Actual source code: ex16.c
slepc-main 2024-11-09
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: */
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";
16: #include <slepcpep.h>
18: int main(int argc,char **argv)
19: {
20: Mat M,C,K,A[3]; /* problem matrices */
21: PEP pep; /* polynomial eigenproblem solver context */
22: PetscInt N,n=10,m,Istart,Iend,II,nev,i,j,nconv;
23: PetscBool flag,terse;
24: PetscReal error,re,im;
25: PetscScalar kr,ki;
26: Vec xr,xi;
27: BV V;
28: PetscRandom rand;
30: PetscFunctionBeginUser;
31: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
33: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
34: PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
35: if (!flag) m=n;
36: N = n*m;
37: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));
39: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40: Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
41: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
43: /* K is the 2-D Laplacian */
44: PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
45: PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N));
46: PetscCall(MatSetFromOptions(K));
47: PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
48: for (II=Istart;II<Iend;II++) {
49: i = II/n; j = II-i*n;
50: if (i>0) PetscCall(MatSetValue(K,II,II-n,-1.0,INSERT_VALUES));
51: if (i<m-1) PetscCall(MatSetValue(K,II,II+n,-1.0,INSERT_VALUES));
52: if (j>0) PetscCall(MatSetValue(K,II,II-1,-1.0,INSERT_VALUES));
53: if (j<n-1) PetscCall(MatSetValue(K,II,II+1,-1.0,INSERT_VALUES));
54: PetscCall(MatSetValue(K,II,II,4.0,INSERT_VALUES));
55: }
56: PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
57: PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));
59: /* C is the 1-D Laplacian on horizontal lines */
60: PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
61: PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N));
62: PetscCall(MatSetFromOptions(C));
63: PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
64: for (II=Istart;II<Iend;II++) {
65: i = II/n; j = II-i*n;
66: if (j>0) PetscCall(MatSetValue(C,II,II-1,-1.0,INSERT_VALUES));
67: if (j<n-1) PetscCall(MatSetValue(C,II,II+1,-1.0,INSERT_VALUES));
68: PetscCall(MatSetValue(C,II,II,2.0,INSERT_VALUES));
69: }
70: PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
71: PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
73: /* M is a diagonal matrix */
74: PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
75: PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N));
76: PetscCall(MatSetFromOptions(M));
77: PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
78: for (II=Istart;II<Iend;II++) PetscCall(MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES));
79: PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
80: PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Create the eigensolver and set various options
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: /*
87: Create eigensolver context
88: */
89: PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
91: /*
92: Set matrices and problem type
93: */
94: A[0] = K; A[1] = C; A[2] = M;
95: PetscCall(PEPSetOperators(pep,3,A));
96: PetscCall(PEPSetProblemType(pep,PEP_HERMITIAN));
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: PetscCall(PEPGetBV(pep,&V));
104: PetscCall(BVGetRandomContext(V,&rand));
105: PetscCall(PetscRandomSetInterval(rand,-1,1));
107: /*
108: Set solver parameters at runtime
109: */
110: PetscCall(PEPSetFromOptions(pep));
112: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: Solve the eigensystem
114: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116: PetscCall(PEPSolve(pep));
118: /*
119: Optional: Get some information from the solver and display it
120: */
121: PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL));
122: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Display solution and clean up
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128: /* show detailed info unless -terse option is given by user */
129: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
130: if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
131: else {
132: PetscCall(PEPGetConverged(pep,&nconv));
133: if (nconv>0) {
134: PetscCall(MatCreateVecs(M,&xr,&xi));
135: /* display eigenvalues and relative errors */
136: PetscCall(PetscPrintf(PETSC_COMM_WORLD,
137: "\n k ||P(k)x||/||kx||\n"
138: " ----------------- ------------------\n"));
139: for (i=0;i<nconv;i++) {
140: /* get converged eigenpairs */
141: PetscCall(PEPGetEigenpair(pep,i,&kr,&ki,xr,xi));
142: /* compute the relative error associated to each eigenpair */
143: PetscCall(PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error));
144: #if defined(PETSC_USE_COMPLEX)
145: re = PetscRealPart(kr);
146: im = PetscImaginaryPart(kr);
147: #else
148: re = kr;
149: im = ki;
150: #endif
151: if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error));
152: else PetscCall(PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error));
153: }
154: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
155: PetscCall(VecDestroy(&xr));
156: PetscCall(VecDestroy(&xi));
157: }
158: }
159: PetscCall(PEPDestroy(&pep));
160: PetscCall(MatDestroy(&M));
161: PetscCall(MatDestroy(&C));
162: PetscCall(MatDestroy(&K));
163: PetscCall(SlepcFinalize());
164: return 0;
165: }
167: /*TEST
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
192: TEST*/