Date: 2022-03-31T04:48:19+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 */
     28:   PetscInt       i,n = 10,col[3],its;
     29:   PetscMPIInt    size;
     30:   PetscScalar    value[3];

     32:   PetscInitialize(&argc,&args,(char*)0,help);
     33:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     35:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

     37:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     38:          Compute the matrix and right-hand-side vector that define
     39:          the linear system, Ax = b.
     40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     42:   /*
     43:      Create vectors.  Note that we form 1 vector from scratch and
     44:      then duplicate as needed.
     45:   */
     46:   VecCreate(PETSC_COMM_WORLD,&x);
     47:   PetscObjectSetName((PetscObject) x, "Solution");
     48:   VecSetSizes(x,PETSC_DECIDE,n);
     49:   VecSetFromOptions(x);
     50:   VecDuplicate(x,&b);
     51:   VecDuplicate(x,&u);

     53:   /*
     54:      Create matrix.  When using MatCreate(), the matrix format can
     55:      be specified at runtime.

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

     66:   /*
     67:      Assemble matrix
     68:   */
     69:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
     70:   for (i=1; i<n-1; i++) {
     71:     col[0] = i-1; col[1] = i; col[2] = i+1;
     72:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
     73:   }
     74:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
     75:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     76:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
     77:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     78:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     79:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     81:   /*
     82:      Set exact solution; then compute right-hand-side vector.
     83:   */
     84:   VecSet(u,1.0);
     85:   MatMult(A,u,b);

     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:                 Create the linear solver and set various options
     89:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     90:   KSPCreate(PETSC_COMM_WORLD,&ksp);

     92:   /*
     93:      Set operators. Here the matrix that defines the linear system
     94:      also serves as the matrix that defines the preconditioner.
     95:   */
     96:   KSPSetOperators(ksp,A,A);

     98:   /*
     99:      Set linear solver defaults for this problem (optional).
    100:      - By extracting the KSP and PC contexts from the KSP context,
    101:        we can then directly call any KSP and PC routines to set
    102:        various options.
    103:      - The following four statements are optional; all of these
    104:        parameters could alternatively be specified at runtime via
    105:        KSPSetFromOptions();
    106:   */
    107:   KSPGetPC(ksp,&pc);
    108:   PCSetType(pc,PCJACOBI);
    109:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

    111:   /*
    112:     Set runtime options, e.g.,
    113:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    114:     These options will override those specified above as long as
    115:     KSPSetFromOptions() is called _after_ any other customization
    116:     routines.
    117:   */
    118:   KSPSetFromOptions(ksp);

    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:                       Solve the linear system
    122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    123:   KSPSolve(ksp,b,x);

    125:   /*
    126:      View solver info; we could instead use the option -ksp_view to
    127:      print this info to the screen at the conclusion of KSPSolve().
    128:   */
    129:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

    131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    132:                       Check the solution and clean up
    133:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    134:   VecAXPY(x,-1.0,u);
    135:   VecNorm(x,NORM_2,&norm);
    136:   KSPGetIterationNumber(ksp,&its);
    137:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

    139:   /*
    140:      Free work space.  All PETSc objects should be destroyed when they
    141:      are no longer needed.
    142:   */
    143:   VecDestroy(&x)); PetscCall(VecDestroy(&u);
    144:   VecDestroy(&b)); PetscCall(MatDestroy(&A);
    145:   KSPDestroy(&ksp);

    147:   /*
    148:      Always call PetscFinalize() before exiting a program.  This routine
    149:        - finalizes the PETSc libraries as well as MPI
    150:        - provides summary and diagnostic information if certain runtime
    151:          options are chosen (e.g., -log_view).
    152:   */
    153:   PetscFinalize();
    154:   return 0;
    155: }

    157: /*TEST

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

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

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

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

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

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

    186: TEST*/