Actual source code: multequal.c

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

  3: /*
  4:   n; try the MatMult variant n times
  5:   flg: return the boolean result, equal or not
  6:   t: 0 => no transpose; 1 => transpose; 2 => Hermitian transpose
  7:   add:  0 => no add (e.g., y = Ax);  1 => add third vector (e.g., z = Ax + y); 2 => add update (e.g., y = Ax + y)
  8: */
  9: static PetscErrorCode MatMultEqual_Private(Mat A, Mat B, PetscInt n, PetscBool *flg, PetscInt t, PetscInt add)
 10: {
 11:   Vec         Ax = NULL, Bx = NULL, s1 = NULL, s2 = NULL, Ay = NULL, By = NULL;
 12:   PetscRandom rctx;
 13:   PetscReal   r1, r2, tol = PETSC_SQRT_MACHINE_EPSILON;
 14:   PetscInt    am, an, bm, bn, k;
 15:   PetscScalar none = -1.0;
 16: #if defined(PETSC_USE_INFO)
 17:   const char *sops[] = {"MatMult", "MatMultAdd", "MatMultAdd (update)", "MatMultTranspose", "MatMultTransposeAdd", "MatMultTransposeAdd (update)", "MatMultHermitianTranspose", "MatMultHermitianTransposeAdd", "MatMultHermitianTransposeAdd (update)"};
 18:   const char *sop;
 19: #endif

 21:   PetscFunctionBegin;
 24:   PetscCheckSameComm(A, 1, B, 2);
 26:   PetscAssertPointer(flg, 4);
 29:   PetscCall(MatGetLocalSize(A, &am, &an));
 30:   PetscCall(MatGetLocalSize(B, &bm, &bn));
 31:   PetscCheck(am == bm && an == bn, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat A,Mat B: local dim %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT, am, bm, an, bn);
 32: #if defined(PETSC_USE_INFO)
 33:   sop = sops[add + 3 * t];
 34: #endif
 35:   PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)A), &rctx));
 36:   PetscCall(PetscRandomSetFromOptions(rctx));
 37:   if (t) {
 38:     PetscCall(MatCreateVecs(A, &s1, &Ax));
 39:     PetscCall(MatCreateVecs(B, &s2, &Bx));
 40:   } else {
 41:     PetscCall(MatCreateVecs(A, &Ax, &s1));
 42:     PetscCall(MatCreateVecs(B, &Bx, &s2));
 43:   }
 44:   if (add) {
 45:     PetscCall(VecDuplicate(s1, &Ay));
 46:     PetscCall(VecDuplicate(s2, &By));
 47:   }

 49:   *flg = PETSC_TRUE;
 50:   for (k = 0; k < n; k++) {
 51:     Vec Aadd = NULL, Badd = NULL;

 53:     PetscCall(VecSetRandom(Ax, rctx));
 54:     PetscCall(VecCopy(Ax, Bx));
 55:     if (add) {
 56:       PetscCall(VecSetRandom(Ay, rctx));
 57:       PetscCall(VecCopy(Ay, By));
 58:       Aadd = Ay;
 59:       Badd = By;
 60:       if (add == 2) {
 61:         PetscCall(VecCopy(Ay, s1));
 62:         PetscCall(VecCopy(By, s2));
 63:         Aadd = s1;
 64:         Badd = s2;
 65:       }
 66:     }
 67:     if (t == 1) {
 68:       if (add) {
 69:         PetscCall(MatMultTransposeAdd(A, Ax, Aadd, s1));
 70:         PetscCall(MatMultTransposeAdd(B, Bx, Badd, s2));
 71:       } else {
 72:         PetscCall(MatMultTranspose(A, Ax, s1));
 73:         PetscCall(MatMultTranspose(B, Bx, s2));
 74:       }
 75:     } else if (t == 2) {
 76:       if (add) {
 77:         PetscCall(MatMultHermitianTransposeAdd(A, Ax, Aadd, s1));
 78:         PetscCall(MatMultHermitianTransposeAdd(B, Bx, Badd, s2));
 79:       } else {
 80:         PetscCall(MatMultHermitianTranspose(A, Ax, s1));
 81:         PetscCall(MatMultHermitianTranspose(B, Bx, s2));
 82:       }
 83:     } else {
 84:       if (add) {
 85:         PetscCall(MatMultAdd(A, Ax, Aadd, s1));
 86:         PetscCall(MatMultAdd(B, Bx, Badd, s2));
 87:       } else {
 88:         PetscCall(MatMult(A, Ax, s1));
 89:         PetscCall(MatMult(B, Bx, s2));
 90:       }
 91:     }
 92:     PetscCall(VecNorm(s2, NORM_INFINITY, &r2));
 93:     if (r2 < tol) {
 94:       PetscCall(VecNorm(s1, NORM_INFINITY, &r1));
 95:     } else {
 96:       PetscCall(VecAXPY(s2, none, s1));
 97:       PetscCall(VecNorm(s2, NORM_INFINITY, &r1));
 98:       r1 /= r2;
 99:     }
100:     if (r1 > tol) {
101:       *flg = PETSC_FALSE;
102:       PetscCall(PetscInfo(A, "Error: %" PetscInt_FMT "-th %s() %g\n", k, sop, (double)r1));
103:       break;
104:     }
105:   }
106:   PetscCall(PetscRandomDestroy(&rctx));
107:   PetscCall(VecDestroy(&Ax));
108:   PetscCall(VecDestroy(&Bx));
109:   PetscCall(VecDestroy(&Ay));
110:   PetscCall(VecDestroy(&By));
111:   PetscCall(VecDestroy(&s1));
112:   PetscCall(VecDestroy(&s2));
113:   PetscFunctionReturn(PETSC_SUCCESS);
114: }

116: static PetscErrorCode MatMatMultEqual_Private(Mat A, Mat B, Mat C, PetscInt n, PetscBool *flg, PetscBool At, PetscBool Bt)
117: {
118:   Vec         Ax, Bx, Cx, s1, s2, s3;
119:   PetscRandom rctx;
120:   PetscReal   r1, r2, tol = PETSC_SQRT_MACHINE_EPSILON;
121:   PetscInt    am, an, bm, bn, cm, cn, k;
122:   PetscScalar none = -1.0;
123: #if defined(PETSC_USE_INFO)
124:   const char *sops[] = {"MatMatMult", "MatTransposeMatMult", "MatMatTransposeMult", "MatTransposeMatTransposeMult"};
125:   const char *sop;
126: #endif

128:   PetscFunctionBegin;
131:   PetscCheckSameComm(A, 1, B, 2);
133:   PetscCheckSameComm(A, 1, C, 3);
135:   PetscAssertPointer(flg, 5);
138:   PetscCall(MatGetLocalSize(A, &am, &an));
139:   PetscCall(MatGetLocalSize(B, &bm, &bn));
140:   PetscCall(MatGetLocalSize(C, &cm, &cn));
141:   if (At) {
142:     PetscInt tt = an;
143:     an          = am;
144:     am          = tt;
145:   }
146:   if (Bt) {
147:     PetscInt tt = bn;
148:     bn          = bm;
149:     bm          = tt;
150:   }
151:   PetscCheck(an == bm && am == cm && bn == cn, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat A, B, C local dim %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT, am, an, bm, bn, cm, cn);

153: #if defined(PETSC_USE_INFO)
154:   sop = sops[(At ? 1 : 0) + 2 * (Bt ? 1 : 0)];
155: #endif
156:   PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)C), &rctx));
157:   PetscCall(PetscRandomSetFromOptions(rctx));
158:   if (Bt) {
159:     PetscCall(MatCreateVecs(B, &s1, &Bx));
160:   } else {
161:     PetscCall(MatCreateVecs(B, &Bx, &s1));
162:   }
163:   if (At) {
164:     PetscCall(MatCreateVecs(A, &s2, &Ax));
165:   } else {
166:     PetscCall(MatCreateVecs(A, &Ax, &s2));
167:   }
168:   PetscCall(MatCreateVecs(C, &Cx, &s3));

170:   *flg = PETSC_TRUE;
171:   for (k = 0; k < n; k++) {
172:     PetscCall(VecSetRandom(Bx, rctx));
173:     if (Bt) {
174:       PetscCall(MatMultTranspose(B, Bx, s1));
175:     } else {
176:       PetscCall(MatMult(B, Bx, s1));
177:     }
178:     PetscCall(VecCopy(s1, Ax));
179:     if (At) {
180:       PetscCall(MatMultTranspose(A, Ax, s2));
181:     } else {
182:       PetscCall(MatMult(A, Ax, s2));
183:     }
184:     PetscCall(VecCopy(Bx, Cx));
185:     PetscCall(MatMult(C, Cx, s3));

187:     PetscCall(VecNorm(s2, NORM_INFINITY, &r2));
188:     if (r2 < tol) {
189:       PetscCall(VecNorm(s3, NORM_INFINITY, &r1));
190:     } else {
191:       PetscCall(VecAXPY(s2, none, s3));
192:       PetscCall(VecNorm(s2, NORM_INFINITY, &r1));
193:       r1 /= r2;
194:     }
195:     if (r1 > tol) {
196:       *flg = PETSC_FALSE;
197:       PetscCall(PetscInfo(A, "Error: %" PetscInt_FMT "-th %s %g\n", k, sop, (double)r1));
198:       break;
199:     }
200:   }
201:   PetscCall(PetscRandomDestroy(&rctx));
202:   PetscCall(VecDestroy(&Ax));
203:   PetscCall(VecDestroy(&Bx));
204:   PetscCall(VecDestroy(&Cx));
205:   PetscCall(VecDestroy(&s1));
206:   PetscCall(VecDestroy(&s2));
207:   PetscCall(VecDestroy(&s3));
208:   PetscFunctionReturn(PETSC_SUCCESS);
209: }

211: /*@
212:   MatMultEqual - Compares matrix-vector products of two matrices.

214:   Collective

216:   Input Parameters:
217: + A - the first matrix
218: . B - the second matrix
219: - n - number of random vectors to be tested

221:   Output Parameter:
222: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

224:   Level: intermediate

226: .seealso: `Mat`, `MatMultAddEqual()`, `MatMultTransposeEqual()`, `MatMultTransposeAddEqual()`, `MatIsLinear()`
227: @*/
228: PetscErrorCode MatMultEqual(Mat A, Mat B, PetscInt n, PetscBool *flg)
229: {
230:   PetscFunctionBegin;
231:   PetscCall(MatMultEqual_Private(A, B, n, flg, 0, 0));
232:   PetscFunctionReturn(PETSC_SUCCESS);
233: }

235: /*@
236:   MatMultAddEqual - Compares matrix-vector product plus vector add of two matrices.

238:   Collective

240:   Input Parameters:
241: + A - the first matrix
242: . B - the second matrix
243: - n - number of random vectors to be tested

245:   Output Parameter:
246: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

248:   Level: intermediate

250: .seealso: `Mat`, `MatMultEqual()`, `MatMultTransposeEqual()`, `MatMultTransposeAddEqual()`
251: @*/
252: PetscErrorCode MatMultAddEqual(Mat A, Mat B, PetscInt n, PetscBool *flg)
253: {
254:   PetscFunctionBegin;
255:   PetscCall(MatMultEqual_Private(A, B, n, flg, 0, 1));
256:   PetscCall(MatMultEqual_Private(A, B, n, flg, 0, 2));
257:   PetscFunctionReturn(PETSC_SUCCESS);
258: }

260: /*@
261:   MatMultTransposeEqual - Compares matrix-vector products of two matrices.

263:   Collective

265:   Input Parameters:
266: + A - the first matrix
267: . B - the second matrix
268: - n - number of random vectors to be tested

270:   Output Parameter:
271: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

273:   Level: intermediate

275: .seealso: `Mat`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeAddEqual()`
276: @*/
277: PetscErrorCode MatMultTransposeEqual(Mat A, Mat B, PetscInt n, PetscBool *flg)
278: {
279:   PetscFunctionBegin;
280:   PetscCall(MatMultEqual_Private(A, B, n, flg, 1, 0));
281:   PetscFunctionReturn(PETSC_SUCCESS);
282: }

284: /*@
285:   MatMultTransposeAddEqual - Compares matrix-vector products of two matrices.

287:   Collective

289:   Input Parameters:
290: + A - the first matrix
291: . B - the second matrix
292: - n - number of random vectors to be tested

294:   Output Parameter:
295: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

297:   Level: intermediate

299: .seealso: `Mat`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
300: @*/
301: PetscErrorCode MatMultTransposeAddEqual(Mat A, Mat B, PetscInt n, PetscBool *flg)
302: {
303:   PetscFunctionBegin;
304:   PetscCall(MatMultEqual_Private(A, B, n, flg, 1, 1));
305:   PetscCall(MatMultEqual_Private(A, B, n, flg, 1, 2));
306:   PetscFunctionReturn(PETSC_SUCCESS);
307: }

309: /*@
310:   MatMultHermitianTransposeEqual - Compares matrix-vector products of two matrices.

312:   Collective

314:   Input Parameters:
315: + A - the first matrix
316: . B - the second matrix
317: - n - number of random vectors to be tested

319:   Output Parameter:
320: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

322:   Level: intermediate

324: .seealso: `Mat`, `MatMatMultEqual()`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
325: @*/
326: PetscErrorCode MatMultHermitianTransposeEqual(Mat A, Mat B, PetscInt n, PetscBool *flg)
327: {
328:   PetscFunctionBegin;
329:   PetscCall(MatMultEqual_Private(A, B, n, flg, 2, 0));
330:   PetscFunctionReturn(PETSC_SUCCESS);
331: }

333: /*@
334:   MatMultHermitianTransposeAddEqual - Compares matrix-vector products of two matrices.

336:   Collective

338:   Input Parameters:
339: + A - the first matrix
340: . B - the second matrix
341: - n - number of random vectors to be tested

343:   Output Parameter:
344: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

346:   Level: intermediate

348: .seealso: `Mat`, `MatMatMultEqual()`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
349: @*/
350: PetscErrorCode MatMultHermitianTransposeAddEqual(Mat A, Mat B, PetscInt n, PetscBool *flg)
351: {
352:   PetscFunctionBegin;
353:   PetscCall(MatMultEqual_Private(A, B, n, flg, 2, 1));
354:   PetscCall(MatMultEqual_Private(A, B, n, flg, 2, 2));
355:   PetscFunctionReturn(PETSC_SUCCESS);
356: }

358: /*@
359:   MatMatMultEqual - Test A*B*x = C*x for n random vector x

361:   Collective

363:   Input Parameters:
364: + A - the first matrix
365: . B - the second matrix
366: . C - the third matrix
367: - n - number of random vectors to be tested

369:   Output Parameter:
370: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

372:   Level: intermediate

374: .seealso: `Mat`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
375: @*/
376: PetscErrorCode MatMatMultEqual(Mat A, Mat B, Mat C, PetscInt n, PetscBool *flg)
377: {
378:   PetscFunctionBegin;
379:   PetscCall(MatMatMultEqual_Private(A, B, C, n, flg, PETSC_FALSE, PETSC_FALSE));
380:   PetscFunctionReturn(PETSC_SUCCESS);
381: }

383: /*@
384:   MatTransposeMatMultEqual - Test A^T*B*x = C*x for n random vector x

386:   Collective

388:   Input Parameters:
389: + A - the first matrix
390: . B - the second matrix
391: . C - the third matrix
392: - n - number of random vectors to be tested

394:   Output Parameter:
395: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

397:   Level: intermediate

399: .seealso: `Mat`, `MatMatMultEqual()`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
400: @*/
401: PetscErrorCode MatTransposeMatMultEqual(Mat A, Mat B, Mat C, PetscInt n, PetscBool *flg)
402: {
403:   PetscFunctionBegin;
404:   PetscCall(MatMatMultEqual_Private(A, B, C, n, flg, PETSC_TRUE, PETSC_FALSE));
405:   PetscFunctionReturn(PETSC_SUCCESS);
406: }

408: /*@
409:   MatMatTransposeMultEqual - Test A*B^T*x = C*x for n random vector x

411:   Collective

413:   Input Parameters:
414: + A - the first matrix
415: . B - the second matrix
416: . C - the third matrix
417: - n - number of random vectors to be tested

419:   Output Parameter:
420: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

422:   Level: intermediate

424: .seealso: `Mat`, `MatMatMultEqual()`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
425: @*/
426: PetscErrorCode MatMatTransposeMultEqual(Mat A, Mat B, Mat C, PetscInt n, PetscBool *flg)
427: {
428:   PetscFunctionBegin;
429:   PetscCall(MatMatMultEqual_Private(A, B, C, n, flg, PETSC_FALSE, PETSC_TRUE));
430:   PetscFunctionReturn(PETSC_SUCCESS);
431: }

433: static PetscErrorCode MatProjMultEqual_Private(Mat A, Mat B, Mat C, PetscInt n, PetscBool rart, PetscBool *flg)
434: {
435:   Vec         x, v1, v2, v3, v4, Cx, Bx;
436:   PetscReal   norm_abs, norm_rel, tol = PETSC_SQRT_MACHINE_EPSILON;
437:   PetscInt    i, am, an, bm, bn, cm, cn;
438:   PetscRandom rdm;
439:   PetscScalar none = -1.0;

441:   PetscFunctionBegin;
442:   PetscCall(MatGetLocalSize(A, &am, &an));
443:   PetscCall(MatGetLocalSize(B, &bm, &bn));
444:   if (rart) {
445:     PetscInt t = bm;
446:     bm         = bn;
447:     bn         = t;
448:   }
449:   PetscCall(MatGetLocalSize(C, &cm, &cn));
450:   PetscCheck(an == bm && bn == cm && bn == cn, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat A, B, C local dim %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT, am, an, bm, bn, cm, cn);

452:   /* Create left vector of A: v2 */
453:   PetscCall(MatCreateVecs(A, &Bx, &v2));

455:   /* Create right vectors of B: x, v3, v4 */
456:   if (rart) {
457:     PetscCall(MatCreateVecs(B, &v1, &x));
458:   } else {
459:     PetscCall(MatCreateVecs(B, &x, &v1));
460:   }
461:   PetscCall(VecDuplicate(x, &v3));

463:   PetscCall(MatCreateVecs(C, &Cx, &v4));
464:   PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rdm));
465:   PetscCall(PetscRandomSetFromOptions(rdm));

467:   *flg = PETSC_TRUE;
468:   for (i = 0; i < n; i++) {
469:     PetscCall(VecSetRandom(x, rdm));
470:     PetscCall(VecCopy(x, Cx));
471:     PetscCall(MatMult(C, Cx, v4)); /* v4 = C*x   */
472:     if (rart) {
473:       PetscCall(MatMultTranspose(B, x, v1));
474:     } else {
475:       PetscCall(MatMult(B, x, v1));
476:     }
477:     PetscCall(VecCopy(v1, Bx));
478:     PetscCall(MatMult(A, Bx, v2)); /* v2 = A*B*x */
479:     PetscCall(VecCopy(v2, v1));
480:     if (rart) {
481:       PetscCall(MatMult(B, v1, v3)); /* v3 = R*A*R^t*x */
482:     } else {
483:       PetscCall(MatMultTranspose(B, v1, v3)); /* v3 = Bt*A*B*x */
484:     }
485:     PetscCall(VecNorm(v4, NORM_2, &norm_abs));
486:     PetscCall(VecAXPY(v4, none, v3));
487:     PetscCall(VecNorm(v4, NORM_2, &norm_rel));

489:     if (norm_abs > tol) norm_rel /= norm_abs;
490:     if (norm_rel > tol) {
491:       *flg = PETSC_FALSE;
492:       PetscCall(PetscInfo(A, "Error: %" PetscInt_FMT "-th Mat%sMult() %g\n", i, rart ? "RARt" : "PtAP", (double)norm_rel));
493:       break;
494:     }
495:   }

497:   PetscCall(PetscRandomDestroy(&rdm));
498:   PetscCall(VecDestroy(&x));
499:   PetscCall(VecDestroy(&Bx));
500:   PetscCall(VecDestroy(&Cx));
501:   PetscCall(VecDestroy(&v1));
502:   PetscCall(VecDestroy(&v2));
503:   PetscCall(VecDestroy(&v3));
504:   PetscCall(VecDestroy(&v4));
505:   PetscFunctionReturn(PETSC_SUCCESS);
506: }

508: /*@
509:   MatPtAPMultEqual - Compares matrix-vector products of C = Bt*A*B

511:   Collective

513:   Input Parameters:
514: + A - the first matrix
515: . B - the second matrix
516: . C - the third matrix
517: - n - number of random vectors to be tested

519:   Output Parameter:
520: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

522:   Level: intermediate

524: .seealso: `Mat`, `MatMatMultEqual()`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
525: @*/
526: PetscErrorCode MatPtAPMultEqual(Mat A, Mat B, Mat C, PetscInt n, PetscBool *flg)
527: {
528:   PetscFunctionBegin;
529:   PetscCall(MatProjMultEqual_Private(A, B, C, n, PETSC_FALSE, flg));
530:   PetscFunctionReturn(PETSC_SUCCESS);
531: }

533: /*@
534:   MatRARtMultEqual - Compares matrix-vector products of C = B*A*B^t

536:   Collective

538:   Input Parameters:
539: + A - the first matrix
540: . B - the second matrix
541: . C - the third matrix
542: - n - number of random vectors to be tested

544:   Output Parameter:
545: . flg - `PETSC_TRUE` if the products are equal; `PETSC_FALSE` otherwise.

547:   Level: intermediate

549: .seealso: `Mat`, `MatMatMultEqual()`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
550: @*/
551: PetscErrorCode MatRARtMultEqual(Mat A, Mat B, Mat C, PetscInt n, PetscBool *flg)
552: {
553:   PetscFunctionBegin;
554:   PetscCall(MatProjMultEqual_Private(A, B, C, n, PETSC_TRUE, flg));
555:   PetscFunctionReturn(PETSC_SUCCESS);
556: }

558: /*@
559:   MatIsLinear - Check if a shell matrix `A` is a linear operator.

561:   Collective

563:   Input Parameters:
564: + A - the shell matrix
565: - n - number of random vectors to be tested

567:   Output Parameter:
568: . flg - `PETSC_TRUE` if the shell matrix is linear; `PETSC_FALSE` otherwise.

570:   Level: intermediate

572: .seealso: `Mat`, `MatMatMultEqual()`, `MatMultEqual()`, `MatMultAddEqual()`, `MatMultTransposeEqual()`
573: @*/
574: PetscErrorCode MatIsLinear(Mat A, PetscInt n, PetscBool *flg)
575: {
576:   Vec         x, y, s1, s2;
577:   PetscRandom rctx;
578:   PetscScalar a;
579:   PetscInt    k;
580:   PetscReal   norm, normA;
581:   MPI_Comm    comm;
582:   PetscMPIInt rank;

584:   PetscFunctionBegin;
586:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
587:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

589:   PetscCall(PetscRandomCreate(comm, &rctx));
590:   PetscCall(PetscRandomSetFromOptions(rctx));
591:   PetscCall(MatCreateVecs(A, &x, &s1));
592:   PetscCall(VecDuplicate(x, &y));
593:   PetscCall(VecDuplicate(s1, &s2));

595:   *flg = PETSC_TRUE;
596:   for (k = 0; k < n; k++) {
597:     PetscCall(VecSetRandom(x, rctx));
598:     PetscCall(VecSetRandom(y, rctx));
599:     if (rank == 0) PetscCall(PetscRandomGetValue(rctx, &a));
600:     PetscCallMPI(MPI_Bcast(&a, 1, MPIU_SCALAR, 0, comm));

602:     /* s2 = a*A*x + A*y */
603:     PetscCall(MatMult(A, y, s2));  /* s2 = A*y */
604:     PetscCall(MatMult(A, x, s1));  /* s1 = A*x */
605:     PetscCall(VecAXPY(s2, a, s1)); /* s2 = a s1 + s2 */

607:     /* s1 = A * (a x + y) */
608:     PetscCall(VecAXPY(y, a, x)); /* y = a x + y */
609:     PetscCall(MatMult(A, y, s1));
610:     PetscCall(VecNorm(s1, NORM_INFINITY, &normA));

612:     PetscCall(VecAXPY(s2, -1.0, s1)); /* s2 = - s1 + s2 */
613:     PetscCall(VecNorm(s2, NORM_INFINITY, &norm));
614:     if (norm / normA > 100. * PETSC_MACHINE_EPSILON) {
615:       *flg = PETSC_FALSE;
616:       PetscCall(PetscInfo(A, "Error: %" PetscInt_FMT "-th |A*(ax+y) - (a*A*x+A*y)|/|A(ax+y)| %g > tol %g\n", k, (double)(norm / normA), (double)(100. * PETSC_MACHINE_EPSILON)));
617:       break;
618:     }
619:   }
620:   PetscCall(PetscRandomDestroy(&rctx));
621:   PetscCall(VecDestroy(&x));
622:   PetscCall(VecDestroy(&y));
623:   PetscCall(VecDestroy(&s1));
624:   PetscCall(VecDestroy(&s2));
625:   PetscFunctionReturn(PETSC_SUCCESS);
626: }