xref: /petsc/src/ksp/ksp/guess/impls/pod/pod.c (revision 6a97282b1349fb5a3dfe842cdf1bbb3075a9a414)
1 #include <petsc/private/kspimpl.h> /*I "petscksp.h" I*/
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";
11 
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;
39 
KSPGuessReset_POD(KSPGuess guess)40 static PetscErrorCode KSPGuessReset_POD(KSPGuess guess)
41 {
42   KSPGuessPOD *pod  = (KSPGuessPOD *)guess->data;
43   PetscLayout  Alay = NULL, vlay = NULL;
44   PetscBool    cong;
45 
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 }
65 
KSPGuessSetUp_POD(KSPGuess guess)66 static PetscErrorCode KSPGuessSetUp_POD(KSPGuess guess)
67 {
68   KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
69 
70   PetscFunctionBegin;
71   if (!pod->corr) {
72     PetscScalar  sdummy;
73     PetscReal    rdummy = 0;
74     PetscBLASInt bN, lierr, idummy = 0;
75 
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     PetscCallBLAS("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, &lierr));
87 #else
88     PetscCallBLAS("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, &lierr));
89 #endif
90     PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to SYEV Lapack routine %" PetscBLASInt_FMT, lierr);
91     PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(sdummy), &pod->lwork));
92     PetscCall(PetscMalloc1(pod->lwork + PetscMax(bN * bN, 6 * bN), &pod->swork));
93   }
94   /* work vectors are sequential, we explicitly use MPI_Allreduce */
95   if (!pod->xsnap) {
96     Vec *v, vseq;
97 
98     PetscCall(KSPCreateVecs(guess->ksp, 1, &v, 0, NULL));
99     PetscCall(VecCreateLocalVector(v[0], &vseq));
100     PetscCall(VecDestroyVecs(1, &v));
101     PetscCall(VecDuplicateVecs(vseq, pod->maxn, &pod->xsnap));
102     PetscCall(VecDestroy(&vseq));
103   }
104   if (!pod->bsnap) {
105     Vec *v, vseq;
106 
107     PetscCall(KSPCreateVecs(guess->ksp, 0, NULL, 1, &v));
108     PetscCall(VecCreateLocalVector(v[0], &vseq));
109     PetscCall(VecDestroyVecs(1, &v));
110     PetscCall(VecDuplicateVecs(vseq, pod->maxn, &pod->bsnap));
111     PetscCall(VecDestroy(&vseq));
112   }
113   if (!pod->work) PetscCall(KSPCreateVecs(guess->ksp, 1, &pod->work, 0, NULL));
114   PetscFunctionReturn(PETSC_SUCCESS);
115 }
116 
KSPGuessDestroy_POD(KSPGuess guess)117 static PetscErrorCode KSPGuessDestroy_POD(KSPGuess guess)
118 {
119   KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
120 
121   PetscFunctionBegin;
122   PetscCall(PetscFree6(pod->corr, pod->eigs, pod->eigv, pod->iwork, pod->yhay, pod->low));
123 #if defined(PETSC_USE_COMPLEX)
124   PetscCall(PetscFree(pod->rwork));
125 #endif
126   /* need to wait for completion before destroying dots_iallreduce */
127   if (pod->ndots_iallreduce) PetscCallMPI(MPI_Wait(&pod->req_iallreduce, MPI_STATUS_IGNORE));
128   PetscCall(PetscFree(pod->dots_iallreduce));
129   PetscCall(PetscFree(pod->swork));
130   PetscCall(VecDestroyVecs(pod->maxn, &pod->bsnap));
131   PetscCall(VecDestroyVecs(pod->maxn, &pod->xsnap));
132   PetscCall(VecDestroyVecs(1, &pod->work));
133   PetscCall(PetscFree(pod));
134   PetscFunctionReturn(PETSC_SUCCESS);
135 }
136 
137 static PetscErrorCode KSPGuessUpdate_POD(KSPGuess, Vec, Vec);
138 
KSPGuessFormGuess_POD(KSPGuess guess,Vec b,Vec x)139 static PetscErrorCode KSPGuessFormGuess_POD(KSPGuess guess, Vec b, Vec x)
140 {
141   KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
142   PetscScalar  one = 1, zero = 0;
143   PetscBLASInt bN, ione      = 1, bNen, lierr;
144   PetscInt     i;
145 
146   PetscFunctionBegin;
147   PetscCall(PetscCitationsRegister(citation, &cited));
148   if (pod->ndots_iallreduce) { /* complete communication and project the linear system */
149     PetscCall(KSPGuessUpdate_POD(guess, NULL, NULL));
150   }
151   if (!pod->nen) PetscFunctionReturn(PETSC_SUCCESS);
152   /* b_low = S * V^T * X^T * b */
153   PetscCall(VecGetLocalVectorRead(b, pod->bsnap[pod->curr]));
154   PetscCall(VecMDot(pod->bsnap[pod->curr], pod->n, pod->xsnap, pod->swork));
155   PetscCall(VecRestoreLocalVectorRead(b, pod->bsnap[pod->curr]));
156   PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + pod->n, pod->n, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
157   PetscCall(PetscBLASIntCast(pod->n, &bN));
158   PetscCall(PetscBLASIntCast(pod->nen, &bNen));
159   PetscCallBLAS("BLASgemv", BLASgemv_("T", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork + pod->n, &ione, &zero, pod->swork, &ione));
160   if (pod->monitor) {
161     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "  KSPGuessPOD alphas = "));
162     for (i = 0; i < pod->nen; i++) {
163 #if defined(PETSC_USE_COMPLEX)
164       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g + %g i", (double)PetscRealPart(pod->swork[i]), (double)PetscImaginaryPart(pod->swork[i])));
165 #else
166       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g ", (double)pod->swork[i]));
167 #endif
168     }
169     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
170   }
171   /* A_low x_low = b_low */
172   if (!pod->Aspd) { /* A is spd -> LOW = Identity */
173     KSP       pksp = guess->ksp;
174     PetscBool tsolve, symm, set;
175 
176     if (pod->monitor) {
177       PetscMPIInt rank;
178       Mat         L;
179 
180       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)guess), &rank));
181       if (rank == 0) {
182         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "  L = "));
183         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->nen, pod->nen, pod->low, &L));
184         PetscCall(MatView(L, NULL));
185         PetscCall(MatDestroy(&L));
186       }
187     }
188     PetscCall(MatIsSymmetricKnown(guess->A, &set, &symm));
189     tsolve = (set && symm) ? PETSC_FALSE : pksp->transpose_solve;
190     PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&bNen, &bNen, pod->low, &bNen, pod->iwork, &lierr));
191     PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, lierr);
192     PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_(tsolve ? "T" : "N", &bNen, &ione, pod->low, &bNen, pod->iwork, pod->swork, &bNen, &lierr));
193     PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRS Lapack routine %" PetscBLASInt_FMT, lierr);
194   }
195   /* x = X * V * S * x_low */
196   PetscCallBLAS("BLASgemv", BLASgemv_("N", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork, &ione, &zero, pod->swork + pod->n, &ione));
197   if (pod->monitor) {
198     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "  KSPGuessPOD sol = "));
199     for (i = 0; i < pod->nen; i++) {
200 #if defined(PETSC_USE_COMPLEX)
201       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g + %g i", (double)PetscRealPart(pod->swork[i + pod->n]), (double)PetscImaginaryPart(pod->swork[i + pod->n])));
202 #else
203       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "%g ", (double)pod->swork[i + pod->n]));
204 #endif
205     }
206     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
207   }
208   PetscCall(VecGetLocalVector(x, pod->bsnap[pod->curr]));
209   PetscCall(VecSet(pod->bsnap[pod->curr], 0));
210   PetscCall(VecMAXPY(pod->bsnap[pod->curr], pod->n, pod->swork + pod->n, pod->xsnap));
211   PetscCall(VecRestoreLocalVector(x, pod->bsnap[pod->curr]));
212   PetscFunctionReturn(PETSC_SUCCESS);
213 }
214 
KSPGuessUpdate_POD(KSPGuess guess,Vec b,Vec x)215 static PetscErrorCode KSPGuessUpdate_POD(KSPGuess guess, Vec b, Vec x)
216 {
217   KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
218   PetscScalar  one = 1, zero = 0;
219   PetscReal    toten, parten, reps = 0; /* dlamch? */
220   PetscBLASInt bN, lierr, idummy   = 0;
221   PetscInt     i;
222   PetscMPIInt  podn;
223 
224   PetscFunctionBegin;
225   if (pod->ndots_iallreduce) goto complete_request;
226   pod->n = pod->n < pod->maxn ? pod->n + 1 : pod->maxn;
227   PetscCall(PetscMPIIntCast(pod->n, &podn));
228   PetscCall(VecCopy(x, pod->xsnap[pod->curr]));
229   PetscCall(KSP_MatMult(guess->ksp, guess->A, x, pod->work[0]));
230   PetscCall(VecCopy(pod->work[0], pod->bsnap[pod->curr]));
231   if (pod->Aspd) {
232     PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->bsnap, pod->swork));
233 #if !defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
234     PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
235 #else
236     PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
237     pod->ndots_iallreduce = 1;
238 #endif
239   } else {
240     PetscInt  off;
241     PetscBool set, herm;
242 
243 #if defined(PETSC_USE_COMPLEX)
244     PetscCall(MatIsHermitianKnown(guess->A, &set, &herm));
245 #else
246     PetscCall(MatIsSymmetricKnown(guess->A, &set, &herm));
247 #endif
248     off = (guess->ksp->transpose_solve && (!set || !herm)) ? 2 * pod->n : pod->n;
249 
250     /* TODO: we may want to use a user-defined dot for the correlation matrix */
251     PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->xsnap, pod->swork));
252     PetscCall(VecMDot(pod->bsnap[pod->curr], pod->n, pod->xsnap, pod->swork + off));
253     if (!set || !herm) {
254       off = (off == pod->n) ? 2 * pod->n : pod->n;
255       PetscCall(VecMDot(pod->xsnap[pod->curr], pod->n, pod->bsnap, pod->swork + off));
256 #if !defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
257       PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, 3 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
258 #else
259       PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, 3 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
260       pod->ndots_iallreduce = 3;
261 #endif
262     } else {
263 #if !defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
264       PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 3 * pod->n, 2 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
265       for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->swork[4 * pod->n + i];
266 #else
267       PetscCallMPI(MPI_Iallreduce(pod->swork, pod->dots_iallreduce, 2 * podn, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess), &pod->req_iallreduce));
268       pod->ndots_iallreduce = 2;
269 #endif
270     }
271   }
272   if (pod->ndots_iallreduce) PetscFunctionReturn(PETSC_SUCCESS);
273 
274 complete_request:
275   if (pod->ndots_iallreduce) {
276     PetscCallMPI(MPI_Wait(&pod->req_iallreduce, MPI_STATUS_IGNORE));
277     switch (pod->ndots_iallreduce) {
278     case 3:
279       for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
280       for (i = 0; i < pod->n; i++) pod->swork[4 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
281       for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->dots_iallreduce[2 * pod->n + i];
282       break;
283     case 2:
284       for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
285       for (i = 0; i < pod->n; i++) pod->swork[4 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
286       for (i = 0; i < pod->n; i++) pod->swork[5 * pod->n + i] = pod->dots_iallreduce[pod->n + i];
287       break;
288     case 1:
289       for (i = 0; i < pod->n; i++) pod->swork[3 * pod->n + i] = pod->dots_iallreduce[i];
290       break;
291     default:
292       SETERRQ(PetscObjectComm((PetscObject)guess), PETSC_ERR_PLIB, "Invalid number of outstanding dots operations: %" PetscInt_FMT, pod->ndots_iallreduce);
293     }
294   }
295   pod->ndots_iallreduce = 0;
296 
297   /* correlation matrix and Y^H A Y (Galerkin) */
298   for (i = 0; i < pod->n; i++) {
299     pod->corr[pod->curr * pod->maxn + i] = pod->swork[3 * pod->n + i];
300     pod->corr[i * pod->maxn + pod->curr] = PetscConj(pod->swork[3 * pod->n + i]);
301     if (!pod->Aspd) {
302       pod->yhay[pod->curr * pod->maxn + i] = pod->swork[4 * pod->n + i];
303       pod->yhay[i * pod->maxn + pod->curr] = PetscConj(pod->swork[5 * pod->n + i]);
304     }
305   }
306   /* syevx changes the input matrix */
307   for (i = 0; i < pod->n; i++) {
308     PetscInt j;
309     for (j = i; j < pod->n; j++) pod->swork[i * pod->n + j] = pod->corr[i * pod->maxn + j];
310   }
311   PetscCall(PetscBLASIntCast(pod->n, &bN));
312 #if !defined(PETSC_USE_COMPLEX)
313   PetscCallBLAS("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, &lierr));
314 #else
315   PetscCallBLAS("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, &lierr));
316 #endif
317   PetscCheck(lierr >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYEV Lapack routine: illegal argument %" PetscBLASInt_FMT, -lierr);
318   PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYEV Lapack routine: %" PetscBLASInt_FMT " eigenvectors failed to converge", lierr);
319 
320   /* dimension of lower dimensional system */
321   pod->st = -1;
322   for (i = 0, toten = 0; i < pod->n; i++) {
323     pod->eigs[i] = PetscMax(pod->eigs[i], 0.0);
324     toten += pod->eigs[i];
325     if (!pod->eigs[i]) pod->st = i;
326   }
327   pod->nen = 0;
328   for (i = pod->n - 1, parten = 0; i > pod->st && toten > 0; i--) {
329     pod->nen++;
330     parten += pod->eigs[i];
331     if (parten + toten * pod->tol >= toten) break;
332   }
333   pod->st = pod->n - pod->nen;
334 
335   /* Compute eigv = V * S */
336   for (i = pod->st; i < pod->n; i++) {
337     const PetscReal v  = 1.0 / PetscSqrtReal(pod->eigs[i]);
338     const PetscInt  st = pod->n * i;
339     PetscInt        j;
340 
341     for (j = 0; j < pod->n; j++) pod->eigv[st + j] *= v;
342   }
343 
344   /* compute S * V^T * X^T * A * X * V * S if needed */
345   if (pod->nen && !pod->Aspd) {
346     PetscBLASInt bNen, bMaxN;
347     PetscInt     st = pod->st * pod->n;
348     PetscCall(PetscBLASIntCast(pod->nen, &bNen));
349     PetscCall(PetscBLASIntCast(pod->maxn, &bMaxN));
350     PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &bNen, &bN, &bN, &one, pod->eigv + st, &bN, pod->yhay, &bMaxN, &zero, pod->swork, &bNen));
351     PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &bNen, &bNen, &bN, &one, pod->swork, &bNen, pod->eigv + st, &bN, &zero, pod->low, &bNen));
352   }
353 
354   if (pod->monitor) {
355     PetscMPIInt rank;
356     Mat         C;
357 
358     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)guess), &rank));
359     if (rank == 0) {
360       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "  C = "));
361       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->n, pod->n, pod->corr, &C));
362       PetscCall(MatDenseSetLDA(C, pod->maxn));
363       PetscCall(MatView(C, NULL));
364       PetscCall(MatDestroy(&C));
365       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "  YHAY = "));
366       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pod->n, pod->n, pod->yhay, &C));
367       PetscCall(MatDenseSetLDA(C, pod->maxn));
368       PetscCall(MatView(C, NULL));
369       PetscCall(MatDestroy(&C));
370     }
371     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "  KSPGuessPOD: basis %" PetscBLASInt_FMT ", energy fractions = ", pod->nen));
372     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));
373     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "\n"));
374     if (PetscDefined(USE_DEBUG)) {
375       for (i = 0; i < pod->n; i++) {
376         Vec          v;
377         PetscInt     j;
378         PetscBLASInt bNen, ione = 1;
379 
380         PetscCall(VecDuplicate(pod->xsnap[i], &v));
381         PetscCall(VecCopy(pod->xsnap[i], v));
382         PetscCall(PetscBLASIntCast(pod->nen, &bNen));
383         PetscCallBLAS("BLASgemv", BLASgemv_("T", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->corr + pod->maxn * i, &ione, &zero, pod->swork, &ione));
384         PetscCallBLAS("BLASgemv", BLASgemv_("N", &bN, &bNen, &one, pod->eigv + pod->st * pod->n, &bN, pod->swork, &ione, &zero, pod->swork + pod->n, &ione));
385         for (j = 0; j < pod->n; j++) pod->swork[j] = -pod->swork[pod->n + j];
386         PetscCall(VecMAXPY(v, pod->n, pod->swork, pod->xsnap));
387         PetscCall(VecDot(v, v, pod->swork));
388         PetscCallMPI(MPIU_Allreduce(pod->swork, pod->swork + 1, 1, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)guess)));
389         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)guess), "  Error projection %" PetscInt_FMT ": %g (expected lower than %g)\n", i, (double)PetscRealPart(pod->swork[1]), (double)(toten - parten)));
390         PetscCall(VecDestroy(&v));
391       }
392     }
393   }
394   /* new tip */
395   pod->curr = (pod->curr + 1) % pod->maxn;
396   PetscFunctionReturn(PETSC_SUCCESS);
397 }
398 
KSPGuessSetFromOptions_POD(KSPGuess guess)399 static PetscErrorCode KSPGuessSetFromOptions_POD(KSPGuess guess)
400 {
401   KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
402 
403   PetscFunctionBegin;
404   PetscOptionsBegin(PetscObjectComm((PetscObject)guess), ((PetscObject)guess)->prefix, "POD initial guess options", "KSPGuess");
405   PetscCall(PetscOptionsInt("-ksp_guess_pod_size", "Number of snapshots", NULL, pod->maxn, &pod->maxn, NULL));
406   PetscCall(PetscOptionsBool("-ksp_guess_pod_monitor", "Monitor initial guess generator", NULL, pod->monitor, &pod->monitor, NULL));
407   PetscCall(PetscOptionsReal("-ksp_guess_pod_tol", "Tolerance to retain eigenvectors", "KSPGuessSetTolerance", pod->tol, &pod->tol, NULL));
408   PetscCall(PetscOptionsBool("-ksp_guess_pod_Ainner", "Use the operator as inner product (must be SPD)", NULL, pod->Aspd, &pod->Aspd, NULL));
409   PetscOptionsEnd();
410   PetscFunctionReturn(PETSC_SUCCESS);
411 }
412 
KSPGuessSetTolerance_POD(KSPGuess guess,PetscReal tol)413 static PetscErrorCode KSPGuessSetTolerance_POD(KSPGuess guess, PetscReal tol)
414 {
415   KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
416 
417   PetscFunctionBegin;
418   pod->tol = tol;
419   PetscFunctionReturn(PETSC_SUCCESS);
420 }
421 
KSPGuessView_POD(KSPGuess guess,PetscViewer viewer)422 static PetscErrorCode KSPGuessView_POD(KSPGuess guess, PetscViewer viewer)
423 {
424   KSPGuessPOD *pod = (KSPGuessPOD *)guess->data;
425   PetscBool    isascii;
426 
427   PetscFunctionBegin;
428   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
429   if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer, "Max size %" PetscInt_FMT ", tolerance %g, Ainner %d\n", pod->maxn, (double)pod->tol, pod->Aspd));
430   PetscFunctionReturn(PETSC_SUCCESS);
431 }
432 
433 /*MC
434     KSPGUESSPOD - Implements a proper orthogonal decomposition based Galerkin scheme for repeated linear system solves.
435 
436   Options Database Keys:
437 +  -ksp_guess_pod_size <size> - Number of snapshots
438 .  -ksp_guess_pod_monitor <true or false> - Monitor initial guess generator
439 .  -ksp_guess_pod_tol <tol> - Tolerance to retain eigenvectors
440 -  -ksp_guess_pod_Ainner <true> - Use the operator as inner product (must be SPD)
441 
442   Level: intermediate
443 
444   Note:
445   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`.
446 
447 .seealso: [](ch_ksp), `KSPGuess`, `KSPGuessType`, `KSPGuessCreate()`, `KSPSetGuess()`, `KSPGetGuess()`
448 M*/
KSPGuessCreate_POD(KSPGuess guess)449 PetscErrorCode KSPGuessCreate_POD(KSPGuess guess)
450 {
451   KSPGuessPOD *pod;
452 
453   PetscFunctionBegin;
454   PetscCall(PetscNew(&pod));
455   pod->maxn   = 10;
456   pod->tol    = PETSC_MACHINE_EPSILON;
457   guess->data = pod;
458 
459   guess->ops->setfromoptions = KSPGuessSetFromOptions_POD;
460   guess->ops->destroy        = KSPGuessDestroy_POD;
461   guess->ops->settolerance   = KSPGuessSetTolerance_POD;
462   guess->ops->setup          = KSPGuessSetUp_POD;
463   guess->ops->view           = KSPGuessView_POD;
464   guess->ops->reset          = KSPGuessReset_POD;
465   guess->ops->update         = KSPGuessUpdate_POD;
466   guess->ops->formguess      = KSPGuessFormGuess_POD;
467   PetscFunctionReturn(PETSC_SUCCESS);
468 }
469