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

  6: #include <petscksp.h>

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

 20:   PetscInitialize(&argc, &args, (char *)0, help);
 21:   MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
 22:   MPI_Comm_size(PETSC_COMM_WORLD, &size);
 23:   PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL);

 25:   /* Create vectors.*/
 26:   VecCreate(PETSC_COMM_WORLD, &x);
 27:   PetscObjectSetName((PetscObject)x, "Solution");
 28:   VecSetSizes(x, PETSC_DECIDE, n);
 29:   VecSetFromOptions(x);
 30:   VecDuplicate(x, &b);
 31:   VecDuplicate(x, &u);
 32:   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:   MatCreate(PETSC_COMM_WORLD, &A);
 37:   MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, n, n);
 38:   MatSetFromOptions(A);
 39:   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:       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:     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:     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:     MatSetValues(A, 1, &i, 1, col, value, INSERT_VALUES);
 66:   }
 67:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
 68:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);

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

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

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

 87:   /* Check the error */
 88:   VecAXPY(x, -1.0, u);
 89:   VecNorm(x, NORM_2, &norm);
 90:   KSPGetIterationNumber(ksp, &its);
 91:   if (norm > tol) 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:   MatMultTranspose(A, u, b);
 95:   KSPSolveTranspose(ksp, b, x2);

 97:   /* Check the error */
 98:   VecAXPY(x2, -1.0, u);
 99:   VecNorm(x2, NORM_2, &norm);
100:   KSPGetIterationNumber(ksp, &its);
101:   if (norm > tol) 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:     MatSetValues(A, 1, &i, 1, col, value, ADD_VALUES);
109:   }
110:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
111:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);

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

116:   /* Check the error */
117:   VecAXPY(x, -1.0, u);
118:   VecNorm(x, NORM_2, &norm);
119:   KSPGetIterationNumber(ksp, &its);
120:   if (norm > tol) 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:   VecDestroy(&x);
124:   VecDestroy(&u);
125:   VecDestroy(&x2);
126:   VecDestroy(&b);
127:   MatDestroy(&A);
128:   KSPDestroy(&ksp);

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

134: /*TEST

136:    test:
137:       requires: mumps

139:    test:
140:       suffix: 2
141:       nsize: 2
142:       requires: mumps
143:       output_file: output/ex53.out

145: TEST*/