Line data Source code
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 1 : int main(int argc,char **argv)
34 : {
35 1 : Mat A[NMAT]; /* problem matrices */
36 1 : FN f[NMAT]; /* functions to define the nonlinear operator */
37 1 : NEP nep; /* nonlinear eigensolver context */
38 1 : RG rg;
39 1 : Vec v,r,z,w;
40 1 : PetscInt n=100,Istart,Iend,i,nconv;
41 1 : PetscReal kappa=1.0,m=1.0,nrm,tol;
42 1 : PetscScalar lambda,sigma,numer[2],denom[2],omega1,omega2;
43 :
44 1 : PetscFunctionBeginUser;
45 1 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
46 :
47 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
48 1 : PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
49 1 : PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
50 1 : sigma = kappa/m;
51 1 : 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 4 : for (i=0;i<NMAT;i++) {
59 3 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
60 3 : PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
61 3 : PetscCall(MatSetFromOptions(A[i]));
62 : }
63 1 : PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
64 :
65 : /* A0 */
66 101 : for (i=Istart;i<Iend;i++) {
67 100 : PetscCall(MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES));
68 100 : if (i>0) PetscCall(MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES));
69 100 : if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES));
70 : }
71 :
72 : /* A1 */
73 101 : for (i=Istart;i<Iend;i++) {
74 100 : PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES));
75 100 : if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES));
76 100 : if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES));
77 : }
78 :
79 : /* A2 */
80 1 : if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES));
81 :
82 : /* assemble matrices */
83 4 : for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
84 4 : 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 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0]));
92 1 : PetscCall(FNSetType(f[0],FNRATIONAL));
93 1 : numer[0] = 1.0;
94 1 : PetscCall(FNRationalSetNumerator(f[0],1,numer));
95 :
96 : /* f2=-lambda */
97 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1]));
98 1 : PetscCall(FNSetType(f[1],FNRATIONAL));
99 1 : numer[0] = -1.0; numer[1] = 0.0;
100 1 : PetscCall(FNRationalSetNumerator(f[1],2,numer));
101 :
102 : /* f3=lambda/(lambda-sigma) */
103 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f[2]));
104 1 : PetscCall(FNSetType(f[2],FNRATIONAL));
105 1 : numer[0] = 1.0; numer[1] = 0.0;
106 1 : denom[0] = 1.0; denom[1] = -sigma;
107 1 : PetscCall(FNRationalSetNumerator(f[2],2,numer));
108 1 : PetscCall(FNRationalSetDenominator(f[2],2,denom));
109 :
110 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111 : Create the eigensolver and solve the problem
112 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
113 :
114 1 : PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
115 1 : PetscCall(NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN));
116 1 : PetscCall(NEPSetProblemType(nep,NEP_RATIONAL));
117 1 : PetscCall(NEPSetDimensions(nep,8,PETSC_DEFAULT,PETSC_DEFAULT));
118 :
119 : /* set two-sided NLEIGS solver */
120 1 : PetscCall(NEPSetType(nep,NEPNLEIGS));
121 1 : PetscCall(NEPNLEIGSSetFullBasis(nep,PETSC_TRUE));
122 1 : PetscCall(NEPSetTwoSided(nep,PETSC_TRUE));
123 1 : PetscCall(NEPGetRG(nep,&rg));
124 1 : PetscCall(RGSetType(rg,RGINTERVAL));
125 : #if defined(PETSC_USE_COMPLEX)
126 1 : 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 1 : PetscCall(NEPSetTarget(nep,5.0));
131 :
132 1 : PetscCall(NEPSetFromOptions(nep));
133 1 : PetscCall(NEPSolve(nep));
134 :
135 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136 : Check left residual
137 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138 1 : PetscCall(MatCreateVecs(A[0],&v,&r));
139 1 : PetscCall(VecDuplicate(v,&w));
140 1 : PetscCall(VecDuplicate(v,&z));
141 1 : PetscCall(NEPGetConverged(nep,&nconv));
142 1 : PetscCall(NEPGetTolerances(nep,&tol,NULL));
143 9 : for (i=0;i<nconv;i++) {
144 8 : PetscCall(NEPGetEigenpair(nep,i,&lambda,NULL,NULL,NULL));
145 8 : PetscCall(NEPGetLeftEigenvector(nep,i,v,NULL));
146 8 : PetscCall(NEPApplyAdjoint(nep,lambda,v,w,r,NULL,NULL));
147 8 : PetscCall(VecNorm(r,NORM_2,&nrm));
148 8 : 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 1 : omega1 = 20.0;
155 1 : omega2 = 150.0;
156 1 : PetscCall(VecSet(v,0.0));
157 1 : PetscCall(VecSetValue(v,0,-1.0,INSERT_VALUES));
158 1 : PetscCall(VecSetValue(v,1,3.0,INSERT_VALUES));
159 1 : PetscCall(VecAssemblyBegin(v));
160 1 : PetscCall(VecAssemblyEnd(v));
161 1 : PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r));
162 1 : PetscCall(VecNorm(r,NORM_2,&nrm));
163 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm));
164 1 : PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r));
165 1 : PetscCall(VecNorm(r,NORM_2,&nrm));
166 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm));
167 1 : PetscCall(VecSet(v,1.0));
168 1 : PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r));
169 1 : PetscCall(VecNorm(r,NORM_2,&nrm));
170 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm));
171 1 : PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r));
172 1 : PetscCall(VecNorm(r,NORM_2,&nrm));
173 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm));
174 :
175 : /* clean up */
176 1 : PetscCall(NEPDestroy(&nep));
177 4 : for (i=0;i<NMAT;i++) {
178 3 : PetscCall(MatDestroy(&A[i]));
179 3 : PetscCall(FNDestroy(&f[i]));
180 : }
181 1 : PetscCall(VecDestroy(&v));
182 1 : PetscCall(VecDestroy(&r));
183 1 : PetscCall(VecDestroy(&w));
184 1 : PetscCall(VecDestroy(&z));
185 1 : PetscCall(SlepcFinalize());
186 : return 0;
187 : }
188 :
189 : /*TEST
190 :
191 : test:
192 : suffix: 1
193 : requires: !single
194 :
195 : TEST*/
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