Actual source code: ex1.c
petsc-3.4.2 2013-07-02

      2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";

      4: /*T
      5:    Concepts: KSP^solving a system of linear equations
      6:    Processors: 1
      7: T*/

      9: /*
     10:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     11:   automatically includes:
     12:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     13:      petscmat.h - matrices
     14:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     15:      petscviewer.h - viewers               petscpc.h  - preconditioners

     17:   Note:  The corresponding parallel example is ex23.c
     18: */
     19: #include <petscksp.h>

     23: int main(int argc,char **args)
     24: {
     25:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
     26:   Mat            A;            /* linear system matrix */
     27:   KSP            ksp;         /* linear solver context */
     28:   PC             pc;           /* preconditioner context */
     29:   PetscReal      norm,tol=1.e-14;  /* norm of solution error */
     31:   PetscInt       i,n = 10,col[3],its;
     32:   PetscMPIInt    size;
     33:   PetscScalar    neg_one      = -1.0,one = 1.0,value[3];
     34:   PetscBool      nonzeroguess = PETSC_FALSE;

     36:   PetscInitialize(&argc,&args,(char*)0,help);
     37:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     38:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
     39:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     40:   PetscOptionsGetBool(NULL,"-nonzero_guess",&nonzeroguess,NULL);

     43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     44:          Compute the matrix and right-hand-side vector that define
     45:          the linear system, Ax = b.
     46:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     48:   /*
     49:      Create vectors.  Note that we form 1 vector from scratch and
     50:      then duplicate as needed.
     51:   */
     52:   VecCreate(PETSC_COMM_WORLD,&x);
     53:   PetscObjectSetName((PetscObject) x, "Solution");
     54:   VecSetSizes(x,PETSC_DECIDE,n);
     55:   VecSetFromOptions(x);
     56:   VecDuplicate(x,&b);
     57:   VecDuplicate(x,&u);

     59:   /*
     60:      Create matrix.  When using MatCreate(), the matrix format can
     61:      be specified at runtime.

     63:      Performance tuning note:  For problems of substantial size,
     64:      preallocation of matrix memory is crucial for attaining good
     65:      performance. See the matrix chapter of the users manual for details.
     66:   */
     67:   MatCreate(PETSC_COMM_WORLD,&A);
     68:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     69:   MatSetFromOptions(A);
     70:   MatSetUp(A);

     72:   /*
     73:      Assemble matrix
     74:   */
     75:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
     76:   for (i=1; i<n-1; i++) {
     77:     col[0] = i-1; col[1] = i; col[2] = i+1;
     78:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
     79:   }
     80:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
     81:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     82:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
     83:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     84:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     85:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     87:   /*
     88:      Set exact solution; then compute right-hand-side vector.
     89:   */
     90:   VecSet(u,one);
     91:   MatMult(A,u,b);

     93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94:                 Create the linear solver and set various options
     95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     96:   /*
     97:      Create linear solver context
     98:   */
     99:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    101:   /*
    102:      Set operators. Here the matrix that defines the linear system
    103:      also serves as the preconditioning matrix.
    104:   */
    105:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

    107:   /*
    108:      Set linear solver defaults for this problem (optional).
    109:      - By extracting the KSP and PC contexts from the KSP context,
    110:        we can then directly call any KSP and PC routines to set
    111:        various options.
    112:      - The following four statements are optional; all of these
    113:        parameters could alternatively be specified at runtime via
    114:        KSPSetFromOptions();
    115:   */
    116:   KSPGetPC(ksp,&pc);
    117:   PCSetType(pc,PCJACOBI);
    118:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

    120:   /*
    121:     Set runtime options, e.g.,
    122:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    123:     These options will override those specified above as long as
    124:     KSPSetFromOptions() is called _after_ any other customization
    125:     routines.
    126:   */
    127:   KSPSetFromOptions(ksp);

    129:   if (nonzeroguess) {
    130:     PetscScalar p = .5;
    131:     VecSet(x,p);
    132:     KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
    133:   }

    135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    136:                       Solve the linear system
    137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    138:   /*
    139:      Solve linear system
    140:   */
    141:   KSPSolve(ksp,b,x);

    143:   /*
    144:      View solver info; we could instead use the option -ksp_view to
    145:      print this info to the screen at the conclusion of KSPSolve().
    146:   */
    147:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    150:                       Check solution and clean up
    151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    152:   /*
    153:      Check the error
    154:   */
    155:   VecAXPY(x,neg_one,u);
    156:   VecNorm(x,NORM_2,&norm);
    157:   KSPGetIterationNumber(ksp,&its);
    158:   if (norm > tol) {
    159:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G, Iterations %D\n",norm,its);
    160:   }

    162:   /*
    163:      Free work space.  All PETSc objects should be destroyed when they
    164:      are no longer needed.
    165:   */
    166:   VecDestroy(&x); VecDestroy(&u);
    167:   VecDestroy(&b); MatDestroy(&A);
    168:   KSPDestroy(&ksp);

    170:   /*
    171:      Always call PetscFinalize() before exiting a program.  This routine
    172:        - finalizes the PETSc libraries as well as MPI
    173:        - provides summary and diagnostic information if certain runtime
    174:          options are chosen (e.g., -log_summary).
    175:   */
    176:   PetscFinalize();
    177:   return 0;
    178: }