Date: 2025-03-29T05:58:28+00:00

Actual source code: ex5.c

      1: static char help[] = "Solves two linear systems in parallel with KSP.  The code\n\
      2: illustrates repeated solution of linear systems with the same preconditioner\n\
      3: method but different matrices (having the same nonzero structure).  The code\n\
      4: also uses multiple profiling stages.  Input arguments are\n\
      5:   -m <size> : problem size\n\
      6:   -mat_nonsym : use nonsymmetric matrix (default is symmetric)\n\n";

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

     18: int main(int argc, char **args)
     19: {
     20:   KSP           ksp;         /* linear solver context */
     21:   Mat           C;           /* matrix */
     22:   Vec           x, u, b;     /* approx solution, RHS, exact solution */
     23:   PetscReal     norm, bnorm; /* norm of solution error */
     24:   PetscScalar   v, none = -1.0;
     25:   PetscInt      Ii, J, ldim, low, high, iglobal, Istart, Iend;
     26:   PetscInt      i, j, m = 3, n = 2, its;
     27:   PetscMPIInt   size, rank;
     28:   PetscBool     mat_nonsymmetric = PETSC_FALSE;
     29:   PetscBool     testnewC = PETSC_FALSE, testscaledMat = PETSC_FALSE, single = PETSC_FALSE;
     30:   PetscLogStage stages[2];

     32:   PetscFunctionBeginUser;
     33:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
     34:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
     35:   PetscCall(PetscOptionsHasName(NULL, NULL, "-pc_precision", &single));
     36:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
     37:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     38:   n = 2 * size;

     40:   /*
     41:      Set flag if we are doing a nonsymmetric problem; the default is symmetric.
     42:   */
     43:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-mat_nonsym", &mat_nonsymmetric, NULL));

     45:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_scaledMat", &testscaledMat, NULL));

     47:   /*
     48:      Register two stages for separate profiling of the two linear solves.
     49:      Use the runtime option -log_view for a printout of performance
     50:      statistics at the program's conlusion.
     51:   */
     52:   PetscCall(PetscLogStageRegister("Original Solve", &stages[0]));
     53:   PetscCall(PetscLogStageRegister("Second Solve", &stages[1]));

     55:   /* -------------- Stage 0: Solve Original System ---------------------- */
     56:   /*
     57:      Indicate to PETSc profiling that we're beginning the first stage
     58:   */
     59:   PetscCall(PetscLogStagePush(stages[0]));

     61:   /*
     62:      Create parallel matrix, specifying only its global dimensions.
     63:      When using MatCreate(), the matrix format can be specified at
     64:      runtime. Also, the parallel partitioning of the matrix is
     65:      determined by PETSc at runtime.
     66:   */
     67:   PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
     68:   PetscCall(MatSetSizes(C, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
     69:   PetscCall(MatSetFromOptions(C));
     70:   PetscCall(MatSetUp(C));

     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:   PetscCall(MatGetOwnershipRange(C, &Istart, &Iend));

     79:   /*
     80:      Set matrix entries matrix 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 row and columns of matrix entries.
     85:   */
     86:   for (Ii = Istart; Ii < Iend; Ii++) {
     87:     v = -1.0;
     88:     i = Ii / n;
     89:     j = Ii - i * n;
     90:     if (i > 0) {
     91:       J = Ii - n;
     92:       PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
     93:     }
     94:     if (i < m - 1) {
     95:       J = Ii + n;
     96:       PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
     97:     }
     98:     if (j > 0) {
     99:       J = Ii - 1;
    100:       PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    101:     }
    102:     if (j < n - 1) {
    103:       J = Ii + 1;
    104:       PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    105:     }
    106:     v = 4.0;
    107:     PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
    108:   }

    110:   /*
    111:      Make the matrix nonsymmetric if desired
    112:   */
    113:   if (mat_nonsymmetric) {
    114:     for (Ii = Istart; Ii < Iend; Ii++) {
    115:       v = -1.5;
    116:       i = Ii / n;
    117:       if (i > 1) {
    118:         J = Ii - n - 1;
    119:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    120:       }
    121:     }
    122:   } else {
    123:     PetscCall(MatSetOption(C, MAT_SYMMETRIC, PETSC_TRUE));
    124:     PetscCall(MatSetOption(C, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
    125:   }

    127:   /*
    128:      Assemble matrix, using the 2-step process:
    129:        MatAssemblyBegin(), MatAssemblyEnd()
    130:      Computations can be done while messages are in transition
    131:      by placing code between these two statements.
    132:   */
    133:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    134:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

    136:   /*
    137:      Create parallel vectors.
    138:       - When using VecSetSizes(), we specify only the vector's global
    139:         dimension; the parallel partitioning is determined at runtime.
    140:       - Note: We form 1 vector from scratch and then duplicate as needed.
    141:   */
    142:   PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
    143:   PetscCall(VecSetSizes(u, PETSC_DECIDE, m * n));
    144:   PetscCall(VecSetFromOptions(u));
    145:   PetscCall(VecDuplicate(u, &b));
    146:   PetscCall(VecDuplicate(b, &x));

    148:   /*
    149:      Currently, all parallel PETSc vectors are partitioned by
    150:      contiguous chunks across the processors.  Determine which
    151:      range of entries are locally owned.
    152:   */
    153:   PetscCall(VecGetOwnershipRange(x, &low, &high));

    155:   /*
    156:     Set elements within the exact solution vector in parallel.
    157:      - Each processor needs to insert only elements that it owns
    158:        locally (but any non-local entries will be sent to the
    159:        appropriate processor during vector assembly).
    160:      - Always specify global locations of vector entries.
    161:   */
    162:   PetscCall(VecGetLocalSize(x, &ldim));
    163:   for (i = 0; i < ldim; i++) {
    164:     iglobal = i + low;
    165:     v       = (PetscScalar)(i + 100 * rank);
    166:     PetscCall(VecSetValues(u, 1, &iglobal, &v, INSERT_VALUES));
    167:   }

    169:   /*
    170:      Assemble vector, using the 2-step process:
    171:        VecAssemblyBegin(), VecAssemblyEnd()
    172:      Computations can be done while messages are in transition,
    173:      by placing code between these two statements.
    174:   */
    175:   PetscCall(VecAssemblyBegin(u));
    176:   PetscCall(VecAssemblyEnd(u));

    178:   /*
    179:      Compute right-hand-side vector
    180:   */
    181:   PetscCall(MatMult(C, u, b));

    183:   /*
    184:     Create linear solver context
    185:   */
    186:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));

    188:   /*
    189:      Set operators. Here the matrix that defines the linear system
    190:      also serves as the preconditioning matrix.
    191:   */
    192:   PetscCall(KSPSetOperators(ksp, C, C));

    194:   /*
    195:      Set runtime options (e.g., -ksp_type <type> -pc_type <type>)
    196:   */
    197:   PetscCall(KSPSetFromOptions(ksp));

    199:   /*
    200:      Solve linear system.  Here we explicitly call KSPSetUp() for more
    201:      detailed performance monitoring of certain preconditioners, such
    202:      as ICC and ILU.  This call is optional, as KSPSetUp() will
    203:      automatically be called within KSPSolve() if it hasn't been
    204:      called already.
    205:   */
    206:   PetscCall(KSPSetUp(ksp));
    207:   PetscCall(KSPSolve(ksp, b, x));

    209:   /*
    210:      Check the residual
    211:   */
    212:   PetscCall(VecAXPY(x, none, u));
    213:   PetscCall(VecNorm(x, NORM_2, &norm));
    214:   PetscCall(VecNorm(b, NORM_2, &bnorm));
    215:   PetscCall(KSPGetIterationNumber(ksp, &its));
    216:   if (!testscaledMat || (!single && norm / bnorm > 1.e-5)) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Relative norm of the residual %g, Iterations %" PetscInt_FMT "\n", (double)norm / (double)bnorm, its));

    218:   /* -------------- Stage 1: Solve Second System ---------------------- */
    219:   /*
    220:      Solve another linear system with the same method.  We reuse the KSP
    221:      context, matrix and vector data structures, and hence save the
    222:      overhead of creating new ones.

    224:      Indicate to PETSc profiling that we're concluding the first
    225:      stage with PetscLogStagePop(), and beginning the second stage with
    226:      PetscLogStagePush().
    227:   */
    228:   PetscCall(PetscLogStagePop());
    229:   PetscCall(PetscLogStagePush(stages[1]));

    231:   /*
    232:      Initialize all matrix entries to zero.  MatZeroEntries() retains the
    233:      nonzero structure of the matrix for sparse formats.
    234:   */
    235:   PetscCall(MatZeroEntries(C));

    237:   /*
    238:      Assemble matrix again.  Note that we retain the same matrix data
    239:      structure and the same nonzero pattern; we just change the values
    240:      of the matrix entries.
    241:   */
    242:   for (i = 0; i < m; i++) {
    243:     for (j = 2 * rank; j < 2 * rank + 2; j++) {
    244:       v  = -1.0;
    245:       Ii = j + n * i;
    246:       if (i > 0) {
    247:         J = Ii - n;
    248:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    249:       }
    250:       if (i < m - 1) {
    251:         J = Ii + n;
    252:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    253:       }
    254:       if (j > 0) {
    255:         J = Ii - 1;
    256:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    257:       }
    258:       if (j < n - 1) {
    259:         J = Ii + 1;
    260:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    261:       }
    262:       v = 6.0;
    263:       PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
    264:     }
    265:   }
    266:   if (mat_nonsymmetric) {
    267:     for (Ii = Istart; Ii < Iend; Ii++) {
    268:       v = -1.5;
    269:       i = Ii / n;
    270:       if (i > 1) {
    271:         J = Ii - n - 1;
    272:         PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, ADD_VALUES));
    273:       }
    274:     }
    275:   }
    276:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    277:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

    279:   if (testscaledMat) {
    280:     PetscRandom rctx;

    282:     /* Scale a(0,0) and a(M-1,M-1) */
    283:     if (rank == 0) {
    284:       v  = 6.0 * 0.00001;
    285:       Ii = 0;
    286:       J  = 0;
    287:       PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    288:     } else if (rank == size - 1) {
    289:       v  = 6.0 * 0.00001;
    290:       Ii = m * n - 1;
    291:       J  = m * n - 1;
    292:       PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    293:     }
    294:     PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    295:     PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

    297:     /* Compute a new right-hand-side vector */
    298:     PetscCall(VecDestroy(&u));
    299:     PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
    300:     PetscCall(VecSetSizes(u, PETSC_DECIDE, m * n));
    301:     PetscCall(VecSetFromOptions(u));

    303:     PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rctx));
    304:     PetscCall(PetscRandomSetFromOptions(rctx));
    305:     PetscCall(VecSetRandom(u, rctx));
    306:     PetscCall(PetscRandomDestroy(&rctx));
    307:     PetscCall(VecAssemblyBegin(u));
    308:     PetscCall(VecAssemblyEnd(u));
    309:   }

    311:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_newMat", &testnewC, NULL));
    312:   if (testnewC) {
    313:     /*
    314:      User may use a new matrix C with same nonzero pattern, e.g.
    315:       ./ex5 -ksp_monitor -mat_type sbaij -pc_type cholesky -pc_factor_mat_solver_type mumps -test_newMat
    316:     */
    317:     Mat Ctmp;
    318:     PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &Ctmp));
    319:     PetscCall(MatDestroy(&C));
    320:     PetscCall(MatDuplicate(Ctmp, MAT_COPY_VALUES, &C));
    321:     PetscCall(MatDestroy(&Ctmp));
    322:   }

    324:   PetscCall(MatMult(C, u, b));

    326:   /*
    327:      Set operators. Here the matrix that defines the linear system
    328:      also serves as the preconditioning matrix.
    329:   */
    330:   PetscCall(KSPSetOperators(ksp, C, C));

    332:   /*
    333:      Solve linear system
    334:   */
    335:   PetscCall(KSPSetUp(ksp));
    336:   PetscCall(KSPSolve(ksp, b, x));

    338:   /*
    339:      Check the residual
    340:   */
    341:   PetscCall(VecAXPY(x, none, u));
    342:   PetscCall(VecNorm(x, NORM_2, &norm));
    343:   PetscCall(KSPGetIterationNumber(ksp, &its));
    344:   if (!testscaledMat || (!single && norm / bnorm > PETSC_SMALL)) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Relative norm of the residual %g, Iterations %" PetscInt_FMT "\n", (double)norm / (double)bnorm, its));

    346:   /*
    347:      Free work space.  All PETSc objects should be destroyed when they
    348:      are no longer needed.
    349:   */
    350:   PetscCall(KSPDestroy(&ksp));
    351:   PetscCall(VecDestroy(&u));
    352:   PetscCall(VecDestroy(&x));
    353:   PetscCall(VecDestroy(&b));
    354:   PetscCall(MatDestroy(&C));

    356:   /*
    357:      Indicate to PETSc profiling that we're concluding the second stage
    358:   */
    359:   PetscCall(PetscLogStagePop());

    361:   PetscCall(PetscFinalize());
    362:   return 0;
    363: }

    365: /*TEST

    367:    test:
    368:       args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    370:    test:
    371:       suffix: 2
    372:       nsize: 2
    373:       args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -ksp_rtol .000001

    375:    test:
    376:       suffix: 5
    377:       nsize: 2
    378:       args: -ksp_gmres_cgs_refinement_type refine_always -ksp_monitor draw::draw_lg -ksp_monitor_true_residual draw::draw_lg

    380:    test:
    381:       suffix: asm
    382:       nsize: 4
    383:       args: -pc_type asm

    385:    test:
    386:       suffix: asm_baij
    387:       nsize: 4
    388:       args: -pc_type asm -mat_type baij
    389:       output_file: output/ex5_asm.out

    391:    test:
    392:       suffix: redundant_0
    393:       args: -m 1000 -pc_type redundant -pc_redundant_number 1 -redundant_ksp_type gmres -redundant_pc_type jacobi

    395:    test:
    396:       suffix: redundant_1
    397:       nsize: 5
    398:       args: -pc_type redundant -pc_redundant_number 1 -redundant_ksp_type gmres -redundant_pc_type jacobi

    400:    test:
    401:       suffix: redundant_2
    402:       nsize: 5
    403:       args: -pc_type redundant -pc_redundant_number 3 -redundant_ksp_type gmres -redundant_pc_type jacobi

    405:    test:
    406:       suffix: redundant_3
    407:       nsize: 5
    408:       args: -pc_type redundant -pc_redundant_number 5 -redundant_ksp_type gmres -redundant_pc_type jacobi

    410:    test:
    411:       suffix: redundant_4
    412:       nsize: 5
    413:       args: -pc_type redundant -pc_redundant_number 3 -redundant_ksp_type gmres -redundant_pc_type jacobi -psubcomm_type interlaced

    415:    test:
    416:       suffix: superlu_dist
    417:       nsize: 15
    418:       requires: superlu_dist
    419:       args: -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_equil false -m 150 -mat_superlu_dist_r 3 -mat_superlu_dist_c 5 -test_scaledMat

    421:    test:
    422:       suffix: superlu_dist_2
    423:       nsize: 15
    424:       requires: superlu_dist
    425:       args: -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_equil false -m 150 -mat_superlu_dist_r 3 -mat_superlu_dist_c 5 -test_scaledMat -mat_superlu_dist_fact SamePattern_SameRowPerm
    426:       output_file: output/ex5_superlu_dist.out

    428:    test:
    429:       suffix: superlu_dist_3
    430:       nsize: 15
    431:       requires: superlu_dist
    432:       args: -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_equil false -m 500 -mat_superlu_dist_r 3 -mat_superlu_dist_c 5 -test_scaledMat -mat_superlu_dist_fact DOFACT
    433:       output_file: output/ex5_superlu_dist.out

    435:    test:
    436:       suffix: superlu_dist_3s
    437:       nsize: 15
    438:       requires: superlu_dist defined(PETSC_HAVE_SUPERLU_DIST_SINGLE)
    439:       args: -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_equil false -m 500 -mat_superlu_dist_r 3 -mat_superlu_dist_c 5 -test_scaledMat -mat_superlu_dist_fact DOFACT -pc_precision single
    440:       output_file: output/ex5_superlu_dist.out

    442:    test:
    443:       suffix: superlu_dist_0
    444:       nsize: 1
    445:       requires: superlu_dist
    446:       args: -pc_type lu -pc_factor_mat_solver_type superlu_dist -test_scaledMat
    447:       output_file: output/ex5_superlu_dist.out

    449: TEST*/