Actual source code: test12.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[] = "Test some NLEIGS interface functions.\n\n"
     12:   "Based on ex27.c. The command line options are:\n"
     13:   "  -n <n>, where <n> = matrix dimension.\n";

     15: /*
     16:    Solve T(lambda)x=0 using NLEIGS solver
     17:       with T(lambda) = -D+sqrt(lambda)*I
     18:       where D is the Laplacian operator in 1 dimension
     19:       and with the interpolation interval [.01,16]
     20: */

     22: #include <slepcnep.h>

     24: /*
     25:    User-defined routines
     26: */
     27: PetscErrorCode ComputeSingularities(NEP,PetscInt*,PetscScalar*,void*);

     29: int main(int argc,char **argv)
     30: {
     31:   NEP            nep;             /* nonlinear eigensolver context */
     32:   Mat            A[2];
     33:   PetscInt       n=100,Istart,Iend,i,ns,nsin;
     34:   PetscBool      terse,fb;
     35:   RG             rg;
     36:   FN             f[2];
     37:   PetscScalar    coeffs,shifts[]={1.06,1.1,1.12,1.15},*rkshifts,val;
     38:   PetscErrorCode (*fsing)(NEP,PetscInt*,PetscScalar*,void*);

     40:   PetscFunctionBeginUser;
     41:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     42:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     43:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%" PetscInt_FMT "\n\n",n));

     45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     46:      Create nonlinear eigensolver and set some options
     47:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     49:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
     50:   PetscCall(NEPSetType(nep,NEPNLEIGS));
     51:   PetscCall(NEPNLEIGSSetSingularitiesFunction(nep,ComputeSingularities,NULL));
     52:   PetscCall(NEPGetRG(nep,&rg));
     53:   PetscCall(RGSetType(rg,RGINTERVAL));
     54: #if defined(PETSC_USE_COMPLEX)
     55:   PetscCall(RGIntervalSetEndpoints(rg,0.01,16.0,-0.001,0.001));
     56: #else
     57:   PetscCall(RGIntervalSetEndpoints(rg,0.01,16.0,0,0));
     58: #endif
     59:   PetscCall(NEPSetTarget(nep,1.1));

     61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     62:      Define the nonlinear problem in split form
     63:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     65:   /* Create matrices */
     66:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A[0]));
     67:   PetscCall(MatSetSizes(A[0],PETSC_DECIDE,PETSC_DECIDE,n,n));
     68:   PetscCall(MatSetFromOptions(A[0]));
     69:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
     70:   for (i=Istart;i<Iend;i++) {
     71:     if (i>0) PetscCall(MatSetValue(A[0],i,i-1,1.0,INSERT_VALUES));
     72:     if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,1.0,INSERT_VALUES));
     73:     PetscCall(MatSetValue(A[0],i,i,-2.0,INSERT_VALUES));
     74:   }
     75:   PetscCall(MatAssemblyBegin(A[0],MAT_FINAL_ASSEMBLY));
     76:   PetscCall(MatAssemblyEnd(A[0],MAT_FINAL_ASSEMBLY));

     78:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&A[1]));

     80:   /* Define functions */
     81:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0]));
     82:   PetscCall(FNSetType(f[0],FNRATIONAL));
     83:   coeffs = 1.0;
     84:   PetscCall(FNRationalSetNumerator(f[0],1,&coeffs));
     85:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1]));
     86:   PetscCall(FNSetType(f[1],FNSQRT));
     87:   PetscCall(NEPSetSplitOperator(nep,2,A,f,SUBSET_NONZERO_PATTERN));

     89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     90:                         Set some options
     91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     93:   PetscCall(NEPNLEIGSSetFullBasis(nep,PETSC_FALSE));
     94:   PetscCall(NEPNLEIGSSetRKShifts(nep,4,shifts));
     95:   PetscCall(NEPSetFromOptions(nep));

     97:   PetscCall(NEPNLEIGSGetFullBasis(nep,&fb));
     98:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Using full basis = %s\n",fb?"true":"false"));
     99:   PetscCall(NEPNLEIGSGetRKShifts(nep,&ns,&rkshifts));
    100:   if (ns) {
    101:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Using %" PetscInt_FMT " RK shifts =",ns));
    102:     for (i=0;i<ns;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %g",(double)PetscRealPart(rkshifts[i])));
    103:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    104:     PetscCall(PetscFree(rkshifts));
    105:   }
    106:   PetscCall(NEPNLEIGSGetSingularitiesFunction(nep,&fsing,NULL));
    107:   nsin = 1;
    108:   PetscCall((*fsing)(nep,&nsin,&val,NULL));
    109:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," First returned singularity = %g\n",(double)PetscRealPart(val)));

    111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112:                       Solve the eigensystem
    113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    114:   PetscCall(NEPSolve(nep));

    116:   /* show detailed info unless -terse option is given by user */
    117:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    118:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL));
    119:   else {
    120:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    121:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    122:     PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    123:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    124:   }
    125:   PetscCall(NEPDestroy(&nep));
    126:   PetscCall(MatDestroy(&A[0]));
    127:   PetscCall(MatDestroy(&A[1]));
    128:   PetscCall(FNDestroy(&f[0]));
    129:   PetscCall(FNDestroy(&f[1]));
    130:   PetscCall(SlepcFinalize());
    131:   return 0;
    132: }

    134: /* ------------------------------------------------------------------- */
    135: /*
    136:    ComputeSingularities - Computes maxnp points (at most) in the complex plane where
    137:    the function T(.) is not analytic.

    139:    In this case, we discretize the singularity region (-inf,0)~(-1e+6,-1e-5)
    140: */
    141: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
    142: {
    143:   PetscReal h;
    144:   PetscInt  i;

    146:   PetscFunctionBeginUser;
    147:   h = 11.0/(*maxnp-1);
    148:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
    149:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
    150:   PetscFunctionReturn(PETSC_SUCCESS);
    151: }

    153: /*TEST

    155:    test:
    156:       suffix: 1
    157:       args: -nep_nev 3 -nep_nleigs_interpolation_degree 20 -terse -nep_view
    158:       requires: double
    159:       filter: grep -v tolerance | sed -e "s/[+-]0\.0*i//g"

    161: TEST*/