Actual source code: ex9.c

      2: static char help[] = "The solution of 2 different linear systems with different linear solvers.\n\
      3: Also, this example illustrates the repeated\n\
      4: solution of linear systems, while reusing matrix, vector, and solver data\n\
      5: structures throughout the process.  Note the various stages of event logging.\n\n";

      7: /*T
      8:    Concepts: KSP^repeatedly solving linear systems;
      9:    Concepts: PetscLog^profiling multiple stages of code;
     10:    Concepts: PetscLog^user-defined event profiling;
     11:    Processors: n
     12: 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>

     26: /*
     27:    Declare user-defined routines
     28: */
     29: extern PetscErrorCode CheckError(Vec,Vec,Vec,PetscInt,PetscReal,PetscLogEvent);
     30: extern PetscErrorCode MyKSPMonitor(KSP,PetscInt,PetscReal,void*);

     32: int main(int argc,char **args)
     33: {
     34:   Vec            x1,b1,x2,b2; /* solution and RHS vectors for systems #1 and #2 */
     35:   Vec            u;              /* exact solution vector */
     36:   Mat            C1,C2;         /* matrices for systems #1 and #2 */
     37:   KSP            ksp1,ksp2;   /* KSP contexts for systems #1 and #2 */
     38:   PetscInt       ntimes = 3;     /* number of times to solve the linear systems */
     39:   PetscLogEvent  CHECK_ERROR;    /* event number for error checking */
     40:   PetscInt       ldim,low,high,iglobal,Istart,Iend,Istart2,Iend2;
     41:   PetscInt       Ii,J,i,j,m = 3,n = 2,its,t;
     43:   PetscBool      flg = PETSC_FALSE, unsym = PETSC_TRUE;
     44:   PetscScalar    v;
     45:   PetscMPIInt    rank,size;
     46: #if defined(PETSC_USE_LOG)
     47:   PetscLogStage stages[3];
     48: #endif

     50:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     51:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     52:   PetscOptionsGetInt(NULL,NULL,"-t",&ntimes,NULL);
     53:   PetscOptionsGetBool(NULL,NULL,"-unsym",&unsym,NULL);
     54:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     55:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     56:   n    = 2*size;

     58:   /*
     59:      Register various stages for profiling
     60:   */
     61:   PetscLogStageRegister("Prelim setup",&stages[0]);
     62:   PetscLogStageRegister("Linear System 1",&stages[1]);
     63:   PetscLogStageRegister("Linear System 2",&stages[2]);

     65:   /*
     66:      Register a user-defined event for profiling (error checking).
     67:   */
     68:   CHECK_ERROR = 0;
     69:   PetscLogEventRegister("Check Error",KSP_CLASSID,&CHECK_ERROR);

     71:   /* - - - - - - - - - - - - Stage 0: - - - - - - - - - - - - - -
     72:                         Preliminary Setup
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     75:   PetscLogStagePush(stages[0]);

     77:   /*
     78:      Create data structures for first linear system.
     79:       - Create parallel matrix, specifying only its global dimensions.
     80:         When using MatCreate(), the matrix format can be specified at
     81:         runtime. Also, the parallel partitioning of the matrix is
     82:         determined by PETSc at runtime.
     83:       - Create parallel vectors.
     84:         - When using VecSetSizes(), we specify only the vector's global
     85:           dimension; the parallel partitioning is determined at runtime.
     86:         - Note: We form 1 vector from scratch and then duplicate as needed.
     87:   */
     88:   MatCreate(PETSC_COMM_WORLD,&C1);
     89:   MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     90:   MatSetFromOptions(C1);
     91:   MatSetUp(C1);
     92:   MatGetOwnershipRange(C1,&Istart,&Iend);
     93:   VecCreate(PETSC_COMM_WORLD,&u);
     94:   VecSetSizes(u,PETSC_DECIDE,m*n);
     95:   VecSetFromOptions(u);
     96:   VecDuplicate(u,&b1);
     97:   VecDuplicate(u,&x1);

     99:   /*
    100:      Create first linear solver context.
    101:      Set runtime options (e.g., -pc_type <type>).
    102:      Note that the first linear system uses the default option
    103:      names, while the second linear system uses a different
    104:      options prefix.
    105:   */
    106:   KSPCreate(PETSC_COMM_WORLD,&ksp1);
    107:   KSPSetFromOptions(ksp1);

    109:   /*
    110:      Set user-defined monitoring routine for first linear system.
    111:   */
    112:   PetscOptionsGetBool(NULL,NULL,"-my_ksp_monitor",&flg,NULL);
    113:   if (flg) {KSPMonitorSet(ksp1,MyKSPMonitor,NULL,0);}

    115:   /*
    116:      Create data structures for second linear system.
    117:   */
    118:   MatCreate(PETSC_COMM_WORLD,&C2);
    119:   MatSetSizes(C2,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
    120:   MatSetFromOptions(C2);
    121:   MatSetUp(C2);
    122:   MatGetOwnershipRange(C2,&Istart2,&Iend2);
    123:   VecDuplicate(u,&b2);
    124:   VecDuplicate(u,&x2);

    126:   /*
    127:      Create second linear solver context
    128:   */
    129:   KSPCreate(PETSC_COMM_WORLD,&ksp2);

    131:   /*
    132:      Set different options prefix for second linear system.
    133:      Set runtime options (e.g., -s2_pc_type <type>)
    134:   */
    135:   KSPAppendOptionsPrefix(ksp2,"s2_");
    136:   KSPSetFromOptions(ksp2);

    138:   /*
    139:      Assemble exact solution vector in parallel.  Note that each
    140:      processor needs to set only its local part of the vector.
    141:   */
    142:   VecGetLocalSize(u,&ldim);
    143:   VecGetOwnershipRange(u,&low,&high);
    144:   for (i=0; i<ldim; i++) {
    145:     iglobal = i + low;
    146:     v       = (PetscScalar)(i + 100*rank);
    147:     VecSetValues(u,1,&iglobal,&v,ADD_VALUES);
    148:   }
    149:   VecAssemblyBegin(u);
    150:   VecAssemblyEnd(u);

    152:   /*
    153:      Log the number of flops for computing vector entries
    154:   */
    155:   PetscLogFlops(2.0*ldim);

    157:   /*
    158:      End curent profiling stage
    159:   */
    160:   PetscLogStagePop();

    162:   /* --------------------------------------------------------------
    163:                         Linear solver loop:
    164:       Solve 2 different linear systems several times in succession
    165:      -------------------------------------------------------------- */

    167:   for (t=0; t<ntimes; t++) {

    169:     /* - - - - - - - - - - - - Stage 1: - - - - - - - - - - - - - -
    170:                  Assemble and solve first linear system
    171:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    173:     /*
    174:        Begin profiling stage #1
    175:     */
    176:     PetscLogStagePush(stages[1]);

    178:     /*
    179:        Initialize all matrix entries to zero.  MatZeroEntries() retains
    180:        the nonzero structure of the matrix for sparse formats.
    181:     */
    182:     if (t > 0) {MatZeroEntries(C1);}

    184:     /*
    185:        Set matrix entries in parallel.  Also, log the number of flops
    186:        for computing matrix entries.
    187:         - Each processor needs to insert only elements that it owns
    188:           locally (but any non-local elements will be sent to the
    189:           appropriate processor during matrix assembly).
    190:         - Always specify global row and columns of matrix entries.
    191:     */
    192:     for (Ii=Istart; Ii<Iend; Ii++) {
    193:       v = -1.0; i = Ii/n; j = Ii - i*n;
    194:       if (i>0)   {J = Ii - n; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    195:       if (i<m-1) {J = Ii + n; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    196:       if (j>0)   {J = Ii - 1; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    197:       if (j<n-1) {J = Ii + 1; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    198:       v = 4.0; MatSetValues(C1,1,&Ii,1,&Ii,&v,ADD_VALUES);
    199:     }
    200:     if (unsym) {
    201:       for (Ii=Istart; Ii<Iend; Ii++) { /* Make matrix nonsymmetric */
    202:         v = -1.0*(t+0.5); i = Ii/n;
    203:         if (i>0)   {J = Ii - n; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    204:       }
    205:       PetscLogFlops(2.0*(Iend-Istart));
    206:     }

    208:     /*
    209:        Assemble matrix, using the 2-step process:
    210:          MatAssemblyBegin(), MatAssemblyEnd()
    211:        Computations can be done while messages are in transition
    212:        by placing code between these two statements.
    213:     */
    214:     MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);
    215:     MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);

    217:     /*
    218:        Indicate same nonzero structure of successive linear system matrices
    219:     */
    220:     MatSetOption(C1,MAT_NEW_NONZERO_LOCATIONS,PETSC_TRUE);

    222:     /*
    223:        Compute right-hand-side vector
    224:     */
    225:     MatMult(C1,u,b1);

    227:     /*
    228:        Set operators. Here the matrix that defines the linear system
    229:        also serves as the preconditioning matrix.
    230:     */
    231:     KSPSetOperators(ksp1,C1,C1);

    233:     /*
    234:        Use the previous solution of linear system #1 as the initial
    235:        guess for the next solve of linear system #1.  The user MUST
    236:        call KSPSetInitialGuessNonzero() in indicate use of an initial
    237:        guess vector; otherwise, an initial guess of zero is used.
    238:     */
    239:     if (t>0) {
    240:       KSPSetInitialGuessNonzero(ksp1,PETSC_TRUE);
    241:     }

    243:     /*
    244:        Solve the first linear system.  Here we explicitly call
    245:        KSPSetUp() for more detailed performance monitoring of
    246:        certain preconditioners, such as ICC and ILU.  This call
    247:        is optional, ase KSPSetUp() will automatically be called
    248:        within KSPSolve() if it hasn't been called already.
    249:     */
    250:     KSPSetUp(ksp1);
    251:     KSPSolve(ksp1,b1,x1);
    252:     KSPGetIterationNumber(ksp1,&its);

    254:     /*
    255:        Check error of solution to first linear system
    256:     */
    257:     CheckError(u,x1,b1,its,1.e-4,CHECK_ERROR);

    259:     /* - - - - - - - - - - - - Stage 2: - - - - - - - - - - - - - -
    260:                  Assemble and solve second linear system
    261:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    263:     /*
    264:        Conclude profiling stage #1; begin profiling stage #2
    265:     */
    266:     PetscLogStagePop();
    267:     PetscLogStagePush(stages[2]);

    269:     /*
    270:        Initialize all matrix entries to zero
    271:     */
    272:     if (t > 0) {MatZeroEntries(C2);}

    274:     /*
    275:        Assemble matrix in parallel. Also, log the number of flops
    276:        for computing matrix entries.
    277:         - To illustrate the features of parallel matrix assembly, we
    278:           intentionally set the values differently from the way in
    279:           which the matrix is distributed across the processors.  Each
    280:           entry that is not owned locally will be sent to the appropriate
    281:           processor during MatAssemblyBegin() and MatAssemblyEnd().
    282:         - For best efficiency the user should strive to set as many
    283:           entries locally as possible.
    284:      */
    285:     for (i=0; i<m; i++) {
    286:       for (j=2*rank; j<2*rank+2; j++) {
    287:         v = -1.0;  Ii = j + n*i;
    288:         if (i>0)   {J = Ii - n; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    289:         if (i<m-1) {J = Ii + n; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    290:         if (j>0)   {J = Ii - 1; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    291:         if (j<n-1) {J = Ii + 1; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    292:         v = 6.0 + t*0.5; MatSetValues(C2,1,&Ii,1,&Ii,&v,ADD_VALUES);
    293:       }
    294:     }
    295:     if (unsym) {
    296:       for (Ii=Istart2; Ii<Iend2; Ii++) { /* Make matrix nonsymmetric */
    297:         v = -1.0*(t+0.5); i = Ii/n;
    298:         if (i>0)   {J = Ii - n; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    299:       }
    300:     }
    301:     MatAssemblyBegin(C2,MAT_FINAL_ASSEMBLY);
    302:     MatAssemblyEnd(C2,MAT_FINAL_ASSEMBLY);
    303:     PetscLogFlops(2.0*(Iend-Istart));

    305:     /*
    306:        Indicate same nonzero structure of successive linear system matrices
    307:     */
    308:     MatSetOption(C2,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);

    310:     /*
    311:        Compute right-hand-side vector
    312:     */
    313:     MatMult(C2,u,b2);

    315:     /*
    316:        Set operators. Here the matrix that defines the linear system
    317:        also serves as the preconditioning matrix.  Indicate same nonzero
    318:        structure of successive preconditioner matrices by setting flag
    319:        SAME_NONZERO_PATTERN.
    320:     */
    321:     KSPSetOperators(ksp2,C2,C2);

    323:     /*
    324:        Solve the second linear system
    325:     */
    326:     KSPSetUp(ksp2);
    327:     KSPSolve(ksp2,b2,x2);
    328:     KSPGetIterationNumber(ksp2,&its);

    330:     /*
    331:        Check error of solution to second linear system
    332:     */
    333:     CheckError(u,x2,b2,its,1.e-4,CHECK_ERROR);

    335:     /*
    336:        Conclude profiling stage #2
    337:     */
    338:     PetscLogStagePop();
    339:   }
    340:   /* --------------------------------------------------------------
    341:                        End of linear solver loop
    342:      -------------------------------------------------------------- */

    344:   /*
    345:      Free work space.  All PETSc objects should be destroyed when they
    346:      are no longer needed.
    347:   */
    348:   KSPDestroy(&ksp1); KSPDestroy(&ksp2);
    349:   VecDestroy(&x1);   VecDestroy(&x2);
    350:   VecDestroy(&b1);   VecDestroy(&b2);
    351:   MatDestroy(&C1);   MatDestroy(&C2);
    352:   VecDestroy(&u);

    354:   PetscFinalize();
    355:   return ierr;
    356: }
    357: /* ------------------------------------------------------------- */
    358: /*
    359:     CheckError - Checks the error of the solution.

    361:     Input Parameters:
    362:     u - exact solution
    363:     x - approximate solution
    364:     b - work vector
    365:     its - number of iterations for convergence
    366:     tol - tolerance
    367:     CHECK_ERROR - the event number for error checking
    368:                   (for use with profiling)

    370:     Notes:
    371:     In order to profile this section of code separately from the
    372:     rest of the program, we register it as an "event" with
    373:     PetscLogEventRegister() in the main program.  Then, we indicate
    374:     the start and end of this event by respectively calling
    375:         PetscLogEventBegin(CHECK_ERROR,u,x,b,0);
    376:         PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
    377:     Here, we specify the objects most closely associated with
    378:     the event (the vectors u,x,b).  Such information is optional;
    379:     we could instead just use 0 instead for all objects.
    380: */
    381: PetscErrorCode CheckError(Vec u,Vec x,Vec b,PetscInt its,PetscReal tol,PetscLogEvent CHECK_ERROR)
    382: {
    383:   PetscScalar    none = -1.0;
    384:   PetscReal      norm;

    387:   PetscLogEventBegin(CHECK_ERROR,u,x,b,0);

    389:   /*
    390:      Compute error of the solution, using b as a work vector.
    391:   */
    392:   VecCopy(x,b);
    393:   VecAXPY(b,none,u);
    394:   VecNorm(b,NORM_2,&norm);
    395:   if (norm > tol) {
    396:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    397:   }
    398:   PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
    399:   return 0;
    400: }
    401: /* ------------------------------------------------------------- */
    402: /*
    403:    MyKSPMonitor - This is a user-defined routine for monitoring
    404:    the KSP iterative solvers.

    406:    Input Parameters:
    407:      ksp   - iterative context
    408:      n     - iteration number
    409:      rnorm - 2-norm (preconditioned) residual value (may be estimated)
    410:      dummy - optional user-defined monitor context (unused here)
    411: */
    412: PetscErrorCode MyKSPMonitor(KSP ksp,PetscInt n,PetscReal rnorm,void *dummy)
    413: {
    414:   Vec            x;

    417:   /*
    418:      Build the solution vector
    419:   */
    420:   KSPBuildSolution(ksp,NULL,&x);

    422:   /*
    423:      Write the solution vector and residual norm to stdout.
    424:       - PetscPrintf() handles output for multiprocessor jobs
    425:         by printing from only one processor in the communicator.
    426:       - The parallel viewer PETSC_VIEWER_STDOUT_WORLD handles
    427:         data from multiple processors so that the output
    428:         is not jumbled.
    429:   */
    430:   PetscPrintf(PETSC_COMM_WORLD,"iteration %D solution vector:\n",n);
    431:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);
    432:   PetscPrintf(PETSC_COMM_WORLD,"iteration %D KSP Residual norm %14.12e \n",n,rnorm);
    433:   return 0;
    434: }

    438: /*TEST

    440:    test:
    441:       args: -t 2 -pc_type jacobi -ksp_monitor_short -ksp_type gmres -ksp_gmres_cgs_refinement_type refine_always -s2_ksp_type bcgs -s2_pc_type jacobi -s2_ksp_monitor_short

    443:    test:
    444:       requires: hpddm
    445:       suffix: hpddm
    446:       args: -t 2 -pc_type jacobi -ksp_monitor_short -ksp_type {{gmres hpddm}} -s2_ksp_type {{gmres hpddm}} -s2_pc_type jacobi -s2_ksp_monitor_short

    448:    test:
    449:       requires: hpddm
    450:       suffix: hpddm_2
    451:       args: -t 2 -pc_type jacobi -ksp_monitor_short -ksp_type gmres -s2_ksp_type hpddm -s2_ksp_hpddm_type gcrodr -s2_ksp_hpddm_recycle 10 -s2_pc_type jacobi -s2_ksp_monitor_short

    453:    testset:
    454:       requires: hpddm
    455:       output_file: output/ex9_hpddm_cg.out
    456:       args: -unsym 0 -t 2 -pc_type jacobi -ksp_monitor_short -s2_pc_type jacobi -s2_ksp_monitor_short -ksp_rtol 1.e-2 -s2_ksp_rtol 1.e-2
    457:       test:
    458:          suffix: hpddm_cg_p_p
    459:          args: -ksp_type cg -s2_ksp_type cg
    460:       test:
    461:          suffix: hpddm_cg_p_h
    462:          args: -ksp_type cg -s2_ksp_type hpddm -s2_ksp_hpddm_type {{cg bcg bfbcg}shared output}
    463:       test:
    464:          suffix: hpddm_cg_h_h
    465:          args: -ksp_type hpddm -ksp_hpddm_type cg -s2_ksp_type hpddm -s2_ksp_hpddm_type {{cg bcg bfbcg}shared output}

    467: TEST*/