Date: 2013-07-02T14:48:41+00:00

Actual source code: ex9.c
petsc-3.4.2 2013-07-02

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

      7: /*T
      8:    Concepts: KSP^repeatedly solving linear systems;
      9:    Concepts: PetscLog^profiling multiple stages of code;
     10:    Concepts: PetscLog^user-defined event profiling;
     11:    Processors: n
     12: T*/

     14: /*
     15:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     16:   automatically includes:
     17:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     18:      petscmat.h - matrices
     19:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     20:      petscviewer.h - viewers               petscpc.h  - preconditioners
     21: */
     22: #include <petscksp.h>

     24: /*
     25:    Declare user-defined routines
     26: */
     27: extern PetscErrorCode CheckError(Vec,Vec,Vec,PetscInt,PetscReal,PetscLogEvent);
     28: extern PetscErrorCode MyKSPMonitor(KSP,PetscInt,PetscReal,void*);

     32: int main(int argc,char **args)
     33: {
     34:   Vec            x1,b1,x2,b2; /* solution and RHS vectors for systems #1 and #2 */
     35:   Vec            u;              /* exact solution vector */
     36:   Mat            C1,C2;         /* matrices for systems #1 and #2 */
     37:   KSP            ksp1,ksp2;   /* KSP contexts for systems #1 and #2 */
     38:   PetscInt       ntimes = 3;     /* number of times to solve the linear systems */
     39:   PetscLogEvent  CHECK_ERROR;    /* event number for error checking */
     40:   PetscInt       ldim,low,high,iglobal,Istart,Iend,Istart2,Iend2;
     41:   PetscInt       Ii,J,i,j,m = 3,n = 2,its,t;
     43:   PetscBool      flg = PETSC_FALSE;
     44:   PetscScalar    v;
     45:   PetscMPIInt    rank,size;
     46: #if defined(PETSC_USE_LOG)
     47:   PetscLogStage stages[3];
     48: #endif

     50:   PetscInitialize(&argc,&args,(char*)0,help);
     51:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
     52:   PetscOptionsGetInt(NULL,"-t",&ntimes,NULL);
     53:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     54:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     55:   n    = 2*size;

     57:   /*
     58:      Register various stages for profiling
     59:   */
     60:   PetscLogStageRegister("Prelim setup",&stages[0]);
     61:   PetscLogStageRegister("Linear System 1",&stages[1]);
     62:   PetscLogStageRegister("Linear System 2",&stages[2]);

     64:   /*
     65:      Register a user-defined event for profiling (error checking).
     66:   */
     67:   CHECK_ERROR = 0;
     68:   PetscLogEventRegister("Check Error",KSP_CLASSID,&CHECK_ERROR);

     70:   /* - - - - - - - - - - - - Stage 0: - - - - - - - - - - - - - -
     71:                         Preliminary Setup
     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     74:   PetscLogStagePush(stages[0]);

     76:   /*
     77:      Create data structures for first linear system.
     78:       - Create parallel matrix, specifying only its global dimensions.
     79:         When using MatCreate(), the matrix format can be specified at
     80:         runtime. Also, the parallel partitioning of the matrix is
     81:         determined by PETSc at runtime.
     82:       - Create parallel vectors.
     83:         - When using VecSetSizes(), we specify only the vector's global
     84:           dimension; the parallel partitioning is determined at runtime.
     85:         - Note: We form 1 vector from scratch and then duplicate as needed.
     86:   */
     87:   MatCreate(PETSC_COMM_WORLD,&C1);
     88:   MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     89:   MatSetFromOptions(C1);
     90:   MatSetUp(C1);
     91:   MatGetOwnershipRange(C1,&Istart,&Iend);
     92:   VecCreate(PETSC_COMM_WORLD,&u);
     93:   VecSetSizes(u,PETSC_DECIDE,m*n);
     94:   VecSetFromOptions(u);
     95:   VecDuplicate(u,&b1);
     96:   VecDuplicate(u,&x1);

     98:   /*
     99:      Create first linear solver context.
    100:      Set runtime options (e.g., -pc_type <type>).
    101:      Note that the first linear system uses the default option
    102:      names, while the second linear systme uses a different
    103:      options prefix.
    104:   */
    105:   KSPCreate(PETSC_COMM_WORLD,&ksp1);
    106:   KSPSetFromOptions(ksp1);

    108:   /*
    109:      Set user-defined monitoring routine for first linear system.
    110:   */
    111:   PetscOptionsGetBool(NULL,"-my_ksp_monitor",&flg,NULL);
    112:   if (flg) {KSPMonitorSet(ksp1,MyKSPMonitor,NULL,0);}

    114:   /*
    115:      Create data structures for second linear system.
    116:   */
    117:   MatCreate(PETSC_COMM_WORLD,&C2);
    118:   MatSetSizes(C2,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
    119:   MatSetFromOptions(C2);
    120:   MatSetUp(C2);
    121:   MatGetOwnershipRange(C2,&Istart2,&Iend2);
    122:   VecDuplicate(u,&b2);
    123:   VecDuplicate(u,&x2);

    125:   /*
    126:      Create second linear solver context
    127:   */
    128:   KSPCreate(PETSC_COMM_WORLD,&ksp2);

    130:   /*
    131:      Set different options prefix for second linear system.
    132:      Set runtime options (e.g., -s2_pc_type <type>)
    133:   */
    134:   KSPAppendOptionsPrefix(ksp2,"s2_");
    135:   KSPSetFromOptions(ksp2);

    137:   /*
    138:      Assemble exact solution vector in parallel.  Note that each
    139:      processor needs to set only its local part of the vector.
    140:   */
    141:   VecGetLocalSize(u,&ldim);
    142:   VecGetOwnershipRange(u,&low,&high);
    143:   for (i=0; i<ldim; i++) {
    144:     iglobal = i + low;
    145:     v       = (PetscScalar)(i + 100*rank);
    146:     VecSetValues(u,1,&iglobal,&v,ADD_VALUES);
    147:   }
    148:   VecAssemblyBegin(u);
    149:   VecAssemblyEnd(u);

    151:   /*
    152:      Log the number of flops for computing vector entries
    153:   */
    154:   PetscLogFlops(2.0*ldim);

    156:   /*
    157:      End curent profiling stage
    158:   */
    159:   PetscLogStagePop();

    161:   /* --------------------------------------------------------------
    162:                         Linear solver loop:
    163:       Solve 2 different linear systems several times in succession
    164:      -------------------------------------------------------------- */

    166:   for (t=0; t<ntimes; t++) {

    168:     /* - - - - - - - - - - - - Stage 1: - - - - - - - - - - - - - -
    169:                  Assemble and solve first linear system
    170:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    172:     /*
    173:        Begin profiling stage #1
    174:     */
    175:     PetscLogStagePush(stages[1]);

    177:     /*
    178:        Initialize all matrix entries to zero.  MatZeroEntries() retains
    179:        the nonzero structure of the matrix for sparse formats.
    180:     */
    181:     if (t > 0) {MatZeroEntries(C1);}

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

    205:     /*
    206:        Assemble matrix, using the 2-step process:
    207:          MatAssemblyBegin(), MatAssemblyEnd()
    208:        Computations can be done while messages are in transition
    209:        by placing code between these two statements.
    210:     */
    211:     MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);
    212:     MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);

    214:     /*
    215:        Indicate same nonzero structure of successive linear system matrices
    216:     */
    217:     MatSetOption(C1,MAT_NEW_NONZERO_LOCATIONS,PETSC_TRUE);

    219:     /*
    220:        Compute right-hand-side vector
    221:     */
    222:     MatMult(C1,u,b1);

    224:     /*
    225:        Set operators. Here the matrix that defines the linear system
    226:        also serves as the preconditioning matrix.
    227:         - The flag SAME_NONZERO_PATTERN indicates that the
    228:           preconditioning matrix has identical nonzero structure
    229:           as during the last linear solve (although the values of
    230:           the entries have changed). Thus, we can save some
    231:           work in setting up the preconditioner (e.g., no need to
    232:           redo symbolic factorization for ILU/ICC preconditioners).
    233:         - If the nonzero structure of the matrix is different during
    234:           the second linear solve, then the flag DIFFERENT_NONZERO_PATTERN
    235:           must be used instead.  If you are unsure whether the
    236:           matrix structure has changed or not, use the flag
    237:           DIFFERENT_NONZERO_PATTERN.
    238:         - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
    239:           believes your assertion and does not check the structure
    240:           of the matrix.  If you erroneously claim that the structure
    241:           is the same when it actually is not, the new preconditioner
    242:           will not function correctly.  Thus, use this optimization
    243:           feature with caution!
    244:     */
    245:     KSPSetOperators(ksp1,C1,C1,SAME_NONZERO_PATTERN);

    247:     /*
    248:        Use the previous solution of linear system #1 as the initial
    249:        guess for the next solve of linear system #1.  The user MUST
    250:        call KSPSetInitialGuessNonzero() in indicate use of an initial
    251:        guess vector; otherwise, an initial guess of zero is used.
    252:     */
    253:     if (t>0) {
    254:       KSPSetInitialGuessNonzero(ksp1,PETSC_TRUE);
    255:     }

    257:     /*
    258:        Solve the first linear system.  Here we explicitly call
    259:        KSPSetUp() for more detailed performance monitoring of
    260:        certain preconditioners, such as ICC and ILU.  This call
    261:        is optional, ase KSPSetUp() will automatically be called
    262:        within KSPSolve() if it hasn't been called already.
    263:     */
    264:     KSPSetUp(ksp1);
    265:     KSPSolve(ksp1,b1,x1);
    266:     KSPGetIterationNumber(ksp1,&its);

    268:     /*
    269:        Check error of solution to first linear system
    270:     */
    271:     CheckError(u,x1,b1,its,1.e-4,CHECK_ERROR);

    273:     /* - - - - - - - - - - - - Stage 2: - - - - - - - - - - - - - -
    274:                  Assemble and solve second linear system
    275:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    277:     /*
    278:        Conclude profiling stage #1; begin profiling stage #2
    279:     */
    280:     PetscLogStagePop();
    281:     PetscLogStagePush(stages[2]);

    283:     /*
    284:        Initialize all matrix entries to zero
    285:     */
    286:     if (t > 0) {MatZeroEntries(C2);}

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

    317:     /*
    318:        Indicate same nonzero structure of successive linear system matrices
    319:     */
    320:     MatSetOption(C2,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);

    322:     /*
    323:        Compute right-hand-side vector
    324:     */
    325:     MatMult(C2,u,b2);

    327:     /*
    328:        Set operators. Here the matrix that defines the linear system
    329:        also serves as the preconditioning matrix.  Indicate same nonzero
    330:        structure of successive preconditioner matrices by setting flag
    331:        SAME_NONZERO_PATTERN.
    332:     */
    333:     KSPSetOperators(ksp2,C2,C2,SAME_NONZERO_PATTERN);

    335:     /*
    336:        Solve the second linear system
    337:     */
    338:     KSPSetUp(ksp2);
    339:     KSPSolve(ksp2,b2,x2);
    340:     KSPGetIterationNumber(ksp2,&its);

    342:     /*
    343:        Check error of solution to second linear system
    344:     */
    345:     CheckError(u,x2,b2,its,1.e-4,CHECK_ERROR);

    347:     /*
    348:        Conclude profiling stage #2
    349:     */
    350:     PetscLogStagePop();
    351:   }
    352:   /* --------------------------------------------------------------
    353:                        End of linear solver loop
    354:      -------------------------------------------------------------- */

    356:   /*
    357:      Free work space.  All PETSc objects should be destroyed when they
    358:      are no longer needed.
    359:   */
    360:   KSPDestroy(&ksp1); KSPDestroy(&ksp2);
    361:   VecDestroy(&x1);   VecDestroy(&x2);
    362:   VecDestroy(&b1);   VecDestroy(&b2);
    363:   MatDestroy(&C1);   MatDestroy(&C2);
    364:   VecDestroy(&u);

    366:   PetscFinalize();
    367:   return 0;
    368: }
    371: /* ------------------------------------------------------------- */
    372: /*
    373:     CheckError - Checks the error of the solution.

    375:     Input Parameters:
    376:     u - exact solution
    377:     x - approximate solution
    378:     b - work vector
    379:     its - number of iterations for convergence
    380:     tol - tolerance
    381:     CHECK_ERROR - the event number for error checking
    382:                   (for use with profiling)

    384:     Notes:
    385:     In order to profile this section of code separately from the
    386:     rest of the program, we register it as an "event" with
    387:     PetscLogEventRegister() in the main program.  Then, we indicate
    388:     the start and end of this event by respectively calling
    389:         PetscLogEventBegin(CHECK_ERROR,u,x,b,0);
    390:         PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
    391:     Here, we specify the objects most closely associated with
    392:     the event (the vectors u,x,b).  Such information is optional;
    393:     we could instead just use 0 instead for all objects.
    394: */
    395: PetscErrorCode CheckError(Vec u,Vec x,Vec b,PetscInt its,PetscReal tol,PetscLogEvent CHECK_ERROR)
    396: {
    397:   PetscScalar    none = -1.0;
    398:   PetscReal      norm;

    401:   PetscLogEventBegin(CHECK_ERROR,u,x,b,0);

    403:   /*
    404:      Compute error of the solution, using b as a work vector.
    405:   */
    406:   VecCopy(x,b);
    407:   VecAXPY(b,none,u);
    408:   VecNorm(b,NORM_2,&norm);
    409:   if (norm > tol) {
    410:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G, Iterations %D\n",norm,its);
    411:   }
    412:   PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
    413:   return 0;
    414: }
    415: /* ------------------------------------------------------------- */
    418: /*
    419:    MyKSPMonitor - This is a user-defined routine for monitoring
    420:    the KSP iterative solvers.

    422:    Input Parameters:
    423:      ksp   - iterative context
    424:      n     - iteration number
    425:      rnorm - 2-norm (preconditioned) residual value (may be estimated)
    426:      dummy - optional user-defined monitor context (unused here)
    427: */
    428: PetscErrorCode MyKSPMonitor(KSP ksp,PetscInt n,PetscReal rnorm,void *dummy)
    429: {
    430:   Vec            x;

    433:   /*
    434:      Build the solution vector
    435:   */
    436:   KSPBuildSolution(ksp,NULL,&x);

    438:   /*
    439:      Write the solution vector and residual norm to stdout.
    440:       - PetscPrintf() handles output for multiprocessor jobs
    441:         by printing from only one processor in the communicator.
    442:       - The parallel viewer PETSC_VIEWER_STDOUT_WORLD handles
    443:         data from multiple processors so that the output
    444:         is not jumbled.
    445:   */
    446:   PetscPrintf(PETSC_COMM_WORLD,"iteration %D solution vector:\n",n);
    447:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);
    448:   PetscPrintf(PETSC_COMM_WORLD,"iteration %D KSP Residual norm %14.12e \n",n,rnorm);
    449:   return 0;
    450: }