Actual source code: ex15.c


  2: static char help[] = "Tests MatNorm(), MatLUFactor(), MatSolve() and MatSolveAdd().\n\n";

  4: #include <petscmat.h>

  6: int main(int argc, char **args)
  7: {
  8:   Mat           C;
  9:   PetscInt      i, j, m = 3, n = 3, Ii, J;
 10:   PetscBool     flg;
 11:   PetscScalar   v;
 12:   IS            perm, iperm;
 13:   Vec           x, u, b, y;
 14:   PetscReal     norm, tol = PETSC_SMALL;
 15:   MatFactorInfo info;
 16:   PetscMPIInt   size;

 18:   PetscFunctionBeginUser;
 19:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 20:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
 21:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
 22:   PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
 23:   PetscCall(MatSetSizes(C, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
 24:   PetscCall(MatSetFromOptions(C));
 25:   PetscCall(MatSetUp(C));
 26:   PetscCall(PetscOptionsHasName(NULL, NULL, "-symmetric", &flg));
 27:   if (flg) { /* Treat matrix as symmetric only if we set this flag */
 28:     PetscCall(MatSetOption(C, MAT_SYMMETRIC, PETSC_TRUE));
 29:     PetscCall(MatSetOption(C, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
 30:   }

 32:   /* Create the matrix for the five point stencil, YET AGAIN */
 33:   for (i = 0; i < m; i++) {
 34:     for (j = 0; j < n; j++) {
 35:       v  = -1.0;
 36:       Ii = j + n * i;
 37:       if (i > 0) {
 38:         J = Ii - n;
 39:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 40:       }
 41:       if (i < m - 1) {
 42:         J = Ii + n;
 43:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 44:       }
 45:       if (j > 0) {
 46:         J = Ii - 1;
 47:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 48:       }
 49:       if (j < n - 1) {
 50:         J = Ii + 1;
 51:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
 52:       }
 53:       v = 4.0;
 54:       PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
 55:     }
 56:   }
 57:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
 58:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
 59:   PetscCall(MatGetOrdering(C, MATORDERINGRCM, &perm, &iperm));
 60:   PetscCall(MatView(C, PETSC_VIEWER_STDOUT_WORLD));
 61:   PetscCall(ISView(perm, PETSC_VIEWER_STDOUT_SELF));
 62:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m * n, &u));
 63:   PetscCall(VecSet(u, 1.0));
 64:   PetscCall(VecDuplicate(u, &x));
 65:   PetscCall(VecDuplicate(u, &b));
 66:   PetscCall(VecDuplicate(u, &y));
 67:   PetscCall(MatMult(C, u, b));
 68:   PetscCall(VecCopy(b, y));
 69:   PetscCall(VecScale(y, 2.0));

 71:   PetscCall(MatNorm(C, NORM_FROBENIUS, &norm));
 72:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "Frobenius norm of matrix %g\n", (double)norm));
 73:   PetscCall(MatNorm(C, NORM_1, &norm));
 74:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "One  norm of matrix %g\n", (double)norm));
 75:   PetscCall(MatNorm(C, NORM_INFINITY, &norm));
 76:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "Infinity norm of matrix %g\n", (double)norm));

 78:   PetscCall(MatFactorInfoInitialize(&info));
 79:   info.fill          = 2.0;
 80:   info.dtcol         = 0.0;
 81:   info.zeropivot     = 1.e-14;
 82:   info.pivotinblocks = 1.0;

 84:   PetscCall(MatLUFactor(C, perm, iperm, &info));

 86:   /* Test MatSolve */
 87:   PetscCall(MatSolve(C, b, x));
 88:   PetscCall(VecView(b, PETSC_VIEWER_STDOUT_SELF));
 89:   PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF));
 90:   PetscCall(VecAXPY(x, -1.0, u));
 91:   PetscCall(VecNorm(x, NORM_2, &norm));
 92:   if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatSolve: Norm of error %g\n", (double)norm));

 94:   /* Test MatSolveAdd */
 95:   PetscCall(MatSolveAdd(C, b, y, x));
 96:   PetscCall(VecAXPY(x, -1.0, y));
 97:   PetscCall(VecAXPY(x, -1.0, u));
 98:   PetscCall(VecNorm(x, NORM_2, &norm));
 99:   if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatSolveAdd(): Norm of error %g\n", (double)norm));

101:   PetscCall(ISDestroy(&perm));
102:   PetscCall(ISDestroy(&iperm));
103:   PetscCall(VecDestroy(&u));
104:   PetscCall(VecDestroy(&y));
105:   PetscCall(VecDestroy(&b));
106:   PetscCall(VecDestroy(&x));
107:   PetscCall(MatDestroy(&C));
108:   PetscCall(PetscFinalize());
109:   return 0;
110: }

112: /*TEST

114:    test:

116: TEST*/