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 : static char help[] = "Simple quadratic eigenvalue problem.\n\n"
12 : "The command line options are:\n"
13 : " -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
14 : " -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";
15 :
16 : #include <slepcpep.h>
17 :
18 6 : int main(int argc,char **argv)
19 : {
20 6 : Mat M,C,K,A[3]; /* problem matrices */
21 6 : PEP pep; /* polynomial eigenproblem solver context */
22 6 : PetscInt N,n=10,m,Istart,Iend,II,nev,i,j,nconv;
23 6 : PetscBool flag,terse;
24 6 : PetscReal error,re,im;
25 6 : PetscScalar kr,ki;
26 6 : Vec xr,xi;
27 6 : BV V;
28 6 : PetscRandom rand;
29 :
30 6 : PetscFunctionBeginUser;
31 6 : PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
32 :
33 6 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
34 6 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
35 6 : if (!flag) m=n;
36 6 : N = n*m;
37 6 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));
38 :
39 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40 : Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
41 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
42 :
43 : /* K is the 2-D Laplacian */
44 6 : PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
45 6 : PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N));
46 6 : PetscCall(MatSetFromOptions(K));
47 6 : PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
48 870 : for (II=Istart;II<Iend;II++) {
49 864 : i = II/n; j = II-i*n;
50 864 : if (i>0) PetscCall(MatSetValue(K,II,II-n,-1.0,INSERT_VALUES));
51 864 : if (i<m-1) PetscCall(MatSetValue(K,II,II+n,-1.0,INSERT_VALUES));
52 864 : if (j>0) PetscCall(MatSetValue(K,II,II-1,-1.0,INSERT_VALUES));
53 864 : if (j<n-1) PetscCall(MatSetValue(K,II,II+1,-1.0,INSERT_VALUES));
54 864 : PetscCall(MatSetValue(K,II,II,4.0,INSERT_VALUES));
55 : }
56 6 : PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
57 6 : PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));
58 :
59 : /* C is the 1-D Laplacian on horizontal lines */
60 6 : PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
61 6 : PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N));
62 6 : PetscCall(MatSetFromOptions(C));
63 6 : PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
64 870 : for (II=Istart;II<Iend;II++) {
65 864 : i = II/n; j = II-i*n;
66 864 : if (j>0) PetscCall(MatSetValue(C,II,II-1,-1.0,INSERT_VALUES));
67 864 : if (j<n-1) PetscCall(MatSetValue(C,II,II+1,-1.0,INSERT_VALUES));
68 864 : PetscCall(MatSetValue(C,II,II,2.0,INSERT_VALUES));
69 : }
70 6 : PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
71 6 : PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
72 :
73 : /* M is a diagonal matrix */
74 6 : PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
75 6 : PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N));
76 6 : PetscCall(MatSetFromOptions(M));
77 6 : PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
78 870 : for (II=Istart;II<Iend;II++) PetscCall(MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES));
79 6 : PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
80 6 : PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));
81 :
82 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83 : Create the eigensolver and set various options
84 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85 :
86 : /*
87 : Create eigensolver context
88 : */
89 6 : PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
90 :
91 : /*
92 : Set matrices and problem type
93 : */
94 6 : A[0] = K; A[1] = C; A[2] = M;
95 6 : PetscCall(PEPSetOperators(pep,3,A));
96 6 : PetscCall(PEPSetProblemType(pep,PEP_HERMITIAN));
97 :
98 : /*
99 : In complex scalars, use a real initial vector since in this example
100 : the matrices are all real, then all vectors generated by the solver
101 : will have a zero imaginary part. This is not really necessary.
102 : */
103 6 : PetscCall(PEPGetBV(pep,&V));
104 6 : PetscCall(BVGetRandomContext(V,&rand));
105 6 : PetscCall(PetscRandomSetInterval(rand,-1,1));
106 :
107 : /*
108 : Set solver parameters at runtime
109 : */
110 6 : PetscCall(PEPSetFromOptions(pep));
111 :
112 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113 : Solve the eigensystem
114 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115 :
116 6 : PetscCall(PEPSolve(pep));
117 :
118 : /*
119 : Optional: Get some information from the solver and display it
120 : */
121 6 : PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL));
122 6 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
123 :
124 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125 : Display solution and clean up
126 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127 :
128 : /* show detailed info unless -terse option is given by user */
129 6 : PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
130 6 : if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
131 : else {
132 0 : PetscCall(PEPGetConverged(pep,&nconv));
133 0 : if (nconv>0) {
134 0 : PetscCall(MatCreateVecs(M,&xr,&xi));
135 : /* display eigenvalues and relative errors */
136 0 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,
137 : "\n k ||P(k)x||/||kx||\n"
138 : " ----------------- ------------------\n"));
139 0 : for (i=0;i<nconv;i++) {
140 : /* get converged eigenpairs */
141 0 : PetscCall(PEPGetEigenpair(pep,i,&kr,&ki,xr,xi));
142 : /* compute the relative error associated to each eigenpair */
143 0 : PetscCall(PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error));
144 : #if defined(PETSC_USE_COMPLEX)
145 0 : re = PetscRealPart(kr);
146 0 : im = PetscImaginaryPart(kr);
147 : #else
148 : re = kr;
149 : im = ki;
150 : #endif
151 0 : if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error));
152 0 : else PetscCall(PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error));
153 : }
154 0 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
155 0 : PetscCall(VecDestroy(&xr));
156 0 : PetscCall(VecDestroy(&xi));
157 : }
158 : }
159 6 : PetscCall(PEPDestroy(&pep));
160 6 : PetscCall(MatDestroy(&M));
161 6 : PetscCall(MatDestroy(&C));
162 6 : PetscCall(MatDestroy(&K));
163 6 : PetscCall(SlepcFinalize());
164 : return 0;
165 : }
166 :
167 : /*TEST
168 :
169 : testset:
170 : args: -pep_nev 4 -pep_ncv 21 -n 12 -terse
171 : output_file: output/ex16_1.out
172 : test:
173 : suffix: 1
174 : args: -pep_type {{toar qarnoldi}}
175 : test:
176 : suffix: 1_linear
177 : args: -pep_type linear -pep_linear_explicitmatrix
178 : requires: !single
179 : test:
180 : suffix: 1_linear_symm
181 : args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_eps_gen_indefinite -pep_scale scalar -pep_linear_bv_definite_tol 1e-12
182 : requires: !single
183 : test:
184 : suffix: 1_stoar
185 : args: -pep_type stoar -pep_scale scalar
186 : requires: double
187 : test:
188 : suffix: 1_stoar_t
189 : args: -pep_type stoar -pep_scale scalar -st_transform
190 : requires: double
191 :
192 : TEST*/
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