Date: 2024-04-26T10:22:25+00:00

Actual source code: test16.c
slepc-3.21.1 2024-04-26
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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[] = "Illustrates use of NEPSetEigenvalueComparison().\n\n"
     12:   "This is a simplified version of ex20.\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions.\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 FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     29: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);
     30: PetscErrorCode MyEigenSort(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*);

     32: /*
     33:    User-defined application context
     34: */
     35: typedef struct {
     36:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     37:   PetscReal   h;       /* mesh spacing */
     38: } ApplicationCtx;

     40: int main(int argc,char **argv)
     41: {
     42:   NEP            nep;             /* nonlinear eigensolver context */
     43:   Mat            F,J;             /* Function and Jacobian matrices */
     44:   ApplicationCtx ctx;             /* user-defined context */
     45:   PetscScalar    target;
     46:   RG             rg;
     47:   PetscInt       n=128;
     48:   PetscBool      terse;

     50:   PetscFunctionBeginUser;
     51:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
     52:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     53:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n));
     54:   ctx.h = 1.0/(PetscReal)n;
     55:   ctx.kappa = 1.0;

     57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     58:                Prepare nonlinear eigensolver context
     59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     61:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));

     63:   PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
     64:   PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
     65:   PetscCall(MatSetFromOptions(F));
     66:   PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
     67:   PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
     68:   PetscCall(NEPSetFunction(nep,F,F,FormFunction,&ctx));

     70:   PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
     71:   PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
     72:   PetscCall(MatSetFromOptions(J));
     73:   PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
     74:   PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
     75:   PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));

     77:   PetscCall(NEPSetType(nep,NEPNLEIGS));
     78:   PetscCall(NEPGetRG(nep,&rg));
     79:   PetscCall(RGSetType(rg,RGINTERVAL));
     80: #if defined(PETSC_USE_COMPLEX)
     81:   PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,-0.001,0.001));
     82: #else
     83:   PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,0,0));
     84: #endif
     85:   PetscCall(NEPSetTarget(nep,25.0));
     86:   PetscCall(NEPSetEigenvalueComparison(nep,MyEigenSort,&target));
     87:   PetscCall(NEPSetTolerances(nep,PETSC_SMALL,PETSC_DEFAULT));
     88:   PetscCall(NEPSetFromOptions(nep));
     89:   PetscCall(NEPGetTarget(nep,&target));

     91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     92:               Solve the eigensystem and display the solution
     93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     95:   PetscCall(NEPSolve(nep));

     97:   /* show detailed info unless -terse option is given by user */
     98:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
     99:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
    100:   else {
    101:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    102:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    103:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    104:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    105:   }

    107:   PetscCall(NEPDestroy(&nep));
    108:   PetscCall(MatDestroy(&F));
    109:   PetscCall(MatDestroy(&J));
    110:   PetscCall(SlepcFinalize());
    111:   return 0;
    112: }

    114: /* ------------------------------------------------------------------- */
    115: /*
    116:    FormFunction - Computes Function matrix  T(lambda)

    118:    Input Parameters:
    119: .  nep    - the NEP context
    120: .  lambda - the scalar argument
    121: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    123:    Output Parameters:
    124: .  fun - Function matrix
    125: .  B   - optionally different preconditioning matrix
    126: */
    127: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    128: {
    129:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    130:   PetscScalar    A[3],c,d;
    131:   PetscReal      h;
    132:   PetscInt       i,n,j[3],Istart,Iend;
    133:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    135:   PetscFunctionBeginUser;
    136:   /*
    137:      Compute Function entries and insert into matrix
    138:   */
    139:   PetscCall(MatGetSize(fun,&n,NULL));
    140:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
    141:   if (Istart==0) FirstBlock=PETSC_TRUE;
    142:   if (Iend==n) LastBlock=PETSC_TRUE;
    143:   h = user->h;
    144:   c = user->kappa/(lambda-user->kappa);
    145:   d = n;

    147:   /*
    148:      Interior grid points
    149:   */
    150:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    151:     j[0] = i-1; j[1] = i; j[2] = i+1;
    152:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    153:     PetscCall(MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES));
    154:   }

    156:   /*
    157:      Boundary points
    158:   */
    159:   if (FirstBlock) {
    160:     i = 0;
    161:     j[0] = 0; j[1] = 1;
    162:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    163:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    164:   }

    166:   if (LastBlock) {
    167:     i = n-1;
    168:     j[0] = n-2; j[1] = n-1;
    169:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    170:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    171:   }

    173:   /*
    174:      Assemble matrix
    175:   */
    176:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    177:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    178:   if (fun != B) {
    179:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    180:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    181:   }
    182:   PetscFunctionReturn(PETSC_SUCCESS);
    183: }

    185: /* ------------------------------------------------------------------- */
    186: /*
    187:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    189:    Input Parameters:
    190: .  nep    - the NEP context
    191: .  lambda - the scalar argument
    192: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    194:    Output Parameters:
    195: .  jac - Jacobian matrix
    196: .  B   - optionally different preconditioning matrix
    197: */
    198: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    199: {
    200:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    201:   PetscScalar    A[3],c;
    202:   PetscReal      h;
    203:   PetscInt       i,n,j[3],Istart,Iend;
    204:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    206:   PetscFunctionBeginUser;
    207:   /*
    208:      Compute Jacobian entries and insert into matrix
    209:   */
    210:   PetscCall(MatGetSize(jac,&n,NULL));
    211:   PetscCall(MatGetOwnershipRange(jac,&Istart,&Iend));
    212:   if (Istart==0) FirstBlock=PETSC_TRUE;
    213:   if (Iend==n) LastBlock=PETSC_TRUE;
    214:   h = user->h;
    215:   c = user->kappa/(lambda-user->kappa);

    217:   /*
    218:      Interior grid points
    219:   */
    220:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    221:     j[0] = i-1; j[1] = i; j[2] = i+1;
    222:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    223:     PetscCall(MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES));
    224:   }

    226:   /*
    227:      Boundary points
    228:   */
    229:   if (FirstBlock) {
    230:     i = 0;
    231:     j[0] = 0; j[1] = 1;
    232:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    233:     PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
    234:   }

    236:   if (LastBlock) {
    237:     i = n-1;
    238:     j[0] = n-2; j[1] = n-1;
    239:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    240:     PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
    241:   }

    243:   /*
    244:      Assemble matrix
    245:   */
    246:   PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
    247:   PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
    248:   PetscFunctionReturn(PETSC_SUCCESS);
    249: }

    251: /*
    252:     Function for user-defined eigenvalue ordering criterion.

    254:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    255:     one of them as the preferred one according to the criterion.
    256:     In this example, eigenvalues are sorted with respect to the target,
    257:     but those on the right of the target are preferred.
    258: */
    259: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    260: {
    261:   PetscReal   a,b;
    262:   PetscScalar target = *(PetscScalar*)ctx;

    264:   PetscFunctionBeginUser;
    265:   if (PetscRealPart(ar-target)<0.0 && PetscRealPart(br-target)>0.0) *r = 1;
    266:   else {
    267:     a = SlepcAbsEigenvalue(ar-target,ai);
    268:     b = SlepcAbsEigenvalue(br-target,bi);
    269:     if (a>b) *r = 1;
    270:     else if (a<b) *r = -1;
    271:     else *r = 0;
    272:   }
    273:   PetscFunctionReturn(PETSC_SUCCESS);
    274: }

    276: /*TEST

    278:    test:
    279:       suffix: 1
    280:       args: -nep_nev 4 -nep_ncv 8 -terse
    281:       requires: double !complex

    283: TEST*/