdummy, &idummy, pod->eigs, pod->eigv, &bN, &sdummy, &pod->lwork, pod->rwork, pod->iwork, pod->iwork + 5 * bN, &info));
89: #endif
90: PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(sdummy), &pod->lwork));
91: PetscCall(PetscMalloc1(pod->lwork + PetscMax(bN * bN, 6 * bN), &pod->swork));
92: }
93: /* work vectors are sequential, we explicitly use MPI_Allreduce */
94: if (!pod->xsnap) {
95: Vec *v, vseq;
97: PetscCall(KSPCreateVecs(guess->ksp, 1, &v, 0, NULL));
98: PetscCall(VecCreateLocalVector(v[0], &vseq));
99: PetscCall(VecDestroyVecs(1, &v));
100: PetscCall(VecDuplicateVecs(vseq, pod->maxn, &pod->xsnap));
101: PetscCall(VecDestroy(&vseq));
102: }
103: if (!pod->bsnap) {
104: Vec *v, vseq;
106: PetscCall(KSPCreateVecs(guess->ksp, 0, NULL, 1, &v));
107: PetscCall(VecCreateLocalVector(v[0], &vseq));
108: PetscCall(VecDestroyVecs(1, &v));
109: PetscCall(VecDuplicateVecs(vseq, pod->maxn, &pod->bsnap));
110: PetscCall(VecDestroy(&vseq));
111: }
112: if (!pod->work) PetscCall(KSPCreateVecs(guess->ksp, 1, &pod->work, 0, NULL));
113: PetscFunctionReturn(PETSC_SUCCESS);
114: }
116: static PetscErrorCode KSPGuessDestroy_POD(KSPGuess guess)
117: {
118: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
120: PetscFunctionBegin;
121: PetscCall(PetscFree6(pod->corr, pod->eigs, pod->eigv, pod->iwork, pod->yhay, pod->low));
122: #if PetscDefined(USE_COMPLEX)
123: PetscCall(PetscFree(pod->rwork));
124: #endif
125: /* need to wait for completion before destroying dots_iallreduce */
126: if (pod->ndots_iallreduce) PetscCallMPI(MPI_Wait(&pod->req_iallreduce, MPI_STATUS_IGNORE));
127: PetscCall(PetscFree(pod->dots_iallreduce));
128: PetscCall(PetscFree(pod->swork));
129: PetscCall(VecDestroyVecs(pod->maxn, &pod->bsnap));
130: PetscCall(VecDestroyVecs(pod->maxn, &pod->xsnap));
131: PetscCall(VecDestroyVecs(1, &pod->work));
132: PetscCall(PetscFree(pod));
133: PetscFunctionReturn(PETSC_SUCCESS);
134: }
136: static PetscErrorCode KSPGuessUpdate_POD(KSPGuess, Vec, Vec);
138: static PetscErrorCode KSPGuessFormGuess_POD(KSPGuess guess, Vec b, Vec x)
139: {
140: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
141: PetscScalar one = 1, zero = 0;
142: PetscBLASInt bN, ione = 1, bNen;
143: PetscInt i;
145: PetscFunctionBegin;
146: PetscCall(PetscCitationsRegister(citation, &cited));
147: if (pod->ndots_iallreduce) { /* complete communication and project the linear system */
148: PetscCall(KSPGuessUpdate_POD(guess, NULL, NULL));
149: }
150: if (!pod->nen) PetscFunctionReturn(PETSC_SUCCESS);
151: /* b_low = S * V^T * X^T * b */
152: PetscCall(VecGetLocalVectorRead(b, pod->bsnap[pod->curr]));
153: PetscCall(VecMDot(pod->bsnap[pod->curr], pod->n, pod->xsnap, pod->swork));
154: PetscCall(VecRestoreLocalVectorRead(b, pod->bsnap[pod->curr]));
155: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + pod->n, pod->n, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
156: PetscCall(PetscBLASIntCast(pod->n, &bN));
157: PetscCall(PetscBLASIntCast(pod->nen, &bNen));
158: PetscCallBLAS("BLASgemv", BLASgemv_("T", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork + pod->n, &ione, &zero, pod->swork, &ione));
159: if (pod->monitor) {
160: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " KSPGuessPOD alphas = "));
161: for (i = 0; i < pod->nen; i++) {
162: if (PetscDefined(USE_COMPLEX)) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g + %g i", (double)PetscRealPart(pod->swork[i]), (double)PetscImaginaryPart(pod->swork[i])));
163: else PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g ", (double)PetscRealPart(pod->swork[i])));
164: }
165: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
166: }
167: /* A_low x_low = b_low */
168: if (!pod->Aspd) { /* A is spd -> LOW = Identity */
169: KSP pksp = guess->ksp;
170: PetscBool tsolve, symm, set;
172: if (pod->monitor) {
173: PetscMPIInt rank;
174: Mat L;
176: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)guess), &rank));
177: if (rank == 0) {
178: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " L = "));
179: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->nen, pod->nen, pod->low, &L));
180: PetscCall(MatView(L, NULL));
181: PetscCall(MatDestroy(&L));
182: }
183: }
184: PetscCall(MatIsSymmetricKnown(guess->A, &set, &symm));
185: tsolve = (set && symm) ? PETSC_FALSE : pksp->transpose_solve;
186: PetscCallLAPACKInfo("LAPACKgetrf", LAPACKgetrf_(&bNen, &bNen, pod->low, &bNen, pod->iwork, &info));
187: PetscCallLAPACKInfo("LAPACKgetrs", LAPACKgetrs_(tsolve ? "T" : "N", &bNen, &ione, pod->low, &bNen, pod->iwork, pod->swork, &bNen, &info));
188: }
189: /* x = X * V * S * x_low */
190: PetscCallBLAS("BLASgemv", BLASgemv_("N", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork, &ione, &zero, pod->swork + pod->n, &ione));
191: if (pod->monitor) {
192: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " KSPGuessPOD sol = "));
193: for (i = 0; i < pod->nen; i++) {
194: if (PetscDefined(USE_COMPLEX)) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g + %g i", (double)PetscRealPart(pod->swork[i + pod->n]), (double)PetscImaginaryPart(pod->swork[i + pod->n])));
195: else PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g ", (double)PetscRealPart(pod->swork[i + pod->n])));
196: }
197: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
198: }
199: PetscCall(VecGetLocalVector(x, pod->bsnap[pod->curr]));
200: PetscCall(VecSet(pod->bsnap[pod->curr], 0));
201: PetscCall(VecMAXPY(pod->bsnap[pod->curr], pod->n, pod->swork + pod->n, pod->xsnap));
202: PetscCall(VecRestoreLocalVector(x, pod->bsnap[pod->curr]));
203: PetscFunctionReturn(PETSC_SUCCESS);
204: }
206: static PetscErrorCode KSPGuessUpdate_POD(KSPGuess guess, Vec b, Vec x)
207: {
208: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
209: PetscScalar one = 1, zero = 0;
210: PetscReal toten, parten, reps = 0; /* dlamch? */
211: PetscBLASInt bN, idummy = 0;
212: PetscInt i;
213: PetscMPIInt podn;
215: PetscFunctionBegin;
216: if (pod->ndots_iallreduce) goto complete_request;
217: pod->n = pod->n < pod->maxn ? pod->n + 1 : pod->maxn;
218: PetscCall(PetscMPIIntCast(pod->n, &podn));
219: PetscCall(VecCopy(x, pod->xsnap[pod->curr]));
220: PetscCall(KSP_MatMult(guess->ksp, guess->A, x, pod->work[0]));
221: PetscCall(VecCopy(pod->work[0], pod->bsnap[pod->curr]));
222: if (pod->Aspd) {
223: PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->bsnap, pod->swork));
224: #if !PetscDefined(HAVE_MPI_NONBLOCKING_COLLECTIVES)
225: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
226: #else
227: PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
228: pod->ndots_iallreduce = 1;
229: #endif
230: } else {
231: PetscInt off;
232: PetscBool set, herm;
234: if (PetscDefined(USE_COMPLEX)) PetscCall(MatIsHermitianKnown(guess->A, &set, &herm));
235: else PetscCall(MatIsSymmetricKnown(guess->A, &set, &herm));
236: off = (guess->ksp->transpose_solve && (!set || !herm)) ? 2 * pod->n : pod->n;
238: /* TODO: we may want to use a user-defined dot for the correlation matrix */
239: PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->xsnap, pod->swork));
240: PetscCall(VecMDot(pod->bsnap[pod->curr], pod->n, pod->xsnap, pod->swork + off));
241: if (!set || !herm) {
242: off = (off == pod->n) ? 2 * pod->n : pod->n;
243: PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->bsnap, pod->swork + off));
244: #if !PetscDefined(HAVE_MPI_NONBLOCKING_COLLECTIVES)
245: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, 3 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
246: #else
247: PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, 3 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
248: pod->ndots_iallreduce = 3;
249: #endif
250: } else {
251: #if !PetscDefined(HAVE_MPI_NONBLOCKING_COLLECTIVES)
252: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, 2 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
253: for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->swork[4 * pod->n + i];
254: #else
255: PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, 2 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
256: pod->ndots_iallreduce = 2;
257: #endif
258: }
259: }
260: if (pod->ndots_iallreduce) PetscFunctionReturn(PETSC_SUCCESS);
262: complete_request:
263: if (pod->ndots_iallreduce) {
264: PetscCallMPI(MPI_Wait(&pod->req_iallreduce, MPI_STATUS_IGNORE));
265: switch (pod->ndots_iallreduce) {
266: case 3:
267: for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
268: for (i = 0; i < pod->n; i++) pod->swork[4 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
269: for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->dots_iallreduce[2 * pod->n + i];
270: break;
271: case 2:
272: for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
273: for (i = 0; i < pod->n; i++) pod->swork[4 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
274: for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
275: break;
276: case 1:
277: for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
278: break;
279: default:
280: SETERRQ(PetscObjectComm((PetscObject)guess), PETSC_ERR_PLIB, "Invalid number of outstanding dots operations: %" PetscInt_FMT, pod->ndots_iallreduce);
281: }
282: }
283: pod->ndots_iallreduce = 0;
285: /* correlation matrix and Y^H A Y (Galerkin) */
286: for (i = 0; i < pod->n; i++) {
287: pod->corr[pod->curr * pod->maxn + i] = pod->swork[3 * pod->n + i];
288: pod->corr[i * pod->maxn + pod->curr] = PetscConj(pod->swork[3 * pod->n + i]);
289: if (!pod->Aspd) {
290: pod->yhay[pod->curr * pod->maxn + i] = pod->swork[4 * pod->n + i];
291: pod->yhay[i * pod->maxn + pod->curr] = PetscConj(pod->swork[5 * pod->n + i]);
292: }
293: }
294: /* syevx changes the input matrix */
295: for (i = 0; i < pod->n; i++) {
296: for (PetscInt j = i; j < pod->n; j++) pod->swork[i * pod->n + j] = pod->corr[i * pod->maxn + j];
297: }
298: PetscCall(PetscBLASIntCast(pod->n, &bN));
299: #if !PetscDefined(USE_COMPLEX)
300: PetscCallLAPACKInfo("LAPACKsyevx", LAPACKsyevx_("V", "A", "L", &bN, pod->swork, &bN, &reps, &reps, &idummy, &idummy, &reps, &idummy, pod->eigs, pod->eigv, &bN, pod->swork + bN * bN, &pod->lwork, pod->iwork, pod->iwork + 5 * bN, &info));
301: #else
302: PetscCallLAPACKInfo("LAPACKsyevx", LAPACKsyevx_("V", "A", "L", &bN, pod->swork, &bN, &reps, &reps, &idummy, &idummy, &reps, &idummy, pod->eigs, pod->eigv, &bN, pod->swork + bN * bN, &pod->lwork, pod->rwork, pod->iwork, pod->iwork + 5 * bN, &info));
303: #endif
305: /* dimension of lower dimensional system */
306: pod->st = -1;
307: for (i = 0, toten = 0; i < pod->n; i++) {
308: pod->eigs[i] = PetscMax(pod->eigs[i], 0.0);
309: toten += pod->eigs[i];
310: if (!pod->eigs[i]) pod->st = i;
311: }
312: pod->nen = 0;
313: for (i = pod->n - 1, parten = 0; i > pod->st && toten > 0; i--) {
314: pod->nen++;
315: parten += pod->eigs[i];
316: if (parten + toten * pod->tol >= toten) break;
317: }
318: pod->st = pod->n - pod->nen;
320: /* Compute eigv = V * S */
321: for (i = pod->st; i < pod->n; i++) {
322: const PetscReal v = 1.0 / PetscSqrtReal(pod->eigs[i]);
323: const PetscInt st = pod->n * i;
325: for (PetscInt j = 0; j < pod->n; j++) pod->eigv[st + j] *= v;
326: }
328: /* compute S * V^T * X^T * A * X * V * S if needed */
329: if (pod->nen && !pod->Aspd) {
330: PetscBLASInt bNen, bMaxN;
331: PetscInt st = pod->st * pod->n;
332: PetscCall(PetscBLASIntCast(pod->nen, &bNen));
333: PetscCall(PetscBLASIntCast(pod->maxn, &bMaxN));
334: PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &bNen, &bN, &bN, &one, pod->eigv + st, &bN, pod->yhay, &bMaxN, &zero, pod->swork, &bNen));
335: PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &bNen, &bNen, &bN, &one, pod->swork, &bNen, pod->eigv + st, &bN, &zero, pod->low, &bNen));
336: }
338: if (pod->monitor) {
339: PetscMPIInt rank;
340: Mat C;
342: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)guess), &rank));
343: if (rank == 0) {
344: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " C = "));
345: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->n, pod->n, pod->corr, &C));
346: PetscCall(MatDenseSetLDA(C, pod->maxn));
347: PetscCall(MatView(C, NULL));
348: PetscCall(MatDestroy(&C));
349: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " YHAY = "));
350: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->n, pod->n, pod->yhay, &C));
351: PetscCall(MatDenseSetLDA(C, pod->maxn));
352: PetscCall(MatView(C, NULL));
353: PetscCall(MatDestroy(&C));
354: }
355: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " KSPGuessPOD: basis %" PetscBLASInt_FMT ", energy fractions = ", pod->nen));
356: for (i = pod->n - 1; i >= 0; i--) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%1.6e (%d) ", (double)(pod->eigs[i] / toten), i >= pod->st ? 1 : 0));
357: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
358: if (PetscDefined(USE_DEBUG)) {
359: for (i = 0; i < pod->n; i++) {
360: Vec v;
361: PetscBLASInt bNen, ione = 1;
363: PetscCall(VecDuplicate(pod->xsnap[i], &v));
364: PetscCall(VecCopy(pod->xsnap[i], v));
365: PetscCall(PetscBLASIntCast(pod->nen, &bNen));
366: PetscCallBLAS("BLASgemv", BLASgemv_("T", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->corr + pod->maxn * i, &ione, &zero, pod->swork, &ione));
367: PetscCallBLAS("BLASgemv", BLASgemv_("N", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork, &ione, &zero, pod->swork + pod->n, &ione));
368: for (PetscInt j = 0; j < pod->n; j++) pod->swork[j] = -pod->swork[pod->n + j];
369: PetscCall(VecMAXPY(v, pod->n, pod->swork, pod->xsnap));
370: PetscCall(VecDot(v, v, pod->swork));
371: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 1, 1, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
372: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " Error projection %" PetscInt_FMT ": %g (expected lower than %g)\n", i, (double)PetscRealPart(pod->swork[1]), (double)(toten - parten)));
373: PetscCall(VecDestroy(&v));
374: }
375: }
376: }
377: /* new tip */
378: pod->curr = (pod->curr + 1) % pod->maxn;
379: PetscFunctionReturn(PETSC_SUCCESS);
380: }
382: static PetscErrorCode KSPGuessSetFromOptions_POD(KSPGuess guess)
383: {
384: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
386: PetscFunctionBegin;
387: PetscOptionsBegin(PetscObjectComm((PetscObject)guess), ((PetscObject)guess)->prefix, "POD initial guess options", "KSPGuess");
388: PetscCall(PetscOptionsInt("-ksp_guess_pod_size", "Number of snapshots", NULL, pod->maxn, &pod->maxn, NULL));
389: PetscCall(PetscOptionsBool("-ksp_guess_pod_monitor", "Monitor initial guess generator", NULL, pod->monitor, &pod->monitor, NULL));
390: PetscCall(PetscOptionsReal("-ksp_guess_pod_tol", "Tolerance to retain eigenvectors", "KSPGuessSetTolerance", pod->tol, &pod->tol, NULL));
391: PetscCall(PetscOptionsBool("-ksp_guess_pod_Ainner", "Use the operator as inner product (must be SPD)", NULL, pod->Aspd, &pod->Aspd, NULL));
392: PetscOptionsEnd();
393: PetscFunctionReturn(PETSC_SUCCESS);
394: }
396: static PetscErrorCode KSPGuessSetTolerance_POD(KSPGuess guess, PetscReal tol)
397: {
398: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
400: PetscFunctionBegin;
401: pod->tol = tol;
402: PetscFunctionReturn(PETSC_SUCCESS);
403: }
405: static PetscErrorCode KSPGuessView_POD(KSPGuess guess, PetscViewer viewer)
406: {
407: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
408: PetscBool isascii;
410: PetscFunctionBegin;
411: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
412: if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer, "Max size %" PetscInt_FMT ", tolerance %g, Ainner %d\n", pod->maxn, (double)pod->tol, pod->Aspd));
413: PetscFunctionReturn(PETSC_SUCCESS);
414: }
416: /*MC
417: KSPGUESSPOD - Implements a proper orthogonal decomposition based Galerkin scheme for repeated linear system solves.
419: Options Database Keys:
420: + -ksp_guess_pod_size size - Number of snapshots
421: . -ksp_guess_pod_monitor (true|false) - Monitor initial guess generator
422: . -ksp_guess_pod_tol tol - Tolerance to retain eigenvectors
423: - -ksp_guess_pod_Ainner (true|false) - Use the operator as inner product (must be SPD)
425: Level: intermediate
427: Note:
428: The initial guess is obtained by solving a small and dense linear system, obtained by Galerkin projection on a lower dimensional space generated by the previous solutions as presented in {cite}`volkwein2013proper`.
430: .seealso: [](ch_ksp), `KSPGuess`, `KSPGuessType`, `KSPGuessCreate()`, `KSPSetGuess()`, `KSPGetGuess()`
431: M*/
432: PetscErrorCode KSPGuessCreate_POD(KSPGuess guess)
433: {
434: KSPGuessPOD *pod;
436: PetscFunctionBegin;
437: PetscCall(PetscNew(&pod));
438: pod->maxn = 10;
439: pod->tol = PETSC_MACHINE_EPSILON;
440: guess->data = pod;
442: guess->ops->setfromoptions = KSPGuessSetFromOptions_POD;
443: guess->ops->destroy = KSPGuessDestroy_POD;
444: guess->ops->settolerance = KSPGuessSetTolerance_POD;
445: guess->ops->setup = KSPGuessSetUp_POD;
446: guess->ops->view = KSPGuessView_POD;
447: guess->ops->reset = KSPGuessReset_POD;
448: guess->ops->update = KSPGuessUpdate_POD;
449: guess->ops->formguess = KSPGuessFormGuess_POD;
450: PetscFunctionReturn(PETSC_SUCCESS);
451: }