1: static char help[] = "Solves a tridiagonal linear system with KSP. \n\
  2:                       Modified from ex1.c to illustrate reuse of preconditioner \n\
  3:                       Written as requested by [petsc-maint #63875] \n\n";

  5: #include <petscksp.h>

  7: int main(int argc, char **args)
  8: {
  9:   Vec         x, x2, b, u; /* approx solution, RHS, exact solution */
 10:   Mat         A;           /* linear system matrix */
 11:   KSP         ksp;         /* linear solver context */
 12:   PC          pc;          /* preconditioner context */
 13:   PetscReal   norm;        /* norm of solution error */
 14:   PetscReal   tol = PetscDefined(USE_REAL___FLOAT128) ? 1e-14 : 100. * PETSC_MACHINE_EPSILON;
 15:   PetscInt    i, n = 10, col[3], its;
 16:   PetscMPIInt rank, size;
 17:   PetscScalar one = 1.0, value[3];

 19:   PetscFunctionBeginUser;
 20:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
 21:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
 22:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
 23:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));

 25:   /* Create vectors.*/
 26:   PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
 27:   PetscCall(PetscObjectSetName((PetscObject)x, "Solution"));
 28:   PetscCall(VecSetSizes(x, PETSC_DECIDE, n));
 29:   PetscCall(VecSetFromOptions(x));
 30:   PetscCall(VecDuplicate(x, &b));
 31:   PetscCall(VecDuplicate(x, &u));
 32:   PetscCall(VecDuplicate(x, &x2));

 34:   /* Create matrix. Only proc[0] sets values - not efficient for parallel processing!
 35:      See ex23.c for efficient parallel assembly matrix */
 36:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
 37:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, n, n));
 38:   PetscCall(MatSetFromOptions(A));
 39:   PetscCall(MatSetUp(A));

 41:   if (rank == 0) {
 42:     value[0] = -1.0;
 43:     value[1] = 2.0;
 44:     value[2] = -1.0;
 45:     for (i = 1; i < n - 1; i++) {
 46:       col[0] = i - 1;
 47:       col[1] = i;
 48:       col[2] = i + 1;
 49:       PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
 50:     }
 51:     i      = n - 1;
 52:     col[0] = n - 2;
 53:     col[1] = n - 1;
 54:     PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
 55:     i        = 0;
 56:     col[0]   = 0;
 57:     col[1]   = 1;
 58:     value[0] = 2.0;
 59:     value[1] = -1.0;
 60:     PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));

 62:     i        = 0;
 63:     col[0]   = n - 1;
 64:     value[0] = 0.5; /* make A non-symmetric */
 65:     PetscCall(MatSetValues(A, 1, &i, 1, col, value, INSERT_VALUES));
 66:   }
 67:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 68:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

 70:   /* Set exact solution */
 71:   PetscCall(VecSet(u, one));

 73:   /* Create linear solver context */
 74:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
 75:   PetscCall(KSPSetOperators(ksp, A, A));
 76:   PetscCall(KSPGetPC(ksp, &pc));
 77:   PetscCall(PCSetType(pc, PCLU));
 78: #if defined(PETSC_HAVE_MUMPS)
 79:   if (size > 1) PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERMUMPS));
 80: #endif
 81:   PetscCall(KSPSetFromOptions(ksp));

 83:   /* 1. Solve linear system A x = b */
 84:   PetscCall(MatMult(A, u, b));
 85:   PetscCall(KSPSolve(ksp, b, x));

 87:   /* Check the error */
 88:   PetscCall(VecAXPY(x, -1.0, u));
 89:   PetscCall(VecNorm(x, NORM_2, &norm));
 90:   PetscCall(KSPGetIterationNumber(ksp, &its));
 91:   if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "1. Norm of error for Ax=b: %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));

 93:   /* 2. Solve linear system A^T x = b*/
 94:   PetscCall(MatMultTranspose(A, u, b));
 95:   PetscCall(KSPSolveTranspose(ksp, b, x2));

 97:   /* Check the error */
 98:   PetscCall(VecAXPY(x2, -1.0, u));
 99:   PetscCall(VecNorm(x2, NORM_2, &norm));
100:   PetscCall(KSPGetIterationNumber(ksp, &its));
101:   if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "2. Norm of error for A^T x=b: %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));

103:   /* 3. Change A and solve A x = b with an iterative solver using A=LU as a preconditioner*/
104:   if (rank == 0) {
105:     i        = 0;
106:     col[0]   = n - 1;
107:     value[0] = 1.e-2;
108:     PetscCall(MatSetValues(A, 1, &i, 1, col, value, ADD_VALUES));
109:   }
110:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
111:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

113:   PetscCall(MatMult(A, u, b));
114:   PetscCall(KSPSolve(ksp, b, x));

116:   /* Check the error */
117:   PetscCall(VecAXPY(x, -1.0, u));
118:   PetscCall(VecNorm(x, NORM_2, &norm));
119:   PetscCall(KSPGetIterationNumber(ksp, &its));
120:   if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "3. Norm of error for (A+Delta) x=b: %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));

122:   /* Free work space. */
123:   PetscCall(VecDestroy(&x));
124:   PetscCall(VecDestroy(&u));
125:   PetscCall(VecDestroy(&x2));
126:   PetscCall(VecDestroy(&b));
127:   PetscCall(MatDestroy(&A));
128:   PetscCall(KSPDestroy(&ksp));

130:   PetscCall(PetscFinalize());
131:   return 0;
132: }

134: /*TEST

136:    test:
137:       requires: mumps
138:       output_file: output/empty.out

140:    test:
141:       suffix: 2
142:       nsize: 2
143:       requires: mumps
144:       output_file: output/empty.out

146: TEST*/