| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
| 4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
| 5 | |||
| 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. | ||
| 17 | |||
| 18 | The loaded_string problem is a rational eigenvalue problem for the | ||
| 19 | finite element model of a loaded vibrating string. | ||
| 20 | */ | ||
| 21 | |||
| 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"; | ||
| 28 | |||
| 29 | #include <slepcnep.h> | ||
| 30 | |||
| 31 | #define NMAT 3 | ||
| 32 | |||
| 33 | 10 | int main(int argc,char **argv) | |
| 34 | { | ||
| 35 | 10 | Mat A[NMAT]; /* problem matrices */ | |
| 36 | 10 | FN f[NMAT]; /* functions to define the nonlinear operator */ | |
| 37 | 10 | NEP nep; /* nonlinear eigensolver context */ | |
| 38 | 10 | RG rg; | |
| 39 | 10 | Vec v,r,z,w; | |
| 40 | 10 | PetscInt n=100,Istart,Iend,i,nconv; | |
| 41 | 10 | PetscReal kappa=1.0,m=1.0,nrm,tol; | |
| 42 | 10 | PetscScalar lambda,sigma,numer[2],denom[2],omega1,omega2; | |
| 43 | |||
| 44 |
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10 | PetscFunctionBeginUser; |
| 45 |
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10 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
| 46 | |||
| 47 |
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10 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
| 48 |
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10 | PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL)); |
| 49 |
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10 | PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL)); |
| 50 | 10 | sigma = kappa/m; | |
| 51 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string, n=%" PetscInt_FMT " kappa=%g m=%g\n\n",n,(double)kappa,(double)m)); |
| 52 | |||
| 53 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 54 | Build the problem matrices | ||
| 55 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 56 | |||
| 57 | /* initialize matrices */ | ||
| 58 |
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40 | for (i=0;i<NMAT;i++) { |
| 59 |
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30 | PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i])); |
| 60 |
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30 | PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n)); |
| 61 |
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30 | PetscCall(MatSetFromOptions(A[i])); |
| 62 | } | ||
| 63 |
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10 | PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend)); |
| 64 | |||
| 65 | /* A0 */ | ||
| 66 |
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1010 | for (i=Istart;i<Iend;i++) { |
| 67 |
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1000 | PetscCall(MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES)); |
| 68 |
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1000 | if (i>0) PetscCall(MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES)); |
| 69 |
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1000 | if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES)); |
| 70 | } | ||
| 71 | |||
| 72 | /* A1 */ | ||
| 73 |
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1010 | for (i=Istart;i<Iend;i++) { |
| 74 |
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1000 | PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES)); |
| 75 |
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1000 | if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES)); |
| 76 |
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1000 | if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES)); |
| 77 | } | ||
| 78 | |||
| 79 | /* A2 */ | ||
| 80 |
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10 | if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES)); |
| 81 | |||
| 82 | /* assemble matrices */ | ||
| 83 |
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40 | for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY)); |
| 84 |
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40 | for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY)); |
| 85 | |||
| 86 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 87 | Create the problem functions | ||
| 88 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 89 | |||
| 90 | /* f1=1 */ | ||
| 91 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0])); |
| 92 |
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10 | PetscCall(FNSetType(f[0],FNRATIONAL)); |
| 93 | 10 | numer[0] = 1.0; | |
| 94 |
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10 | PetscCall(FNRationalSetNumerator(f[0],1,numer)); |
| 95 | |||
| 96 | /* f2=-lambda */ | ||
| 97 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1])); |
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10 | PetscCall(FNSetType(f[1],FNRATIONAL)); |
| 99 | 10 | numer[0] = -1.0; numer[1] = 0.0; | |
| 100 |
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10 | PetscCall(FNRationalSetNumerator(f[1],2,numer)); |
| 101 | |||
| 102 | /* f3=lambda/(lambda-sigma) */ | ||
| 103 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f[2])); |
| 104 |
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10 | PetscCall(FNSetType(f[2],FNRATIONAL)); |
| 105 | 10 | numer[0] = 1.0; numer[1] = 0.0; | |
| 106 | 10 | denom[0] = 1.0; denom[1] = -sigma; | |
| 107 |
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10 | PetscCall(FNRationalSetNumerator(f[2],2,numer)); |
| 108 |
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10 | PetscCall(FNRationalSetDenominator(f[2],2,denom)); |
| 109 | |||
| 110 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 111 | Create the eigensolver and solve the problem | ||
| 112 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 113 | |||
| 114 |
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10 | PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep)); |
| 115 |
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10 | PetscCall(NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN)); |
| 116 |
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10 | PetscCall(NEPSetProblemType(nep,NEP_RATIONAL)); |
| 117 |
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10 | PetscCall(NEPSetDimensions(nep,8,PETSC_DETERMINE,PETSC_DETERMINE)); |
| 118 | |||
| 119 | /* set two-sided NLEIGS solver */ | ||
| 120 |
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10 | PetscCall(NEPSetType(nep,NEPNLEIGS)); |
| 121 |
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10 | PetscCall(NEPNLEIGSSetFullBasis(nep,PETSC_TRUE)); |
| 122 |
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10 | PetscCall(NEPSetTwoSided(nep,PETSC_TRUE)); |
| 123 |
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10 | PetscCall(NEPGetRG(nep,&rg)); |
| 124 |
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10 | PetscCall(RGSetType(rg,RGINTERVAL)); |
| 125 | #if defined(PETSC_USE_COMPLEX) | ||
| 126 |
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5 | PetscCall(RGIntervalSetEndpoints(rg,4.0,700.0,-0.001,0.001)); |
| 127 | #else | ||
| 128 |
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5 | PetscCall(RGIntervalSetEndpoints(rg,4.0,700.0,0,0)); |
| 129 | #endif | ||
| 130 |
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10 | PetscCall(NEPSetTarget(nep,5.0)); |
| 131 | |||
| 132 |
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10 | PetscCall(NEPSetFromOptions(nep)); |
| 133 |
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10 | PetscCall(NEPSolve(nep)); |
| 134 | |||
| 135 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 136 | Check left residual | ||
| 137 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 138 |
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10 | PetscCall(MatCreateVecs(A[0],&v,&r)); |
| 139 |
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10 | PetscCall(VecDuplicate(v,&w)); |
| 140 |
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10 | PetscCall(VecDuplicate(v,&z)); |
| 141 |
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10 | PetscCall(NEPGetConverged(nep,&nconv)); |
| 142 |
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10 | PetscCall(NEPGetTolerances(nep,&tol,NULL)); |
| 143 |
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90 | for (i=0;i<nconv;i++) { |
| 144 |
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80 | PetscCall(NEPGetEigenpair(nep,i,&lambda,NULL,NULL,NULL)); |
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80 | PetscCall(NEPGetLeftEigenvector(nep,i,v,NULL)); |
| 146 |
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80 | PetscCall(NEPApplyAdjoint(nep,lambda,v,w,r,NULL,NULL)); |
| 147 |
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80 | PetscCall(VecNorm(r,NORM_2,&nrm)); |
| 148 |
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80 | 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 | } | ||
| 150 | |||
| 151 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 152 | Operate with resolvent | ||
| 153 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
| 154 | 10 | omega1 = 20.0; | |
| 155 | 10 | omega2 = 150.0; | |
| 156 |
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10 | PetscCall(VecSet(v,0.0)); |
| 157 |
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10 | PetscCall(VecSetValue(v,0,-1.0,INSERT_VALUES)); |
| 158 |
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10 | PetscCall(VecSetValue(v,1,3.0,INSERT_VALUES)); |
| 159 |
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10 | PetscCall(VecAssemblyBegin(v)); |
| 160 |
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10 | PetscCall(VecAssemblyEnd(v)); |
| 161 |
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10 | PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r)); |
| 162 |
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10 | PetscCall(VecNorm(r,NORM_2,&nrm)); |
| 163 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm)); |
| 164 |
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10 | PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r)); |
| 165 |
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10 | PetscCall(VecNorm(r,NORM_2,&nrm)); |
| 166 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm)); |
| 167 |
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10 | PetscCall(VecSet(v,1.0)); |
| 168 |
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10 | PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r)); |
| 169 |
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10 | PetscCall(VecNorm(r,NORM_2,&nrm)); |
| 170 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm)); |
| 171 |
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10 | PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r)); |
| 172 |
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10 | PetscCall(VecNorm(r,NORM_2,&nrm)); |
| 173 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm)); |
| 174 | |||
| 175 | /* clean up */ | ||
| 176 |
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10 | PetscCall(NEPDestroy(&nep)); |
| 177 |
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40 | for (i=0;i<NMAT;i++) { |
| 178 |
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30 | PetscCall(MatDestroy(&A[i])); |
| 179 |
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30 | PetscCall(FNDestroy(&f[i])); |
| 180 | } | ||
| 181 |
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10 | PetscCall(VecDestroy(&v)); |
| 182 |
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10 | PetscCall(VecDestroy(&r)); |
| 183 |
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10 | PetscCall(VecDestroy(&w)); |
| 184 |
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10 | PetscCall(VecDestroy(&z)); |
| 185 |
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10 | PetscCall(SlepcFinalize()); |
| 186 | return 0; | ||
| 187 | } | ||
| 188 | |||
| 189 | /*TEST | ||
| 190 | |||
| 191 | test: | ||
| 192 | suffix: 1 | ||
| 193 | requires: !single | ||
| 194 | |||
| 195 | TEST*/ | ||
| 196 |