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 defined(PETSC_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 defined(PETSC_USE_COMPLEX)
78: PetscCall(PetscMalloc1(7 * pod->maxn, &pod->rwork));
79: #endif
80: #if defined(PETSC_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 !defined(PETSC_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 defined(PETSC_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 defined(PETSC_USE_COMPLEX)
163: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g + %g i", (double)PetscRealPart(pod->swork[i]), (double)PetscImaginaryPart(pod->swork[i])));
164: #else
165: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g ", (double)pod->swork[i]));
166: #endif
167: }
168: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
169: }
170: /* A_low x_low = b_low */
171: if (!pod->Aspd) { /* A is spd -> LOW = Identity */
172: KSP pksp = guess->ksp;
173: PetscBool tsolve, symm, set;
175: if (pod->monitor) {
176: PetscMPIInt rank;
177: Mat L;
179: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)guess), &rank));
180: if (rank == 0) {
181: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " L = "));
182: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->nen, pod->nen, pod->low, &L));
183: PetscCall(MatView(L, NULL));
184: PetscCall(MatDestroy(&L));
185: }
186: }
187: PetscCall(MatIsSymmetricKnown(guess->A, &set, &symm));
188: tsolve = (set && symm) ? PETSC_FALSE : pksp->transpose_solve;
189: PetscCallLAPACKInfo("LAPACKgetrf", LAPACKgetrf_(&bNen, &bNen, pod->low, &bNen, pod->iwork, &info));
190: PetscCallLAPACKInfo("LAPACKgetrs", LAPACKgetrs_(tsolve ? "T" : "N", &bNen, &ione, pod->low, &bNen, pod->iwork, pod->swork, &bNen, &info));
191: }
192: /* x = X * V * S * x_low */
193: PetscCallBLAS("BLASgemv", BLASgemv_("N", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork, &ione, &zero, pod->swork + pod->n, &ione));
194: if (pod->monitor) {
195: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " KSPGuessPOD sol = "));
196: for (i = 0; i < pod->nen; i++) {
197: #if defined(PETSC_USE_COMPLEX)
198: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g + %g i", (double)PetscRealPart(pod->swork[i + pod->n]), (double)PetscImaginaryPart(pod->swork[i + pod->n])));
199: #else
200: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g ", (double)pod->swork[i + pod->n]));
201: #endif
202: }
203: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
204: }
205: PetscCall(VecGetLocalVector(x, pod->bsnap[pod->curr]));
206: PetscCall(VecSet(pod->bsnap[pod->curr], 0));
207: PetscCall(VecMAXPY(pod->bsnap[pod->curr], pod->n, pod->swork + pod->n, pod->xsnap));
208: PetscCall(VecRestoreLocalVector(x, pod->bsnap[pod->curr]));
209: PetscFunctionReturn(PETSC_SUCCESS);
210: }
212: static PetscErrorCode KSPGuessUpdate_POD(KSPGuess guess, Vec b, Vec x)
213: {
214: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
215: PetscScalar one = 1, zero = 0;
216: PetscReal toten, parten, reps = 0; /* dlamch? */
217: PetscBLASInt bN, idummy = 0;
218: PetscInt i;
219: PetscMPIInt podn;
221: PetscFunctionBegin;
222: if (pod->ndots_iallreduce) goto complete_request;
223: pod->n = pod->n < pod->maxn ? pod->n + 1 : pod->maxn;
224: PetscCall(PetscMPIIntCast(pod->n, &podn));
225: PetscCall(VecCopy(x, pod->xsnap[pod->curr]));
226: PetscCall(KSP_MatMult(guess->ksp, guess->A, x, pod->work[0]));
227: PetscCall(VecCopy(pod->work[0], pod->bsnap[pod->curr]));
228: if (pod->Aspd) {
229: PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->bsnap, pod->swork));
230: #if !defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
231: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
232: #else
233: PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
234: pod->ndots_iallreduce = 1;
235: #endif
236: } else {
237: PetscInt off;
238: PetscBool set, herm;
240: #if defined(PETSC_USE_COMPLEX)
241: PetscCall(MatIsHermitianKnown(guess->A, &set, &herm));
242: #else
243: PetscCall(MatIsSymmetricKnown(guess->A, &set, &herm));
244: #endif
245: off = (guess->ksp->transpose_solve && (!set || !herm)) ? 2 * pod->n : pod->n;
247: /* TODO: we may want to use a user-defined dot for the correlation matrix */
248: PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->xsnap, pod->swork));
249: PetscCall(VecMDot(pod->bsnap[pod->curr], pod->n, pod->xsnap, pod->swork + off));
250: if (!set || !herm) {
251: off = (off == pod->n) ? 2 * pod->n : pod->n;
252: PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->bsnap, pod->swork + off));
253: #if !defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
254: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, 3 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
255: #else
256: PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, 3 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
257: pod->ndots_iallreduce = 3;
258: #endif
259: } else {
260: #if !defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
261: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, 2 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
262: for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->swork[4 * pod->n + i];
263: #else
264: PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, 2 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
265: pod->ndots_iallreduce = 2;
266: #endif
267: }
268: }
269: if (pod->ndots_iallreduce) PetscFunctionReturn(PETSC_SUCCESS);
271: complete_request:
272: if (pod->ndots_iallreduce) {
273: PetscCallMPI(MPI_Wait(&pod->req_iallreduce, MPI_STATUS_IGNORE));
274: switch (pod->ndots_iallreduce) {
275: case 3:
276: for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
277: for (i = 0; i < pod->n; i++) pod->swork[4 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
278: for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->dots_iallreduce[2 * pod->n + i];
279: break;
280: case 2:
281: for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
282: for (i = 0; i < pod->n; i++) pod->swork[4 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
283: for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
284: break;
285: case 1:
286: for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
287: break;
288: default:
289: SETERRQ(PetscObjectComm((PetscObject)guess), PETSC_ERR_PLIB, "Invalid number of outstanding dots operations: %" PetscInt_FMT, pod->ndots_iallreduce);
290: }
291: }
292: pod->ndots_iallreduce = 0;
294: /* correlation matrix and Y^H A Y (Galerkin) */
295: for (i = 0; i < pod->n; i++) {
296: pod->corr[pod->curr * pod->maxn + i] = pod->swork[3 * pod->n + i];
297: pod->corr[i * pod->maxn + pod->curr] = PetscConj(pod->swork[3 * pod->n + i]);
298: if (!pod->Aspd) {
299: pod->yhay[pod->curr * pod->maxn + i] = pod->swork[4 * pod->n + i];
300: pod->yhay[i * pod->maxn + pod->curr] = PetscConj(pod->swork[5 * pod->n + i]);
301: }
302: }
303: /* syevx changes the input matrix */
304: for (i = 0; i < pod->n; i++) {
305: for (PetscInt j = i; j < pod->n; j++) pod->swork[i * pod->n + j] = pod->corr[i * pod->maxn + j];
306: }
307: PetscCall(PetscBLASIntCast(pod->n, &bN));
308: #if !defined(PETSC_USE_COMPLEX)
309: 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));
310: #else
311: 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));
312: #endif
314: /* dimension of lower dimensional system */
315: pod->st = -1;
316: for (i = 0, toten = 0; i < pod->n; i++) {
317: pod->eigs[i] = PetscMax(pod->eigs[i], 0.0);
318: toten += pod->eigs[i];
319: if (!pod->eigs[i]) pod->st = i;
320: }
321: pod->nen = 0;
322: for (i = pod->n - 1, parten = 0; i > pod->st && toten > 0; i--) {
323: pod->nen++;
324: parten += pod->eigs[i];
325: if (parten + toten * pod->tol >= toten) break;
326: }
327: pod->st = pod->n - pod->nen;
329: /* Compute eigv = V * S */
330: for (i = pod->st; i < pod->n; i++) {
331: const PetscReal v = 1.0 / PetscSqrtReal(pod->eigs[i]);
332: const PetscInt st = pod->n * i;
334: for (PetscInt j = 0; j < pod->n; j++) pod->eigv[st + j] *= v;
335: }
337: /* compute S * V^T * X^T * A * X * V * S if needed */
338: if (pod->nen && !pod->Aspd) {
339: PetscBLASInt bNen, bMaxN;
340: PetscInt st = pod->st * pod->n;
341: PetscCall(PetscBLASIntCast(pod->nen, &bNen));
342: PetscCall(PetscBLASIntCast(pod->maxn, &bMaxN));
343: PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &bNen, &bN, &bN, &one, pod->eigv + st, &bN, pod->yhay, &bMaxN, &zero, pod->swork, &bNen));
344: PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &bNen, &bNen, &bN, &one, pod->swork, &bNen, pod->eigv + st, &bN, &zero, pod->low, &bNen));
345: }
347: if (pod->monitor) {
348: PetscMPIInt rank;
349: Mat C;
351: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)guess), &rank));
352: if (rank == 0) {
353: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " C = "));
354: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->n, pod->n, pod->corr, &C));
355: PetscCall(MatDenseSetLDA(C, pod->maxn));
356: PetscCall(MatView(C, NULL));
357: PetscCall(MatDestroy(&C));
358: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " YHAY = "));
359: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->n, pod->n, pod->yhay, &C));
360: PetscCall(MatDenseSetLDA(C, pod->maxn));
361: PetscCall(MatView(C, NULL));
362: PetscCall(MatDestroy(&C));
363: }
364: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " KSPGuessPOD: basis %" PetscBLASInt_FMT ", energy fractions = ", pod->nen));
365: 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));
366: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
367: if (PetscDefined(USE_DEBUG)) {
368: for (i = 0; i < pod->n; i++) {
369: Vec v;
370: PetscBLASInt bNen, ione = 1;
372: PetscCall(VecDuplicate(pod->xsnap[i], &v));
373: PetscCall(VecCopy(pod->xsnap[i], v));
374: PetscCall(PetscBLASIntCast(pod->nen, &bNen));
375: PetscCallBLAS("BLASgemv", BLASgemv_("T", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->corr + pod->maxn * i, &ione, &zero, pod->swork, &ione));
376: PetscCallBLAS("BLASgemv", BLASgemv_("N", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork, &ione, &zero, pod->swork + pod->n, &ione));
377: for (PetscInt j = 0; j < pod->n; j++) pod->swork[j] = -pod->swork[pod->n + j];
378: PetscCall(VecMAXPY(v, pod->n, pod->swork, pod->xsnap));
379: PetscCall(VecDot(v, v, pod->swork));
380: PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 1, 1, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
381: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), " Error projection %" PetscInt_FMT ": %g (expected lower than %g)\n", i, (double)PetscRealPart(pod->swork[1]), (double)(toten - parten)));
382: PetscCall(VecDestroy(&v));
383: }
384: }
385: }
386: /* new tip */
387: pod->curr = (pod->curr + 1) % pod->maxn;
388: PetscFunctionReturn(PETSC_SUCCESS);
389: }
391: static PetscErrorCode KSPGuessSetFromOptions_POD(KSPGuess guess)
392: {
393: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
395: PetscFunctionBegin;
396: PetscOptionsBegin(PetscObjectComm((PetscObject)guess), ((PetscObject)guess)->prefix, "POD initial guess options", "KSPGuess");
397: PetscCall(PetscOptionsInt("-ksp_guess_pod_size", "Number of snapshots", NULL, pod->maxn, &pod->maxn, NULL));
398: PetscCall(PetscOptionsBool("-ksp_guess_pod_monitor", "Monitor initial guess generator", NULL, pod->monitor, &pod->monitor, NULL));
399: PetscCall(PetscOptionsReal("-ksp_guess_pod_tol", "Tolerance to retain eigenvectors", "KSPGuessSetTolerance", pod->tol, &pod->tol, NULL));
400: PetscCall(PetscOptionsBool("-ksp_guess_pod_Ainner", "Use the operator as inner product (must be SPD)", NULL, pod->Aspd, &pod->Aspd, NULL));
401: PetscOptionsEnd();
402: PetscFunctionReturn(PETSC_SUCCESS);
403: }
405: static PetscErrorCode KSPGuessSetTolerance_POD(KSPGuess guess, PetscReal tol)
406: {
407: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
409: PetscFunctionBegin;
410: pod->tol = tol;
411: PetscFunctionReturn(PETSC_SUCCESS);
412: }
414: static PetscErrorCode KSPGuessView_POD(KSPGuess guess, PetscViewer viewer)
415: {
416: KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
417: PetscBool isascii;
419: PetscFunctionBegin;
420: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
421: if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer, "Max size %" PetscInt_FMT ", tolerance %g, Ainner %d\n", pod->maxn, (double)pod->tol, pod->Aspd));
422: PetscFunctionReturn(PETSC_SUCCESS);
423: }
425: /*MC
426: KSPGUESSPOD - Implements a proper orthogonal decomposition based Galerkin scheme for repeated linear system solves.
428: Options Database Keys:
429: + -ksp_guess_pod_size size - Number of snapshots
430: . -ksp_guess_pod_monitor (true|false) - Monitor initial guess generator
431: . -ksp_guess_pod_tol tol - Tolerance to retain eigenvectors
432: - -ksp_guess_pod_Ainner (true|false) - Use the operator as inner product (must be SPD)
434: Level: intermediate
436: Note:
437: 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`.
439: .seealso: [](ch_ksp), `KSPGuess`, `KSPGuessType`, `KSPGuessCreate()`, `KSPSetGuess()`, `KSPGetGuess()`
440: M*/
441: PetscErrorCode KSPGuessCreate_POD(KSPGuess guess)
442: {
443: KSPGuessPOD *pod;
445: PetscFunctionBegin;
446: PetscCall(PetscNew(&pod));
447: pod->maxn = 10;
448: pod->tol = PETSC_MACHINE_EPSILON;
449: guess->data = pod;
451: guess->ops->setfromoptions = KSPGuessSetFromOptions_POD;
452: guess->ops->destroy = KSPGuessDestroy_POD;
453: guess->ops->settolerance = KSPGuessSetTolerance_POD;
454: guess->ops->setup = KSPGuessSetUp_POD;
455: guess->ops->view = KSPGuessView_POD;
456: guess->ops->reset = KSPGuessReset_POD;
457: guess->ops->update = KSPGuessUpdate_POD;
458: guess->ops->formguess = KSPGuessFormGuess_POD;
459: PetscFunctionReturn(PETSC_SUCCESS);
460: }