Actual source code: lrc.c

  1: #include <petsc/private/matimpl.h>

  3: PETSC_EXTERN PetscErrorCode VecGetRootType_Private(Vec, VecType *);

  5: typedef struct {
  6:   Mat A;            /* sparse matrix */
  7:   Mat U, V;         /* dense tall-skinny matrices */
  8:   Vec c;            /* sequential vector containing the diagonal of C */
  9:   Vec work1, work2; /* sequential vectors that hold partial products */
 10:   Vec xl, yl;       /* auxiliary sequential vectors for matmult operation */
 11: } Mat_LRC;

 13: static PetscErrorCode MatMult_LRC_kernel(Mat N, Vec x, Vec y, PetscBool transpose)
 14: {
 15:   Mat_LRC    *Na = (Mat_LRC *)N->data;
 16:   PetscMPIInt size;
 17:   Mat         U, V;

 19:   PetscFunctionBegin;
 20:   U = transpose ? Na->V : Na->U;
 21:   V = transpose ? Na->U : Na->V;
 22:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)N), &size));
 23:   if (size == 1) {
 24:     PetscCall(MatMultHermitianTranspose(V, x, Na->work1));
 25:     if (Na->c) PetscCall(VecPointwiseMult(Na->work1, Na->c, Na->work1));
 26:     if (Na->A) {
 27:       if (transpose) {
 28:         PetscCall(MatMultTranspose(Na->A, x, y));
 29:       } else {
 30:         PetscCall(MatMult(Na->A, x, y));
 31:       }
 32:       PetscCall(MatMultAdd(U, Na->work1, y, y));
 33:     } else {
 34:       PetscCall(MatMult(U, Na->work1, y));
 35:     }
 36:   } else {
 37:     Mat                Uloc, Vloc;
 38:     Vec                yl, xl;
 39:     const PetscScalar *w1;
 40:     PetscScalar       *w2;
 41:     PetscInt           nwork;

 43:     xl = transpose ? Na->yl : Na->xl;
 44:     yl = transpose ? Na->xl : Na->yl;
 45:     PetscCall(VecGetLocalVector(y, yl));
 46:     PetscCall(MatDenseGetLocalMatrix(U, &Uloc));
 47:     PetscCall(MatDenseGetLocalMatrix(V, &Vloc));

 49:     /* multiply the local part of V with the local part of x */
 50:     PetscCall(VecGetLocalVectorRead(x, xl));
 51:     PetscCall(MatMultHermitianTranspose(Vloc, xl, Na->work1));
 52:     PetscCall(VecRestoreLocalVectorRead(x, xl));

 54:     /* form the sum of all the local multiplies: this is work2 = V'*x =
 55:        sum_{all processors} work1 */
 56:     PetscCall(VecGetArrayRead(Na->work1, &w1));
 57:     PetscCall(VecGetArrayWrite(Na->work2, &w2));
 58:     PetscCall(VecGetLocalSize(Na->work1, &nwork));
 59:     PetscCallMPI(MPIU_Allreduce(w1, w2, nwork, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)N)));
 60:     PetscCall(VecRestoreArrayRead(Na->work1, &w1));
 61:     PetscCall(VecRestoreArrayWrite(Na->work2, &w2));

 63:     if (Na->c) { /* work2 = C*work2 */
 64:       PetscCall(VecPointwiseMult(Na->work2, Na->c, Na->work2));
 65:     }

 67:     if (Na->A) {
 68:       /* form y = A*x or A^t*x */
 69:       if (transpose) {
 70:         PetscCall(MatMultTranspose(Na->A, x, y));
 71:       } else {
 72:         PetscCall(MatMult(Na->A, x, y));
 73:       }
 74:       /* multiply-add y = y + U*work2 */
 75:       PetscCall(MatMultAdd(Uloc, Na->work2, yl, yl));
 76:     } else {
 77:       /* multiply y = U*work2 */
 78:       PetscCall(MatMult(Uloc, Na->work2, yl));
 79:     }

 81:     PetscCall(VecRestoreLocalVector(y, yl));
 82:   }
 83:   PetscFunctionReturn(PETSC_SUCCESS);
 84: }

 86: static PetscErrorCode MatMult_LRC(Mat N, Vec x, Vec y)
 87: {
 88:   PetscFunctionBegin;
 89:   PetscCall(MatMult_LRC_kernel(N, x, y, PETSC_FALSE));
 90:   PetscFunctionReturn(PETSC_SUCCESS);
 91: }

 93: static PetscErrorCode MatMultTranspose_LRC(Mat N, Vec x, Vec y)
 94: {
 95:   PetscFunctionBegin;
 96:   PetscCall(MatMult_LRC_kernel(N, x, y, PETSC_TRUE));
 97:   PetscFunctionReturn(PETSC_SUCCESS);
 98: }

100: static PetscErrorCode MatDestroy_LRC(Mat N)
101: {
102:   Mat_LRC *Na = (Mat_LRC *)N->data;

104:   PetscFunctionBegin;
105:   PetscCall(MatDestroy(&Na->A));
106:   PetscCall(MatDestroy(&Na->U));
107:   PetscCall(MatDestroy(&Na->V));
108:   PetscCall(VecDestroy(&Na->c));
109:   PetscCall(VecDestroy(&Na->work1));
110:   PetscCall(VecDestroy(&Na->work2));
111:   PetscCall(VecDestroy(&Na->xl));
112:   PetscCall(VecDestroy(&Na->yl));
113:   PetscCall(PetscFree(N->data));
114:   PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatLRCGetMats_C", NULL));
115:   PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatLRCSetMats_C", NULL));
116:   PetscFunctionReturn(PETSC_SUCCESS);
117: }

119: static PetscErrorCode MatLRCGetMats_LRC(Mat N, Mat *A, Mat *U, Vec *c, Mat *V)
120: {
121:   Mat_LRC *Na = (Mat_LRC *)N->data;

123:   PetscFunctionBegin;
124:   if (A) *A = Na->A;
125:   if (U) *U = Na->U;
126:   if (c) *c = Na->c;
127:   if (V) *V = Na->V;
128:   PetscFunctionReturn(PETSC_SUCCESS);
129: }

131: static PetscErrorCode MatLRCSetMats_LRC(Mat N, Mat A, Mat U, Vec c, Mat V)
132: {
133:   Mat_LRC *Na = (Mat_LRC *)N->data;

135:   PetscFunctionBegin;
136:   PetscCall(PetscObjectReference((PetscObject)A));
137:   PetscCall(PetscObjectReference((PetscObject)U));
138:   PetscCall(PetscObjectReference((PetscObject)V));
139:   PetscCall(PetscObjectReference((PetscObject)c));
140:   PetscCall(MatDestroy(&Na->A));
141:   PetscCall(MatDestroy(&Na->U));
142:   PetscCall(MatDestroy(&Na->V));
143:   PetscCall(VecDestroy(&Na->c));
144:   Na->A = A;
145:   Na->U = U;
146:   Na->c = c;
147:   Na->V = V;
148:   PetscFunctionReturn(PETSC_SUCCESS);
149: }

151: /*@
152:   MatLRCGetMats - Returns the constituents of an LRC matrix

154:   Not collective

156:   Input Parameter:
157: . N - matrix of type `MATLRC`

159:   Output Parameters:
160: + A - the (sparse) matrix
161: . U - first dense rectangular (tall and skinny) matrix
162: . c - a sequential vector containing the diagonal of C
163: - V - second dense rectangular (tall and skinny) matrix

165:   Level: intermediate

167:   Notes:
168:   The returned matrices should not be destroyed by the caller.

170:   `U`, `c`, `V` may be `NULL` if not needed

172: .seealso: [](ch_matrices), `MatLRCSetMats()`, `Mat`, `MATLRC`, `MatCreateLRC()`
173: @*/
174: PetscErrorCode MatLRCGetMats(Mat N, Mat *A, Mat *U, Vec *c, Mat *V)
175: {
176:   PetscFunctionBegin;
177:   PetscUseMethod(N, "MatLRCGetMats_C", (Mat, Mat *, Mat *, Vec *, Mat *), (N, A, U, c, V));
178:   PetscFunctionReturn(PETSC_SUCCESS);
179: }

181: /*@
182:   MatLRCSetMats - Sets the constituents of an LRC matrix

184:   Logically collective

186:   Input Parameters:
187: + N - matrix of type `MATLRC`
188: . A - the (sparse) matrix
189: . U - first dense rectangular (tall and skinny) matrix
190: . c - a sequential vector containing the diagonal of C
191: - V - second dense rectangular (tall and skinny) matrix

193:   Level: intermediate

195:   Note:
196:   If `V` is `NULL`, then it is assumed to be identical to `U`.

198: .seealso: [](ch_matrices), `MatLRCGetMats()`, `Mat`, `MATLRC`, `MatCreateLRC()`
199: @*/
200: PetscErrorCode MatLRCSetMats(Mat N, Mat A, Mat U, Vec c, Mat V)
201: {
202:   PetscInt  k, k1, m, n, m1, n1;
203:   PetscBool match;

205:   PetscFunctionBegin;
209:   if (V) {
211:     PetscCheckSameComm(U, 3, V, 5);
212:   }
213:   if (A) PetscCheckSameComm(A, 2, U, 3);
214:   if (!V) V = U;
215:   PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)U, &match, MATSEQDENSE, MATMPIDENSE, ""));
216:   PetscCheck(match, PetscObjectComm((PetscObject)U), PETSC_ERR_SUP, "Matrix U must be of type dense, found %s", ((PetscObject)U)->type_name);
217:   PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)V, &match, MATSEQDENSE, MATMPIDENSE, ""));
218:   PetscCheck(match, PetscObjectComm((PetscObject)U), PETSC_ERR_SUP, "Matrix V must be of type dense, found %s", ((PetscObject)V)->type_name);
219:   PetscCall(PetscStrcmp(U->defaultvectype, V->defaultvectype, &match));
220:   PetscCheck(match, PetscObjectComm((PetscObject)U), PETSC_ERR_ARG_WRONG, "Matrix U and V must have the same VecType %s != %s", U->defaultvectype, V->defaultvectype);
221:   if (A) {
222:     PetscCall(PetscStrcmp(A->defaultvectype, U->defaultvectype, &match));
223:     PetscCheck(match, PetscObjectComm((PetscObject)U), PETSC_ERR_ARG_WRONG, "Matrix A and U must have the same VecType %s != %s", A->defaultvectype, U->defaultvectype);
224:   }
225:   PetscCall(MatGetSize(U, NULL, &k));
226:   PetscCall(MatGetSize(V, NULL, &k1));
227:   PetscCheck(k == k1, PetscObjectComm((PetscObject)U), PETSC_ERR_ARG_INCOMP, "U and V have different number of columns (%" PetscInt_FMT " vs %" PetscInt_FMT ")", k, k1);
228:   PetscCall(MatGetLocalSize(U, &m, NULL));
229:   PetscCall(MatGetLocalSize(V, &n, NULL));
230:   if (A) {
231:     PetscCall(MatGetLocalSize(A, &m1, &n1));
232:     PetscCheck(m == m1, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local dimensions of U %" PetscInt_FMT " and A %" PetscInt_FMT " do not match", m, m1);
233:     PetscCheck(n == n1, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local dimensions of V %" PetscInt_FMT " and A %" PetscInt_FMT " do not match", n, n1);
234:   }
235:   if (c) {
236:     PetscMPIInt size, csize;

238:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)U), &size));
239:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)c), &csize));
240:     PetscCall(VecGetSize(c, &k1));
241:     PetscCheck(k == k1, PetscObjectComm((PetscObject)c), PETSC_ERR_ARG_INCOMP, "The length of c %" PetscInt_FMT " does not match the number of columns of U and V (%" PetscInt_FMT ")", k1, k);
242:     PetscCheck(csize == 1 || csize == size, PetscObjectComm((PetscObject)c), PETSC_ERR_ARG_INCOMP, "U and c must have the same communicator size %d != %d", size, csize);
243:   }
244:   PetscCall(MatSetSizes(N, m, n, PETSC_DECIDE, PETSC_DECIDE));

246:   PetscUseMethod(N, "MatLRCSetMats_C", (Mat, Mat, Mat, Vec, Mat), (N, A, U, c, V));
247:   PetscFunctionReturn(PETSC_SUCCESS);
248: }

250: static PetscErrorCode MatSetUp_LRC(Mat N)
251: {
252:   Mat_LRC    *Na = (Mat_LRC *)N->data;
253:   Mat         A  = Na->A;
254:   Mat         U  = Na->U;
255:   Mat         V  = Na->V;
256:   Vec         c  = Na->c;
257:   Mat         Uloc;
258:   PetscMPIInt size, csize = 0;
259:   PetscBool   sym = (PetscBool)(U == V), dummy;

261:   PetscFunctionBegin;
262:   PetscCall(MatSetVecType(N, U->defaultvectype));
263:   // Flag matrix as symmetric if A is symmetric and U == V
264:   if (A && sym) PetscCall(MatIsSymmetricKnown(A, &dummy, &sym));
265:   PetscCall(MatSetOption(N, MAT_SYMMETRIC, sym));
266:   PetscCall(MatDenseGetLocalMatrix(Na->U, &Uloc));
267:   PetscCall(MatCreateVecs(Uloc, &Na->work1, NULL));

269:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)U), &size));
270:   if (c) PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)c), &csize));
271:   if (size != 1) {
272:     Mat Vloc;

274:     if (Na->c && csize != 1) { /* scatter parallel vector to sequential */
275:       VecScatter sct;

277:       PetscCall(VecScatterCreateToAll(Na->c, &sct, &c));
278:       PetscCall(VecScatterBegin(sct, Na->c, c, INSERT_VALUES, SCATTER_FORWARD));
279:       PetscCall(VecScatterEnd(sct, Na->c, c, INSERT_VALUES, SCATTER_FORWARD));
280:       PetscCall(VecScatterDestroy(&sct));
281:       PetscCall(VecDestroy(&Na->c));
282:       Na->c = c;
283:     }
284:     PetscCall(MatDenseGetLocalMatrix(Na->V, &Vloc));
285:     PetscCall(VecDuplicate(Na->work1, &Na->work2));
286:     PetscCall(MatCreateVecs(Vloc, NULL, &Na->xl));
287:     PetscCall(MatCreateVecs(Uloc, NULL, &Na->yl));
288:   }
289:   // Internally create a scaling vector if roottypes do not match
290:   if (Na->c) {
291:     VecType   rt1, rt2;
292:     PetscBool match;

294:     PetscCall(VecGetRootType_Private(Na->work1, &rt1));
295:     PetscCall(VecGetRootType_Private(Na->c, &rt2));
296:     PetscCall(PetscStrcmp(rt1, rt2, &match));
297:     if (!match) {
298:       PetscCall(VecDuplicate(Na->c, &c));
299:       PetscCall(VecCopy(Na->c, c));
300:       PetscCall(VecDestroy(&Na->c));
301:       Na->c = c;
302:     }
303:   }
304:   N->assembled    = PETSC_TRUE;
305:   N->preallocated = PETSC_TRUE;
306:   PetscFunctionReturn(PETSC_SUCCESS);
307: }

309: PETSC_EXTERN PetscErrorCode MatCreate_LRC(Mat N)
310: {
311:   Mat_LRC *Na;

313:   PetscFunctionBegin;
314:   PetscCall(PetscObjectChangeTypeName((PetscObject)N, MATLRC));
315:   PetscCall(PetscNew(&Na));
316:   N->data               = (void *)Na;
317:   N->ops->destroy       = MatDestroy_LRC;
318:   N->ops->setup         = MatSetUp_LRC;
319:   N->ops->mult          = MatMult_LRC;
320:   N->ops->multtranspose = MatMultTranspose_LRC;

322:   PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatLRCGetMats_C", MatLRCGetMats_LRC));
323:   PetscCall(PetscObjectComposeFunction((PetscObject)N, "MatLRCSetMats_C", MatLRCSetMats_LRC));
324:   PetscFunctionReturn(PETSC_SUCCESS);
325: }

327: /*MC
328:   MATLRC -  "lrc" - a matrix object that behaves like A + U*C*V'

330:   Note:
331:    The matrix A + U*C*V' is not formed! Rather the matrix  object performs the matrix-vector product `MatMult()`, by first multiplying by
332:    A and then adding the other term.

334:   Level: advanced

336: .seealso: [](ch_matrices), `Mat`, `MatCreateLRC()`, `MatMult()`, `MatLRCGetMats()`, `MatLRCSetMats()`
337: M*/

339: /*@
340:   MatCreateLRC - Creates a new matrix object that behaves like A + U*C*V' of type `MATLRC`

342:   Collective

344:   Input Parameters:
345: + A - the (sparse) matrix (can be `NULL`)
346: . U - dense rectangular (tall and skinny) matrix
347: . V - dense rectangular (tall and skinny) matrix
348: - c - a vector containing the diagonal of C (can be `NULL`)

350:   Output Parameter:
351: . N - the matrix that represents A + U*C*V'

353:   Level: intermediate

355:   Notes:
356:   The matrix A + U*C*V' is not formed! Rather the new matrix
357:   object performs the matrix-vector product `MatMult()`, by first multiplying by
358:   A and then adding the other term.

360:   `C` is a diagonal matrix (represented as a vector) of order k,
361:   where k is the number of columns of both `U` and `V`.

363:   If `A` is `NULL` then the new object behaves like a low-rank matrix U*C*V'.

365:   Use `V`=`U` (or `V`=`NULL`) for a symmetric low-rank correction, A + U*C*U'.

367:   If `c` is `NULL` then the low-rank correction is just U*V'.
368:   If a sequential `c` vector is used for a parallel matrix,
369:   PETSc assumes that the values of the vector are consistently set across processors.

371: .seealso: [](ch_matrices), `Mat`, `MATLRC`, `MatLRCGetMats()`
372: @*/
373: PetscErrorCode MatCreateLRC(Mat A, Mat U, Vec c, Mat V, Mat *N)
374: {
375:   PetscFunctionBegin;
376:   PetscCall(MatCreate(PetscObjectComm((PetscObject)U), N));
377:   PetscCall(MatSetType(*N, MATLRC));
378:   PetscCall(MatLRCSetMats(*N, A, U, c, V));
379:   PetscCall(MatSetUp(*N));
380:   PetscFunctionReturn(PETSC_SUCCESS);
381: }