Actual source code: ex30.c

  1: static char help[] = "Tests ILU and ICC factorization with and without matrix ordering on seqaij format, and illustrates drawing of matrix sparsity structure with MatView().\n\
  2:   Input parameters are:\n\
  3:   -lf <level> : level of fill for ILU (default is 0)\n\
  4:   -lu : use full LU or Cholesky factorization\n\
  5:   -m <value>,-n <value> : grid dimensions\n\
  6: Note that most users should employ the KSP interface to the\n\
  7: linear solvers instead of using the factorization routines\n\
  8: directly.\n\n";

 10: #include <petscmat.h>

 12: int main(int argc, char **args)
 13: {
 14:   Mat           C, A;
 15:   PetscInt      i, j, m = 5, n = 5, Ii, J, lf = 0;
 16:   PetscBool     LU = PETSC_FALSE, CHOLESKY, TRIANGULAR = PETSC_FALSE, MATDSPL = PETSC_FALSE, flg, matordering;
 17:   PetscScalar   v;
 18:   IS            row, col;
 19:   PetscViewer   viewer1, viewer2;
 20:   MatFactorInfo info;
 21:   Vec           x, y, b, ytmp;
 22:   PetscReal     norm2, norm2_inplace, tol = 100. * PETSC_MACHINE_EPSILON;
 23:   PetscRandom   rdm;
 24:   PetscMPIInt   size;

 26:   PetscFunctionBeginUser;
 27:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 28:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
 29:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
 30:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
 31:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
 32:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-lf", &lf, NULL));

 34:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 0, 0, 400, 400, &viewer1));
 35:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 400, 0, 400, 400, &viewer2));

 37:   PetscCall(MatCreate(PETSC_COMM_SELF, &C));
 38:   PetscCall(MatSetSizes(C, m * n, m * n, m * n, m * n));
 39:   PetscCall(MatSetFromOptions(C));
 40:   PetscCall(MatSetUp(C));

 42:   /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */
 43:   for (i = 0; i < m; i++) {
 44:     for (j = 0; j < n; j++) {
 45:       v  = -1.0;
 46:       Ii = j + n * i;
 47:       J  = Ii - n;
 48:       if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 49:       J = Ii + n;
 50:       if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 51:       J = Ii - 1;
 52:       if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 53:       J = Ii + 1;
 54:       if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 55:       v = 4.0;
 56:       PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
 57:     }
 58:   }
 59:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
 60:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

 62:   PetscCall(MatIsSymmetric(C, 0.0, &flg));
 63:   PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "C is non-symmetric");

 65:   /* Create vectors for error checking */
 66:   PetscCall(MatCreateVecs(C, &x, &b));
 67:   PetscCall(VecDuplicate(x, &y));
 68:   PetscCall(VecDuplicate(x, &ytmp));
 69:   PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm));
 70:   PetscCall(PetscRandomSetFromOptions(rdm));
 71:   PetscCall(VecSetRandom(x, rdm));
 72:   PetscCall(MatMult(C, x, b));

 74:   PetscCall(PetscOptionsHasName(NULL, NULL, "-mat_ordering", &matordering));
 75:   if (matordering) {
 76:     PetscCall(MatGetOrdering(C, MATORDERINGRCM, &row, &col));
 77:   } else {
 78:     PetscCall(MatGetOrdering(C, MATORDERINGNATURAL, &row, &col));
 79:   }

 81:   PetscCall(PetscOptionsHasName(NULL, NULL, "-display_matrices", &MATDSPL));
 82:   if (MATDSPL) {
 83:     printf("original matrix:\n");
 84:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF, PETSC_VIEWER_ASCII_INFO));
 85:     PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
 86:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF));
 87:     PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
 88:     PetscCall(MatView(C, viewer1));
 89:   }

 91:   /* Compute LU or ILU factor A */
 92:   PetscCall(MatFactorInfoInitialize(&info));

 94:   info.fill          = 1.0;
 95:   info.diagonal_fill = 0;
 96:   info.zeropivot     = 0.0;

 98:   PetscCall(PetscOptionsHasName(NULL, NULL, "-lu", &LU));
 99:   if (LU) {
100:     printf("Test LU...\n");
101:     PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_LU, &A));
102:     PetscCall(MatLUFactorSymbolic(A, C, row, col, &info));
103:   } else {
104:     printf("Test ILU...\n");
105:     info.levels = lf;

107:     PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ILU, &A));
108:     PetscCall(MatILUFactorSymbolic(A, C, row, col, &info));
109:   }
110:   PetscCall(MatLUFactorNumeric(A, C, &info));

112:   /* Solve A*y = b, then check the error */
113:   PetscCall(MatSolve(A, b, y));
114:   PetscCall(VecAXPY(y, -1.0, x));
115:   PetscCall(VecNorm(y, NORM_2, &norm2));
116:   PetscCall(MatDestroy(&A));

118:   /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
119:   if (!LU && lf == 0) {
120:     PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &A));
121:     PetscCall(MatILUFactor(A, row, col, &info));
122:     /*
123:     printf("In-place factored matrix:\n");
124:     PetscCall(MatView(C,PETSC_VIEWER_STDOUT_SELF));
125:     */
126:     PetscCall(MatSolve(A, b, y));
127:     PetscCall(VecAXPY(y, -1.0, x));
128:     PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
129:     PetscCheck(PetscAbs(norm2 - norm2_inplace) <= tol, PETSC_COMM_SELF, PETSC_ERR_PLIB, "ILU(0) %g and in-place ILU(0) %g give different residuals", (double)norm2, (double)norm2_inplace);
130:     PetscCall(MatDestroy(&A));
131:   }

133:   /* Test Cholesky and ICC on seqaij matrix with matrix reordering on aij matrix C */
134:   CHOLESKY = LU;
135:   if (CHOLESKY) {
136:     printf("Test Cholesky...\n");
137:     lf = -1;
138:     PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &A));
139:     PetscCall(MatCholeskyFactorSymbolic(A, C, row, &info));
140:   } else {
141:     printf("Test ICC...\n");
142:     info.levels        = lf;
143:     info.fill          = 1.0;
144:     info.diagonal_fill = 0;
145:     info.zeropivot     = 0.0;

147:     PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ICC, &A));
148:     PetscCall(MatICCFactorSymbolic(A, C, row, &info));
149:   }
150:   PetscCall(MatCholeskyFactorNumeric(A, C, &info));

152:   /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */
153:   if (lf == -1) {
154:     PetscCall(PetscOptionsHasName(NULL, NULL, "-triangular_solve", &TRIANGULAR));
155:     if (TRIANGULAR) {
156:       printf("Test MatForwardSolve...\n");
157:       PetscCall(MatForwardSolve(A, b, ytmp));
158:       printf("Test MatBackwardSolve...\n");
159:       PetscCall(MatBackwardSolve(A, ytmp, y));
160:       PetscCall(VecAXPY(y, -1.0, x));
161:       PetscCall(VecNorm(y, NORM_2, &norm2));
162:       if (norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatForwardSolve and BackwardSolve: Norm of error=%g\n", (double)norm2));
163:     }
164:   }

166:   PetscCall(MatSolve(A, b, y));
167:   PetscCall(MatDestroy(&A));
168:   PetscCall(VecAXPY(y, -1.0, x));
169:   PetscCall(VecNorm(y, NORM_2, &norm2));
170:   if (lf == -1 && norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ:   Cholesky/ICC levels %" PetscInt_FMT ", residual %g\n", lf, (double)norm2));

172:   /* Test in-place ICC(0) and compare it with the out-place ICC(0) */
173:   if (!CHOLESKY && lf == 0 && !matordering) {
174:     PetscCall(MatConvert(C, MATSBAIJ, MAT_INITIAL_MATRIX, &A));
175:     PetscCall(MatICCFactor(A, row, &info));
176:     /*
177:     printf("In-place factored matrix:\n");
178:     PetscCall(MatView(A,PETSC_VIEWER_STDOUT_SELF));
179:     */
180:     PetscCall(MatSolve(A, b, y));
181:     PetscCall(VecAXPY(y, -1.0, x));
182:     PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
183:     PetscCheck(PetscAbs(norm2 - norm2_inplace) <= tol, PETSC_COMM_SELF, PETSC_ERR_PLIB, "ICC(0) %g and in-place ICC(0) %g give different residuals", (double)norm2, (double)norm2_inplace);
184:     PetscCall(MatDestroy(&A));
185:   }

187:   /* Free data structures */
188:   PetscCall(ISDestroy(&row));
189:   PetscCall(ISDestroy(&col));
190:   PetscCall(MatDestroy(&C));
191:   PetscCall(PetscViewerDestroy(&viewer1));
192:   PetscCall(PetscViewerDestroy(&viewer2));
193:   PetscCall(PetscRandomDestroy(&rdm));
194:   PetscCall(VecDestroy(&x));
195:   PetscCall(VecDestroy(&y));
196:   PetscCall(VecDestroy(&ytmp));
197:   PetscCall(VecDestroy(&b));
198:   PetscCall(PetscFinalize());
199:   return 0;
200: }

202: /*TEST

204:    test:
205:       args: -mat_ordering -display_matrices -nox
206:       filter: grep -v " MPI process"

208:    test:
209:       suffix: 2
210:       args: -mat_ordering -display_matrices -nox -lu

212:    test:
213:       suffix: 3
214:       args: -mat_ordering -lu -triangular_solve

216:    test:
217:       suffix: 4

219:    test:
220:       suffix: 5
221:       args: -lu

223:    test:
224:       suffix: 6
225:       args: -lu -triangular_solve
226:       output_file: output/ex30_3.out

228: TEST*/