Actual source code: ex1.c
petsc-3.13.6 2020-09-29
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      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);

     39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     40:          Compute the matrix and right-hand-side vector that define
     41:          the linear system, Ax = b.
     42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

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

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

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

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

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

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

    149:   /*
    150:      Always call PetscFinalize() before exiting a program.  This routine
    151:        - finalizes the PETSc libraries as well as MPI
    152:        - provides summary and diagnostic information if certain runtime
    153:          options are chosen (e.g., -log_view).
    154:   */
    155:   PetscFinalize();
    156:   return ierr;
    157: }

    159: /*TEST

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

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

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

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

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

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

    188: TEST*/