Date: 2022-10-01T06:40:39+00:00

Actual source code: test12.c
slepc-3.18.0 2022-10-01
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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[] = "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*);

     41:   SlepcInitialize(&argc,&argv,(char*)0,help);
     42:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     43:   PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%" PetscInt_FMT "\n\n",n);

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

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

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

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

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

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

     90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     91:                         Set some options
     92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

    117:   /* show detailed info unless -terse option is given by user */
    118:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    119:   if (terse) NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL);
    120:   else {
    121:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    122:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    123:     NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    124:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    125:   }
    126:   NEPDestroy(&nep);
    127:   MatDestroy(&A[0]);
    128:   MatDestroy(&A[1]);
    129:   FNDestroy(&f[0]);
    130:   FNDestroy(&f[1]);
    131:   SlepcFinalize();
    132:   return 0;
    133: }

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

    140:    In this case, we discretize the singularity region (-inf,0)~(-10e+6,-10e-6)
    141: */
    142: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
    143: {
    144:   PetscReal h;
    145:   PetscInt  i;

    148:   h = 11.0/(*maxnp-1);
    149:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
    150:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
    151:   return 0;
    152: }

    154: /*TEST

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

    162: TEST*/