Actual source code: test16.c

      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 MyEigenSort(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*);

     31: /*
     32:    User-defined application context
     33: */
     34: typedef struct {
     35:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     36:   PetscReal   h;       /* mesh spacing */
     37: } ApplicationCtx;

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

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

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:                Prepare nonlinear eigensolver context
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

     69:   PetscCall(NEPSetType(nep,NEPNLEIGS));
     70:   PetscCall(NEPGetRG(nep,&rg));
     71:   PetscCall(RGSetType(rg,RGINTERVAL));
     72: #if defined(PETSC_USE_COMPLEX)
     73:   PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,-0.001,0.001));
     74: #else
     75:   PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,0,0));
     76: #endif
     77:   PetscCall(NEPSetTarget(nep,25.0));
     78:   PetscCall(NEPSetEigenvalueComparison(nep,MyEigenSort,&target));
     79:   PetscCall(NEPSetTolerances(nep,PETSC_SMALL,PETSC_CURRENT));
     80:   PetscCall(NEPSetFromOptions(nep));
     81:   PetscCall(NEPGetTarget(nep,&target));

     83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     84:               Solve the eigensystem and display the solution
     85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     87:   PetscCall(NEPSolve(nep));

     89:   /* show detailed info unless -terse option is given by user */
     90:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
     91:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
     92:   else {
     93:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
     94:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
     95:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
     96:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
     97:   }

     99:   PetscCall(NEPDestroy(&nep));
    100:   PetscCall(MatDestroy(&F));
    101:   PetscCall(SlepcFinalize());
    102:   return 0;
    103: }

    105: /* ------------------------------------------------------------------- */
    106: /*
    107:    FormFunction - Computes Function matrix  T(lambda)

    109:    Input Parameters:
    110: .  nep    - the NEP context
    111: .  lambda - the scalar argument
    112: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    114:    Output Parameters:
    115: .  fun - Function matrix
    116: .  B   - optionally different preconditioning matrix
    117: */
    118: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    119: {
    120:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    121:   PetscScalar    A[3],c,d;
    122:   PetscReal      h;
    123:   PetscInt       i,n,j[3],Istart,Iend;
    124:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    126:   PetscFunctionBeginUser;
    127:   /*
    128:      Compute Function entries and insert into matrix
    129:   */
    130:   PetscCall(MatGetSize(fun,&n,NULL));
    131:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
    132:   if (Istart==0) FirstBlock=PETSC_TRUE;
    133:   if (Iend==n) LastBlock=PETSC_TRUE;
    134:   h = user->h;
    135:   c = user->kappa/(lambda-user->kappa);
    136:   d = n;

    138:   /*
    139:      Interior grid points
    140:   */
    141:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    142:     j[0] = i-1; j[1] = i; j[2] = i+1;
    143:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    144:     PetscCall(MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES));
    145:   }

    147:   /*
    148:      Boundary points
    149:   */
    150:   if (FirstBlock) {
    151:     i = 0;
    152:     j[0] = 0; j[1] = 1;
    153:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    154:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    155:   }

    157:   if (LastBlock) {
    158:     i = n-1;
    159:     j[0] = n-2; j[1] = n-1;
    160:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    161:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    162:   }

    164:   /*
    165:      Assemble matrix
    166:   */
    167:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    168:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    169:   if (fun != B) {
    170:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    171:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    172:   }
    173:   PetscFunctionReturn(PETSC_SUCCESS);
    174: }

    176: /*
    177:     Function for user-defined eigenvalue ordering criterion.

    179:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    180:     one of them as the preferred one according to the criterion.
    181:     In this example, eigenvalues are sorted with respect to the target,
    182:     but those on the right of the target are preferred.
    183: */
    184: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    185: {
    186:   PetscReal   a,b;
    187:   PetscScalar target = *(PetscScalar*)ctx;

    189:   PetscFunctionBeginUser;
    190:   if (PetscRealPart(ar-target)<0.0 && PetscRealPart(br-target)>0.0) *r = 1;
    191:   else {
    192:     a = SlepcAbsEigenvalue(ar-target,ai);
    193:     b = SlepcAbsEigenvalue(br-target,bi);
    194:     if (a>b) *r = 1;
    195:     else if (a<b) *r = -1;
    196:     else *r = 0;
    197:   }
    198:   PetscFunctionReturn(PETSC_SUCCESS);
    199: }

    201: /*TEST

    203:    test:
    204:       suffix: 1
    205:       args: -nep_nev 4 -nep_ncv 8 -terse
    206:       requires: double !complex

    208: TEST*/