Date: 2017-05-17T08:27:30+00:00

Actual source code: ex20.c
slepc-3.7.4 2017-05-17
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, 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.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     25:   "  -draw_sol, to draw the computed solution.\n\n";

     27: /*
     28:    Solve 1-D PDE
     29:             -u'' = lambda*u
     30:    on [0,1] subject to
     31:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
     32: */

     34: #include <slepcnep.h>

     36: /*
     37:    User-defined routines
     38: */
     39: PetscErrorCode FormInitialGuess(Vec);
     40: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     41: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);
     42: PetscErrorCode CheckSolution(PetscScalar,Vec,PetscReal*,void*);
     43: PetscErrorCode FixSign(Vec);

     45: /*
     46:    User-defined application context
     47: */
     48: typedef struct {
     49:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     50:   PetscReal   h;       /* mesh spacing */
     51: } ApplicationCtx;

     55: int main(int argc,char **argv)
     56: {
     57:   NEP            nep;             /* nonlinear eigensolver context */
     58:   Vec            x;               /* eigenvector */
     59:   PetscScalar    lambda;          /* eigenvalue */
     60:   Mat            F,J;             /* Function and Jacobian matrices */
     61:   ApplicationCtx ctx;             /* user-defined context */
     62:   NEPType        type;
     63:   PetscInt       n=128,nev,i,its,maxit,nconv;
     64:   PetscReal      re,im,tol,norm,error;
     65:   PetscBool      draw_sol;

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

     75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     76:      Create nonlinear eigensolver context
     77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     79:   NEPCreate(PETSC_COMM_WORLD,&nep);

     81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     82:      Create matrix data structure; set Function evaluation routine
     83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     85:   MatCreate(PETSC_COMM_WORLD,&F);
     86:   MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
     87:   MatSetFromOptions(F);
     88:   MatSeqAIJSetPreallocation(F,3,NULL);
     89:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
     90:   MatSetUp(F);

     92:   /*
     93:      Set Function matrix data structure and default Function evaluation
     94:      routine
     95:   */
     96:   NEPSetFunction(nep,F,F,FormFunction,&ctx);

     98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99:      Create matrix data structure; set Jacobian evaluation routine
    100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    102:   MatCreate(PETSC_COMM_WORLD,&J);
    103:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
    104:   MatSetFromOptions(J);
    105:   MatSeqAIJSetPreallocation(J,3,NULL);
    106:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
    107:   MatSetUp(J);

    109:   /*
    110:      Set Jacobian matrix data structure and default Jacobian evaluation
    111:      routine
    112:   */
    113:   NEPSetJacobian(nep,J,FormJacobian,&ctx);

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:      Customize nonlinear solver; set runtime options
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    119:   NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
    120:   NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);

    122:   /*
    123:      Set solver parameters at runtime
    124:   */
    125:   NEPSetFromOptions(nep);

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:                       Initialize application
    129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    131:   /*
    132:      Evaluate initial guess
    133:   */
    134:   MatCreateVecs(F,&x,NULL);
    135:   FormInitialGuess(x);
    136:   NEPSetInitialSpace(nep,1,&x);

    138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    139:                       Solve the eigensystem
    140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    142:   NEPSolve(nep);
    143:   NEPGetIterationNumber(nep,&its);
    144:   PetscPrintf(PETSC_COMM_WORLD," Number of NEP iterations = %D\n\n",its);

    146:   /*
    147:      Optional: Get some information from the solver and display it
    148:   */
    149:   NEPGetType(nep,&type);
    150:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
    151:   NEPGetDimensions(nep,&nev,NULL,NULL);
    152:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
    153:   NEPGetTolerances(nep,&tol,&maxit);
    154:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%g, maxit=%D\n",(double)tol,maxit);

    156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    157:                     Display solution and clean up
    158:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    160:   /*
    161:      Get number of converged approximate eigenpairs
    162:   */
    163:   NEPGetConverged(nep,&nconv);
    164:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %D\n\n",nconv);

    166:   if (nconv>0) {
    167:     /*
    168:        Display eigenvalues and relative errors
    169:     */
    170:     PetscPrintf(PETSC_COMM_WORLD,
    171:          "           k              ||T(k)x||           error\n"
    172:          "   ----------------- ------------------ ------------------\n");
    173:     for (i=0;i<nconv;i++) {
    174:       /*
    175:         Get converged eigenpairs (in this example they are always real)
    176:       */
    177:       NEPGetEigenpair(nep,i,&lambda,NULL,x,NULL);
    178:       FixSign(x);
    179:       /*
    180:          Compute residual norm and error
    181:       */
    182:       NEPComputeError(nep,i,NEP_ERROR_RELATIVE,&norm);
    183:       CheckSolution(lambda,x,&error,&ctx);

    185: #if defined(PETSC_USE_COMPLEX)
    186:       re = PetscRealPart(lambda);
    187:       im = PetscImaginaryPart(lambda);
    188: #else
    189:       re = lambda;
    190:       im = 0.0;
    191: #endif
    192:       if (im!=0.0) {
    193:         PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g     %12g\n",(double)re,(double)im,(double)norm,(double)error);
    194:       } else {
    195:         PetscPrintf(PETSC_COMM_WORLD,"   %12f         %12g     %12g\n",(double)re,(double)norm,(double)error);
    196:       }
    197:       if (draw_sol) {
    198:         PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
    199:         VecView(x,PETSC_VIEWER_DRAW_WORLD);
    200:       }
    201:     }
    202:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    203:   }

    205:   NEPDestroy(&nep);
    206:   MatDestroy(&F);
    207:   MatDestroy(&J);
    208:   VecDestroy(&x);
    209:   SlepcFinalize();
    210:   return ierr;
    211: }

    213: /* ------------------------------------------------------------------- */
    216: /*
    217:    FormInitialGuess - Computes initial guess.

    219:    Input/Output Parameter:
    220: .  x - the solution vector
    221: */
    222: PetscErrorCode FormInitialGuess(Vec x)
    223: {

    227:   VecSet(x,1.0);
    228:   return(0);
    229: }

    231: /* ------------------------------------------------------------------- */
    234: /*
    235:    FormFunction - Computes Function matrix  T(lambda)

    237:    Input Parameters:
    238: .  nep    - the NEP context
    239: .  lambda - the scalar argument
    240: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    242:    Output Parameters:
    243: .  fun - Function matrix
    244: .  B   - optionally different preconditioning matrix
    245: */
    246: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    247: {
    249:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    250:   PetscScalar    A[3],c,d;
    251:   PetscReal      h;
    252:   PetscInt       i,n,j[3],Istart,Iend;
    253:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    256:   /*
    257:      Compute Function entries and insert into matrix
    258:   */
    259:   MatGetSize(fun,&n,NULL);
    260:   MatGetOwnershipRange(fun,&Istart,&Iend);
    261:   if (Istart==0) FirstBlock=PETSC_TRUE;
    262:   if (Iend==n) LastBlock=PETSC_TRUE;
    263:   h = user->h;
    264:   c = user->kappa/(lambda-user->kappa);
    265:   d = n;

    267:   /*
    268:      Interior grid points
    269:   */
    270:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    271:     j[0] = i-1; j[1] = i; j[2] = i+1;
    272:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    273:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
    274:   }

    276:   /*
    277:      Boundary points
    278:   */
    279:   if (FirstBlock) {
    280:     i = 0;
    281:     j[0] = 0; j[1] = 1;
    282:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    283:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    284:   }

    286:   if (LastBlock) {
    287:     i = n-1;
    288:     j[0] = n-2; j[1] = n-1;
    289:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    290:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    291:   }

    293:   /*
    294:      Assemble matrix
    295:   */
    296:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    297:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    298:   if (fun != B) {
    299:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    300:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    301:   }
    302:   return(0);
    303: }

    305: /* ------------------------------------------------------------------- */
    308: /*
    309:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    311:    Input Parameters:
    312: .  nep    - the NEP context
    313: .  lambda - the scalar argument
    314: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    316:    Output Parameters:
    317: .  jac - Jacobian matrix
    318: .  B   - optionally different preconditioning matrix
    319: */
    320: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    321: {
    323:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    324:   PetscScalar    A[3],c;
    325:   PetscReal      h;
    326:   PetscInt       i,n,j[3],Istart,Iend;
    327:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    330:   /*
    331:      Compute Jacobian entries and insert into matrix
    332:   */
    333:   MatGetSize(jac,&n,NULL);
    334:   MatGetOwnershipRange(jac,&Istart,&Iend);
    335:   if (Istart==0) FirstBlock=PETSC_TRUE;
    336:   if (Iend==n) LastBlock=PETSC_TRUE;
    337:   h = user->h;
    338:   c = user->kappa/(lambda-user->kappa);

    340:   /*
    341:      Interior grid points
    342:   */
    343:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    344:     j[0] = i-1; j[1] = i; j[2] = i+1;
    345:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    346:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    347:   }

    349:   /*
    350:      Boundary points
    351:   */
    352:   if (FirstBlock) {
    353:     i = 0;
    354:     j[0] = 0; j[1] = 1;
    355:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    356:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    357:   }

    359:   if (LastBlock) {
    360:     i = n-1;
    361:     j[0] = n-2; j[1] = n-1;
    362:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    363:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    364:   }

    366:   /*
    367:      Assemble matrix
    368:   */
    369:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    370:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    371:   return(0);
    372: }

    374: /* ------------------------------------------------------------------- */
    377: /*
    378:    CheckSolution - Given a computed solution (lambda,x) check if it
    379:    satisfies the analytic solution.

    381:    Input Parameters:
    382: +  lambda - the computed eigenvalue
    383: -  y      - the computed eigenvector

    385:    Output Parameter:
    386: .  error - norm of difference between the computed and exact eigenvector
    387: */
    388: PetscErrorCode CheckSolution(PetscScalar lambda,Vec y,PetscReal *error,void *ctx)
    389: {
    391:   PetscScalar    nu,*uu;
    392:   PetscInt       i,n,Istart,Iend;
    393:   PetscReal      x;
    394:   Vec            u;
    395:   ApplicationCtx *user = (ApplicationCtx*)ctx;

    398:   nu = PetscSqrtScalar(lambda);
    399:   VecDuplicate(y,&u);
    400:   VecGetSize(u,&n);
    401:   VecGetOwnershipRange(y,&Istart,&Iend);
    402:   VecGetArray(u,&uu);
    403:   for (i=Istart;i<Iend;i++) {
    404:     x = (i+1)*user->h;
    405:     uu[i-Istart] = PetscSinReal(nu*x);
    406:   }
    407:   VecRestoreArray(u,&uu);
    408:   VecNormalize(u,NULL);
    409:   VecAXPY(u,-1.0,y);
    410:   VecNorm(u,NORM_2,error);
    411:   VecDestroy(&u);
    412:   return(0);
    413: }

    415: /* ------------------------------------------------------------------- */
    418: /*
    419:    FixSign - Force the eigenfunction to be real and positive, since
    420:    some eigensolvers may return the eigenvector multiplied by a
    421:    complex number of modulus one.

    423:    Input/Output Parameter:
    424: .  x - the computed vector
    425: */
    426: PetscErrorCode FixSign(Vec x)
    427: {
    428:   PetscErrorCode    ierr;
    429:   PetscMPIInt       rank;
    430:   PetscScalar       sign;
    431:   const PetscScalar *xx;

    434:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
    435:   if (!rank) {
    436:     VecGetArrayRead(x,&xx);
    437:     sign = *xx/PetscAbsScalar(*xx);
    438:     VecRestoreArrayRead(x,&xx);
    439:   }
    440:   MPI_Bcast(&sign,1,MPIU_SCALAR,0,PETSC_COMM_WORLD);
    441:   VecScale(x,1.0/sign);
    442:   return(0);
    443: }