Date: 2013-07-02T14:48:45+00:00

Actual source code: ex18.c
petsc-3.4.2 2013-07-02

      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_n>       : number of mesh points in y-direction\n\n";

      9: /*T
     10:    Concepts: KSP^basic parallel example;
     11:    Concepts: KSP^Laplacian, 2d
     12:    Concepts: Laplacian, 2d
     13:    Processors: n
     14: T*/

     16: /*
     17:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     18:   automatically includes:
     19:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     20:      petscmat.h - matrices
     21:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     22:      petscviewer.h - viewers               petscpc.h  - preconditioners
     23: */
     24: #include <petscksp.h>

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

     45:   PetscInitialize(&argc,&args,(char*)0,help);
     46:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Poisson example options","");
     47:   {
     48:     m                = 8;
     49:     PetscOptionsInt("-m","Number of grid points in x direction","",m,&m,NULL);
     50:     n                = m-1;
     51:     PetscOptionsInt("-n","Number of grid points in y direction","",n,&n,NULL);
     52:     random_exact_sol = PETSC_FALSE;
     53:     PetscOptionsBool("-random_exact_sol","Choose a random exact solution","",random_exact_sol,&random_exact_sol,NULL);
     54:     view_exact_sol   = PETSC_FALSE;
     55:     PetscOptionsBool("-view_exact_sol","View exact solution","",view_exact_sol,&view_exact_sol,NULL);
     56:     permute          = PETSC_FALSE;
     57:     PetscOptionsList("-permute","Permute matrix and vector to solving in new ordering","",MatOrderingList,ordering,ordering,sizeof(ordering),&permute);
     58:   }
     59:   PetscOptionsEnd();
     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:          Compute the matrix and right-hand-side vector that define
     62:          the linear system, Ax = b.
     63:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     64:   /*
     65:      Create parallel matrix, specifying only its global dimensions.
     66:      When using MatCreate(), the matrix format can be specified at
     67:      runtime. Also, the parallel partitioning of the matrix is
     68:      determined by PETSc at runtime.

     70:      Performance tuning note:  For problems of substantial size,
     71:      preallocation of matrix memory is crucial for attaining good
     72:      performance. See the matrix chapter of the users manual for details.
     73:   */
     74:   MatCreate(PETSC_COMM_WORLD,&A);
     75:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     76:   MatSetFromOptions(A);
     77:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
     78:   MatSeqAIJSetPreallocation(A,5,NULL);
     79:   MatSetUp(A);

     81:   /*
     82:      Currently, all PETSc parallel matrix formats are partitioned by
     83:      contiguous chunks of rows across the processors.  Determine which
     84:      rows of the matrix are locally owned.
     85:   */
     86:   MatGetOwnershipRange(A,&Istart,&Iend);

     88:   /*
     89:      Set matrix elements for the 2-D, five-point stencil in parallel.
     90:       - Each processor needs to insert only elements that it owns
     91:         locally (but any non-local elements will be sent to the
     92:         appropriate processor during matrix assembly).
     93:       - Always specify global rows and columns of matrix entries.

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

    100:    */
    101:   PetscLogStageRegister("Assembly", &stage);
    102:   PetscLogStagePush(stage);
    103:   for (Ii=Istart; Ii<Iend; Ii++) {
    104:     v = -1.0; i = Ii/n; j = Ii - i*n;
    105:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    106:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    107:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    108:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    109:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
    110:   }

    112:   /*
    113:      Assemble matrix, using the 2-step process:
    114:        MatAssemblyBegin(), MatAssemblyEnd()
    115:      Computations can be done while messages are in transition
    116:      by placing code between these two statements.
    117:   */
    118:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    119:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    120:   PetscLogStagePop();

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

    125:   /*
    126:      Create parallel vectors.
    127:       - We form 1 vector from scratch and then duplicate as needed.
    128:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
    129:         in this example, we specify only the
    130:         vector's global dimension; the parallel partitioning is determined
    131:         at runtime.
    132:       - When solving a linear system, the vectors and matrices MUST
    133:         be partitioned accordingly.  PETSc automatically generates
    134:         appropriately partitioned matrices and vectors when MatCreate()
    135:         and VecCreate() are used with the same communicator.
    136:       - The user can alternatively specify the local vector and matrix
    137:         dimensions when more sophisticated partitioning is needed
    138:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
    139:         below).
    140:   */
    141:   VecCreate(PETSC_COMM_WORLD,&u);
    142:   VecSetSizes(u,PETSC_DECIDE,m*n);
    143:   VecSetFromOptions(u);
    144:   VecDuplicate(u,&b);
    145:   VecDuplicate(b,&x);

    147:   /*
    148:      Set exact solution; then compute right-hand-side vector.
    149:      By default we use an exact solution of a vector with all
    150:      elements of 1.0;  Alternatively, using the runtime option
    151:      -random_sol forms a solution vector with random components.
    152:   */
    153:   if (random_exact_sol) {
    154:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    155:     PetscRandomSetFromOptions(rctx);
    156:     VecSetRandom(u,rctx);
    157:     PetscRandomDestroy(&rctx);
    158:   } else {
    159:     VecSet(u,1.0);
    160:   }
    161:   MatMult(A,u,b);

    163:   /*
    164:      View the exact solution vector if desired
    165:   */
    166:   if (view_exact_sol) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

    168:   if (permute) {
    169:     Mat Aperm;
    170:     MatGetOrdering(A,ordering,&rowperm,&colperm);
    171:     MatPermute(A,rowperm,colperm,&Aperm);
    172:     VecPermute(b,colperm,PETSC_FALSE);
    173:     MatDestroy(&A);
    174:     A    = Aperm;               /* Replace original operator with permuted version */
    175:   }

    177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    178:                 Create the linear solver and set various options
    179:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    181:   /*
    182:      Create linear solver context
    183:   */
    184:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    186:   /*
    187:      Set operators. Here the matrix that defines the linear system
    188:      also serves as the preconditioning matrix.
    189:   */
    190:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

    192:   /*
    193:      Set linear solver defaults for this problem (optional).
    194:      - By extracting the KSP and PC contexts from the KSP context,
    195:        we can then directly call any KSP and PC routines to set
    196:        various options.
    197:      - The following two statements are optional; all of these
    198:        parameters could alternatively be specified at runtime via
    199:        KSPSetFromOptions().  All of these defaults can be
    200:        overridden at runtime, as indicated below.
    201:   */
    202:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
    203:                           PETSC_DEFAULT);

    205:   /*
    206:     Set runtime options, e.g.,
    207:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    208:     These options will override those specified above as long as
    209:     KSPSetFromOptions() is called _after_ any other customization
    210:     routines.
    211:   */
    212:   KSPSetFromOptions(ksp);

    214:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    215:                       Solve the linear system
    216:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    218:   KSPSolve(ksp,b,x);

    220:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    221:                       Check solution and clean up
    222:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    224:   if (permute) {VecPermute(x,rowperm,PETSC_TRUE);}

    226:   /*
    227:      Check the error
    228:   */
    229:   VecAXPY(x,-1.0,u);
    230:   VecNorm(x,NORM_2,&norm);
    231:   KSPGetIterationNumber(ksp,&its);

    233:   /*
    234:      Print convergence information.  PetscPrintf() produces a single
    235:      print statement from all processes that share a communicator.
    236:      An alternative is PetscFPrintf(), which prints to a file.
    237:   */
    238:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G iterations %D\n",
    239:                      norm,its);

    241:   /*
    242:      Free work space.  All PETSc objects should be destroyed when they
    243:      are no longer needed.
    244:   */
    245:   KSPDestroy(&ksp);
    246:   VecDestroy(&u);  VecDestroy(&x);
    247:   VecDestroy(&b);  MatDestroy(&A);
    248:   ISDestroy(&rowperm);  ISDestroy(&colperm);

    250:   /*
    251:      Always call PetscFinalize() before exiting a program.  This routine
    252:        - finalizes the PETSc libraries as well as MPI
    253:        - provides summary and diagnostic information if certain runtime
    254:          options are chosen (e.g., -log_summary).
    255:   */
    256:   PetscFinalize();
    257:   return 0;
    258: }