Date: 2026-05-01T10:02:28+00:00

Actual source code: ex42.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: */
     10: /*
     11:    This example implements one of the problems found at
     12:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     13:        The University of Manchester.
     14:    The details of the collection can be found at:
     15:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     16:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     18:    The loaded_string problem is a rational eigenvalue problem for the
     19:    finite element model of a loaded vibrating string.
     20: */

     22: static char help[] = "Illustrates computation of left eigenvectors and resolvent.\n\n"
     23:   "This is based on loaded_string from the NLEVP collection.\n"
     24:   "The command line options are:\n"
     25:   "  -n <n>, dimension of the matrices.\n"
     26:   "  -kappa <kappa>, stiffness of elastic spring.\n"
     27:   "  -mass <m>, mass of the attached load.\n\n";

     29: #include <slepcnep.h>

     31: #define NMAT 3

     33: int main(int argc,char **argv)
     34: {
     35:   Mat            A[NMAT];         /* problem matrices */
     36:   FN             f[NMAT];         /* functions to define the nonlinear operator */
     37:   NEP            nep;             /* nonlinear eigensolver context */
     38:   RG             rg;
     39:   Vec            v,r,z,w;
     40:   PetscInt       n=100,Istart,Iend,i,nconv;
     41:   PetscReal      kappa=1.0,m=1.0,nrm,tol;
     42:   PetscScalar    lambda,sigma,numer[2],denom[2],omega1,omega2;

     44:   PetscFunctionBeginUser;
     45:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     47:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     48:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
     49:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
     50:   sigma = kappa/m;
     51:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string, n=%" PetscInt_FMT " kappa=%g m=%g\n\n",n,(double)kappa,(double)m));

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:                        Build the problem matrices
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     57:   /* initialize matrices */
     58:   for (i=0;i<NMAT;i++) {
     59:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
     60:     PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
     61:     PetscCall(MatSetFromOptions(A[i]));
     62:   }
     63:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

     65:   /* A0 */
     66:   for (i=Istart;i<Iend;i++) {
     67:     PetscCall(MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES));
     68:     if (i>0) PetscCall(MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES));
     69:     if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES));
     70:   }

     72:   /* A1 */
     73:   for (i=Istart;i<Iend;i++) {
     74:     PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES));
     75:     if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES));
     76:     if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES));
     77:   }

     79:   /* A2 */
     80:   if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES));

     82:   /* assemble matrices */
     83:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
     84:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:                        Create the problem functions
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     90:   /* f1=1 */
     91:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0]));
     92:   PetscCall(FNSetType(f[0],FNRATIONAL));
     93:   numer[0] = 1.0;
     94:   PetscCall(FNRationalSetNumerator(f[0],1,numer));

     96:   /* f2=-lambda */
     97:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1]));
     98:   PetscCall(FNSetType(f[1],FNRATIONAL));
     99:   numer[0] = -1.0; numer[1] = 0.0;
    100:   PetscCall(FNRationalSetNumerator(f[1],2,numer));

    102:   /* f3=lambda/(lambda-sigma) */
    103:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[2]));
    104:   PetscCall(FNSetType(f[2],FNRATIONAL));
    105:   numer[0] = 1.0; numer[1] = 0.0;
    106:   denom[0] = 1.0; denom[1] = -sigma;
    107:   PetscCall(FNRationalSetNumerator(f[2],2,numer));
    108:   PetscCall(FNRationalSetDenominator(f[2],2,denom));

    110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    111:                 Create the eigensolver and solve the problem
    112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    114:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
    115:   PetscCall(NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN));
    116:   PetscCall(NEPSetProblemType(nep,NEP_RATIONAL));
    117:   PetscCall(NEPSetDimensions(nep,8,PETSC_DETERMINE,PETSC_DETERMINE));

    119:   /* set two-sided NLEIGS solver */
    120:   PetscCall(NEPSetType(nep,NEPNLEIGS));
    121:   PetscCall(NEPNLEIGSSetFullBasis(nep,PETSC_TRUE));
    122:   PetscCall(NEPSetTwoSided(nep,PETSC_TRUE));
    123:   PetscCall(NEPGetRG(nep,&rg));
    124:   PetscCall(RGSetType(rg,RGINTERVAL));
    125: #if defined(PETSC_USE_COMPLEX)
    126:   PetscCall(RGIntervalSetEndpoints(rg,4.0,700.0,-0.001,0.001));
    127: #else
    128:   PetscCall(RGIntervalSetEndpoints(rg,4.0,700.0,0,0));
    129: #endif
    130:   PetscCall(NEPSetTarget(nep,5.0));

    132:   PetscCall(NEPSetFromOptions(nep));
    133:   PetscCall(NEPSolve(nep));

    135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    136:                        Check left residual
    137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    138:   PetscCall(MatCreateVecs(A[0],&v,&r));
    139:   PetscCall(VecDuplicate(v,&w));
    140:   PetscCall(VecDuplicate(v,&z));
    141:   PetscCall(NEPGetConverged(nep,&nconv));
    142:   PetscCall(NEPGetTolerances(nep,&tol,NULL));
    143:   for (i=0;i<nconv;i++) {
    144:     PetscCall(NEPGetEigenpair(nep,i,&lambda,NULL,NULL,NULL));
    145:     PetscCall(NEPGetLeftEigenvector(nep,i,v,NULL));
    146:     PetscCall(NEPApplyAdjoint(nep,lambda,v,w,r,NULL,NULL));
    147:     PetscCall(VecNorm(r,NORM_2,&nrm));
    148:     if (nrm>tol*PetscAbsScalar(lambda)) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Left residual i=%" PetscInt_FMT " is above tolerance --> %g\n",i,(double)(nrm/PetscAbsScalar(lambda))));
    149:   }

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    152:                       Operate with resolvent
    153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    154:   omega1 = 20.0;
    155:   omega2 = 150.0;
    156:   PetscCall(VecSet(v,0.0));
    157:   PetscCall(VecSetValue(v,0,-1.0,INSERT_VALUES));
    158:   PetscCall(VecSetValue(v,1,3.0,INSERT_VALUES));
    159:   PetscCall(VecAssemblyBegin(v));
    160:   PetscCall(VecAssemblyEnd(v));
    161:   PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r));
    162:   PetscCall(VecNorm(r,NORM_2,&nrm));
    163:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm));
    164:   PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r));
    165:   PetscCall(VecNorm(r,NORM_2,&nrm));
    166:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm));
    167:   PetscCall(VecSet(v,1.0));
    168:   PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r));
    169:   PetscCall(VecNorm(r,NORM_2,&nrm));
    170:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm));
    171:   PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r));
    172:   PetscCall(VecNorm(r,NORM_2,&nrm));
    173:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm));

    175:   /* clean up */
    176:   PetscCall(NEPDestroy(&nep));
    177:   for (i=0;i<NMAT;i++) {
    178:     PetscCall(MatDestroy(&A[i]));
    179:     PetscCall(FNDestroy(&f[i]));
    180:   }
    181:   PetscCall(VecDestroy(&v));
    182:   PetscCall(VecDestroy(&r));
    183:   PetscCall(VecDestroy(&w));
    184:   PetscCall(VecDestroy(&z));
    185:   PetscCall(SlepcFinalize());
    186:   return 0;
    187: }

    189: /*TEST

    191:    test:
    192:       suffix: 1
    193:       requires: !single

    195: TEST*/