Date: 2021-02-01T14:42:18+00:00

Actual source code: ex20.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     14:   "  -draw_sol, to draw the computed solution.\n\n";

     16: /*
     17:    Solve 1-D PDE
     18:             -u'' = lambda*u
     19:    on [0,1] subject to
     20:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
     21: */

     23: #include <slepcnep.h>

     25: /*
     26:    User-defined routines
     27: */
     28: PetscErrorCode FormInitialGuess(Vec);
     29: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     30: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);
     31: PetscErrorCode CheckSolution(PetscScalar,Vec,PetscReal*,void*);
     32: PetscErrorCode FixSign(Vec);

     34: /*
     35:    User-defined application context
     36: */
     37: typedef struct {
     38:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     39:   PetscReal   h;       /* mesh spacing */
     40: } ApplicationCtx;

     42: int main(int argc,char **argv)
     43: {
     44:   NEP            nep;             /* nonlinear eigensolver context */
     45:   Vec            x;               /* eigenvector */
     46:   PetscScalar    lambda;          /* eigenvalue */
     47:   Mat            F,J;             /* Function and Jacobian matrices */
     48:   ApplicationCtx ctx;             /* user-defined context */
     49:   NEPType        type;
     50:   PetscInt       n=128,nev,i,its,maxit,nconv;
     51:   PetscReal      re,im,tol,norm,error;
     52:   PetscBool      draw_sol=PETSC_FALSE;

     55:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     56:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     57:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%D\n\n",n);
     58:   ctx.h = 1.0/(PetscReal)n;
     59:   ctx.kappa = 1.0;
     60:   PetscOptionsGetBool(NULL,NULL,"-draw_sol",&draw_sol,NULL);

     62:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     63:      Create nonlinear eigensolver context
     64:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     66:   NEPCreate(PETSC_COMM_WORLD,&nep);

     68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69:      Create matrix data structure; set Function evaluation routine
     70:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     72:   MatCreate(PETSC_COMM_WORLD,&F);
     73:   MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
     74:   MatSetFromOptions(F);
     75:   MatSeqAIJSetPreallocation(F,3,NULL);
     76:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
     77:   MatSetUp(F);

     79:   /*
     80:      Set Function matrix data structure and default Function evaluation
     81:      routine
     82:   */
     83:   NEPSetFunction(nep,F,F,FormFunction,&ctx);

     85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     86:      Create matrix data structure; set Jacobian evaluation routine
     87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     89:   MatCreate(PETSC_COMM_WORLD,&J);
     90:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
     91:   MatSetFromOptions(J);
     92:   MatSeqAIJSetPreallocation(J,3,NULL);
     93:   MatMPIAIJSetPreallocation(J,3,NULL,1,NULL);
     94:   MatSetUp(J);

     96:   /*
     97:      Set Jacobian matrix data structure and default Jacobian evaluation
     98:      routine
     99:   */
    100:   NEPSetJacobian(nep,J,FormJacobian,&ctx);

    102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    103:      Customize nonlinear solver; set runtime options
    104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    106:   NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
    107:   NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);

    109:   /*
    110:      Set solver parameters at runtime
    111:   */
    112:   NEPSetFromOptions(nep);

    114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115:                       Initialize application
    116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    118:   /*
    119:      Evaluate initial guess
    120:   */
    121:   MatCreateVecs(F,&x,NULL);
    122:   FormInitialGuess(x);
    123:   NEPSetInitialSpace(nep,1,&x);

    125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    126:                       Solve the eigensystem
    127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    129:   NEPSolve(nep);
    130:   NEPGetIterationNumber(nep,&its);
    131:   PetscPrintf(PETSC_COMM_WORLD," Number of NEP iterations = %D\n\n",its);

    133:   /*
    134:      Optional: Get some information from the solver and display it
    135:   */
    136:   NEPGetType(nep,&type);
    137:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
    138:   NEPGetDimensions(nep,&nev,NULL,NULL);
    139:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
    140:   NEPGetTolerances(nep,&tol,&maxit);
    141:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%g, maxit=%D\n",(double)tol,maxit);

    143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144:                     Display solution and clean up
    145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    147:   /*
    148:      Get number of converged approximate eigenpairs
    149:   */
    150:   NEPGetConverged(nep,&nconv);
    151:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %D\n\n",nconv);

    153:   if (nconv>0) {
    154:     /*
    155:        Display eigenvalues and relative errors
    156:     */
    157:     PetscPrintf(PETSC_COMM_WORLD,
    158:          "           k              ||T(k)x||           error\n"
    159:          "   ----------------- ------------------ ------------------\n");
    160:     for (i=0;i<nconv;i++) {
    161:       /*
    162:         Get converged eigenpairs (in this example they are always real)
    163:       */
    164:       NEPGetEigenpair(nep,i,&lambda,NULL,x,NULL);
    165:       FixSign(x);
    166:       /*
    167:          Compute residual norm and error
    168:       */
    169:       NEPComputeError(nep,i,NEP_ERROR_RELATIVE,&norm);
    170:       CheckSolution(lambda,x,&error,&ctx);

    172: #if defined(PETSC_USE_COMPLEX)
    173:       re = PetscRealPart(lambda);
    174:       im = PetscImaginaryPart(lambda);
    175: #else
    176:       re = lambda;
    177:       im = 0.0;
    178: #endif
    179:       if (im!=0.0) {
    180:         PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g     %12g\n",(double)re,(double)im,(double)norm,(double)error);
    181:       } else {
    182:         PetscPrintf(PETSC_COMM_WORLD,"   %12f         %12g     %12g\n",(double)re,(double)norm,(double)error);
    183:       }
    184:       if (draw_sol) {
    185:         PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
    186:         VecView(x,PETSC_VIEWER_DRAW_WORLD);
    187:       }
    188:     }
    189:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    190:   }

    192:   NEPDestroy(&nep);
    193:   MatDestroy(&F);
    194:   MatDestroy(&J);
    195:   VecDestroy(&x);
    196:   SlepcFinalize();
    197:   return ierr;
    198: }

    200: /* ------------------------------------------------------------------- */
    201: /*
    202:    FormInitialGuess - Computes initial guess.

    204:    Input/Output Parameter:
    205: .  x - the solution vector
    206: */
    207: PetscErrorCode FormInitialGuess(Vec x)
    208: {

    212:   VecSet(x,1.0);
    213:   return(0);
    214: }

    216: /* ------------------------------------------------------------------- */
    217: /*
    218:    FormFunction - Computes Function matrix  T(lambda)

    220:    Input Parameters:
    221: .  nep    - the NEP context
    222: .  lambda - the scalar argument
    223: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    225:    Output Parameters:
    226: .  fun - Function matrix
    227: .  B   - optionally different preconditioning matrix
    228: */
    229: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    230: {
    232:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    233:   PetscScalar    A[3],c,d;
    234:   PetscReal      h;
    235:   PetscInt       i,n,j[3],Istart,Iend;
    236:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    239:   /*
    240:      Compute Function entries and insert into matrix
    241:   */
    242:   MatGetSize(fun,&n,NULL);
    243:   MatGetOwnershipRange(fun,&Istart,&Iend);
    244:   if (Istart==0) FirstBlock=PETSC_TRUE;
    245:   if (Iend==n) LastBlock=PETSC_TRUE;
    246:   h = user->h;
    247:   c = user->kappa/(lambda-user->kappa);
    248:   d = n;

    250:   /*
    251:      Interior grid points
    252:   */
    253:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    254:     j[0] = i-1; j[1] = i; j[2] = i+1;
    255:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    256:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
    257:   }

    259:   /*
    260:      Boundary points
    261:   */
    262:   if (FirstBlock) {
    263:     i = 0;
    264:     j[0] = 0; j[1] = 1;
    265:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    266:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    267:   }

    269:   if (LastBlock) {
    270:     i = n-1;
    271:     j[0] = n-2; j[1] = n-1;
    272:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    273:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    274:   }

    276:   /*
    277:      Assemble matrix
    278:   */
    279:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    280:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    281:   if (fun != B) {
    282:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    283:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    284:   }
    285:   return(0);
    286: }

    288: /* ------------------------------------------------------------------- */
    289: /*
    290:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    292:    Input Parameters:
    293: .  nep    - the NEP context
    294: .  lambda - the scalar argument
    295: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    297:    Output Parameters:
    298: .  jac - Jacobian matrix
    299: */
    300: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    301: {
    303:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    304:   PetscScalar    A[3],c;
    305:   PetscReal      h;
    306:   PetscInt       i,n,j[3],Istart,Iend;
    307:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    310:   /*
    311:      Compute Jacobian entries and insert into matrix
    312:   */
    313:   MatGetSize(jac,&n,NULL);
    314:   MatGetOwnershipRange(jac,&Istart,&Iend);
    315:   if (Istart==0) FirstBlock=PETSC_TRUE;
    316:   if (Iend==n) LastBlock=PETSC_TRUE;
    317:   h = user->h;
    318:   c = user->kappa/(lambda-user->kappa);

    320:   /*
    321:      Interior grid points
    322:   */
    323:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    324:     j[0] = i-1; j[1] = i; j[2] = i+1;
    325:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    326:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    327:   }

    329:   /*
    330:      Boundary points
    331:   */
    332:   if (FirstBlock) {
    333:     i = 0;
    334:     j[0] = 0; j[1] = 1;
    335:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    336:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    337:   }

    339:   if (LastBlock) {
    340:     i = n-1;
    341:     j[0] = n-2; j[1] = n-1;
    342:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    343:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    344:   }

    346:   /*
    347:      Assemble matrix
    348:   */
    349:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    350:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    351:   return(0);
    352: }

    354: /* ------------------------------------------------------------------- */
    355: /*
    356:    CheckSolution - Given a computed solution (lambda,x) check if it
    357:    satisfies the analytic solution.

    359:    Input Parameters:
    360: +  lambda - the computed eigenvalue
    361: -  y      - the computed eigenvector

    363:    Output Parameter:
    364: .  error - norm of difference between the computed and exact eigenvector
    365: */
    366: PetscErrorCode CheckSolution(PetscScalar lambda,Vec y,PetscReal *error,void *ctx)
    367: {
    369:   PetscScalar    nu,*uu;
    370:   PetscInt       i,n,Istart,Iend;
    371:   PetscReal      x;
    372:   Vec            u;
    373:   ApplicationCtx *user = (ApplicationCtx*)ctx;

    376:   nu = PetscSqrtScalar(lambda);
    377:   VecDuplicate(y,&u);
    378:   VecGetSize(u,&n);
    379:   VecGetOwnershipRange(y,&Istart,&Iend);
    380:   VecGetArray(u,&uu);
    381:   for (i=Istart;i<Iend;i++) {
    382:     x = (i+1)*user->h;
    383:     uu[i-Istart] = PetscSinReal(nu*x);
    384:   }
    385:   VecRestoreArray(u,&uu);
    386:   VecNormalize(u,NULL);
    387:   VecAXPY(u,-1.0,y);
    388:   VecNorm(u,NORM_2,error);
    389:   VecDestroy(&u);
    390:   return(0);
    391: }

    393: /* ------------------------------------------------------------------- */
    394: /*
    395:    FixSign - Force the eigenfunction to be real and positive, since
    396:    some eigensolvers may return the eigenvector multiplied by a
    397:    complex number of modulus one.

    399:    Input/Output Parameter:
    400: .  x - the computed vector
    401: */
    402: PetscErrorCode FixSign(Vec x)
    403: {
    404:   PetscErrorCode    ierr;
    405:   PetscMPIInt       rank;
    406:   PetscScalar       sign=0.0;
    407:   const PetscScalar *xx;

    410:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
    411:   if (!rank) {
    412:     VecGetArrayRead(x,&xx);
    413:     sign = *xx/PetscAbsScalar(*xx);
    414:     VecRestoreArrayRead(x,&xx);
    415:   }
    416:   MPI_Bcast(&sign,1,MPIU_SCALAR,0,PETSC_COMM_WORLD);
    417:   VecScale(x,1.0/sign);
    418:   return(0);
    419: }

    421: /*TEST

    423:    build:
    424:       requires: !single

    426:    test:
    427:       suffix: 1
    428:       args: -nep_target 4
    429:       filter: sed -e "s/[0-9]\.[0-9]*e-\([0-9]*\)/removed/g" -e "s/ Number of NEP iterations = \([0-9]*\)/ Number of NEP iterations = /"
    430:       requires: !single

    432:    testset:
    433:       args: -nep_type nleigs -nep_target 10 -nep_nev 4
    434:       test:
    435:          suffix: 2
    436:          filter: sed -e "s/[0-9]\.[0-9]*e-\([0-9]*\)/removed/g" -e "s/0\.\([0-9]*\)/removed/g" -e "s/ Number of NEP iterations = \([0-9]*\)/ Number of NEP iterations = /"
    437:          args: -rg_interval_endpoints 4,900
    438:          requires: !single !complex
    439:       test:
    440:          suffix: 2_complex
    441:          filter: sed -e "s/[+-]0.[0-9]*i//" -e "s/[0-9]\.[0-9]*e-\([0-9]*\)/removed/g" -e "s/0\.\([0-9]*\)/removed/g" -e "s/ Number of NEP iterations = \([0-9]*\)/ Number of NEP iterations = /"
    442:          output_file: output/ex20_2.out
    443:          args: -rg_interval_endpoints 4,900,-.1,.1 -nep_target_real
    444:          requires: !single complex

    446:    testset:
    447:       args: -nep_type nleigs -nep_target 10 -nep_nev 4 -nep_ncv 18 -nep_two_sided {{0 1}} -nep_nleigs_full_basis
    448:       test:
    449:          suffix: 3
    450:          filter: sed -e "s/[0-9]\.[0-9]*e-\([0-9]*\)/removed/g" -e "s/0\.\([0-9]*\)/removed/g" -e "s/ Number of NEP iterations = \([0-9]*\)/ Number of NEP iterations = /"
    451:          output_file: output/ex20_2.out
    452:          args: -rg_interval_endpoints 4,900
    453:          requires: !single !complex
    454:       test:
    455:          suffix: 3_complex
    456:          filter: sed -e "s/[+-]0.[0-9]*i//" -e "s/[0-9]\.[0-9]*e-\([0-9]*\)/removed/g" -e "s/0\.\([0-9]*\)/removed/g" -e "s/ Number of NEP iterations = \([0-9]*\)/ Number of NEP iterations = /"
    457:          output_file: output/ex20_2.out
    458:          args: -rg_interval_endpoints 4,900,-.1,.1
    459:          requires: !single complex

    461:    test:
    462:       suffix: 4
    463:       args: -n 256 -nep_nev 2 -nep_target 10
    464:       filter: sed -e "s/[+-]0\.0*i//g" -e "s/[0-9]\.[0-9]*e-\([0-9]*\)/removed/g" -e "s/ Number of NEP iterations = \([0-9]*\)/ Number of NEP iterations = /"
    465:       requires: !single

    467: TEST*/