Actual source code: ex52.c

      1: static char help[] = "Solves a linear system in parallel with KSP. Modified from ex2.c \n\
      2:                       Illustrate how to use external packages MUMPS, SUPERLU and STRUMPACK \n\
      3: Input parameters include:\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_y>       : number of mesh points in y-direction\n\n";

      9: #include <petscksp.h>

     11: #if defined(PETSC_HAVE_MUMPS)
     12: /* Subroutine contributed by Varun Hiremath */
     13: PetscErrorCode printMumpsMemoryInfo(Mat F)
     14: {
     15:   PetscInt maxMem, sumMem;

     17:   PetscFunctionBeginUser;
     18:   PetscCall(MatMumpsGetInfog(F, 16, &maxMem));
     19:   PetscCall(MatMumpsGetInfog(F, 17, &sumMem));
     20:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n MUMPS INFOG(16) :: Max memory in MB = %" PetscInt_FMT, maxMem));
     21:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n MUMPS INFOG(17) :: Sum memory in MB = %" PetscInt_FMT "\n", sumMem));
     22:   PetscFunctionReturn(PETSC_SUCCESS);
     23: }
     24: #endif

     26: int main(int argc, char **args)
     27: {
     28:   Vec         x, b, u; /* approx solution, RHS, exact solution */
     29:   Mat         A, F;
     30:   KSP         ksp; /* linear solver context */
     31:   PC          pc;
     32:   PetscRandom rctx; /* random number generator context */
     33:   PetscReal   norm; /* norm of solution error */
     34:   PetscInt    i, j, Ii, J, Istart, Iend, m = 8, n = 7, its;
     35:   PetscBool   flg = PETSC_FALSE, flg_ilu = PETSC_FALSE, flg_ch = PETSC_FALSE;
     36: #if defined(PETSC_HAVE_MUMPS)
     37:   PetscBool flg_mumps = PETSC_FALSE, flg_mumps_ch = PETSC_FALSE;
     38: #endif
     39: #if defined(PETSC_HAVE_SUPERLU) || defined(PETSC_HAVE_SUPERLU_DIST)
     40:   PetscBool flg_superlu = PETSC_FALSE;
     41: #endif
     42: #if defined(PETSC_HAVE_STRUMPACK)
     43:   PetscBool flg_strumpack = PETSC_FALSE;
     44: #endif
     45:   PetscScalar   v;
     46:   PetscMPIInt   rank, size;
     47:   PetscLogStage stage;

     49: #if defined(PETSC_HAVE_STRUMPACK) && defined(PETSC_HAVE_SLATE)
     50:   PETSC_MPI_THREAD_REQUIRED = MPI_THREAD_MULTIPLE;
     51: #endif
     52:   PetscFunctionBeginUser;
     53:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
     54:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
     55:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     56:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
     57:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
     58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     59:          Compute the matrix and right-hand-side vector that define
     60:          the linear system, Ax = b.
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     62:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
     63:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n));
     64:   PetscCall(MatSetFromOptions(A));
     65:   PetscCall(MatMPIAIJSetPreallocation(A, 5, NULL, 5, NULL));
     66:   PetscCall(MatSeqAIJSetPreallocation(A, 5, NULL));
     67:   PetscCall(MatSetUp(A));

     69:   /*
     70:      Currently, all PETSc parallel matrix formats are partitioned by
     71:      contiguous chunks of rows across the processors.  Determine which
     72:      rows of the matrix are locally owned.
     73:   */
     74:   PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));

     76:   /*
     77:      Set matrix elements for the 2-D, five-point stencil in parallel.
     78:       - Each processor needs to insert only elements that it owns
     79:         locally (but any non-local elements will be sent to the
     80:         appropriate processor during matrix assembly).
     81:       - Always specify global rows and columns of matrix entries.

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

     88:    */
     89:   PetscCall(PetscLogStageRegister("Assembly", &stage));
     90:   PetscCall(PetscLogStagePush(stage));
     91:   for (Ii = Istart; Ii < Iend; Ii++) {
     92:     v = -1.0;
     93:     i = Ii / n;
     94:     j = Ii - i * n;
     95:     if (i > 0) {
     96:       J = Ii - n;
     97:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
     98:     }
     99:     if (i < m - 1) {
    100:       J = Ii + n;
    101:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    102:     }
    103:     if (j > 0) {
    104:       J = Ii - 1;
    105:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    106:     }
    107:     if (j < n - 1) {
    108:       J = Ii + 1;
    109:       PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    110:     }
    111:     v = 4.0;
    112:     PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    113:   }

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

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

    128:   /* Create parallel vectors */
    129:   PetscCall(MatCreateVecs(A, &u, &b));
    130:   PetscCall(VecDuplicate(u, &x));

    132:   /*
    133:      Set exact solution; then compute right-hand-side vector.
    134:      By default we use an exact solution of a vector with all
    135:      elements of 1.0;  Alternatively, using the runtime option
    136:      -random_sol forms a solution vector with random components.
    137:   */
    138:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-random_exact_sol", &flg, NULL));
    139:   if (flg) {
    140:     PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rctx));
    141:     PetscCall(PetscRandomSetFromOptions(rctx));
    142:     PetscCall(VecSetRandom(u, rctx));
    143:     PetscCall(PetscRandomDestroy(&rctx));
    144:   } else {
    145:     PetscCall(VecSet(u, 1.0));
    146:   }
    147:   PetscCall(MatMult(A, u, b));

    149:   /*
    150:      View the exact solution vector if desired
    151:   */
    152:   flg = PETSC_FALSE;
    153:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_exact_sol", &flg, NULL));
    154:   if (flg) PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD));

    156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    157:                 Create the linear solver and set various options
    158:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    160:   /*
    161:      Create linear solver context
    162:   */
    163:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
    164:   PetscCall(KSPSetOperators(ksp, A, A));

    166:   /*
    167:     Example of how to use external package MUMPS
    168:     Note: runtime options
    169:           '-ksp_type preonly -pc_type lu -pc_factor_mat_solver_type mumps -mat_mumps_icntl_7 3 -mat_mumps_icntl_1 0.0'
    170:           are equivalent to these procedural calls
    171:   */
    172: #if defined(PETSC_HAVE_MUMPS)
    173:   flg_mumps    = PETSC_FALSE;
    174:   flg_mumps_ch = PETSC_FALSE;
    175:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_mumps_lu", &flg_mumps, NULL));
    176:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_mumps_ch", &flg_mumps_ch, NULL));
    177:   if (flg_mumps || flg_mumps_ch) {
    178:     PetscCall(KSPSetType(ksp, KSPPREONLY));
    179:     PetscInt  ival, icntl;
    180:     PetscReal val;
    181:     PetscCall(KSPGetPC(ksp, &pc));
    182:     if (flg_mumps) {
    183:       PetscCall(PCSetType(pc, PCLU));
    184:     } else if (flg_mumps_ch) {
    185:       PetscCall(MatSetOption(A, MAT_SPD, PETSC_TRUE)); /* set MUMPS id%SYM=1 */
    186:       PetscCall(PCSetType(pc, PCCHOLESKY));
    187:     }
    188:     PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERMUMPS));
    189:     PetscCall(PCFactorSetUpMatSolverType(pc)); /* call MatGetFactor() to create F */
    190:     PetscCall(PCFactorGetMatrix(pc, &F));
    191:     PetscCall(MatMumpsSetIcntl(F, 24, 1));
    192:     PetscCall(MatMumpsGetIcntl(F, 24, &ival));
    193:     PetscCheck(ival == 1, PetscObjectComm((PetscObject)F), PETSC_ERR_LIB, "ICNTL(24) = %" PetscInt_FMT " (!= 1)", ival);
    194:     PetscCall(MatMumpsSetCntl(F, 3, 1e-6));
    195:     PetscCall(MatMumpsGetCntl(F, 3, &val));
    196:     PetscCheck(PetscEqualReal(val, 1e-6), PetscObjectComm((PetscObject)F), PETSC_ERR_LIB, "CNTL(3) = %g (!= %g)", (double)val, 1e-6);
    197:     if (flg_mumps) {
    198:       /* Zero the first and last rows in the rank, they should then show up in corresponding null pivot rows output via
    199:          MatMumpsGetNullPivots */
    200:       flg = PETSC_FALSE;
    201:       PetscCall(PetscOptionsGetBool(NULL, NULL, "-zero_first_and_last_rows", &flg, NULL));
    202:       if (flg) {
    203:         PetscInt rows[2];
    204:         rows[0] = Istart;   /* first row of the rank */
    205:         rows[1] = Iend - 1; /* last row of the rank */
    206:         PetscCall(MatZeroRows(A, 2, rows, 0.0, NULL, NULL));
    207:       }
    208:       /* Get memory estimates from MUMPS' MatLUFactorSymbolic(), e.g. INFOG(16), INFOG(17).
    209:          KSPSetUp() below will do nothing inside MatLUFactorSymbolic() */
    210:       MatFactorInfo info;
    211:       PetscCall(MatLUFactorSymbolic(F, A, NULL, NULL, &info));
    212:       flg = PETSC_FALSE;
    213:       PetscCall(PetscOptionsGetBool(NULL, NULL, "-print_mumps_memory", &flg, NULL));
    214:       if (flg) PetscCall(printMumpsMemoryInfo(F));
    215:     }

    217:     /* sequential ordering */
    218:     icntl = 7;
    219:     ival  = 2;
    220:     PetscCall(MatMumpsSetIcntl(F, icntl, ival));

    222:     /* threshold for row pivot detection */
    223:     PetscCall(MatMumpsGetIcntl(F, 24, &ival));
    224:     PetscCheck(ival == 1, PetscObjectComm((PetscObject)F), PETSC_ERR_LIB, "ICNTL(24) = %" PetscInt_FMT " (!= 1)", ival);
    225:     icntl = 3;
    226:     PetscCall(MatMumpsGetCntl(F, icntl, &val));
    227:     PetscCheck(PetscEqualReal(val, 1e-6), PetscObjectComm((PetscObject)F), PETSC_ERR_LIB, "CNTL(3) = %g (!= %g)", (double)val, 1e-6);

    229:     /* compute determinant of A */
    230:     PetscCall(MatMumpsSetIcntl(F, 33, 1));
    231:   }
    232: #endif

    234:   /*
    235:     Example of how to use external package SuperLU
    236:     Note: runtime options
    237:           '-ksp_type preonly -pc_type ilu -pc_factor_mat_solver_type superlu -mat_superlu_ilu_droptol 1.e-8'
    238:           are equivalent to these procedual calls
    239:   */
    240: #if defined(PETSC_HAVE_SUPERLU) || defined(PETSC_HAVE_SUPERLU_DIST)
    241:   flg_ilu     = PETSC_FALSE;
    242:   flg_superlu = PETSC_FALSE;
    243:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_superlu_lu", &flg_superlu, NULL));
    244:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_superlu_ilu", &flg_ilu, NULL));
    245:   if (flg_superlu || flg_ilu) {
    246:     PetscCall(KSPSetType(ksp, KSPPREONLY));
    247:     PetscCall(KSPGetPC(ksp, &pc));
    248:     if (flg_superlu) PetscCall(PCSetType(pc, PCLU));
    249:     else if (flg_ilu) PetscCall(PCSetType(pc, PCILU));
    250:     if (size == 1) {
    251:   #if !defined(PETSC_HAVE_SUPERLU)
    252:       SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "This test requires SUPERLU");
    253:   #else
    254:       PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERSUPERLU));
    255:   #endif
    256:     } else {
    257:   #if !defined(PETSC_HAVE_SUPERLU_DIST)
    258:       SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "This test requires SUPERLU_DIST");
    259:   #else
    260:       PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERSUPERLU_DIST));
    261:   #endif
    262:     }
    263:     PetscCall(PCFactorSetUpMatSolverType(pc)); /* call MatGetFactor() to create F */
    264:     PetscCall(PCFactorGetMatrix(pc, &F));
    265:   #if defined(PETSC_HAVE_SUPERLU)
    266:     if (size == 1) PetscCall(MatSuperluSetILUDropTol(F, 1.e-8));
    267:   #endif
    268:   }
    269: #endif

    271:   /*
    272:     Example of how to use external package STRUMPACK
    273:     Note: runtime options
    274:           '-pc_type lu/ilu \
    275:            -pc_factor_mat_solver_type strumpack \
    276:            -mat_strumpack_reordering GEOMETRIC \
    277:            -mat_strumpack_geometric_xyz n,m \
    278:            -mat_strumpack_colperm 0 \
    279:            -mat_strumpack_compression_rel_tol 1.e-3 \
    280:            -mat_strumpack_compression_min_sep_size 15 \
    281:            -mat_strumpack_leaf_size 4'
    282:        are equivalent to these procedural calls

    284:     We refer to the STRUMPACK manual for more info on
    285:     how to tune the preconditioner, see for instance:
    286:      https://portal.nersc.gov/project/sparse/strumpack/master/prec.html
    287:   */
    288: #if defined(PETSC_HAVE_STRUMPACK)
    289:   flg_ilu       = PETSC_FALSE;
    290:   flg_strumpack = PETSC_FALSE;
    291:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_strumpack_lu", &flg_strumpack, NULL));
    292:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_strumpack_ilu", &flg_ilu, NULL));
    293:   if (flg_strumpack || flg_ilu) {
    294:     PetscCall(KSPSetType(ksp, KSPPREONLY));
    295:     PetscCall(KSPGetPC(ksp, &pc));
    296:     if (flg_strumpack) PetscCall(PCSetType(pc, PCLU));
    297:     else if (flg_ilu) PetscCall(PCSetType(pc, PCILU));
    298:   #if !defined(PETSC_HAVE_STRUMPACK)
    299:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "This test requires STRUMPACK");
    300:   #endif
    301:     PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERSTRUMPACK));
    302:     PetscCall(PCFactorSetUpMatSolverType(pc)); /* call MatGetFactor() to create F */
    303:     PetscCall(PCFactorGetMatrix(pc, &F));

    305:     /* Set the fill-reducing reordering, MAT_STRUMPACK_METIS is       */
    306:     /* always supported, but is sequential. Parallel alternatives are */
    307:     /* MAT_STRUMPACK_PARMETIS and MAT_STRUMPACK_PTSCOTCH, but         */
    308:     /* strumpack needs to be configured with support for these.       */
    309:     /*PetscCall(MatSTRUMPACKSetReordering(F, MAT_STRUMPACK_METIS));   */
    310:     /* However, since this is a problem on a regular grid, we can use */
    311:     /* a simple geometric nested dissection implementation, which     */
    312:     /* requires passing the grid dimensions to strumpack.             */
    313:     PetscCall(MatSTRUMPACKSetReordering(F, MAT_STRUMPACK_GEOMETRIC));
    314:     PetscCall(MatSTRUMPACKSetGeometricNxyz(F, n, m, PETSC_DECIDE));
    315:     /* These are optional, defaults are 1                             */
    316:     PetscCall(MatSTRUMPACKSetGeometricComponents(F, 1));
    317:     PetscCall(MatSTRUMPACKSetGeometricWidth(F, 1));

    319:     /* Since this is a simple discretization, the diagonal is always  */
    320:     /* nonzero, and there is no need for the extra MC64 permutation.  */
    321:     PetscCall(MatSTRUMPACKSetColPerm(F, PETSC_FALSE));

    323:     if (flg_ilu) {
    324:       /* The compression tolerance used when doing low-rank compression */
    325:       /* in the preconditioner. This is problem specific!               */
    326:       PetscCall(MatSTRUMPACKSetCompRelTol(F, 1.e-3));

    328:       /* Set a small minimum (dense) matrix size for compression to     */
    329:       /* demonstrate the preconditioner on small problems.              */
    330:       /* For performance the default value should be better.            */
    331:       /* This size corresponds to the size of separators in the graph.  */
    332:       /* For instance on an m x n mesh, the top level separator is of   */
    333:       /* size m (if m <= n)                                             */
    334:       /*PetscCall(MatSTRUMPACKSetCompMinSepSize(F,15));*/

    336:       /* Set the size of the diagonal blocks (the leafs) in the HSS     */
    337:       /* approximation. The default value should be better for real     */
    338:       /* problems. This is mostly for illustration on a small problem.  */
    339:       /*PetscCall(MatSTRUMPACKSetCompLeafSize(F,4));*/
    340:     }
    341:   }
    342: #endif

    344:   /*
    345:     Example of how to use procedural calls that are equivalent to
    346:           '-ksp_type preonly -pc_type lu/ilu -pc_factor_mat_solver_type petsc'
    347:   */
    348:   flg     = PETSC_FALSE;
    349:   flg_ilu = PETSC_FALSE;
    350:   flg_ch  = PETSC_FALSE;
    351:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_petsc_lu", &flg, NULL));
    352:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_petsc_ilu", &flg_ilu, NULL));
    353:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_petsc_ch", &flg_ch, NULL));
    354:   if (flg || flg_ilu || flg_ch) {
    355:     Vec diag;

    357:     PetscCall(KSPSetType(ksp, KSPPREONLY));
    358:     PetscCall(KSPGetPC(ksp, &pc));
    359:     if (flg) PetscCall(PCSetType(pc, PCLU));
    360:     else if (flg_ilu) PetscCall(PCSetType(pc, PCILU));
    361:     else if (flg_ch) PetscCall(PCSetType(pc, PCCHOLESKY));
    362:     PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERPETSC));
    363:     PetscCall(PCFactorSetUpMatSolverType(pc)); /* call MatGetFactor() to create F */
    364:     PetscCall(PCFactorGetMatrix(pc, &F));

    366:     /* Test MatGetDiagonal() */
    367:     PetscCall(KSPSetUp(ksp));
    368:     PetscCall(VecDuplicate(x, &diag));
    369:     PetscCall(MatGetDiagonal(F, diag));
    370:     /* PetscCall(VecView(diag,PETSC_VIEWER_STDOUT_WORLD)); */
    371:     PetscCall(VecDestroy(&diag));
    372:   }

    374:   PetscCall(KSPSetFromOptions(ksp));

    376:   /* Get info from matrix factors */
    377:   PetscCall(KSPSetUp(ksp));

    379: #if defined(PETSC_HAVE_MUMPS)
    380:   if (flg_mumps || flg_mumps_ch) {
    381:     PetscInt  icntl, infog34, num_null_pivots, *null_pivots;
    382:     PetscReal cntl, rinfo12, rinfo13;
    383:     icntl = 3;
    384:     PetscCall(MatMumpsGetCntl(F, icntl, &cntl));

    386:     /* compute determinant and check for any null pivots*/
    387:     if (rank == 0) {
    388:       PetscCall(MatMumpsGetInfog(F, 34, &infog34));
    389:       PetscCall(MatMumpsGetRinfog(F, 12, &rinfo12));
    390:       PetscCall(MatMumpsGetRinfog(F, 13, &rinfo13));
    391:       PetscCall(MatMumpsGetNullPivots(F, &num_null_pivots, &null_pivots));
    392:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Mumps row pivot threshold = %g\n", cntl));
    393:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Mumps determinant = (%g, %g) * 2^%" PetscInt_FMT " \n", (double)rinfo12, (double)rinfo13, infog34));
    394:       if (num_null_pivots > 0) {
    395:         PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Mumps num of null pivots detected = %" PetscInt_FMT "\n", num_null_pivots));
    396:         PetscCall(PetscSortInt(num_null_pivots, null_pivots)); /* just make the printf deterministic */
    397:         for (j = 0; j < num_null_pivots; j++) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Mumps row with null pivots is = %" PetscInt_FMT "\n", null_pivots[j]));
    398:       }
    399:       PetscCall(PetscFree(null_pivots));
    400:     }
    401:   }
    402: #endif

    404:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    405:                       Solve the linear system
    406:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    407:   PetscCall(KSPSolve(ksp, b, x));

    409:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    410:                       Check solution and clean up
    411:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    412:   PetscCall(VecAXPY(x, -1.0, u));
    413:   PetscCall(VecNorm(x, NORM_2, &norm));
    414:   PetscCall(KSPGetIterationNumber(ksp, &its));

    416:   /*
    417:      Print convergence information.  PetscPrintf() produces a single
    418:      print statement from all processes that share a communicator.
    419:      An alternative is PetscFPrintf(), which prints to a file.
    420:   */
    421:   if (norm < 1.e-12) {
    422:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error < 1.e-12 iterations %" PetscInt_FMT "\n", its));
    423:   } else {
    424:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g iterations %" PetscInt_FMT "\n", (double)norm, its));
    425:   }

    427:   /*
    428:      Free work space.  All PETSc objects should be destroyed when they
    429:      are no longer needed.
    430:   */
    431:   PetscCall(KSPDestroy(&ksp));
    432:   PetscCall(VecDestroy(&u));
    433:   PetscCall(VecDestroy(&x));
    434:   PetscCall(VecDestroy(&b));
    435:   PetscCall(MatDestroy(&A));

    437:   /*
    438:      Always call PetscFinalize() before exiting a program.  This routine
    439:        - finalizes the PETSc libraries as well as MPI
    440:        - provides summary and diagnostic information if certain runtime
    441:          options are chosen (e.g., -log_view).
    442:   */
    443:   PetscCall(PetscFinalize());
    444:   return 0;
    445: }

    447: /*TEST

    449:    test:
    450:       args: -use_petsc_lu
    451:       output_file: output/ex52_2.out

    453:    test:
    454:       suffix: mumps
    455:       nsize: 3
    456:       requires: mumps
    457:       args: -use_mumps_lu
    458:       output_file: output/ex52_1.out

    460:    test:
    461:       suffix: mumps_2
    462:       nsize: 3
    463:       requires: mumps
    464:       args: -use_mumps_ch
    465:       output_file: output/ex52_1.out

    467:    test:
    468:       suffix: mumps_3
    469:       nsize: 3
    470:       requires: mumps
    471:       args: -use_mumps_ch -mat_type sbaij
    472:       output_file: output/ex52_1.out

    474:    test:
    475:       suffix: mumps_4
    476:       nsize: 3
    477:       requires: mumps !complex !single
    478:       args: -use_mumps_lu -m 50 -n 50 -print_mumps_memory
    479:       output_file: output/ex52_4.out

    481:    test:
    482:       suffix: mumps_5
    483:       nsize: 3
    484:       requires: mumps !complex !single
    485:       args: -use_mumps_lu -m 50 -n 50 -zero_first_and_last_rows
    486:       output_file: output/ex52_5.out

    488:    test:
    489:       suffix: mumps_omp_2
    490:       nsize: 4
    491:       requires: mumps hwloc openmp pthread defined(PETSC_HAVE_MPI_PROCESS_SHARED_MEMORY)
    492:       args: -use_mumps_lu -mat_mumps_use_omp_threads 2
    493:       output_file: output/ex52_1.out

    495:    test:
    496:       suffix: mumps_omp_3
    497:       nsize: 4
    498:       requires: mumps hwloc openmp pthread defined(PETSC_HAVE_MPI_PROCESS_SHARED_MEMORY)
    499:       args: -use_mumps_ch -mat_mumps_use_omp_threads 3 -mat_mumps_icntl_48 0
    500:       # Ignore the warning since we are intentionally testing the imbalanced case
    501:       filter: grep -v "Warning: number of OpenMP threads"
    502:       output_file: output/ex52_1.out

    504:    test:
    505:       suffix: mumps_omp_4
    506:       nsize: 4
    507:       requires: mumps hwloc openmp pthread defined(PETSC_HAVE_MPI_PROCESS_SHARED_MEMORY)
    508:       # let PETSc guess a proper number for threads
    509:       args: -use_mumps_ch -mat_type sbaij -mat_mumps_use_omp_threads
    510:       output_file: output/ex52_1.out

    512:    testset:
    513:       suffix: strumpack_2
    514:       nsize: {{1 2}}
    515:       requires: strumpack
    516:       args: -use_strumpack_lu
    517:       output_file: output/ex52_3.out

    519:       test:
    520:         suffix: aij
    521:         args: -mat_type aij

    523:       test:
    524:         requires: kokkos_kernels
    525:         suffix: kok
    526:         args: -mat_type aijkokkos

    528:       test:
    529:         requires: cuda
    530:         suffix: cuda
    531:         args: -mat_type aijcusparse

    533:       test:
    534:         requires: hip
    535:         suffix: hip
    536:         args: -mat_type aijhipsparse

    538:    test:
    539:       suffix: strumpack_ilu
    540:       nsize: {{1 2}}
    541:       requires: strumpack
    542:       args: -use_strumpack_ilu
    543:       output_file: output/ex52_3.out

    545:    testset:
    546:       suffix: superlu_dist
    547:       nsize: {{1 2}}
    548:       requires: superlu superlu_dist
    549:       args: -use_superlu_lu
    550:       output_file: output/ex52_2.out

    552:       test:
    553:         suffix: aij
    554:         args: -mat_type aij

    556:       test:
    557:         requires: kokkos_kernels
    558:         suffix: kok
    559:         args: -mat_type aijkokkos

    561:       test:
    562:         requires: cuda
    563:         suffix: cuda
    564:         args: -mat_type aijcusparse

    566:       test:
    567:         requires: hip
    568:         suffix: hip
    569:         args: -mat_type aijhipsparse

    571:    test:
    572:       suffix: superlu_ilu
    573:       requires: superlu superlu_dist
    574:       args: -use_superlu_ilu
    575:       output_file: output/ex52_2.out

    577: TEST*/