Date: 2022-08-02T03:14:46+00:00

Actual source code: ex18.c

      1: static const char help[] = "Solves a (permuted) linear system in parallel with KSP.\n\
      2: Input parameters include:\n\
      3:   -permute <natural,rcm,nd,...> : solve system in permuted indexing\n\
      4:   -random_exact_sol : use a random exact solution vector\n\
      5:   -view_exact_sol   : write exact solution vector to stdout\n\
      6:   -m <mesh_x>       : number of mesh points in x-direction\n\
      7:   -n <mesh_y>       : number of mesh points in y-direction\n\n";

      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
     16: */
     17: #include <petscksp.h>

     19: int main(int argc,char **args)
     20: {
     21:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
     22:   Mat            A;        /* linear system matrix */
     23:   KSP            ksp;     /* linear solver context */
     24:   PetscRandom    rctx;     /* random number generator context */
     25:   PetscReal      norm;     /* norm of solution error */
     26:   PetscInt       i,j,Ii,J,Istart,Iend,m,n,its;
     28:   PetscBool      random_exact_sol,view_exact_sol,permute;
     29:   char           ordering[256] = MATORDERINGRCM;
     30:   IS             rowperm       = NULL,colperm = NULL;
     31:   PetscScalar    v;
     32: #if defined(PETSC_USE_LOG)
     33:   PetscLogStage stage;
     34: #endif

     36:   PetscInitialize(&argc,&args,(char*)0,help);
     37:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Poisson example options","");
     38:   {
     39:     m                = 8;
     40:     PetscOptionsInt("-m","Number of grid points in x direction","",m,&m,NULL);
     41:     n                = m-1;
     42:     PetscOptionsInt("-n","Number of grid points in y direction","",n,&n,NULL);
     43:     random_exact_sol = PETSC_FALSE;
     44:     PetscOptionsBool("-random_exact_sol","Choose a random exact solution","",random_exact_sol,&random_exact_sol,NULL);
     45:     view_exact_sol   = PETSC_FALSE;
     46:     PetscOptionsBool("-view_exact_sol","View exact solution","",view_exact_sol,&view_exact_sol,NULL);
     47:     permute          = PETSC_FALSE;
     48:     PetscOptionsFList("-permute","Permute matrix and vector to solving in new ordering","",MatOrderingList,ordering,ordering,sizeof(ordering),&permute);
     49:   }
     50:   PetscOptionsEnd();
     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:          Compute the matrix and right-hand-side vector that define
     53:          the linear system, Ax = b.
     54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     55:   /*
     56:      Create parallel matrix, specifying only its global dimensions.
     57:      When using MatCreate(), the matrix format can be specified at
     58:      runtime. Also, the parallel partitioning of the matrix is
     59:      determined by PETSc at runtime.

     61:      Performance tuning note:  For problems of substantial size,
     62:      preallocation of matrix memory is crucial for attaining good
     63:      performance. See the matrix chapter of the users manual for details.
     64:   */
     65:   MatCreate(PETSC_COMM_WORLD,&A);
     66:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     67:   MatSetFromOptions(A);
     68:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
     69:   MatSeqAIJSetPreallocation(A,5,NULL);
     70:   MatSetUp(A);

     72:   /*
     73:      Currently, all PETSc parallel matrix formats are partitioned by
     74:      contiguous chunks of rows across the processors.  Determine which
     75:      rows of the matrix are locally owned.
     76:   */
     77:   MatGetOwnershipRange(A,&Istart,&Iend);

     79:   /*
     80:      Set matrix elements for the 2-D, five-point stencil in parallel.
     81:       - Each processor needs to insert only elements that it owns
     82:         locally (but any non-local elements will be sent to the
     83:         appropriate processor during matrix assembly).
     84:       - Always specify global rows and columns of matrix entries.

     86:      Note: this uses the less common natural ordering that orders first
     87:      all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
     88:      instead of J = I +- m as you might expect. The more standard ordering
     89:      would first do all variables for y = h, then y = 2h etc.

     91:    */
     92:   PetscLogStageRegister("Assembly", &stage);
     93:   PetscLogStagePush(stage);
     94:   for (Ii=Istart; Ii<Iend; Ii++) {
     95:     v = -1.0; i = Ii/n; j = Ii - i*n;
     96:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     97:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     98:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     99:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    100:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
    101:   }

    103:   /*
    104:      Assemble matrix, using the 2-step process:
    105:        MatAssemblyBegin(), MatAssemblyEnd()
    106:      Computations can be done while messages are in transition
    107:      by placing code between these two statements.
    108:   */
    109:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    110:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    111:   PetscLogStagePop();

    113:   /* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
    114:   MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);

    116:   /*
    117:      Create parallel vectors.
    118:       - We form 1 vector from scratch and then duplicate as needed.
    119:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
    120:         in this example, we specify only the
    121:         vector's global dimension; the parallel partitioning is determined
    122:         at runtime.
    123:       - When solving a linear system, the vectors and matrices MUST
    124:         be partitioned accordingly.  PETSc automatically generates
    125:         appropriately partitioned matrices and vectors when MatCreate()
    126:         and VecCreate() are used with the same communicator.
    127:       - The user can alternatively specify the local vector and matrix
    128:         dimensions when more sophisticated partitioning is needed
    129:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
    130:         below).
    131:   */
    132:   VecCreate(PETSC_COMM_WORLD,&u);
    133:   VecSetSizes(u,PETSC_DECIDE,m*n);
    134:   VecSetFromOptions(u);
    135:   VecDuplicate(u,&b);
    136:   VecDuplicate(b,&x);

    138:   /*
    139:      Set exact solution; then compute right-hand-side vector.
    140:      By default we use an exact solution of a vector with all
    141:      elements of 1.0;  Alternatively, using the runtime option
    142:      -random_sol forms a solution vector with random components.
    143:   */
    144:   if (random_exact_sol) {
    145:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    146:     PetscRandomSetFromOptions(rctx);
    147:     VecSetRandom(u,rctx);
    148:     PetscRandomDestroy(&rctx);
    149:   } else {
    150:     VecSet(u,1.0);
    151:   }
    152:   MatMult(A,u,b);

    154:   /*
    155:      View the exact solution vector if desired
    156:   */
    157:   if (view_exact_sol) VecView(u,PETSC_VIEWER_STDOUT_WORLD);

    159:   if (permute) {
    160:     Mat Aperm;
    161:     MatGetOrdering(A,ordering,&rowperm,&colperm);
    162:     MatPermute(A,rowperm,colperm,&Aperm);
    163:     VecPermute(b,colperm,PETSC_FALSE);
    164:     MatDestroy(&A);
    165:     A    = Aperm;               /* Replace original operator with permuted version */
    166:   }

    168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    169:                 Create the linear solver and set various options
    170:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    172:   /*
    173:      Create linear solver context
    174:   */
    175:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    177:   /*
    178:      Set operators. Here the matrix that defines the linear system
    179:      also serves as the preconditioning matrix.
    180:   */
    181:   KSPSetOperators(ksp,A,A);

    183:   /*
    184:      Set linear solver defaults for this problem (optional).
    185:      - By extracting the KSP and PC contexts from the KSP context,
    186:        we can then directly call any KSP and PC routines to set
    187:        various options.
    188:      - The following two statements are optional; all of these
    189:        parameters could alternatively be specified at runtime via
    190:        KSPSetFromOptions().  All of these defaults can be
    191:        overridden at runtime, as indicated below.
    192:   */
    193:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),PETSC_DEFAULT,PETSC_DEFAULT,
    194:                           PETSC_DEFAULT);

    196:   /*
    197:     Set runtime options, e.g.,
    198:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    199:     These options will override those specified above as long as
    200:     KSPSetFromOptions() is called _after_ any other customization
    201:     routines.
    202:   */
    203:   KSPSetFromOptions(ksp);

    205:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    206:                       Solve the linear system
    207:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    209:   KSPSolve(ksp,b,x);

    211:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    212:                       Check solution and clean up
    213:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    215:   if (permute) VecPermute(x,rowperm,PETSC_TRUE);

    217:   /*
    218:      Check the error
    219:   */
    220:   VecAXPY(x,-1.0,u);
    221:   VecNorm(x,NORM_2,&norm);
    222:   KSPGetIterationNumber(ksp,&its);

    224:   /*
    225:      Print convergence information.  PetscPrintf() produces a single
    226:      print statement from all processes that share a communicator.
    227:      An alternative is PetscFPrintf(), which prints to a file.
    228:   */
    229:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

    231:   /*
    232:      Free work space.  All PETSc objects should be destroyed when they
    233:      are no longer needed.
    234:   */
    235:   KSPDestroy(&ksp);
    236:   VecDestroy(&u));  PetscCall(VecDestroy(&x);
    237:   VecDestroy(&b));  PetscCall(MatDestroy(&A);
    238:   ISDestroy(&rowperm));  PetscCall(ISDestroy(&colperm);

    240:   /*
    241:      Always call PetscFinalize() before exiting a program.  This routine
    242:        - finalizes the PETSc libraries as well as MPI
    243:        - provides summary and diagnostic information if certain runtime
    244:          options are chosen (e.g., -log_view).
    245:   */
    246:   PetscFinalize();
    247:   return 0;
    248: }

    250: /*TEST

    252:    test:
    253:       nsize: 3
    254:       args: -m 39 -n 18 -ksp_monitor_short -permute nd
    255:       requires: !single

    257:    test:
    258:       suffix: 2
    259:       nsize: 3
    260:       args: -m 39 -n 18 -ksp_monitor_short -permute rcm
    261:       requires: !single

    263:    test:
    264:       suffix: 3
    265:       nsize: 3
    266:       args: -m 13 -n 17 -ksp_monitor_short -ksp_type cg -ksp_cg_single_reduction
    267:       requires: !single

    269:    test:
    270:       suffix: bas
    271:       args: -m 13 -n 17 -ksp_monitor_short -ksp_type cg -pc_type icc -pc_factor_mat_solver_type bas -ksp_view -pc_factor_levels 1
    272:       filter: grep -v "variant "
    273:       requires: !single

    275: TEST*/