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

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: /*
      8:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
      9:   automatically includes:
     10:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     11:      petscmat.h - matrices
     12:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     13:      petscviewer.h - viewers               petscpc.h  - preconditioners
     14: */
     15: #include <petscksp.h>

     17: /*
     18:    Declare user-defined routines
     19: */
     20: extern PetscErrorCode CheckError(Vec,Vec,Vec,PetscInt,PetscReal,PetscLogEvent);
     21: extern PetscErrorCode MyKSPMonitor(KSP,PetscInt,PetscReal,void*);

     23: int main(int argc,char **args)
     24: {
     25:   Vec            x1,b1,x2,b2; /* solution and RHS vectors for systems #1 and #2 */
     26:   Vec            u;              /* exact solution vector */
     27:   Mat            C1,C2;         /* matrices for systems #1 and #2 */
     28:   KSP            ksp1,ksp2;   /* KSP contexts for systems #1 and #2 */
     29:   PetscInt       ntimes = 3;     /* number of times to solve the linear systems */
     30:   PetscLogEvent  CHECK_ERROR;    /* event number for error checking */
     31:   PetscInt       ldim,low,high,iglobal,Istart,Iend,Istart2,Iend2;
     32:   PetscInt       Ii,J,i,j,m = 3,n = 2,its,t;
     33:   PetscBool      flg = PETSC_FALSE, unsym = PETSC_TRUE;
     34:   PetscScalar    v;
     35:   PetscMPIInt    rank,size;
     36: #if defined(PETSC_USE_LOG)
     37:   PetscLogStage stages[3];
     38: #endif

     40:   PetscInitialize(&argc,&args,(char*)0,help);
     41:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     42:   PetscOptionsGetInt(NULL,NULL,"-t",&ntimes,NULL);
     43:   PetscOptionsGetBool(NULL,NULL,"-unsym",&unsym,NULL);
     44:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     45:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     46:   n    = 2*size;

     48:   /*
     49:      Register various stages for profiling
     50:   */
     51:   PetscLogStageRegister("Prelim setup",&stages[0]);
     52:   PetscLogStageRegister("Linear System 1",&stages[1]);
     53:   PetscLogStageRegister("Linear System 2",&stages[2]);

     55:   /*
     56:      Register a user-defined event for profiling (error checking).
     57:   */
     58:   CHECK_ERROR = 0;
     59:   PetscLogEventRegister("Check Error",KSP_CLASSID,&CHECK_ERROR);

     61:   /* - - - - - - - - - - - - Stage 0: - - - - - - - - - - - - - -
     62:                         Preliminary Setup
     63:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     65:   PetscLogStagePush(stages[0]);

     67:   /*
     68:      Create data structures for first linear system.
     69:       - Create parallel matrix, specifying only its global dimensions.
     70:         When using MatCreate(), the matrix format can be specified at
     71:         runtime. Also, the parallel partitioning of the matrix is
     72:         determined by PETSc at runtime.
     73:       - Create parallel vectors.
     74:         - When using VecSetSizes(), we specify only the vector's global
     75:           dimension; the parallel partitioning is determined at runtime.
     76:         - Note: We form 1 vector from scratch and then duplicate as needed.
     77:   */
     78:   MatCreate(PETSC_COMM_WORLD,&C1);
     79:   MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     80:   MatSetFromOptions(C1);
     81:   MatSetUp(C1);
     82:   MatGetOwnershipRange(C1,&Istart,&Iend);
     83:   VecCreate(PETSC_COMM_WORLD,&u);
     84:   VecSetSizes(u,PETSC_DECIDE,m*n);
     85:   VecSetFromOptions(u);
     86:   VecDuplicate(u,&b1);
     87:   VecDuplicate(u,&x1);

     89:   /*
     90:      Create first linear solver context.
     91:      Set runtime options (e.g., -pc_type <type>).
     92:      Note that the first linear system uses the default option
     93:      names, while the second linear system uses a different
     94:      options prefix.
     95:   */
     96:   KSPCreate(PETSC_COMM_WORLD,&ksp1);
     97:   KSPSetFromOptions(ksp1);

     99:   /*
    100:      Set user-defined monitoring routine for first linear system.
    101:   */
    102:   PetscOptionsGetBool(NULL,NULL,"-my_ksp_monitor",&flg,NULL);
    103:   if (flg) KSPMonitorSet(ksp1,MyKSPMonitor,NULL,0);

    105:   /*
    106:      Create data structures for second linear system.
    107:   */
    108:   MatCreate(PETSC_COMM_WORLD,&C2);
    109:   MatSetSizes(C2,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
    110:   MatSetFromOptions(C2);
    111:   MatSetUp(C2);
    112:   MatGetOwnershipRange(C2,&Istart2,&Iend2);
    113:   VecDuplicate(u,&b2);
    114:   VecDuplicate(u,&x2);

    116:   /*
    117:      Create second linear solver context
    118:   */
    119:   KSPCreate(PETSC_COMM_WORLD,&ksp2);

    121:   /*
    122:      Set different options prefix for second linear system.
    123:      Set runtime options (e.g., -s2_pc_type <type>)
    124:   */
    125:   KSPAppendOptionsPrefix(ksp2,"s2_");
    126:   KSPSetFromOptions(ksp2);

    128:   /*
    129:      Assemble exact solution vector in parallel.  Note that each
    130:      processor needs to set only its local part of the vector.
    131:   */
    132:   VecGetLocalSize(u,&ldim);
    133:   VecGetOwnershipRange(u,&low,&high);
    134:   for (i=0; i<ldim; i++) {
    135:     iglobal = i + low;
    136:     v       = (PetscScalar)(i + 100*rank);
    137:     VecSetValues(u,1,&iglobal,&v,ADD_VALUES);
    138:   }
    139:   VecAssemblyBegin(u);
    140:   VecAssemblyEnd(u);

    142:   /*
    143:      Log the number of flops for computing vector entries
    144:   */
    145:   PetscLogFlops(2.0*ldim);

    147:   /*
    148:      End curent profiling stage
    149:   */
    150:   PetscLogStagePop();

    152:   /* --------------------------------------------------------------
    153:                         Linear solver loop:
    154:       Solve 2 different linear systems several times in succession
    155:      -------------------------------------------------------------- */

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

    159:     /* - - - - - - - - - - - - Stage 1: - - - - - - - - - - - - - -
    160:                  Assemble and solve first linear system
    161:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    163:     /*
    164:        Begin profiling stage #1
    165:     */
    166:     PetscLogStagePush(stages[1]);

    168:     /*
    169:        Initialize all matrix entries to zero.  MatZeroEntries() retains
    170:        the nonzero structure of the matrix for sparse formats.
    171:     */
    172:     if (t > 0) MatZeroEntries(C1);

    174:     /*
    175:        Set matrix entries in parallel.  Also, log the number of flops
    176:        for computing matrix entries.
    177:         - Each processor needs to insert only elements that it owns
    178:           locally (but any non-local elements will be sent to the
    179:           appropriate processor during matrix assembly).
    180:         - Always specify global row and columns of matrix entries.
    181:     */
    182:     for (Ii=Istart; Ii<Iend; Ii++) {
    183:       v = -1.0; i = Ii/n; j = Ii - i*n;
    184:       if (i>0)   {J = Ii - n; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    185:       if (i<m-1) {J = Ii + n; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    186:       if (j>0)   {J = Ii - 1; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    187:       if (j<n-1) {J = Ii + 1; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    188:       v = 4.0; MatSetValues(C1,1,&Ii,1,&Ii,&v,ADD_VALUES);
    189:     }
    190:     if (unsym) {
    191:       for (Ii=Istart; Ii<Iend; Ii++) { /* Make matrix nonsymmetric */
    192:         v = -1.0*(t+0.5); i = Ii/n;
    193:         if (i>0)   {J = Ii - n; MatSetValues(C1,1,&Ii,1,&J,&v,ADD_VALUES);}
    194:       }
    195:       PetscLogFlops(2.0*(Iend-Istart));
    196:     }

    198:     /*
    199:        Assemble matrix, using the 2-step process:
    200:          MatAssemblyBegin(), MatAssemblyEnd()
    201:        Computations can be done while messages are in transition
    202:        by placing code between these two statements.
    203:     */
    204:     MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);
    205:     MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);

    207:     /*
    208:        Indicate same nonzero structure of successive linear system matrices
    209:     */
    210:     MatSetOption(C1,MAT_NEW_NONZERO_LOCATIONS,PETSC_TRUE);

    212:     /*
    213:        Compute right-hand-side vector
    214:     */
    215:     MatMult(C1,u,b1);

    217:     /*
    218:        Set operators. Here the matrix that defines the linear system
    219:        also serves as the preconditioning matrix.
    220:     */
    221:     KSPSetOperators(ksp1,C1,C1);

    223:     /*
    224:        Use the previous solution of linear system #1 as the initial
    225:        guess for the next solve of linear system #1.  The user MUST
    226:        call KSPSetInitialGuessNonzero() in indicate use of an initial
    227:        guess vector; otherwise, an initial guess of zero is used.
    228:     */
    229:     if (t>0) {
    230:       KSPSetInitialGuessNonzero(ksp1,PETSC_TRUE);
    231:     }

    233:     /*
    234:        Solve the first linear system.  Here we explicitly call
    235:        KSPSetUp() for more detailed performance monitoring of
    236:        certain preconditioners, such as ICC and ILU.  This call
    237:        is optional, ase KSPSetUp() will automatically be called
    238:        within KSPSolve() if it hasn't been called already.
    239:     */
    240:     KSPSetUp(ksp1);
    241:     KSPSolve(ksp1,b1,x1);
    242:     KSPGetIterationNumber(ksp1,&its);

    244:     /*
    245:        Check error of solution to first linear system
    246:     */
    247:     CheckError(u,x1,b1,its,1.e-4,CHECK_ERROR);

    249:     /* - - - - - - - - - - - - Stage 2: - - - - - - - - - - - - - -
    250:                  Assemble and solve second linear system
    251:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    253:     /*
    254:        Conclude profiling stage #1; begin profiling stage #2
    255:     */
    256:     PetscLogStagePop();
    257:     PetscLogStagePush(stages[2]);

    259:     /*
    260:        Initialize all matrix entries to zero
    261:     */
    262:     if (t > 0) MatZeroEntries(C2);

    264:     /*
    265:        Assemble matrix in parallel. Also, log the number of flops
    266:        for computing matrix entries.
    267:         - To illustrate the features of parallel matrix assembly, we
    268:           intentionally set the values differently from the way in
    269:           which the matrix is distributed across the processors.  Each
    270:           entry that is not owned locally will be sent to the appropriate
    271:           processor during MatAssemblyBegin() and MatAssemblyEnd().
    272:         - For best efficiency the user should strive to set as many
    273:           entries locally as possible.
    274:      */
    275:     for (i=0; i<m; i++) {
    276:       for (j=2*rank; j<2*rank+2; j++) {
    277:         v = -1.0;  Ii = j + n*i;
    278:         if (i>0)   {J = Ii - n; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    279:         if (i<m-1) {J = Ii + n; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    280:         if (j>0)   {J = Ii - 1; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    281:         if (j<n-1) {J = Ii + 1; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    282:         v = 6.0 + t*0.5; MatSetValues(C2,1,&Ii,1,&Ii,&v,ADD_VALUES);
    283:       }
    284:     }
    285:     if (unsym) {
    286:       for (Ii=Istart2; Ii<Iend2; Ii++) { /* Make matrix nonsymmetric */
    287:         v = -1.0*(t+0.5); i = Ii/n;
    288:         if (i>0)   {J = Ii - n; MatSetValues(C2,1,&Ii,1,&J,&v,ADD_VALUES);}
    289:       }
    290:     }
    291:     MatAssemblyBegin(C2,MAT_FINAL_ASSEMBLY);
    292:     MatAssemblyEnd(C2,MAT_FINAL_ASSEMBLY);
    293:     PetscLogFlops(2.0*(Iend-Istart));

    295:     /*
    296:        Indicate same nonzero structure of successive linear system matrices
    297:     */
    298:     MatSetOption(C2,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);

    300:     /*
    301:        Compute right-hand-side vector
    302:     */
    303:     MatMult(C2,u,b2);

    305:     /*
    306:        Set operators. Here the matrix that defines the linear system
    307:        also serves as the preconditioning matrix.  Indicate same nonzero
    308:        structure of successive preconditioner matrices by setting flag
    309:        SAME_NONZERO_PATTERN.
    310:     */
    311:     KSPSetOperators(ksp2,C2,C2);

    313:     /*
    314:        Solve the second linear system
    315:     */
    316:     KSPSetUp(ksp2);
    317:     KSPSolve(ksp2,b2,x2);
    318:     KSPGetIterationNumber(ksp2,&its);

    320:     /*
    321:        Check error of solution to second linear system
    322:     */
    323:     CheckError(u,x2,b2,its,1.e-4,CHECK_ERROR);

    325:     /*
    326:        Conclude profiling stage #2
    327:     */
    328:     PetscLogStagePop();
    329:   }
    330:   /* --------------------------------------------------------------
    331:                        End of linear solver loop
    332:      -------------------------------------------------------------- */

    334:   /*
    335:      Free work space.  All PETSc objects should be destroyed when they
    336:      are no longer needed.
    337:   */
    338:   KSPDestroy(&ksp1)); PetscCall(KSPDestroy(&ksp2);
    339:   VecDestroy(&x1));   PetscCall(VecDestroy(&x2);
    340:   VecDestroy(&b1));   PetscCall(VecDestroy(&b2);
    341:   MatDestroy(&C1));   PetscCall(MatDestroy(&C2);
    342:   VecDestroy(&u);

    344:   PetscFinalize();
    345:   return 0;
    346: }
    347: /* ------------------------------------------------------------- */
    348: /*
    349:     CheckError - Checks the error of the solution.

    351:     Input Parameters:
    352:     u - exact solution
    353:     x - approximate solution
    354:     b - work vector
    355:     its - number of iterations for convergence
    356:     tol - tolerance
    357:     CHECK_ERROR - the event number for error checking
    358:                   (for use with profiling)

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

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

    378:   /*
    379:      Compute error of the solution, using b as a work vector.
    380:   */
    381:   VecCopy(x,b);
    382:   VecAXPY(b,none,u);
    383:   VecNorm(b,NORM_2,&norm);
    384:   if (norm > tol) {
    385:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    386:   }
    387:   PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
    388:   return 0;
    389: }
    390: /* ------------------------------------------------------------- */
    391: /*
    392:    MyKSPMonitor - This is a user-defined routine for monitoring
    393:    the KSP iterative solvers.

    395:    Input Parameters:
    396:      ksp   - iterative context
    397:      n     - iteration number
    398:      rnorm - 2-norm (preconditioned) residual value (may be estimated)
    399:      dummy - optional user-defined monitor context (unused here)
    400: */
    401: PetscErrorCode MyKSPMonitor(KSP ksp,PetscInt n,PetscReal rnorm,void *dummy)
    402: {
    403:   Vec            x;

    405:   /*
    406:      Build the solution vector
    407:   */
    408:   KSPBuildSolution(ksp,NULL,&x);

    410:   /*
    411:      Write the solution vector and residual norm to stdout.
    412:       - PetscPrintf() handles output for multiprocessor jobs
    413:         by printing from only one processor in the communicator.
    414:       - The parallel viewer PETSC_VIEWER_STDOUT_WORLD handles
    415:         data from multiple processors so that the output
    416:         is not jumbled.
    417:   */
    418:   PetscPrintf(PETSC_COMM_WORLD,"iteration %D solution vector:\n",n);
    419:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);
    420:   PetscPrintf(PETSC_COMM_WORLD,"iteration %D KSP Residual norm %14.12e \n",n,rnorm);
    421:   return 0;
    422: }

    424: /*TEST

    426:    test:
    427:       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

    429:    test:
    430:       requires: hpddm
    431:       suffix: hpddm
    432:       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

    434:    test:
    435:       requires: hpddm
    436:       suffix: hpddm_2
    437:       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

    439:    testset:
    440:       requires: hpddm
    441:       output_file: output/ex9_hpddm_cg.out
    442:       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
    443:       test:
    444:          suffix: hpddm_cg_p_p
    445:          args: -ksp_type cg -s2_ksp_type cg
    446:       test:
    447:          suffix: hpddm_cg_p_h
    448:          args: -ksp_type cg -s2_ksp_type hpddm -s2_ksp_hpddm_type {{cg bcg bfbcg}shared output}
    449:       test:
    450:          suffix: hpddm_cg_h_h
    451:          args: -ksp_type hpddm -ksp_hpddm_type cg -s2_ksp_type hpddm -s2_ksp_hpddm_type {{cg bcg bfbcg}shared output}

    453: TEST*/