Actual source code: ex74.c


  2: static char help[] = "Tests the various sequential routines in MATSEQSBAIJ format.\n";

  4: #include <petscmat.h>

  6: int main(int argc, char **args)
  7: {
  8:   PetscMPIInt   size;
  9:   Vec           x, y, b, s1, s2;
 10:   Mat           A;                     /* linear system matrix */
 11:   Mat           sA, sB, sFactor, B, C; /* symmetric matrices */
 12:   PetscInt      n, mbs = 16, bs = 1, nz = 3, prob = 1, i, j, k1, k2, col[3], lf, block, row, Ii, J, n1, inc;
 13:   PetscReal     norm1, norm2, rnorm, tol = 10 * PETSC_SMALL;
 14:   PetscScalar   neg_one = -1.0, four = 4.0, value[3];
 15:   IS            perm, iscol;
 16:   PetscRandom   rdm;
 17:   PetscBool     doIcc = PETSC_TRUE, equal;
 18:   MatInfo       minfo1, minfo2;
 19:   MatFactorInfo factinfo;
 20:   MatType       type;

 22:   PetscFunctionBeginUser;
 23:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 24:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
 25:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
 26:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-bs", &bs, NULL));
 27:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-mbs", &mbs, NULL));

 29:   n = mbs * bs;
 30:   PetscCall(MatCreate(PETSC_COMM_SELF, &A));
 31:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
 32:   PetscCall(MatSetType(A, MATSEQBAIJ));
 33:   PetscCall(MatSetFromOptions(A));
 34:   PetscCall(MatSeqBAIJSetPreallocation(A, bs, nz, NULL));

 36:   PetscCall(MatCreate(PETSC_COMM_SELF, &sA));
 37:   PetscCall(MatSetSizes(sA, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
 38:   PetscCall(MatSetType(sA, MATSEQSBAIJ));
 39:   PetscCall(MatSetFromOptions(sA));
 40:   PetscCall(MatGetType(sA, &type));
 41:   PetscCall(PetscObjectTypeCompare((PetscObject)sA, MATSEQSBAIJ, &doIcc));
 42:   PetscCall(MatSeqSBAIJSetPreallocation(sA, bs, nz, NULL));
 43:   PetscCall(MatSetOption(sA, MAT_IGNORE_LOWER_TRIANGULAR, PETSC_TRUE));

 45:   /* Test MatGetOwnershipRange() */
 46:   PetscCall(MatGetOwnershipRange(A, &Ii, &J));
 47:   PetscCall(MatGetOwnershipRange(sA, &i, &j));
 48:   if (i - Ii || j - J) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: MatGetOwnershipRange() in MatSBAIJ format\n"));

 50:   /* Assemble matrix */
 51:   if (bs == 1) {
 52:     PetscCall(PetscOptionsGetInt(NULL, NULL, "-test_problem", &prob, NULL));
 53:     if (prob == 1) { /* tridiagonal matrix */
 54:       value[0] = -1.0;
 55:       value[1] = 2.0;
 56:       value[2] = -1.0;
 57:       for (i = 1; i < n - 1; i++) {
 58:         col[0] = i - 1;
 59:         col[1] = i;
 60:         col[2] = i + 1;
 61:         PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
 62:         PetscCall(MatSetValues(sA, 1, &i, 3, col, value, INSERT_VALUES));
 63:       }
 64:       i      = n - 1;
 65:       col[0] = 0;
 66:       col[1] = n - 2;
 67:       col[2] = n - 1;

 69:       value[0] = 0.1;
 70:       value[1] = -1;
 71:       value[2] = 2;

 73:       PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
 74:       PetscCall(MatSetValues(sA, 1, &i, 3, col, value, INSERT_VALUES));

 76:       i        = 0;
 77:       col[0]   = n - 1;
 78:       col[1]   = 1;
 79:       col[2]   = 0;
 80:       value[0] = 0.1;
 81:       value[1] = -1.0;
 82:       value[2] = 2;

 84:       PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
 85:       PetscCall(MatSetValues(sA, 1, &i, 3, col, value, INSERT_VALUES));

 87:     } else if (prob == 2) { /* matrix for the five point stencil */
 88:       n1 = (PetscInt)(PetscSqrtReal((PetscReal)n) + 0.001);
 89:       PetscCheck(n1 * n1 == n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "sqrt(n) must be a positive integer!");
 90:       for (i = 0; i < n1; i++) {
 91:         for (j = 0; j < n1; j++) {
 92:           Ii = j + n1 * i;
 93:           if (i > 0) {
 94:             J = Ii - n1;
 95:             PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
 96:             PetscCall(MatSetValues(sA, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
 97:           }
 98:           if (i < n1 - 1) {
 99:             J = Ii + n1;
100:             PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
101:             PetscCall(MatSetValues(sA, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
102:           }
103:           if (j > 0) {
104:             J = Ii - 1;
105:             PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
106:             PetscCall(MatSetValues(sA, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
107:           }
108:           if (j < n1 - 1) {
109:             J = Ii + 1;
110:             PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
111:             PetscCall(MatSetValues(sA, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
112:           }
113:           PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &four, INSERT_VALUES));
114:           PetscCall(MatSetValues(sA, 1, &Ii, 1, &Ii, &four, INSERT_VALUES));
115:         }
116:       }
117:     }

119:   } else { /* bs > 1 */
120:     for (block = 0; block < n / bs; block++) {
121:       /* diagonal blocks */
122:       value[0] = -1.0;
123:       value[1] = 4.0;
124:       value[2] = -1.0;
125:       for (i = 1 + block * bs; i < bs - 1 + block * bs; i++) {
126:         col[0] = i - 1;
127:         col[1] = i;
128:         col[2] = i + 1;
129:         PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
130:         PetscCall(MatSetValues(sA, 1, &i, 3, col, value, INSERT_VALUES));
131:       }
132:       i      = bs - 1 + block * bs;
133:       col[0] = bs - 2 + block * bs;
134:       col[1] = bs - 1 + block * bs;

136:       value[0] = -1.0;
137:       value[1] = 4.0;

139:       PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
140:       PetscCall(MatSetValues(sA, 1, &i, 2, col, value, INSERT_VALUES));

142:       i      = 0 + block * bs;
143:       col[0] = 0 + block * bs;
144:       col[1] = 1 + block * bs;

146:       value[0] = 4.0;
147:       value[1] = -1.0;

149:       PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
150:       PetscCall(MatSetValues(sA, 1, &i, 2, col, value, INSERT_VALUES));
151:     }
152:     /* off-diagonal blocks */
153:     value[0] = -1.0;
154:     for (i = 0; i < (n / bs - 1) * bs; i++) {
155:       col[0] = i + bs;

157:       PetscCall(MatSetValues(A, 1, &i, 1, col, value, INSERT_VALUES));
158:       PetscCall(MatSetValues(sA, 1, &i, 1, col, value, INSERT_VALUES));

160:       col[0] = i;
161:       row    = i + bs;

163:       PetscCall(MatSetValues(A, 1, &row, 1, col, value, INSERT_VALUES));
164:       PetscCall(MatSetValues(sA, 1, &row, 1, col, value, INSERT_VALUES));
165:     }
166:   }
167:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
168:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

170:   PetscCall(MatAssemblyBegin(sA, MAT_FINAL_ASSEMBLY));
171:   PetscCall(MatAssemblyEnd(sA, MAT_FINAL_ASSEMBLY));

173:   /* Test MatGetInfo() of A and sA */
174:   PetscCall(MatGetInfo(A, MAT_LOCAL, &minfo1));
175:   PetscCall(MatGetInfo(sA, MAT_LOCAL, &minfo2));
176:   i  = (int)(minfo1.nz_used - minfo2.nz_used);
177:   j  = (int)(minfo1.nz_allocated - minfo2.nz_allocated);
178:   k1 = (int)(minfo1.nz_allocated - minfo1.nz_used);
179:   k2 = (int)(minfo2.nz_allocated - minfo2.nz_used);
180:   if (i < 0 || j < 0 || k1 < 0 || k2 < 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error (compare A and sA): MatGetInfo()\n"));

182:   /* Test MatDuplicate() */
183:   PetscCall(MatNorm(A, NORM_FROBENIUS, &norm1));
184:   PetscCall(MatDuplicate(sA, MAT_COPY_VALUES, &sB));
185:   PetscCall(MatEqual(sA, sB, &equal));
186:   PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_ARG_NOTSAMETYPE, "Error in MatDuplicate()");

188:   /* Test MatNorm() */
189:   PetscCall(MatNorm(A, NORM_FROBENIUS, &norm1));
190:   PetscCall(MatNorm(sB, NORM_FROBENIUS, &norm2));
191:   rnorm = PetscAbsReal(norm1 - norm2) / norm2;
192:   if (rnorm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: MatNorm_FROBENIUS, NormA=%16.14e NormsB=%16.14e\n", (double)norm1, (double)norm2));
193:   PetscCall(MatNorm(A, NORM_INFINITY, &norm1));
194:   PetscCall(MatNorm(sB, NORM_INFINITY, &norm2));
195:   rnorm = PetscAbsReal(norm1 - norm2) / norm2;
196:   if (rnorm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n", (double)norm1, (double)norm2));
197:   PetscCall(MatNorm(A, NORM_1, &norm1));
198:   PetscCall(MatNorm(sB, NORM_1, &norm2));
199:   rnorm = PetscAbsReal(norm1 - norm2) / norm2;
200:   if (rnorm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n", (double)norm1, (double)norm2));

202:   /* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
203:   PetscCall(MatGetInfo(A, MAT_LOCAL, &minfo1));
204:   PetscCall(MatGetInfo(sB, MAT_LOCAL, &minfo2));
205:   i  = (int)(minfo1.nz_used - minfo2.nz_used);
206:   j  = (int)(minfo1.nz_allocated - minfo2.nz_allocated);
207:   k1 = (int)(minfo1.nz_allocated - minfo1.nz_used);
208:   k2 = (int)(minfo2.nz_allocated - minfo2.nz_used);
209:   if (i < 0 || j < 0 || k1 < 0 || k2 < 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error(compare A and sB): MatGetInfo()\n"));

211:   PetscCall(MatGetSize(A, &Ii, &J));
212:   PetscCall(MatGetSize(sB, &i, &j));
213:   if (i - Ii || j - J) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: MatGetSize()\n"));

215:   PetscCall(MatGetBlockSize(A, &Ii));
216:   PetscCall(MatGetBlockSize(sB, &i));
217:   if (i - Ii) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: MatGetBlockSize()\n"));

219:   PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm));
220:   PetscCall(PetscRandomSetFromOptions(rdm));
221:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &x));
222:   PetscCall(VecDuplicate(x, &s1));
223:   PetscCall(VecDuplicate(x, &s2));
224:   PetscCall(VecDuplicate(x, &y));
225:   PetscCall(VecDuplicate(x, &b));
226:   PetscCall(VecSetRandom(x, rdm));

228:   /* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
229: #if !defined(PETSC_USE_COMPLEX)
230:   /* Scaling matrix with complex numbers results non-spd matrix,
231:      causing crash of MatForwardSolve() and MatBackwardSolve() */
232:   PetscCall(MatDiagonalScale(A, x, x));
233:   PetscCall(MatDiagonalScale(sB, x, x));
234:   PetscCall(MatMultEqual(A, sB, 10, &equal));
235:   PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_ARG_NOTSAMETYPE, "Error in MatDiagonalScale");

237:   PetscCall(MatGetDiagonal(A, s1));
238:   PetscCall(MatGetDiagonal(sB, s2));
239:   PetscCall(VecAXPY(s2, neg_one, s1));
240:   PetscCall(VecNorm(s2, NORM_1, &norm1));
241:   if (norm1 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error:MatGetDiagonal(), ||s1-s2||=%g\n", (double)norm1));

243:   {
244:     PetscScalar alpha = 0.1;
245:     PetscCall(MatScale(A, alpha));
246:     PetscCall(MatScale(sB, alpha));
247:   }
248: #endif

250:   /* Test MatGetRowMaxAbs() */
251:   PetscCall(MatGetRowMaxAbs(A, s1, NULL));
252:   PetscCall(MatGetRowMaxAbs(sB, s2, NULL));
253:   PetscCall(VecNorm(s1, NORM_1, &norm1));
254:   PetscCall(VecNorm(s2, NORM_1, &norm2));
255:   norm1 -= norm2;
256:   if (norm1 < -tol || norm1 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error:MatGetRowMaxAbs() \n"));

258:   /* Test MatMult() */
259:   for (i = 0; i < 40; i++) {
260:     PetscCall(VecSetRandom(x, rdm));
261:     PetscCall(MatMult(A, x, s1));
262:     PetscCall(MatMult(sB, x, s2));
263:     PetscCall(VecNorm(s1, NORM_1, &norm1));
264:     PetscCall(VecNorm(s2, NORM_1, &norm2));
265:     norm1 -= norm2;
266:     if (norm1 < -tol || norm1 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: MatMult(), norm1-norm2: %g\n", (double)norm1));
267:   }

269:   /* MatMultAdd() */
270:   for (i = 0; i < 40; i++) {
271:     PetscCall(VecSetRandom(x, rdm));
272:     PetscCall(VecSetRandom(y, rdm));
273:     PetscCall(MatMultAdd(A, x, y, s1));
274:     PetscCall(MatMultAdd(sB, x, y, s2));
275:     PetscCall(VecNorm(s1, NORM_1, &norm1));
276:     PetscCall(VecNorm(s2, NORM_1, &norm2));
277:     norm1 -= norm2;
278:     if (norm1 < -tol || norm1 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error:MatMultAdd(), norm1-norm2: %g\n", (double)norm1));
279:   }

281:   /* Test MatMatMult() for sbaij and dense matrices */
282:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n, 5 * n, NULL, &B));
283:   PetscCall(MatSetRandom(B, rdm));
284:   PetscCall(MatMatMult(sA, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &C));
285:   PetscCall(MatMatMultEqual(sA, B, C, 5 * n, &equal));
286:   PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatMatMult()");
287:   PetscCall(MatDestroy(&C));
288:   PetscCall(MatDestroy(&B));

290:   /* Test MatCholeskyFactor(), MatICCFactor() with natural ordering */
291:   PetscCall(MatGetOrdering(A, MATORDERINGNATURAL, &perm, &iscol));
292:   PetscCall(ISDestroy(&iscol));
293:   norm1 = tol;
294:   inc   = bs;

296:   /* initialize factinfo */
297:   PetscCall(PetscMemzero(&factinfo, sizeof(MatFactorInfo)));

299:   for (lf = -1; lf < 10; lf += inc) {
300:     if (lf == -1) { /* Cholesky factor of sB (duplicate sA) */
301:       factinfo.fill = 5.0;

303:       PetscCall(MatGetFactor(sB, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &sFactor));
304:       PetscCall(MatCholeskyFactorSymbolic(sFactor, sB, perm, &factinfo));
305:     } else if (!doIcc) break;
306:     else { /* incomplete Cholesky factor */ factinfo.fill = 5.0;
307:       factinfo.levels                                     = lf;

309:       PetscCall(MatGetFactor(sB, MATSOLVERPETSC, MAT_FACTOR_ICC, &sFactor));
310:       PetscCall(MatICCFactorSymbolic(sFactor, sB, perm, &factinfo));
311:     }
312:     PetscCall(MatCholeskyFactorNumeric(sFactor, sB, &factinfo));
313:     /* MatView(sFactor, PETSC_VIEWER_DRAW_WORLD); */

315:     /* test MatGetDiagonal on numeric factor */
316:     /*
317:     if (lf == -1) {
318:       PetscCall(MatGetDiagonal(sFactor,s1));
319:       printf(" in ex74.c, diag: \n");
320:       PetscCall(VecView(s1,PETSC_VIEWER_STDOUT_SELF));
321:     }
322:     */

324:     PetscCall(MatMult(sB, x, b));

326:     /* test MatForwardSolve() and MatBackwardSolve() */
327:     if (lf == -1) {
328:       PetscCall(MatForwardSolve(sFactor, b, s1));
329:       PetscCall(MatBackwardSolve(sFactor, s1, s2));
330:       PetscCall(VecAXPY(s2, neg_one, x));
331:       PetscCall(VecNorm(s2, NORM_2, &norm2));
332:       if (10 * norm1 < norm2) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatForwardSolve and BackwardSolve: Norm of error=%g, bs=%" PetscInt_FMT "\n", (double)norm2, bs));
333:     }

335:     /* test MatSolve() */
336:     PetscCall(MatSolve(sFactor, b, y));
337:     PetscCall(MatDestroy(&sFactor));
338:     /* Check the error */
339:     PetscCall(VecAXPY(y, neg_one, x));
340:     PetscCall(VecNorm(y, NORM_2, &norm2));
341:     if (10 * norm1 < norm2 && lf - inc != -1) PetscCall(PetscPrintf(PETSC_COMM_SELF, "lf=%" PetscInt_FMT ", %" PetscInt_FMT ", Norm of error=%g, %g\n", lf - inc, lf, (double)norm1, (double)norm2));
342:     norm1 = norm2;
343:     if (norm2 < tol && lf != -1) break;
344:   }

346: #if defined(PETSC_HAVE_MUMPS)
347:   PetscCall(MatGetFactor(sA, MATSOLVERMUMPS, MAT_FACTOR_CHOLESKY, &sFactor));
348:   PetscCall(MatCholeskyFactorSymbolic(sFactor, sA, NULL, NULL));
349:   PetscCall(MatCholeskyFactorNumeric(sFactor, sA, NULL));
350:   for (i = 0; i < 10; i++) {
351:     PetscCall(VecSetRandom(b, rdm));
352:     PetscCall(MatSolve(sFactor, b, y));
353:     /* Check the error */
354:     PetscCall(MatMult(sA, y, x));
355:     PetscCall(VecAXPY(x, neg_one, b));
356:     PetscCall(VecNorm(x, NORM_2, &norm2));
357:     if (norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error:MatSolve(), norm2: %g\n", (double)norm2));
358:   }
359:   PetscCall(MatDestroy(&sFactor));
360: #endif

362:   PetscCall(ISDestroy(&perm));

364:   PetscCall(MatDestroy(&A));
365:   PetscCall(MatDestroy(&sB));
366:   PetscCall(MatDestroy(&sA));
367:   PetscCall(VecDestroy(&x));
368:   PetscCall(VecDestroy(&y));
369:   PetscCall(VecDestroy(&s1));
370:   PetscCall(VecDestroy(&s2));
371:   PetscCall(VecDestroy(&b));
372:   PetscCall(PetscRandomDestroy(&rdm));

374:   PetscCall(PetscFinalize());
375:   return 0;
376: }

378: /*TEST

380:    test:
381:       args: -bs {{1 2 3 4 5 6 7 8}}

383: TEST*/