Date: 2022-03-31T04:48:19+00:00

Actual source code: ex5.c

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

      9: /*T
     10:    Concepts: KSP^repeatedly solving linear systems;
     11:    Concepts: PetscLog^profiling multiple stages of code;
     12:    Processors: n
     13: T*/

     15: /*
     16:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     17:   automatically includes:
     18:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     19:      petscmat.h - matrices
     20:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     21:      petscviewer.h - viewers               petscpc.h  - preconditioners
     22: */
     23: #include <petscksp.h>

     25: int main(int argc,char **args)
     26: {
     27:   KSP            ksp;              /* linear solver context */
     28:   Mat            C;                /* matrix */
     29:   Vec            x,u,b;            /* approx solution, RHS, exact solution */
     30:   PetscReal      norm;             /* norm of solution error */
     31:   PetscScalar    v,none = -1.0;
     32:   PetscInt       Ii,J,ldim,low,high,iglobal,Istart,Iend;
     33:   PetscInt       i,j,m = 3,n = 2,its;
     34:   PetscMPIInt    size,rank;
     35:   PetscBool      mat_nonsymmetric = PETSC_FALSE;
     36:   PetscBool      testnewC = PETSC_FALSE,testscaledMat=PETSC_FALSE;
     37: #if defined(PETSC_USE_LOG)
     38:   PetscLogStage stages[2];
     39: #endif

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

     47:   /*
     48:      Set flag if we are doing a nonsymmetric problem; the default is symmetric.
     49:   */
     50:   PetscOptionsGetBool(NULL,NULL,"-mat_nonsym",&mat_nonsymmetric,NULL);

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

     54:   /*
     55:      Register two stages for separate profiling of the two linear solves.
     56:      Use the runtime option -log_view for a printout of performance
     57:      statistics at the program's conlusion.
     58:   */
     59:   PetscLogStageRegister("Original Solve",&stages[0]);
     60:   PetscLogStageRegister("Second Solve",&stages[1]);

     62:   /* -------------- Stage 0: Solve Original System ---------------------- */
     63:   /*
     64:      Indicate to PETSc profiling that we're beginning the first stage
     65:   */
     66:   PetscLogStagePush(stages[0]);

     68:   /*
     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:   */
     74:   MatCreate(PETSC_COMM_WORLD,&C);
     75:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     76:   MatSetFromOptions(C);
     77:   MatSetUp(C);

     79:   /*
     80:      Currently, all PETSc parallel matrix formats are partitioned by
     81:      contiguous chunks of rows across the processors.  Determine which
     82:      rows of the matrix are locally owned.
     83:   */
     84:   MatGetOwnershipRange(C,&Istart,&Iend);

     86:   /*
     87:      Set matrix entries matrix in parallel.
     88:       - Each processor needs to insert only elements that it owns
     89:         locally (but any non-local elements will be sent to the
     90:         appropriate processor during matrix assembly).
     91:       - Always specify global row and columns of matrix entries.
     92:   */
     93:   for (Ii=Istart; Ii<Iend; Ii++) {
     94:     v = -1.0; i = Ii/n; j = Ii - i*n;
     95:     if (i>0)   {J = Ii - n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     96:     if (i<m-1) {J = Ii + n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     97:     if (j>0)   {J = Ii - 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     98:     if (j<n-1) {J = Ii + 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     99:     v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,ADD_VALUES);
    100:   }

    102:   /*
    103:      Make the matrix nonsymmetric if desired
    104:   */
    105:   if (mat_nonsymmetric) {
    106:     for (Ii=Istart; Ii<Iend; Ii++) {
    107:       v = -1.5; i = Ii/n;
    108:       if (i>1)   {J = Ii-n-1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    109:     }
    110:   } else {
    111:     MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE);
    112:     MatSetOption(C,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
    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:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    122:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    124:   /*
    125:      Create parallel vectors.
    126:       - When using VecSetSizes(), we specify only the vector's global
    127:         dimension; the parallel partitioning is determined at runtime.
    128:       - Note: We form 1 vector from scratch and then duplicate as needed.
    129:   */
    130:   VecCreate(PETSC_COMM_WORLD,&u);
    131:   VecSetSizes(u,PETSC_DECIDE,m*n);
    132:   VecSetFromOptions(u);
    133:   VecDuplicate(u,&b);
    134:   VecDuplicate(b,&x);

    136:   /*
    137:      Currently, all parallel PETSc vectors are partitioned by
    138:      contiguous chunks across the processors.  Determine which
    139:      range of entries are locally owned.
    140:   */
    141:   VecGetOwnershipRange(x,&low,&high);

    143:   /*
    144:     Set elements within the exact solution vector in parallel.
    145:      - Each processor needs to insert only elements that it owns
    146:        locally (but any non-local entries will be sent to the
    147:        appropriate processor during vector assembly).
    148:      - Always specify global locations of vector entries.
    149:   */
    150:   VecGetLocalSize(x,&ldim);
    151:   for (i=0; i<ldim; i++) {
    152:     iglobal = i + low;
    153:     v       = (PetscScalar)(i + 100*rank);
    154:     VecSetValues(u,1,&iglobal,&v,INSERT_VALUES);
    155:   }

    157:   /*
    158:      Assemble vector, using the 2-step process:
    159:        VecAssemblyBegin(), VecAssemblyEnd()
    160:      Computations can be done while messages are in transition,
    161:      by placing code between these two statements.
    162:   */
    163:   VecAssemblyBegin(u);
    164:   VecAssemblyEnd(u);

    166:   /*
    167:      Compute right-hand-side vector
    168:   */
    169:   MatMult(C,u,b);

    171:   /*
    172:     Create linear solver context
    173:   */
    174:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    176:   /*
    177:      Set operators. Here the matrix that defines the linear system
    178:      also serves as the preconditioning matrix.
    179:   */
    180:   KSPSetOperators(ksp,C,C);

    182:   /*
    183:      Set runtime options (e.g., -ksp_type <type> -pc_type <type>)
    184:   */
    185:   KSPSetFromOptions(ksp);

    187:   /*
    188:      Solve linear system.  Here we explicitly call KSPSetUp() for more
    189:      detailed performance monitoring of certain preconditioners, such
    190:      as ICC and ILU.  This call is optional, as KSPSetUp() will
    191:      automatically be called within KSPSolve() if it hasn't been
    192:      called already.
    193:   */
    194:   KSPSetUp(ksp);
    195:   KSPSolve(ksp,b,x);

    197:   /*
    198:      Check the error
    199:   */
    200:   VecAXPY(x,none,u);
    201:   VecNorm(x,NORM_2,&norm);
    202:   KSPGetIterationNumber(ksp,&its);
    203:   if (!testscaledMat || norm > 1.e-7) {
    204:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    205:   }

    207:   /* -------------- Stage 1: Solve Second System ---------------------- */
    208:   /*
    209:      Solve another linear system with the same method.  We reuse the KSP
    210:      context, matrix and vector data structures, and hence save the
    211:      overhead of creating new ones.

    213:      Indicate to PETSc profiling that we're concluding the first
    214:      stage with PetscLogStagePop(), and beginning the second stage with
    215:      PetscLogStagePush().
    216:   */
    217:   PetscLogStagePop();
    218:   PetscLogStagePush(stages[1]);

    220:   /*
    221:      Initialize all matrix entries to zero.  MatZeroEntries() retains the
    222:      nonzero structure of the matrix for sparse formats.
    223:   */
    224:   MatZeroEntries(C);

    226:   /*
    227:      Assemble matrix again.  Note that we retain the same matrix data
    228:      structure and the same nonzero pattern; we just change the values
    229:      of the matrix entries.
    230:   */
    231:   for (i=0; i<m; i++) {
    232:     for (j=2*rank; j<2*rank+2; j++) {
    233:       v = -1.0;  Ii = j + n*i;
    234:       if (i>0)   {J = Ii - n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    235:       if (i<m-1) {J = Ii + n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    236:       if (j>0)   {J = Ii - 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    237:       if (j<n-1) {J = Ii + 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    238:       v = 6.0; MatSetValues(C,1,&Ii,1,&Ii,&v,ADD_VALUES);
    239:     }
    240:   }
    241:   if (mat_nonsymmetric) {
    242:     for (Ii=Istart; Ii<Iend; Ii++) {
    243:       v = -1.5; i = Ii/n;
    244:       if (i>1)   {J = Ii-n-1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    245:     }
    246:   }
    247:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    248:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    250:   if (testscaledMat) {
    251:     PetscRandom    rctx;

    253:     /* Scale a(0,0) and a(M-1,M-1) */
    254:     if (rank == 0) {
    255:       v = 6.0*0.00001; Ii = 0; J = 0;
    256:       MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
    257:     } else if (rank == size -1) {
    258:       v = 6.0*0.00001; Ii = m*n-1; J = m*n-1;
    259:       MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
    260:     }
    261:     MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    262:     MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    264:     /* Compute a new right-hand-side vector */
    265:     VecDestroy(&u);
    266:     VecCreate(PETSC_COMM_WORLD,&u);
    267:     VecSetSizes(u,PETSC_DECIDE,m*n);
    268:     VecSetFromOptions(u);

    270:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    271:     PetscRandomSetFromOptions(rctx);
    272:     VecSetRandom(u,rctx);
    273:     PetscRandomDestroy(&rctx);
    274:     VecAssemblyBegin(u);
    275:     VecAssemblyEnd(u);
    276:   }

    278:   PetscOptionsGetBool(NULL,NULL,"-test_newMat",&testnewC,NULL);
    279:   if (testnewC) {
    280:     /*
    281:      User may use a new matrix C with same nonzero pattern, e.g.
    282:       ./ex5 -ksp_monitor -mat_type sbaij -pc_type cholesky -pc_factor_mat_solver_type mumps -test_newMat
    283:     */
    284:     Mat Ctmp;
    285:     MatDuplicate(C,MAT_COPY_VALUES,&Ctmp);
    286:     MatDestroy(&C);
    287:     MatDuplicate(Ctmp,MAT_COPY_VALUES,&C);
    288:     MatDestroy(&Ctmp);
    289:   }

    291:   MatMult(C,u,b);

    293:   /*
    294:      Set operators. Here the matrix that defines the linear system
    295:      also serves as the preconditioning matrix.
    296:   */
    297:   KSPSetOperators(ksp,C,C);

    299:   /*
    300:      Solve linear system
    301:   */
    302:   KSPSetUp(ksp);
    303:   KSPSolve(ksp,b,x);

    305:   /*
    306:      Check the error
    307:   */
    308:   VecAXPY(x,none,u);
    309:   VecNorm(x,NORM_2,&norm);
    310:   KSPGetIterationNumber(ksp,&its);
    311:   if (!testscaledMat || norm > 1.e-7) {
    312:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    313:   }

    315:   /*
    316:      Free work space.  All PETSc objects should be destroyed when they
    317:      are no longer needed.
    318:   */
    319:   KSPDestroy(&ksp);
    320:   VecDestroy(&u);
    321:   VecDestroy(&x);
    322:   VecDestroy(&b);
    323:   MatDestroy(&C);

    325:   /*
    326:      Indicate to PETSc profiling that we're concluding the second stage
    327:   */
    328:   PetscLogStagePop();

    330:   PetscFinalize();
    331:   return 0;
    332: }

    334: /*TEST

    336:    test:
    337:       args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    339:    test:
    340:       suffix: 2
    341:       nsize: 2
    342:       args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -ksp_rtol .000001

    344:    test:
    345:       suffix: 5
    346:       nsize: 2
    347:       args: -ksp_gmres_cgs_refinement_type refine_always -ksp_monitor draw::draw_lg -ksp_monitor_true_residual draw::draw_lg

    349:    test:
    350:       suffix: asm
    351:       nsize: 4
    352:       args: -pc_type asm

    354:    test:
    355:       suffix: asm_baij
    356:       nsize: 4
    357:       args: -pc_type asm -mat_type baij
    358:       output_file: output/ex5_asm.out

    360:    test:
    361:       suffix: redundant_0
    362:       args: -m 1000 -pc_type redundant -pc_redundant_number 1 -redundant_ksp_type gmres -redundant_pc_type jacobi

    364:    test:
    365:       suffix: redundant_1
    366:       nsize: 5
    367:       args: -pc_type redundant -pc_redundant_number 1 -redundant_ksp_type gmres -redundant_pc_type jacobi

    369:    test:
    370:       suffix: redundant_2
    371:       nsize: 5
    372:       args: -pc_type redundant -pc_redundant_number 3 -redundant_ksp_type gmres -redundant_pc_type jacobi

    374:    test:
    375:       suffix: redundant_3
    376:       nsize: 5
    377:       args: -pc_type redundant -pc_redundant_number 5 -redundant_ksp_type gmres -redundant_pc_type jacobi

    379:    test:
    380:       suffix: redundant_4
    381:       nsize: 5
    382:       args: -pc_type redundant -pc_redundant_number 3 -redundant_ksp_type gmres -redundant_pc_type jacobi -psubcomm_type interlaced

    384:    test:
    385:       suffix: superlu_dist
    386:       nsize: 15
    387:       requires: superlu_dist
    388:       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

    390:    test:
    391:       suffix: superlu_dist_2
    392:       nsize: 15
    393:       requires: superlu_dist
    394:       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
    395:       output_file: output/ex5_superlu_dist.out

    397:    test:
    398:       suffix: superlu_dist_3
    399:       nsize: 15
    400:       requires: superlu_dist
    401:       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
    402:       output_file: output/ex5_superlu_dist.out

    404:    test:
    405:       suffix: superlu_dist_0
    406:       nsize: 1
    407:       requires: superlu_dist
    408:       args: -pc_type lu -pc_factor_mat_solver_type superlu_dist -test_scaledMat
    409:       output_file: output/ex5_superlu_dist.out

    411: TEST*/