Date: 2022-10-01T06:40:41+00:00

Actual source code: ex21.c
slepc-3.18.0 2022-10-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Simple 1-D nonlinear eigenproblem (matrix-free version).\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions\n\n";

     15: /*
     16:    Solve 1-D PDE
     17:             -u'' = lambda*u
     18:    on [0,1] subject to
     19:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
     20: */

     22: #include <slepcnep.h>

     24: /*
     25:    User-defined routines
     26: */
     27: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     28: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);

     30: /*
     31:    Matrix operations and context
     32: */
     33: PetscErrorCode MatMult_Fun(Mat,Vec,Vec);
     34: PetscErrorCode MatGetDiagonal_Fun(Mat,Vec);
     35: PetscErrorCode MatDestroy_Fun(Mat);
     36: PetscErrorCode MatDuplicate_Fun(Mat,MatDuplicateOption,Mat*);
     37: PetscErrorCode MatMult_Jac(Mat,Vec,Vec);
     38: PetscErrorCode MatGetDiagonal_Jac(Mat,Vec);
     39: PetscErrorCode MatDestroy_Jac(Mat);

     41: typedef struct {
     42:   PetscScalar lambda,kappa;
     43:   PetscReal   h;
     44:   PetscMPIInt next,prev;
     45: } MatCtx;

     47: /*
     48:    User-defined application context
     49: */
     50: typedef struct {
     51:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     52:   PetscReal   h;       /* mesh spacing */
     53: } ApplicationCtx;

     55: int main(int argc,char **argv)
     56: {
     57:   NEP            nep;             /* nonlinear eigensolver context */
     58:   Mat            F,J;             /* Function and Jacobian matrices */
     59:   ApplicationCtx ctx;             /* user-defined context */
     60:   MatCtx         *ctxF,*ctxJ;     /* contexts for shell matrices */
     61:   PetscInt       n=128,nev;
     62:   KSP            ksp;
     63:   PC             pc;
     64:   PetscMPIInt    rank,size;
     65:   PetscBool      terse;

     68:   SlepcInitialize(&argc,&argv,(char*)0,help);
     69:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     70:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     71:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     72:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n);
     73:   ctx.h = 1.0/(PetscReal)n;
     74:   ctx.kappa = 1.0;

     76:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     77:      Create nonlinear eigensolver context
     78:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     80:   NEPCreate(PETSC_COMM_WORLD,&nep);

     82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     83:      Create matrix data structure; set Function evaluation routine
     84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     86:   PetscNew(&ctxF);
     87:   ctxF->h = ctx.h;
     88:   ctxF->kappa = ctx.kappa;
     89:   ctxF->next = rank==size-1? MPI_PROC_NULL: rank+1;
     90:   ctxF->prev = rank==0? MPI_PROC_NULL: rank-1;

     92:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,(void*)ctxF,&F);
     93:   MatShellSetOperation(F,MATOP_MULT,(void(*)(void))MatMult_Fun);
     94:   MatShellSetOperation(F,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Fun);
     95:   MatShellSetOperation(F,MATOP_DESTROY,(void(*)(void))MatDestroy_Fun);
     96:   MatShellSetOperation(F,MATOP_DUPLICATE,(void(*)(void))MatDuplicate_Fun);

     98:   /*
     99:      Set Function matrix data structure and default Function evaluation
    100:      routine
    101:   */
    102:   NEPSetFunction(nep,F,F,FormFunction,NULL);

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:      Create matrix data structure; set Jacobian evaluation routine
    106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    108:   PetscNew(&ctxJ);
    109:   ctxJ->h = ctx.h;
    110:   ctxJ->kappa = ctx.kappa;
    111:   ctxJ->next = rank==size-1? MPI_PROC_NULL: rank+1;
    112:   ctxJ->prev = rank==0? MPI_PROC_NULL: rank-1;

    114:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,(void*)ctxJ,&J);
    115:   MatShellSetOperation(J,MATOP_MULT,(void(*)(void))MatMult_Jac);
    116:   MatShellSetOperation(J,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Jac);
    117:   MatShellSetOperation(J,MATOP_DESTROY,(void(*)(void))MatDestroy_Jac);

    119:   /*
    120:      Set Jacobian matrix data structure and default Jacobian evaluation
    121:      routine
    122:   */
    123:   NEPSetJacobian(nep,J,FormJacobian,NULL);

    125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    126:      Customize nonlinear solver; set runtime options
    127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    129:   NEPSetType(nep,NEPRII);
    130:   NEPRIISetLagPreconditioner(nep,0);
    131:   NEPRIIGetKSP(nep,&ksp);
    132:   KSPSetType(ksp,KSPBCGS);
    133:   KSPGetPC(ksp,&pc);
    134:   PCSetType(pc,PCJACOBI);

    136:   /*
    137:      Set solver parameters at runtime
    138:   */
    139:   NEPSetFromOptions(nep);

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:                       Solve the eigensystem
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    145:   NEPSolve(nep);
    146:   NEPGetDimensions(nep,&nev,NULL,NULL);
    147:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    150:                     Display solution and clean up
    151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    153:   /* show detailed info unless -terse option is given by user */
    154:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    155:   if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    156:   else {
    157:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    158:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    159:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    160:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    161:   }
    162:   NEPDestroy(&nep);
    163:   MatDestroy(&F);
    164:   MatDestroy(&J);
    165:   SlepcFinalize();
    166:   return 0;
    167: }

    169: /* ------------------------------------------------------------------- */
    170: /*
    171:    FormFunction - Computes Function matrix  T(lambda)

    173:    Input Parameters:
    174: .  nep    - the NEP context
    175: .  lambda - real part of the scalar argument
    176: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    178:    Output Parameters:
    179: .  fun - Function matrix
    180: .  B   - optionally different preconditioning matrix
    181: */
    182: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    183: {
    184:   MatCtx         *ctxF;

    187:   MatShellGetContext(fun,&ctxF);
    188:   ctxF->lambda = lambda;
    189:   return 0;
    190: }

    192: /* ------------------------------------------------------------------- */
    193: /*
    194:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    196:    Input Parameters:
    197: .  nep    - the NEP context
    198: .  lambda - real part of the scalar argument
    199: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    201:    Output Parameters:
    202: .  jac - Jacobian matrix
    203: */
    204: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    205: {
    206:   MatCtx         *ctxJ;

    209:   MatShellGetContext(jac,&ctxJ);
    210:   ctxJ->lambda = lambda;
    211:   return 0;
    212: }

    214: /* ------------------------------------------------------------------- */
    215: PetscErrorCode MatMult_Fun(Mat A,Vec x,Vec y)
    216: {
    217:   MatCtx            *ctx;
    218:   PetscInt          i,n,N;
    219:   const PetscScalar *px;
    220:   PetscScalar       *py,c,d,de,oe,upper=0.0,lower=0.0;
    221:   PetscReal         h;
    222:   MPI_Comm          comm;

    225:   MatShellGetContext(A,&ctx);
    226:   VecGetArrayRead(x,&px);
    227:   VecGetArray(y,&py);
    228:   VecGetSize(x,&N);
    229:   VecGetLocalSize(x,&n);

    231:   PetscObjectGetComm((PetscObject)A,&comm);
    232:   MPI_Sendrecv(px,1,MPIU_SCALAR,ctx->prev,0,&lower,1,MPIU_SCALAR,ctx->next,0,comm,MPI_STATUS_IGNORE);
    233:   MPI_Sendrecv(px+n-1,1,MPIU_SCALAR,ctx->next,0,&upper,1,MPIU_SCALAR,ctx->prev,0,comm,MPI_STATUS_IGNORE);

    235:   h = ctx->h;
    236:   c = ctx->kappa/(ctx->lambda-ctx->kappa);
    237:   d = N;
    238:   de = 2.0*(d-ctx->lambda*h/3.0);   /* diagonal entry */
    239:   oe = -d-ctx->lambda*h/6.0;        /* offdiagonal entry */
    240:   py[0] = oe*upper + de*px[0] + oe*px[1];
    241:   for (i=1;i<n-1;i++) py[i] = oe*px[i-1] +de*px[i] + oe*px[i+1];
    242:   if (ctx->next==MPI_PROC_NULL) de = d-ctx->lambda*h/3.0+ctx->lambda*c;   /* diagonal entry of last row */
    243:   py[n-1] = oe*px[n-2] + de*px[n-1] + oe*lower;

    245:   VecRestoreArrayRead(x,&px);
    246:   VecRestoreArray(y,&py);
    247:   return 0;
    248: }

    250: /* ------------------------------------------------------------------- */
    251: PetscErrorCode MatGetDiagonal_Fun(Mat A,Vec diag)
    252: {
    253:   MatCtx         *ctx;
    254:   PetscInt       n,N;
    255:   PetscScalar    *pd,c,d;
    256:   PetscReal      h;

    259:   MatShellGetContext(A,&ctx);
    260:   VecGetSize(diag,&N);
    261:   VecGetLocalSize(diag,&n);
    262:   h = ctx->h;
    263:   c = ctx->kappa/(ctx->lambda-ctx->kappa);
    264:   d = N;
    265:   VecSet(diag,2.0*(d-ctx->lambda*h/3.0));
    266:   VecGetArray(diag,&pd);
    267:   pd[n-1] = d-ctx->lambda*h/3.0+ctx->lambda*c;
    268:   VecRestoreArray(diag,&pd);
    269:   return 0;
    270: }

    272: /* ------------------------------------------------------------------- */
    273: PetscErrorCode MatDestroy_Fun(Mat A)
    274: {
    275:   MatCtx         *ctx;

    277:   MatShellGetContext(A,&ctx);
    278:   PetscFree(ctx);
    279:   return 0;
    280: }

    282: /* ------------------------------------------------------------------- */
    283: PetscErrorCode MatDuplicate_Fun(Mat A,MatDuplicateOption op,Mat *B)
    284: {
    285:   MatCtx         *actx,*bctx;
    286:   PetscInt       m,n,M,N;
    287:   MPI_Comm       comm;

    289:   MatShellGetContext(A,&actx);
    290:   MatGetSize(A,&M,&N);
    291:   MatGetLocalSize(A,&m,&n);

    293:   PetscNew(&bctx);
    294:   bctx->h      = actx->h;
    295:   bctx->kappa  = actx->kappa;
    296:   bctx->lambda = actx->lambda;
    297:   bctx->next   = actx->next;
    298:   bctx->prev   = actx->prev;

    300:   PetscObjectGetComm((PetscObject)A,&comm);
    301:   MatCreateShell(comm,m,n,M,N,(void*)bctx,B);
    302:   MatShellSetOperation(*B,MATOP_MULT,(void(*)(void))MatMult_Fun);
    303:   MatShellSetOperation(*B,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Fun);
    304:   MatShellSetOperation(*B,MATOP_DESTROY,(void(*)(void))MatDestroy_Fun);
    305:   MatShellSetOperation(*B,MATOP_DUPLICATE,(void(*)(void))MatDuplicate_Fun);
    306:   return 0;
    307: }

    309: /* ------------------------------------------------------------------- */
    310: PetscErrorCode MatMult_Jac(Mat A,Vec x,Vec y)
    311: {
    312:   MatCtx            *ctx;
    313:   PetscInt          i,n;
    314:   const PetscScalar *px;
    315:   PetscScalar       *py,c,de,oe,upper=0.0,lower=0.0;
    316:   PetscReal         h;
    317:   MPI_Comm          comm;

    320:   MatShellGetContext(A,&ctx);
    321:   VecGetArrayRead(x,&px);
    322:   VecGetArray(y,&py);
    323:   VecGetLocalSize(x,&n);

    325:   PetscObjectGetComm((PetscObject)A,&comm);
    326:   MPI_Sendrecv(px,1,MPIU_SCALAR,ctx->prev,0,&lower,1,MPIU_SCALAR,ctx->next,0,comm,MPI_STATUS_IGNORE);
    327:   MPI_Sendrecv(px+n-1,1,MPIU_SCALAR,ctx->next,0,&upper,1,MPIU_SCALAR,ctx->prev,0,comm,MPI_STATUS_IGNORE);

    329:   h = ctx->h;
    330:   c = ctx->kappa/(ctx->lambda-ctx->kappa);
    331:   de = -2.0*h/3.0;    /* diagonal entry */
    332:   oe = -h/6.0;        /* offdiagonal entry */
    333:   py[0] = oe*upper + de*px[0] + oe*px[1];
    334:   for (i=1;i<n-1;i++) py[i] = oe*px[i-1] +de*px[i] + oe*px[i+1];
    335:   if (ctx->next==MPI_PROC_NULL) de = -h/3.0-c*c;    /* diagonal entry of last row */
    336:   py[n-1] = oe*px[n-2] + de*px[n-1] + oe*lower;

    338:   VecRestoreArrayRead(x,&px);
    339:   VecRestoreArray(y,&py);
    340:   return 0;
    341: }

    343: /* ------------------------------------------------------------------- */
    344: PetscErrorCode MatGetDiagonal_Jac(Mat A,Vec diag)
    345: {
    346:   MatCtx         *ctx;
    347:   PetscInt       n;
    348:   PetscScalar    *pd,c;
    349:   PetscReal      h;

    352:   MatShellGetContext(A,&ctx);
    353:   VecGetLocalSize(diag,&n);
    354:   h = ctx->h;
    355:   c = ctx->kappa/(ctx->lambda-ctx->kappa);
    356:   VecSet(diag,-2.0*h/3.0);
    357:   VecGetArray(diag,&pd);
    358:   pd[n-1] = -h/3.0-c*c;
    359:   VecRestoreArray(diag,&pd);
    360:   return 0;
    361: }

    363: /* ------------------------------------------------------------------- */
    364: PetscErrorCode MatDestroy_Jac(Mat A)
    365: {
    366:   MatCtx         *ctx;

    368:   MatShellGetContext(A,&ctx);
    369:   PetscFree(ctx);
    370:   return 0;
    371: }

    373: /*TEST

    375:    testset:
    376:       nsize: {{1 2}}
    377:       args: -terse
    378:       requires: !single
    379:       output_file: output/ex21_1.out
    380:       filter: sed -e "s/[+-]0\.0*i//g" -e "s/+0i//g"
    381:       test:
    382:          suffix: 1_rii
    383:          args: -nep_type rii -nep_target 4
    384:       test:
    385:          suffix: 1_slp
    386:          args: -nep_type slp -nep_slp_pc_type jacobi -nep_slp_ksp_type bcgs -nep_target 10

    388: TEST*/