Date: 2021-02-01T14:42:17+00:00

Actual source code: test12.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[] = "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;
     35:   PetscBool      terse,fb;
     36:   RG             rg;
     37:   FN             f[2];
     38:   PetscScalar    coeffs,shifts[]={1.06,1.1,1.12,1.15},*rkshifts,val;
     39:   PetscErrorCode (*fsing)(NEP,PetscInt*,PetscScalar*,void*);

     41:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     42:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     43:   PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%D\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:   MatCreate(PETSC_COMM_WORLD,&A[1]);
     80:   MatSetSizes(A[1],PETSC_DECIDE,PETSC_DECIDE,n,n);
     81:   MatSetFromOptions(A[1]);
     82:   MatSetUp(A[1]);
     83:   MatAssemblyBegin(A[1],MAT_FINAL_ASSEMBLY);
     84:   MatAssemblyEnd(A[1],MAT_FINAL_ASSEMBLY);
     85:   MatShift(A[1],1.0);

     87:   /* Define functions */
     88:   FNCreate(PETSC_COMM_WORLD,&f[0]);
     89:   FNSetType(f[0],FNRATIONAL);
     90:   coeffs = 1.0;
     91:   FNRationalSetNumerator(f[0],1,&coeffs);
     92:   FNCreate(PETSC_COMM_WORLD,&f[1]);
     93:   FNSetType(f[1],FNSQRT);
     94:   NEPSetSplitOperator(nep,2,A,f,SUBSET_NONZERO_PATTERN);

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:                         Set some options
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    100:   NEPNLEIGSSetFullBasis(nep,PETSC_FALSE);
    101:   NEPNLEIGSSetRKShifts(nep,4,shifts);
    102:   NEPSetFromOptions(nep);

    104:   NEPNLEIGSGetFullBasis(nep,&fb);
    105:   PetscPrintf(PETSC_COMM_WORLD," Using full basis = %s\n",fb?"true":"false");
    106:   NEPNLEIGSGetRKShifts(nep,&ns,&rkshifts);
    107:   if (ns) {
    108:     PetscPrintf(PETSC_COMM_WORLD," Using %d RK shifts =",ns);
    109:     for (i=0;i<ns;i++) {
    110:       PetscPrintf(PETSC_COMM_WORLD," %g",(double)PetscRealPart(rkshifts[i]));
    111:     }
    112:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    113:     PetscFree(rkshifts);
    114:   }
    115:   NEPNLEIGSGetSingularitiesFunction(nep,&fsing,NULL);
    116:   nsin = 1;
    117:   (*fsing)(nep,&nsin,&val,NULL);
    118:   PetscPrintf(PETSC_COMM_WORLD," First returned singularity = %g\n",(double)PetscRealPart(val));

    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:                       Solve the eigensystem
    122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    123:   NEPSolve(nep);

    125:   /* show detailed info unless -terse option is given by user */
    126:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    127:   if (terse) {
    128:     NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL);
    129:   } else {
    130:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    131:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    132:     NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    133:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    134:   }
    135:   NEPDestroy(&nep);
    136:   MatDestroy(&A[0]);
    137:   MatDestroy(&A[1]);
    138:   FNDestroy(&f[0]);
    139:   FNDestroy(&f[1]);
    140:   SlepcFinalize();
    141:   return ierr;
    142: }

    144: /* ------------------------------------------------------------------- */
    145: /*
    146:    ComputeSingularities - Computes maxnp points (at most) in the complex plane where
    147:    the function T(.) is not analytic.

    149:    In this case, we discretize the singularity region (-inf,0)~(-10e+6,-10e-6)
    150: */
    151: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
    152: {
    153:   PetscReal h;
    154:   PetscInt  i;

    157:   h = 11.0/(*maxnp-1);
    158:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
    159:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
    160:   return(0);
    161: }

    163: /*TEST

    165:    test:
    166:       suffix: 1
    167:       args: -nep_nev 3 -nep_nleigs_interpolation_degree 90 -terse -nep_view
    168:       requires: double
    169:       filter: grep -v tolerance

    171: TEST*/