Date: 2022-08-02T03:14:46+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: /*
     10:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     11:   automatically includes:
     12:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     13:      petscmat.h - matrices
     14:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     15:      petscviewer.h - viewers               petscpc.h  - preconditioners
     16: */
     17: #include <petscksp.h>

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

     35:   PetscInitialize(&argc,&args,(char*)0,help);
     36:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     37:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     38:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     39:   n    = 2*size;

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

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

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

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

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

     73:   /*
     74:      Currently, all PETSc parallel matrix formats are partitioned by
     75:      contiguous chunks of rows across the processors.  Determine which
     76:      rows of the matrix are locally owned.
     77:   */
     78:   MatGetOwnershipRange(C,&Istart,&Iend);

     80:   /*
     81:      Set matrix entries matrix in parallel.
     82:       - Each processor needs to insert only elements that it owns
     83:         locally (but any non-local elements will be sent to the
     84:         appropriate processor during matrix assembly).
     85:       - Always specify global row and columns of matrix entries.
     86:   */
     87:   for (Ii=Istart; Ii<Iend; Ii++) {
     88:     v = -1.0; i = Ii/n; j = Ii - i*n;
     89:     if (i>0)   {J = Ii - n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     90:     if (i<m-1) {J = Ii + n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     91:     if (j>0)   {J = Ii - 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     92:     if (j<n-1) {J = Ii + 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     93:     v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,ADD_VALUES);
     94:   }

     96:   /*
     97:      Make the matrix nonsymmetric if desired
     98:   */
     99:   if (mat_nonsymmetric) {
    100:     for (Ii=Istart; Ii<Iend; Ii++) {
    101:       v = -1.5; i = Ii/n;
    102:       if (i>1)   {J = Ii-n-1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    103:     }
    104:   } else {
    105:     MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE);
    106:     MatSetOption(C,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
    107:   }

    109:   /*
    110:      Assemble matrix, using the 2-step process:
    111:        MatAssemblyBegin(), MatAssemblyEnd()
    112:      Computations can be done while messages are in transition
    113:      by placing code between these two statements.
    114:   */
    115:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    116:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    118:   /*
    119:      Create parallel vectors.
    120:       - When using VecSetSizes(), we specify only the vector's global
    121:         dimension; the parallel partitioning is determined at runtime.
    122:       - Note: We form 1 vector from scratch and then duplicate as needed.
    123:   */
    124:   VecCreate(PETSC_COMM_WORLD,&u);
    125:   VecSetSizes(u,PETSC_DECIDE,m*n);
    126:   VecSetFromOptions(u);
    127:   VecDuplicate(u,&b);
    128:   VecDuplicate(b,&x);

    130:   /*
    131:      Currently, all parallel PETSc vectors are partitioned by
    132:      contiguous chunks across the processors.  Determine which
    133:      range of entries are locally owned.
    134:   */
    135:   VecGetOwnershipRange(x,&low,&high);

    137:   /*
    138:     Set elements within the exact solution vector in parallel.
    139:      - Each processor needs to insert only elements that it owns
    140:        locally (but any non-local entries will be sent to the
    141:        appropriate processor during vector assembly).
    142:      - Always specify global locations of vector entries.
    143:   */
    144:   VecGetLocalSize(x,&ldim);
    145:   for (i=0; i<ldim; i++) {
    146:     iglobal = i + low;
    147:     v       = (PetscScalar)(i + 100*rank);
    148:     VecSetValues(u,1,&iglobal,&v,INSERT_VALUES);
    149:   }

    151:   /*
    152:      Assemble vector, using the 2-step process:
    153:        VecAssemblyBegin(), VecAssemblyEnd()
    154:      Computations can be done while messages are in transition,
    155:      by placing code between these two statements.
    156:   */
    157:   VecAssemblyBegin(u);
    158:   VecAssemblyEnd(u);

    160:   /*
    161:      Compute right-hand-side vector
    162:   */
    163:   MatMult(C,u,b);

    165:   /*
    166:     Create linear solver context
    167:   */
    168:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    170:   /*
    171:      Set operators. Here the matrix that defines the linear system
    172:      also serves as the preconditioning matrix.
    173:   */
    174:   KSPSetOperators(ksp,C,C);

    176:   /*
    177:      Set runtime options (e.g., -ksp_type <type> -pc_type <type>)
    178:   */
    179:   KSPSetFromOptions(ksp);

    181:   /*
    182:      Solve linear system.  Here we explicitly call KSPSetUp() for more
    183:      detailed performance monitoring of certain preconditioners, such
    184:      as ICC and ILU.  This call is optional, as KSPSetUp() will
    185:      automatically be called within KSPSolve() if it hasn't been
    186:      called already.
    187:   */
    188:   KSPSetUp(ksp);
    189:   KSPSolve(ksp,b,x);

    191:   /*
    192:      Check the error
    193:   */
    194:   VecAXPY(x,none,u);
    195:   VecNorm(x,NORM_2,&norm);
    196:   KSPGetIterationNumber(ksp,&its);
    197:   if (!testscaledMat || norm > 1.e-7) {
    198:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    199:   }

    201:   /* -------------- Stage 1: Solve Second System ---------------------- */
    202:   /*
    203:      Solve another linear system with the same method.  We reuse the KSP
    204:      context, matrix and vector data structures, and hence save the
    205:      overhead of creating new ones.

    207:      Indicate to PETSc profiling that we're concluding the first
    208:      stage with PetscLogStagePop(), and beginning the second stage with
    209:      PetscLogStagePush().
    210:   */
    211:   PetscLogStagePop();
    212:   PetscLogStagePush(stages[1]);

    214:   /*
    215:      Initialize all matrix entries to zero.  MatZeroEntries() retains the
    216:      nonzero structure of the matrix for sparse formats.
    217:   */
    218:   MatZeroEntries(C);

    220:   /*
    221:      Assemble matrix again.  Note that we retain the same matrix data
    222:      structure and the same nonzero pattern; we just change the values
    223:      of the matrix entries.
    224:   */
    225:   for (i=0; i<m; i++) {
    226:     for (j=2*rank; j<2*rank+2; j++) {
    227:       v = -1.0;  Ii = j + n*i;
    228:       if (i>0)   {J = Ii - n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    229:       if (i<m-1) {J = Ii + n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    230:       if (j>0)   {J = Ii - 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    231:       if (j<n-1) {J = Ii + 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    232:       v = 6.0; MatSetValues(C,1,&Ii,1,&Ii,&v,ADD_VALUES);
    233:     }
    234:   }
    235:   if (mat_nonsymmetric) {
    236:     for (Ii=Istart; Ii<Iend; Ii++) {
    237:       v = -1.5; i = Ii/n;
    238:       if (i>1)   {J = Ii-n-1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
    239:     }
    240:   }
    241:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    242:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    244:   if (testscaledMat) {
    245:     PetscRandom    rctx;

    247:     /* Scale a(0,0) and a(M-1,M-1) */
    248:     if (rank == 0) {
    249:       v = 6.0*0.00001; Ii = 0; J = 0;
    250:       MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
    251:     } else if (rank == size -1) {
    252:       v = 6.0*0.00001; Ii = m*n-1; J = m*n-1;
    253:       MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
    254:     }
    255:     MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    256:     MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    258:     /* Compute a new right-hand-side vector */
    259:     VecDestroy(&u);
    260:     VecCreate(PETSC_COMM_WORLD,&u);
    261:     VecSetSizes(u,PETSC_DECIDE,m*n);
    262:     VecSetFromOptions(u);

    264:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    265:     PetscRandomSetFromOptions(rctx);
    266:     VecSetRandom(u,rctx);
    267:     PetscRandomDestroy(&rctx);
    268:     VecAssemblyBegin(u);
    269:     VecAssemblyEnd(u);
    270:   }

    272:   PetscOptionsGetBool(NULL,NULL,"-test_newMat",&testnewC,NULL);
    273:   if (testnewC) {
    274:     /*
    275:      User may use a new matrix C with same nonzero pattern, e.g.
    276:       ./ex5 -ksp_monitor -mat_type sbaij -pc_type cholesky -pc_factor_mat_solver_type mumps -test_newMat
    277:     */
    278:     Mat Ctmp;
    279:     MatDuplicate(C,MAT_COPY_VALUES,&Ctmp);
    280:     MatDestroy(&C);
    281:     MatDuplicate(Ctmp,MAT_COPY_VALUES,&C);
    282:     MatDestroy(&Ctmp);
    283:   }

    285:   MatMult(C,u,b);

    287:   /*
    288:      Set operators. Here the matrix that defines the linear system
    289:      also serves as the preconditioning matrix.
    290:   */
    291:   KSPSetOperators(ksp,C,C);

    293:   /*
    294:      Solve linear system
    295:   */
    296:   KSPSetUp(ksp);
    297:   KSPSolve(ksp,b,x);

    299:   /*
    300:      Check the error
    301:   */
    302:   VecAXPY(x,none,u);
    303:   VecNorm(x,NORM_2,&norm);
    304:   KSPGetIterationNumber(ksp,&its);
    305:   if (!testscaledMat || norm > 1.e-7) {
    306:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    307:   }

    309:   /*
    310:      Free work space.  All PETSc objects should be destroyed when they
    311:      are no longer needed.
    312:   */
    313:   KSPDestroy(&ksp);
    314:   VecDestroy(&u);
    315:   VecDestroy(&x);
    316:   VecDestroy(&b);
    317:   MatDestroy(&C);

    319:   /*
    320:      Indicate to PETSc profiling that we're concluding the second stage
    321:   */
    322:   PetscLogStagePop();

    324:   PetscFinalize();
    325:   return 0;
    326: }

    328: /*TEST

    330:    test:
    331:       args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    333:    test:
    334:       suffix: 2
    335:       nsize: 2
    336:       args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -ksp_rtol .000001

    338:    test:
    339:       suffix: 5
    340:       nsize: 2
    341:       args: -ksp_gmres_cgs_refinement_type refine_always -ksp_monitor draw::draw_lg -ksp_monitor_true_residual draw::draw_lg

    343:    test:
    344:       suffix: asm
    345:       nsize: 4
    346:       args: -pc_type asm

    348:    test:
    349:       suffix: asm_baij
    350:       nsize: 4
    351:       args: -pc_type asm -mat_type baij
    352:       output_file: output/ex5_asm.out

    354:    test:
    355:       suffix: redundant_0
    356:       args: -m 1000 -pc_type redundant -pc_redundant_number 1 -redundant_ksp_type gmres -redundant_pc_type jacobi

    358:    test:
    359:       suffix: redundant_1
    360:       nsize: 5
    361:       args: -pc_type redundant -pc_redundant_number 1 -redundant_ksp_type gmres -redundant_pc_type jacobi

    363:    test:
    364:       suffix: redundant_2
    365:       nsize: 5
    366:       args: -pc_type redundant -pc_redundant_number 3 -redundant_ksp_type gmres -redundant_pc_type jacobi

    368:    test:
    369:       suffix: redundant_3
    370:       nsize: 5
    371:       args: -pc_type redundant -pc_redundant_number 5 -redundant_ksp_type gmres -redundant_pc_type jacobi

    373:    test:
    374:       suffix: redundant_4
    375:       nsize: 5
    376:       args: -pc_type redundant -pc_redundant_number 3 -redundant_ksp_type gmres -redundant_pc_type jacobi -psubcomm_type interlaced

    378:    test:
    379:       suffix: superlu_dist
    380:       nsize: 15
    381:       requires: superlu_dist
    382:       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

    384:    test:
    385:       suffix: superlu_dist_2
    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 -mat_superlu_dist_fact SamePattern_SameRowPerm
    389:       output_file: output/ex5_superlu_dist.out

    391:    test:
    392:       suffix: superlu_dist_3
    393:       nsize: 15
    394:       requires: superlu_dist
    395:       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
    396:       output_file: output/ex5_superlu_dist.out

    398:    test:
    399:       suffix: superlu_dist_0
    400:       nsize: 1
    401:       requires: superlu_dist
    402:       args: -pc_type lu -pc_factor_mat_solver_type superlu_dist -test_scaledMat
    403:       output_file: output/ex5_superlu_dist.out

    405: TEST*/