Date: 2015-09-03T15:06:03+00:00

Actual source code: ex21.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

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

     26: /*
     27:    Solve 1-D PDE
     28:             -u'' = lambda*u
     29:    on [0,1] subject to
     30:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
     31: */

     33: #include <slepcnep.h>

     35: /*
     36:    User-defined routines
     37: */
     38: PetscErrorCode FormInitialGuess(Vec);
     39: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     40: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);

     42: /*
     43:    Matrix operations and context
     44: */
     45: PetscErrorCode MatMult_Fun(Mat,Vec,Vec);
     46: PetscErrorCode MatGetDiagonal_Fun(Mat,Vec);
     47: PetscErrorCode MatDestroy_Fun(Mat);
     48: PetscErrorCode MatDuplicate_Fun(Mat,MatDuplicateOption,Mat*);
     49: PetscErrorCode MatMult_Jac(Mat,Vec,Vec);
     50: PetscErrorCode MatDestroy_Jac(Mat);

     52: typedef struct {
     53:   PetscScalar lambda,kappa;
     54:   PetscReal   h;
     55: } MatCtx;

     57: /*
     58:    User-defined application context
     59: */
     60: typedef struct {
     61:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     62:   PetscReal   h;       /* mesh spacing */
     63: } ApplicationCtx;

     67: int main(int argc,char **argv)
     68: {
     69:   NEP            nep;             /* nonlinear eigensolver context */
     70:   Mat            F,J;             /* Function and Jacobian matrices */
     71:   ApplicationCtx ctx;             /* user-defined context */
     72:   MatCtx         *ctxF,*ctxJ;     /* contexts for shell matrices */
     73:   NEPType        type;
     74:   PetscInt       n=128,nev,its;
     75:   KSP            ksp;
     76:   PC             pc;
     77:   PetscMPIInt    size;
     78:   PetscBool      terse;

     81:   SlepcInitialize(&argc,&argv,(char*)0,help);
     82:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     83:   if (size != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This is a uniprocessor example only!");
     84:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     85:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%D\n\n",n);
     86:   ctx.h = 1.0/(PetscReal)n;
     87:   ctx.kappa = 1.0;

     89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     90:      Create nonlinear eigensolver context
     91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     93:   NEPCreate(PETSC_COMM_WORLD,&nep);

     95:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     96:      Create matrix data structure; set Function evaluation routine
     97:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     99:   PetscNew(&ctxF);
    100:   ctxF->h = ctx.h;
    101:   ctxF->kappa = ctx.kappa;

    103:   MatCreateShell(PETSC_COMM_WORLD,n,n,n,n,(void*)ctxF,&F);
    104:   MatShellSetOperation(F,MATOP_MULT,(void(*)())MatMult_Fun);
    105:   MatShellSetOperation(F,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Fun);
    106:   MatShellSetOperation(F,MATOP_DESTROY,(void(*)())MatDestroy_Fun);
    107:   MatShellSetOperation(F,MATOP_DUPLICATE,(void(*)())MatDuplicate_Fun);

    109:   /*
    110:      Set Function matrix data structure and default Function evaluation
    111:      routine
    112:   */
    113:   NEPSetFunction(nep,F,F,FormFunction,NULL);

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:      Create matrix data structure; set Jacobian evaluation routine
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    119:   PetscNew(&ctxJ);
    120:   ctxJ->h = ctx.h;
    121:   ctxJ->kappa = ctx.kappa;

    123:   MatCreateShell(PETSC_COMM_WORLD,n,n,n,n,(void*)ctxJ,&J);
    124:   MatShellSetOperation(J,MATOP_MULT,(void(*)())MatMult_Jac);
    125:   MatShellSetOperation(J,MATOP_DESTROY,(void(*)())MatDestroy_Jac);

    127:   /*
    128:      Set Jacobian matrix data structure and default Jacobian evaluation
    129:      routine
    130:   */
    131:   NEPSetJacobian(nep,J,FormJacobian,NULL);

    133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    134:      Customize nonlinear solver; set runtime options
    135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    137:   NEPGetKSP(nep,&ksp);
    138:   KSPSetType(ksp,KSPBCGS);
    139:   KSPGetPC(ksp,&pc);
    140:   PCSetType(pc,PCJACOBI);

    142:   /*
    143:      Set solver parameters at runtime
    144:   */
    145:   NEPSetFromOptions(nep);

    147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    148:                       Solve the eigensystem
    149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    151:   NEPSolve(nep);
    152:   NEPGetIterationNumber(nep,&its);
    153:   PetscPrintf(PETSC_COMM_WORLD," Number of NEP iterations = %D\n\n",its);

    155:   /*
    156:      Optional: Get some information from the solver and display it
    157:   */
    158:   NEPGetType(nep,&type);
    159:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
    160:   NEPGetDimensions(nep,&nev,NULL,NULL);
    161:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:                     Display solution and clean up
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    167:   /* show detailed info unless -terse option is given by user */
    168:   PetscOptionsHasName(NULL,"-terse",&terse);
    169:   if (terse) {
    170:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    171:   } else {
    172:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    173:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    174:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    175:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    176:   }
    177:   NEPDestroy(&nep);
    178:   MatDestroy(&F);
    179:   MatDestroy(&J);
    180:   SlepcFinalize();
    181:   return 0;
    182: }

    184: /* ------------------------------------------------------------------- */
    187: /*
    188:    FormInitialGuess - Computes initial guess.

    190:    Input/Output Parameter:
    191: .  x - the solution vector
    192: */
    193: PetscErrorCode FormInitialGuess(Vec x)
    194: {

    198:   VecSet(x,1.0);
    199:   return(0);
    200: }

    202: /* ------------------------------------------------------------------- */
    205: /*
    206:    FormFunction - Computes Function matrix  T(lambda)

    208:    Input Parameters:
    209: .  nep    - the NEP context
    210: .  lambda - real part of the scalar argument
    211: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    213:    Output Parameters:
    214: .  fun - Function matrix
    215: .  B   - optionally different preconditioning matrix
    216: */
    217: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    218: {
    220:   MatCtx         *ctxF;

    223:   MatShellGetContext(fun,(void**)&ctxF);
    224:   ctxF->lambda = lambda;
    225:   return(0);
    226: }

    228: /* ------------------------------------------------------------------- */
    231: /*
    232:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    234:    Input Parameters:
    235: .  nep    - the NEP context
    236: .  lambda - real part of the scalar argument
    237: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    239:    Output Parameters:
    240: .  jac - Jacobian matrix
    241: .  B   - optionally different preconditioning matrix
    242: */
    243: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    244: {
    246:   MatCtx         *ctxJ;

    249:   MatShellGetContext(jac,(void**)&ctxJ);
    250:   ctxJ->lambda = lambda;
    251:   return(0);
    252: }

    254: /* ------------------------------------------------------------------- */
    257: PetscErrorCode MatMult_Fun(Mat A,Vec x,Vec y)
    258: {
    259:   PetscErrorCode    ierr;
    260:   MatCtx            *ctx;
    261:   PetscInt          i,n;
    262:   const PetscScalar *px;
    263:   PetscScalar       *py,c,d,de,oe;
    264:   PetscReal         h;

    267:   MatShellGetContext(A,(void**)&ctx);
    268:   VecGetArrayRead(x,&px);
    269:   VecGetArray(y,&py);

    271:   VecGetSize(x,&n);
    272:   h = ctx->h;
    273:   c = ctx->kappa/(ctx->lambda-ctx->kappa);
    274:   d = n;
    275:   de = 2.0*(d-ctx->lambda*h/3.0);   /* diagonal entry */
    276:   oe = -d-ctx->lambda*h/6.0;        /* offdiagonal entry */
    277:   py[0] = de*px[0] + oe*px[1];
    278:   for (i=1;i<n-1;i++) py[i] = oe*px[i-1] +de*px[i] + oe*px[i+1];
    279:   de = d-ctx->lambda*h/3.0+ctx->lambda*c;   /* diagonal entry of last row */
    280:   py[n-1] = oe*px[n-2] + de*px[n-1];

    282:   VecRestoreArrayRead(x,&px);
    283:   VecRestoreArray(y,&py);
    284:   return(0);
    285: }

    287: /* ------------------------------------------------------------------- */
    290: PetscErrorCode MatGetDiagonal_Fun(Mat A,Vec diag)
    291: {
    292:   PetscErrorCode    ierr;
    293:   MatCtx            *ctx;
    294:   PetscInt          n;
    295:   PetscScalar       *pd,c,d;
    296:   PetscReal         h;

    299:   MatShellGetContext(A,(void**)&ctx);
    300:   VecGetSize(diag,&n);
    301:   h = ctx->h;
    302:   c = ctx->kappa/(ctx->lambda-ctx->kappa);
    303:   d = n;
    304:   VecSet(diag,2.0*(d-ctx->lambda*h/3.0));
    305:   VecGetArray(diag,&pd);
    306:   pd[n-1] = d-ctx->lambda*h/3.0+ctx->lambda*c;
    307:   VecRestoreArray(diag,&pd);
    308:   return(0);
    309: }

    311: /* ------------------------------------------------------------------- */
    314: PetscErrorCode MatDestroy_Fun(Mat A)
    315: {
    316:   MatCtx         *ctx;

    320:   MatShellGetContext(A,(void**)&ctx);
    321:   PetscFree(ctx);
    322:   return(0);
    323: }

    325: /* ------------------------------------------------------------------- */
    328: PetscErrorCode MatDuplicate_Fun(Mat A,MatDuplicateOption op,Mat *B)
    329: {
    330:   MatCtx         *actx,*bctx;
    331:   PetscInt       n;
    332:   MPI_Comm       comm;

    336:   MatShellGetContext(A,(void**)&actx);
    337:   MatGetSize(A,&n,NULL);

    339:   PetscNew(&bctx);
    340:   bctx->h      = actx->h;
    341:   bctx->kappa  = actx->kappa;
    342:   bctx->lambda = actx->lambda;

    344:   PetscObjectGetComm((PetscObject)A,&comm);
    345:   MatCreateShell(comm,n,n,n,n,(void*)bctx,B);
    346:   MatShellSetOperation(*B,MATOP_MULT,(void(*)())MatMult_Fun);
    347:   MatShellSetOperation(*B,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Fun);
    348:   MatShellSetOperation(*B,MATOP_DESTROY,(void(*)())MatDestroy_Fun);
    349:   MatShellSetOperation(*B,MATOP_DUPLICATE,(void(*)())MatDuplicate_Fun);
    350:   return(0);
    351: }

    353: /* ------------------------------------------------------------------- */
    356: PetscErrorCode MatMult_Jac(Mat A,Vec x,Vec y)
    357: {
    358:   PetscErrorCode    ierr;
    359:   MatCtx            *ctx;
    360:   PetscInt          i,n;
    361:   const PetscScalar *px;
    362:   PetscScalar       *py,c,de,oe;
    363:   PetscReal         h;

    366:   MatShellGetContext(A,(void**)&ctx);
    367:   VecGetArrayRead(x,&px);
    368:   VecGetArray(y,&py);

    370:   VecGetSize(x,&n);
    371:   h = ctx->h;
    372:   c = ctx->kappa/(ctx->lambda-ctx->kappa);
    373:   de = -2.0*h/3.0;    /* diagonal entry */
    374:   oe = -h/6.0;        /* offdiagonal entry */
    375:   py[0] = de*px[0] + oe*px[1];
    376:   for (i=1;i<n-1;i++) py[i] = oe*px[i-1] +de*px[i] + oe*px[i+1];
    377:   de = -h/3.0-c*c;    /* diagonal entry of last row */
    378:   py[n-1] = oe*px[n-2] + de*px[n-1];

    380:   VecRestoreArrayRead(x,&px);
    381:   VecRestoreArray(y,&py);
    382:   return(0);
    383: }

    385: /* ------------------------------------------------------------------- */
    388: PetscErrorCode MatDestroy_Jac(Mat A)
    389: {
    390:   MatCtx         *ctx;

    394:   MatShellGetContext(A,(void**)&ctx);
    395:   PetscFree(ctx);
    396:   return(0);
    397: }