Actual source code: ex58.c
petsc-3.12.4 2020-02-04
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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:   Modified from ex1.c for testing matrix operations when matrix structure is changed.
     11:   Contributed by Jose E. Roman, Feb. 2012.
     12: */
     13:  #include <petscksp.h>

     15: int main(int argc,char **args)
     16: {
     17:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
     18:   Mat            A,B,C;        /* linear system matrix */
     19:   KSP            ksp;          /* linear solver context */
     20:   PC             pc;           /* preconditioner context */
     21:   PetscReal      norm;         /* norm of solution error */
     23:   PetscInt       i,n = 20,col[3],its;
     24:   PetscMPIInt    size;
     25:   PetscScalar    one = 1.0,value[3];
     26:   PetscBool      nonzeroguess = PETSC_FALSE;

     28:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     29:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     30:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
     31:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     32:   PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);

     35:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     36:          Compute the matrix and right-hand-side vector that define
     37:          the linear system, Ax = b.
     38:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     40:   /*
     41:      Create vectors.  Note that we form 1 vector from scratch and
     42:      then duplicate as needed.
     43:   */
     44:   VecCreate(PETSC_COMM_WORLD,&x);
     45:   PetscObjectSetName((PetscObject) x, "Solution");
     46:   VecSetSizes(x,PETSC_DECIDE,n);
     47:   VecSetFromOptions(x);
     48:   VecDuplicate(x,&b);
     49:   VecDuplicate(x,&u);

     51:   /*
     52:      Create matrix.  When using MatCreate(), the matrix format can
     53:      be specified at runtime.

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

     64:   /*
     65:      Assemble matrix
     66:   */
     67:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
     68:   for (i=1; i<n-1; i++) {
     69:     col[0] = i-1; col[1] = i; col[2] = i+1;
     70:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
     71:   }
     72:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
     73:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     74:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
     75:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     76:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     77:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     79:   /*
     80:      jroman: added matrices
     81:   */
     82:   MatCreate(PETSC_COMM_WORLD,&B);
     83:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
     84:   MatSetFromOptions(B);
     85:   MatSetUp(B);
     86:   for (i=0; i<n; i++) {
     87:     MatSetValue(B,i,i,value[1],INSERT_VALUES);
     88:     if (n-i+n/3<n) {
     89:       MatSetValue(B,n-i+n/3,i,value[0],INSERT_VALUES);
     90:       MatSetValue(B,i,n-i+n/3,value[0],INSERT_VALUES);
     91:     }
     92:   }
     93:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     94:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     95:   MatDuplicate(A,MAT_COPY_VALUES,&C);
     96:   MatAXPY(C,2.0,B,DIFFERENT_NONZERO_PATTERN);

     98:   /*
     99:      Set exact solution; then compute right-hand-side vector.
    100:   */
    101:   VecSet(u,one);
    102:   MatMult(C,u,b);

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:                 Create the linear solver and set various options
    106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    107:   /*
    108:      Create linear solver context
    109:   */
    110:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    112:   /*
    113:      Set operators. Here the matrix that defines the linear system
    114:      also serves as the preconditioning matrix.
    115:   */
    116:   KSPSetOperators(ksp,C,C);

    118:   /*
    119:      Set linear solver defaults for this problem (optional).
    120:      - By extracting the KSP and PC contexts from the KSP context,
    121:        we can then directly call any KSP and PC routines to set
    122:        various options.
    123:      - The following four statements are optional; all of these
    124:        parameters could alternatively be specified at runtime via
    125:        KSPSetFromOptions();
    126:   */
    127:   KSPGetPC(ksp,&pc);
    128:   PCSetType(pc,PCJACOBI);
    129:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

    131:   /*
    132:     Set runtime options, e.g.,
    133:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    134:     These options will override those specified above as long as
    135:     KSPSetFromOptions() is called _after_ any other customization
    136:     routines.
    137:   */
    138:   KSPSetFromOptions(ksp);

    140:   if (nonzeroguess) {
    141:     PetscScalar p = .5;
    142:     VecSet(x,p);
    143:     KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
    144:   }

    146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    147:                       Solve the linear system
    148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    149:   /*
    150:      Solve linear system
    151:   */
    152:   KSPSolve(ksp,b,x);

    154:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    155:                       Check solution and clean up
    156:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    157:   /*
    158:      Check the error
    159:   */
    160:   VecAXPY(x,-1.0,u);
    161:   VecNorm(x,NORM_2,&norm);
    162:   KSPGetIterationNumber(ksp,&its);
    163:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

    165:   /*
    166:      Free work space.  All PETSc objects should be destroyed when they
    167:      are no longer needed.
    168:   */
    169:   VecDestroy(&x); VecDestroy(&u);
    170:   VecDestroy(&b); MatDestroy(&A);
    171:   MatDestroy(&B);
    172:   MatDestroy(&C);
    173:   KSPDestroy(&ksp);

    175:   /*
    176:      Always call PetscFinalize() before exiting a program.  This routine
    177:        - finalizes the PETSc libraries as well as MPI
    178:        - provides summary and diagnostic information if certain runtime
    179:          options are chosen (e.g., -log_view).
    180:   */
    181:   PetscFinalize();
    182:   return ierr;
    183: }

    186: /*TEST

    188:    test:
    189:       args: -mat_type aij
    190:       output_file: output/ex58.out

    192:    test:
    193:       suffix: baij
    194:       args: -mat_type baij
    195:       output_file: output/ex58.out

    197:    test:
    198:       suffix: sbaij
    199:       args: -mat_type sbaij
    200:       output_file: output/ex58.out

    202: TEST*/