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>

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

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

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

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

 42:   if (!rank) {
 43:     value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 44:     for (i=1; i<n-1; i++) {
 45:       col[0] = i-1; col[1] = i; col[2] = i+1;
 46:       MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 47:     }
 48:     i    = n - 1; col[0] = n - 2; col[1] = n - 1;
 49:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 50:     i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 51:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);

 53:     i    = 0; col[0] = n-1; value[0] = 0.5; /* make A non-symmetric */
 54:     MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
 55:   }
 56:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 57:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 59:   /* Set exact solution */
 60:   VecSet(u,one);

 62:   /* Create linear solver context */
 63:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 64:   KSPSetOperators(ksp,A,A);
 65:   KSPGetPC(ksp,&pc);
 66:   PCSetType(pc,PCLU);
 67: #if defined(PETSC_HAVE_MUMPS)
 68:   PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);
 69: #endif
 70:   KSPSetFromOptions(ksp);

 72:   /* 1. Solve linear system A x = b */
 73:   MatMult(A,u,b);
 74:   KSPSolve(ksp,b,x);

 76:   /* Check the error */
 77:   VecAXPY(x,neg_one,u);
 78:   VecNorm(x,NORM_2,&norm);
 79:   KSPGetIterationNumber(ksp,&its);
 80:   if (norm > tol) {
 81:     PetscPrintf(PETSC_COMM_WORLD,"1. Norm of error for Ax=b: %g, Iterations %D\n",(double)norm,its);
 82:   }

 84:   /* 2. Solve linear system A^T x = b*/
 85:   MatMultTranspose(A,u,b);
 86:   KSPSolveTranspose(ksp,b,x2);

 88:   /* Check the error */
 89:   VecAXPY(x2,neg_one,u);
 90:   VecNorm(x2,NORM_2,&norm);
 91:   KSPGetIterationNumber(ksp,&its);
 92:   if (norm > tol) {
 93:     PetscPrintf(PETSC_COMM_WORLD,"2. Norm of error for A^T x=b: %g, Iterations %D\n",(double)norm,its);
 94:   }

 96:   /* 3. Change A and solve A x = b with an iterative solver using A=LU as a preconditioner*/
 97:   if (!rank) {
 98:     i    = 0; col[0] = n-1; value[0] = 1.e-2;
 99:     MatSetValues(A,1,&i,1,col,value,ADD_VALUES);
100:   }
101:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
102:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

104:   MatMult(A,u,b);
105:   KSPSolve(ksp,b,x);

107:   /* Check the error */
108:   VecAXPY(x,neg_one,u);
109:   VecNorm(x,NORM_2,&norm);
110:   KSPGetIterationNumber(ksp,&its);
111:   if (norm > tol) {
112:     PetscPrintf(PETSC_COMM_WORLD,"3. Norm of error for (A+Delta) x=b: %g, Iterations %D\n",(double)norm,its);
113:   }

115:   /* Free work space. */
116:   VecDestroy(&x);
117:   VecDestroy(&u);
118:   VecDestroy(&x2);
119:   VecDestroy(&b);
120:   MatDestroy(&A);
121:   KSPDestroy(&ksp);

123:   PetscFinalize();
124:   return 0;
125: }