Date: 2026-03-31T05:46:15+00:00

Actual source code: ex9.c

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

      6: /*
      7:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
      8:   automatically includes:
      9:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     10:      petscmat.h - matrices
     11:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     12:      petscviewer.h - viewers               petscpc.h  - preconditioners
     13: */
     14: #include <petscksp.h>

     16: /*
     17:    Declare user-defined routines
     18: */
     19: extern PetscErrorCode CheckError(Vec, Vec, Vec, PetscInt, PetscReal, PetscLogEvent);
     20: extern PetscErrorCode MyKSPMonitor(KSP, PetscInt, PetscReal, void *);

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

     37:   PetscFunctionBeginUser;
     38:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
     39:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
     40:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-t", &ntimes, NULL));
     41:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-unsym", &unsym, NULL));
     42:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
     43:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     44:   n = 2 * size;

     46:   /*
     47:      Register various stages for profiling
     48:   */
     49:   PetscCall(PetscLogStageRegister("Prelim setup", &stages[0]));
     50:   PetscCall(PetscLogStageRegister("Linear System 1", &stages[1]));
     51:   PetscCall(PetscLogStageRegister("Linear System 2", &stages[2]));

     53:   /*
     54:      Register a user-defined event for profiling (error checking).
     55:   */
     56:   CHECK_ERROR = 0;
     57:   PetscCall(PetscLogEventRegister("Check Error", KSP_CLASSID, &CHECK_ERROR));

     59:   /* - - - - - - - - - - - - Stage 0: - - - - - - - - - - - - - -
     60:                         Preliminary Setup
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   PetscCall(PetscLogStagePush(stages[0]));

     65:   /*
     66:      Create data structures for first linear system.
     67:       - Create parallel matrix, specifying only its global dimensions.
     68:         When using MatCreate(), the matrix format can be specified at
     69:         runtime. Also, the parallel partitioning of the matrix is
     70:         determined by PETSc at runtime.
     71:       - Create parallel vectors.
     72:         - When using VecSetSizes(), we specify only the vector's global
     73:           dimension; the parallel partitioning is determined at runtime.
     74:         - Note: We form 1 vector from scratch and then duplicate as needed.
     75:   */
     76:   PetscCall(MatCreate(PETSC_COMM_WORLD, &C1));
     77:   PetscCall(MatSetSizes(C1, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
     78:   PetscCall(MatSetFromOptions(C1));
     79:   PetscCall(MatSetUp(C1));
     80:   PetscCall(MatGetOwnershipRange(C1, &Istart, &Iend));
     81:   PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
     82:   PetscCall(VecSetSizes(u, PETSC_DECIDE, m * n));
     83:   PetscCall(VecSetFromOptions(u));
     84:   PetscCall(VecDuplicate(u, &b1));
     85:   PetscCall(VecDuplicate(u, &x1));

     87:   /*
     88:      Create first linear solver context.
     89:      Set runtime options (e.g., -pc_type <type>).
     90:      Note that the first linear system uses the default option
     91:      names, while the second linear system uses a different
     92:      options prefix.
     93:   */
     94:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp1));
     95:   PetscCall(KSPSetFromOptions(ksp1));

     97:   /*
     98:      Set user-defined monitoring routine for first linear system.
     99:   */
    100:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-my_ksp_monitor", &flg, NULL));
    101:   if (flg) PetscCall(KSPMonitorSet(ksp1, MyKSPMonitor, NULL, 0));

    103:   /*
    104:      Create data structures for second linear system.
    105:   */
    106:   PetscCall(MatCreate(PETSC_COMM_WORLD, &C2));
    107:   PetscCall(MatSetSizes(C2, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
    108:   PetscCall(MatSetFromOptions(C2));
    109:   PetscCall(MatSetUp(C2));
    110:   PetscCall(MatGetOwnershipRange(C2, &Istart2, &Iend2));
    111:   PetscCall(VecDuplicate(u, &b2));
    112:   PetscCall(VecDuplicate(u, &x2));

    114:   /*
    115:      Create second linear solver context
    116:   */
    117:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp2));

    119:   /*
    120:      Set different options prefix for second linear system.
    121:      Set runtime options (e.g., -s2_pc_type <type>)
    122:   */
    123:   PetscCall(KSPAppendOptionsPrefix(ksp2, "s2_"));
    124:   PetscCall(KSPSetFromOptions(ksp2));

    126:   /*
    127:      Assemble exact solution vector in parallel.  Note that each
    128:      processor needs to set only its local part of the vector.
    129:   */
    130:   PetscCall(VecGetLocalSize(u, &ldim));
    131:   PetscCall(VecGetOwnershipRange(u, &low, &high));
    132:   for (i = 0; i < ldim; i++) {
    133:     iglobal = i + low;
    134:     v       = (PetscScalar)(i + 100 * rank);
    135:     PetscCall(VecSetValues(u, 1, &iglobal, &v, ADD_VALUES));
    136:   }
    137:   PetscCall(VecAssemblyBegin(u));
    138:   PetscCall(VecAssemblyEnd(u));

    140:   /*
    141:      Log the number of flops for computing vector entries
    142:   */
    143:   PetscCall(PetscLogFlops(2.0 * ldim));

    145:   /*
    146:      End current profiling stage
    147:   */
    148:   PetscCall(PetscLogStagePop());

    150:   /* --------------------------------------------------------------
    151:                         Linear solver loop:
    152:       Solve 2 different linear systems several times in succession
    153:      -------------------------------------------------------------- */

    155:   for (t = 0; t < ntimes; t++) {
    156:     /* - - - - - - - - - - - - Stage 1: - - - - - - - - - - - - - -
    157:                  Assemble and solve first linear system
    158:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    160:     /*
    161:        Begin profiling stage #1
    162:     */
    163:     PetscCall(PetscLogStagePush(stages[1]));

    165:     /*
    166:        Initialize all matrix entries to zero.  MatZeroEntries() retains
    167:        the nonzero structure of the matrix for sparse formats.
    168:     */
    169:     if (t > 0) PetscCall(MatZeroEntries(C1));

    171:     /*
    172:        Set matrix entries in parallel.  Also, log the number of flops
    173:        for computing matrix entries.
    174:         - Each processor needs to insert only elements that it owns
    175:           locally (but any non-local elements will be sent to the
    176:           appropriate processor during matrix assembly).
    177:         - Always specify global row and columns of matrix entries.
    178:     */
    179:     for (Ii = Istart; Ii < Iend; Ii++) {
    180:       v = -1.0;
    181:       i = Ii / n;
    182:       j = Ii - i * n;
    183:       if (i > 0) {
    184:         J = Ii - n;
    185:         PetscCall(MatSetValues(C1, 1, &Ii, 1, &J, &v, ADD_VALUES));
    186:       }
    187:       if (i < m - 1) {
    188:         J = Ii + n;
    189:         PetscCall(MatSetValues(C1, 1, &Ii, 1, &J, &v, ADD_VALUES));
    190:       }
    191:       if (j > 0) {
    192:         J = Ii - 1;
    193:         PetscCall(MatSetValues(C1, 1, &Ii, 1, &J, &v, ADD_VALUES));
    194:       }
    195:       if (j < n - 1) {
    196:         J = Ii + 1;
    197:         PetscCall(MatSetValues(C1, 1, &Ii, 1, &J, &v, ADD_VALUES));
    198:       }
    199:       v = 4.0;
    200:       PetscCall(MatSetValues(C1, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
    201:     }
    202:     if (unsym) {
    203:       for (Ii = Istart; Ii < Iend; Ii++) { /* Make matrix nonsymmetric */
    204:         v = -1.0 * (t + 0.5);
    205:         i = Ii / n;
    206:         if (i > 0) {
    207:           J = Ii - n;
    208:           PetscCall(MatSetValues(C1, 1, &Ii, 1, &J, &v, ADD_VALUES));
    209:         }
    210:       }
    211:       PetscCall(PetscLogFlops(2.0 * (Iend - Istart)));
    212:     }

    214:     /*
    215:        Assemble matrix, using the 2-step process:
    216:          MatAssemblyBegin(), MatAssemblyEnd()
    217:        Computations can be done while messages are in transition
    218:        by placing code between these two statements.
    219:     */
    220:     PetscCall(MatAssemblyBegin(C1, MAT_FINAL_ASSEMBLY));
    221:     PetscCall(MatAssemblyEnd(C1, MAT_FINAL_ASSEMBLY));

    223:     /*
    224:        Indicate same nonzero structure of successive linear system matrices
    225:     */
    226:     PetscCall(MatSetOption(C1, MAT_NEW_NONZERO_LOCATIONS, PETSC_TRUE));

    228:     /*
    229:        Compute right-hand-side vector
    230:     */
    231:     PetscCall(MatMult(C1, u, b1));

    233:     /*
    234:        Set operators. Here the matrix that defines the linear system
    235:        also serves as the matrix from which the preconditioner is constructed.
    236:     */
    237:     PetscCall(KSPSetOperators(ksp1, C1, C1));

    239:     /*
    240:        Use the previous solution of linear system #1 as the initial
    241:        guess for the next solve of linear system #1.  The user MUST
    242:        call KSPSetInitialGuessNonzero() in indicate use of an initial
    243:        guess vector; otherwise, an initial guess of zero is used.
    244:     */
    245:     if (t > 0) PetscCall(KSPSetInitialGuessNonzero(ksp1, PETSC_TRUE));

    247:     /*
    248:        Solve the first linear system.  Here we explicitly call
    249:        KSPSetUp() for more detailed performance monitoring of
    250:        certain preconditioners, such as ICC and ILU.  This call
    251:        is optional, ase KSPSetUp() will automatically be called
    252:        within KSPSolve() if it hasn't been called already.
    253:     */
    254:     PetscCall(KSPSetUp(ksp1));
    255:     PetscCall(KSPSolve(ksp1, b1, x1));
    256:     PetscCall(KSPGetIterationNumber(ksp1, &its));

    258:     /*
    259:        Check error of solution to first linear system
    260:     */
    261:     PetscCall(CheckError(u, x1, b1, its, 1.e-4, CHECK_ERROR));

    263:     /* - - - - - - - - - - - - Stage 2: - - - - - - - - - - - - - -
    264:                  Assemble and solve second linear system
    265:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    267:     /*
    268:        Conclude profiling stage #1; begin profiling stage #2
    269:     */
    270:     PetscCall(PetscLogStagePop());
    271:     PetscCall(PetscLogStagePush(stages[2]));

    273:     /*
    274:        Initialize all matrix entries to zero
    275:     */
    276:     if (t > 0) PetscCall(MatZeroEntries(C2));

    278:     /*
    279:        Assemble matrix in parallel. Also, log the number of flops
    280:        for computing matrix entries.
    281:         - To illustrate the features of parallel matrix assembly, we
    282:           intentionally set the values differently from the way in
    283:           which the matrix is distributed across the processors.  Each
    284:           entry that is not owned locally will be sent to the appropriate
    285:           processor during MatAssemblyBegin() and MatAssemblyEnd().
    286:         - For best efficiency the user should strive to set as many
    287:           entries locally as possible.
    288:      */
    289:     for (i = 0; i < m; i++) {
    290:       for (j = 2 * rank; j < 2 * rank + 2; j++) {
    291:         v  = -1.0;
    292:         Ii = j + n * i;
    293:         if (i > 0) {
    294:           J = Ii - n;
    295:           PetscCall(MatSetValues(C2, 1, &Ii, 1, &J, &v, ADD_VALUES));
    296:         }
    297:         if (i < m - 1) {
    298:           J = Ii + n;
    299:           PetscCall(MatSetValues(C2, 1, &Ii, 1, &J, &v, ADD_VALUES));
    300:         }
    301:         if (j > 0) {
    302:           J = Ii - 1;
    303:           PetscCall(MatSetValues(C2, 1, &Ii, 1, &J, &v, ADD_VALUES));
    304:         }
    305:         if (j < n - 1) {
    306:           J = Ii + 1;
    307:           PetscCall(MatSetValues(C2, 1, &Ii, 1, &J, &v, ADD_VALUES));
    308:         }
    309:         v = 6.0 + t * 0.5;
    310:         PetscCall(MatSetValues(C2, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
    311:       }
    312:     }
    313:     if (unsym) {
    314:       for (Ii = Istart2; Ii < Iend2; Ii++) { /* Make matrix nonsymmetric */
    315:         v = -1.0 * (t + 0.5);
    316:         i = Ii / n;
    317:         if (i > 0) {
    318:           J = Ii - n;
    319:           PetscCall(MatSetValues(C2, 1, &Ii, 1, &J, &v, ADD_VALUES));
    320:         }
    321:       }
    322:     }
    323:     PetscCall(MatAssemblyBegin(C2, MAT_FINAL_ASSEMBLY));
    324:     PetscCall(MatAssemblyEnd(C2, MAT_FINAL_ASSEMBLY));
    325:     PetscCall(PetscLogFlops(2.0 * (Iend - Istart)));

    327:     /*
    328:        Indicate same nonzero structure of successive linear system matrices
    329:     */
    330:     PetscCall(MatSetOption(C2, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE));

    332:     /*
    333:        Compute right-hand-side vector
    334:     */
    335:     PetscCall(MatMult(C2, u, b2));

    337:     /*
    338:        Set operators. Here the matrix that defines the linear system
    339:        also serves as the matrix from which the preconditioner is constructed.  Indicate same nonzero
    340:        structure of successive preconditioner matrices by setting flag
    341:        SAME_NONZERO_PATTERN.
    342:     */
    343:     PetscCall(KSPSetOperators(ksp2, C2, C2));

    345:     /*
    346:        Solve the second linear system
    347:     */
    348:     PetscCall(KSPSetUp(ksp2));
    349:     PetscCall(KSPSolve(ksp2, b2, x2));
    350:     PetscCall(KSPGetIterationNumber(ksp2, &its));

    352:     /*
    353:        Check error of solution to second linear system
    354:     */
    355:     PetscCall(CheckError(u, x2, b2, its, 1.e-4, CHECK_ERROR));

    357:     /*
    358:        Conclude profiling stage #2
    359:     */
    360:     PetscCall(PetscLogStagePop());
    361:   }
    362:   /* --------------------------------------------------------------
    363:                        End of linear solver loop
    364:      -------------------------------------------------------------- */

    366:   /*
    367:      Free work space.  All PETSc objects should be destroyed when they
    368:      are no longer needed.
    369:   */
    370:   PetscCall(KSPDestroy(&ksp1));
    371:   PetscCall(KSPDestroy(&ksp2));
    372:   PetscCall(VecDestroy(&x1));
    373:   PetscCall(VecDestroy(&x2));
    374:   PetscCall(VecDestroy(&b1));
    375:   PetscCall(VecDestroy(&b2));
    376:   PetscCall(MatDestroy(&C1));
    377:   PetscCall(MatDestroy(&C2));
    378:   PetscCall(VecDestroy(&u));

    380:   PetscCall(PetscFinalize());
    381:   return 0;
    382: }
    383: /* ------------------------------------------------------------- */
    384: /*
    385:     CheckError - Checks the error of the solution.

    387:     Input Parameters:
    388:     u - exact solution
    389:     x - approximate solution
    390:     b - work vector
    391:     its - number of iterations for convergence
    392:     tol - tolerance
    393:     CHECK_ERROR - the event number for error checking
    394:                   (for use with profiling)

    396:     Notes:
    397:     In order to profile this section of code separately from the
    398:     rest of the program, we register it as an "event" with
    399:     PetscLogEventRegister() in the main program.  Then, we indicate
    400:     the start and end of this event by respectively calling
    401:         PetscLogEventBegin(CHECK_ERROR,u,x,b,0);
    402:         PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
    403:     Here, we specify the objects most closely associated with
    404:     the event (the vectors u,x,b).  Such information is optional;
    405:     we could instead just use 0 instead for all objects.
    406: */
    407: PetscErrorCode CheckError(Vec u, Vec x, Vec b, PetscInt its, PetscReal tol, PetscLogEvent CHECK_ERROR)
    408: {
    409:   PetscScalar none = -1.0;
    410:   PetscReal   norm;

    412:   PetscFunctionBeginUser;
    413:   PetscCall(PetscLogEventBegin(CHECK_ERROR, u, x, b, 0));

    415:   /*
    416:      Compute error of the solution, using b as a work vector.
    417:   */
    418:   PetscCall(VecCopy(x, b));
    419:   PetscCall(VecAXPY(b, none, u));
    420:   PetscCall(VecNorm(b, NORM_2, &norm));
    421:   if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));
    422:   PetscCall(PetscLogEventEnd(CHECK_ERROR, u, x, b, 0));
    423:   PetscFunctionReturn(PETSC_SUCCESS);
    424: }
    425: /* ------------------------------------------------------------- */
    426: /*
    427:    MyKSPMonitor - This is a user-defined routine for monitoring
    428:    the KSP iterative solvers.

    430:    Input Parameters:
    431:      ksp   - iterative context
    432:      n     - iteration number
    433:      rnorm - 2-norm (preconditioned) residual value (may be estimated)
    434:      unused - optional user-defined monitor context (unused here)
    435: */
    436: PetscErrorCode MyKSPMonitor(KSP ksp, PetscInt n, PetscReal rnorm, void *unused)
    437: {
    438:   Vec x;

    440:   PetscFunctionBeginUser;
    441:   /*
    442:      Build the solution vector
    443:   */
    444:   PetscCall(KSPBuildSolution(ksp, NULL, &x));

    446:   /*
    447:      Write the solution vector and residual norm to stdout.
    448:       - PetscPrintf() handles output for multiprocessor jobs
    449:         by printing from only one processor in the communicator.
    450:       - The parallel viewer PETSC_VIEWER_STDOUT_WORLD handles
    451:         data from multiple processors so that the output
    452:         is not jumbled.
    453:   */
    454:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "iteration %" PetscInt_FMT " solution vector:\n", n));
    455:   PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD));
    456:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "iteration %" PetscInt_FMT " KSP Residual norm %14.12e\n", n, (double)rnorm));
    457:   PetscFunctionReturn(PETSC_SUCCESS);
    458: }

    460: /*TEST

    462:    test:
    463:       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

    465:    test:
    466:       requires: hpddm
    467:       suffix: hpddm
    468:       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

    470:    test:
    471:       requires: hpddm
    472:       suffix: hpddm_2
    473:       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

    475:    testset:
    476:       requires: hpddm
    477:       output_file: output/ex9_hpddm_cg.out
    478:       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
    479:       test:
    480:          suffix: hpddm_cg_p_p
    481:          args: -ksp_type cg -s2_ksp_type cg
    482:       test:
    483:          suffix: hpddm_cg_p_h
    484:          args: -ksp_type cg -s2_ksp_type hpddm -s2_ksp_hpddm_type {{cg bcg bfbcg}shared output}
    485:       test:
    486:          suffix: hpddm_cg_h_h
    487:          args: -ksp_type hpddm -ksp_hpddm_type cg -s2_ksp_type hpddm -s2_ksp_hpddm_type {{cg bcg bfbcg}shared output}

    489: TEST*/