Date: 2022-03-04T17:39:12+00:00

Actual source code: ex1.c

      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              petscpc.h  - preconditioners
     14:      petscis.h     - index sets
     15:      petscviewer.h - viewers

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

     21: int main(int argc,char **args)
     22: {
     23:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
     24:   Mat            A;            /* linear system matrix */
     25:   KSP            ksp;          /* linear solver context */
     26:   PC             pc;           /* preconditioner context */
     27:   PetscReal      norm;         /* norm of solution error */
     29:   PetscInt       i,n = 10,col[3],its;
     30:   PetscMPIInt    size;
     31:   PetscScalar    value[3];

     33:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     35:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
     36:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

     38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     39:          Compute the matrix and right-hand-side vector that define
     40:          the linear system, Ax = b.
     41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     43:   /*
     44:      Create vectors.  Note that we form 1 vector from scratch and
     45:      then duplicate as needed.
     46:   */
     47:   VecCreate(PETSC_COMM_WORLD,&x);
     48:   PetscObjectSetName((PetscObject) x, "Solution");
     49:   VecSetSizes(x,PETSC_DECIDE,n);
     50:   VecSetFromOptions(x);
     51:   VecDuplicate(x,&b);
     52:   VecDuplicate(x,&u);

     54:   /*
     55:      Create matrix.  When using MatCreate(), the matrix format can
     56:      be specified at runtime.

     58:      Performance tuning note:  For problems of substantial size,
     59:      preallocation of matrix memory is crucial for attaining good
     60:      performance. See the matrix chapter of the users manual for details.
     61:   */
     62:   MatCreate(PETSC_COMM_WORLD,&A);
     63:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     64:   MatSetFromOptions(A);
     65:   MatSetUp(A);

     67:   /*
     68:      Assemble matrix
     69:   */
     70:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
     71:   for (i=1; i<n-1; i++) {
     72:     col[0] = i-1; col[1] = i; col[2] = i+1;
     73:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
     74:   }
     75:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
     76:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     77:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
     78:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     79:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     80:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     82:   /*
     83:      Set exact solution; then compute right-hand-side vector.
     84:   */
     85:   VecSet(u,1.0);
     86:   MatMult(A,u,b);

     88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     89:                 Create the linear solver and set various options
     90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     91:   KSPCreate(PETSC_COMM_WORLD,&ksp);

     93:   /*
     94:      Set operators. Here the matrix that defines the linear system
     95:      also serves as the matrix that defines the preconditioner.
     96:   */
     97:   KSPSetOperators(ksp,A,A);

     99:   /*
    100:      Set linear solver defaults for this problem (optional).
    101:      - By extracting the KSP and PC contexts from the KSP context,
    102:        we can then directly call any KSP and PC routines to set
    103:        various options.
    104:      - The following four statements are optional; all of these
    105:        parameters could alternatively be specified at runtime via
    106:        KSPSetFromOptions();
    107:   */
    108:   KSPGetPC(ksp,&pc);
    109:   PCSetType(pc,PCJACOBI);
    110:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

    112:   /*
    113:     Set runtime options, e.g.,
    114:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    115:     These options will override those specified above as long as
    116:     KSPSetFromOptions() is called _after_ any other customization
    117:     routines.
    118:   */
    119:   KSPSetFromOptions(ksp);

    121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    122:                       Solve the linear system
    123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    124:   KSPSolve(ksp,b,x);

    126:   /*
    127:      View solver info; we could instead use the option -ksp_view to
    128:      print this info to the screen at the conclusion of KSPSolve().
    129:   */
    130:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

    132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    133:                       Check the solution and clean up
    134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    135:   VecAXPY(x,-1.0,u);
    136:   VecNorm(x,NORM_2,&norm);
    137:   KSPGetIterationNumber(ksp,&its);
    138:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

    140:   /*
    141:      Free work space.  All PETSc objects should be destroyed when they
    142:      are no longer needed.
    143:   */
    144:   VecDestroy(&x); VecDestroy(&u);
    145:   VecDestroy(&b); MatDestroy(&A);
    146:   KSPDestroy(&ksp);

    148:   /*
    149:      Always call PetscFinalize() before exiting a program.  This routine
    150:        - finalizes the PETSc libraries as well as MPI
    151:        - provides summary and diagnostic information if certain runtime
    152:          options are chosen (e.g., -log_view).
    153:   */
    154:   PetscFinalize();
    155:   return ierr;
    156: }

    158: /*TEST

    160:    test:
    161:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    163:    test:
    164:       suffix: 2
    165:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    167:    test:
    168:       suffix: 2_aijcusparse
    169:       requires: cuda
    170:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

    172:    test:
    173:       suffix: 3
    174:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    176:    test:
    177:       suffix: 3_aijcusparse
    178:       requires: cuda
    179:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

    181:    test:
    182:       suffix: aijcusparse
    183:       requires: cuda
    184:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda
    185:       output_file: output/ex1_1_aijcusparse.out

    187: TEST*/