Actual source code: ex30.c


  2: 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\
  3:   Input parameters are:\n\
  4:   -lf <level> : level of fill for ILU (default is 0)\n\
  5:   -lu : use full LU or Cholesky factorization\n\
  6:   -m <value>,-n <value> : grid dimensions\n\
  7: Note that most users should employ the KSP interface to the\n\
  8: linear solvers instead of using the factorization routines\n\
  9: directly.\n\n";

 11: #include <petscmat.h>

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

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

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

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

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

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

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

 75:   PetscCall(PetscOptionsHasName(NULL, NULL, "-mat_ordering", &matordering));
 76:   if (matordering) {
 77:     PetscCall(MatGetOrdering(C, MATORDERINGRCM, &row, &col));
 78:   } else {
 79:     PetscCall(MatGetOrdering(C, MATORDERINGNATURAL, &row, &col));
 80:   }

 82:   PetscCall(PetscOptionsHasName(NULL, NULL, "-display_matrices", &MATDSPL));
 83:   if (MATDSPL) {
 84:     printf("original matrix:\n");
 85:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF, PETSC_VIEWER_ASCII_INFO));
 86:     PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
 87:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF));
 88:     PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
 89:     PetscCall(MatView(C, viewer1));
 90:   }

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

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

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

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

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

119:   /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
120:   if (!LU && lf == 0) {
121:     PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &A));
122:     PetscCall(MatILUFactor(A, row, col, &info));
123:     /*
124:     printf("In-place factored matrix:\n");
125:     PetscCall(MatView(C,PETSC_VIEWER_STDOUT_SELF));
126:     */
127:     PetscCall(MatSolve(A, b, y));
128:     PetscCall(VecAXPY(y, -1.0, x));
129:     PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
130:     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);
131:     PetscCall(MatDestroy(&A));
132:   }

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

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

153:   /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */
154:   if (lf == -1) {
155:     PetscCall(PetscOptionsHasName(NULL, NULL, "-triangular_solve", &TRIANGULAR));
156:     if (TRIANGULAR) {
157:       printf("Test MatForwardSolve...\n");
158:       PetscCall(MatForwardSolve(A, b, ytmp));
159:       printf("Test MatBackwardSolve...\n");
160:       PetscCall(MatBackwardSolve(A, ytmp, y));
161:       PetscCall(VecAXPY(y, -1.0, x));
162:       PetscCall(VecNorm(y, NORM_2, &norm2));
163:       if (norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatForwardSolve and BackwardSolve: Norm of error=%g\n", (double)norm2));
164:     }
165:   }

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

173:   /* Test in-place ICC(0) and compare it with the out-place ICC(0) */
174:   if (!CHOLESKY && lf == 0 && !matordering) {
175:     PetscCall(MatConvert(C, MATSBAIJ, MAT_INITIAL_MATRIX, &A));
176:     PetscCall(MatICCFactor(A, row, &info));
177:     /*
178:     printf("In-place factored matrix:\n");
179:     PetscCall(MatView(A,PETSC_VIEWER_STDOUT_SELF));
180:     */
181:     PetscCall(MatSolve(A, b, y));
182:     PetscCall(VecAXPY(y, -1.0, x));
183:     PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
184:     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);
185:     PetscCall(MatDestroy(&A));
186:   }

188:   /* Free data structures */
189:   PetscCall(ISDestroy(&row));
190:   PetscCall(ISDestroy(&col));
191:   PetscCall(MatDestroy(&C));
192:   PetscCall(PetscViewerDestroy(&viewer1));
193:   PetscCall(PetscViewerDestroy(&viewer2));
194:   PetscCall(PetscRandomDestroy(&rdm));
195:   PetscCall(VecDestroy(&x));
196:   PetscCall(VecDestroy(&y));
197:   PetscCall(VecDestroy(&ytmp));
198:   PetscCall(VecDestroy(&b));
199:   PetscCall(PetscFinalize());
200:   return 0;
201: }

203: /*TEST

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

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

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

217:    test:
218:       suffix: 4

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

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

229: TEST*/