Actual source code: ex16.c
slepc-3.19.0 2023-03-31
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,(char*)0,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(MatSetUp(K));
48: PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
49: for (II=Istart;II<Iend;II++) {
50: i = II/n; j = II-i*n;
51: if (i>0) PetscCall(MatSetValue(K,II,II-n,-1.0,INSERT_VALUES));
52: if (i<m-1) PetscCall(MatSetValue(K,II,II+n,-1.0,INSERT_VALUES));
53: if (j>0) PetscCall(MatSetValue(K,II,II-1,-1.0,INSERT_VALUES));
54: if (j<n-1) PetscCall(MatSetValue(K,II,II+1,-1.0,INSERT_VALUES));
55: PetscCall(MatSetValue(K,II,II,4.0,INSERT_VALUES));
56: }
57: PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
58: PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));
60: /* C is the 1-D Laplacian on horizontal lines */
61: PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
62: PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N));
63: PetscCall(MatSetFromOptions(C));
64: PetscCall(MatSetUp(C));
65: PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
66: for (II=Istart;II<Iend;II++) {
67: i = II/n; j = II-i*n;
68: if (j>0) PetscCall(MatSetValue(C,II,II-1,-1.0,INSERT_VALUES));
69: if (j<n-1) PetscCall(MatSetValue(C,II,II+1,-1.0,INSERT_VALUES));
70: PetscCall(MatSetValue(C,II,II,2.0,INSERT_VALUES));
71: }
72: PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
73: PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
75: /* M is a diagonal matrix */
76: PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
77: PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N));
78: PetscCall(MatSetFromOptions(M));
79: PetscCall(MatSetUp(M));
80: PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
81: for (II=Istart;II<Iend;II++) PetscCall(MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES));
82: PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
83: PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));
85: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
86: Create the eigensolver and set various options
87: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: /*
90: Create eigensolver context
91: */
92: PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
94: /*
95: Set matrices and problem type
96: */
97: A[0] = K; A[1] = C; A[2] = M;
98: PetscCall(PEPSetOperators(pep,3,A));
99: PetscCall(PEPSetProblemType(pep,PEP_HERMITIAN));
101: /*
102: In complex scalars, use a real initial vector since in this example
103: the matrices are all real, then all vectors generated by the solver
104: will have a zero imaginary part. This is not really necessary.
105: */
106: PetscCall(PEPGetBV(pep,&V));
107: PetscCall(BVGetRandomContext(V,&rand));
108: PetscCall(PetscRandomSetInterval(rand,-1,1));
110: /*
111: Set solver parameters at runtime
112: */
113: PetscCall(PEPSetFromOptions(pep));
115: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: Solve the eigensystem
117: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119: PetscCall(PEPSolve(pep));
121: /*
122: Optional: Get some information from the solver and display it
123: */
124: PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL));
125: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Display solution and clean up
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: /* show detailed info unless -terse option is given by user */
132: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
133: if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
134: else {
135: PetscCall(PEPGetConverged(pep,&nconv));
136: if (nconv>0) {
137: PetscCall(MatCreateVecs(M,&xr,&xi));
138: /* display eigenvalues and relative errors */
139: PetscCall(PetscPrintf(PETSC_COMM_WORLD,
140: "\n k ||P(k)x||/||kx||\n"
141: " ----------------- ------------------\n"));
142: for (i=0;i<nconv;i++) {
143: /* get converged eigenpairs */
144: PetscCall(PEPGetEigenpair(pep,i,&kr,&ki,xr,xi));
145: /* compute the relative error associated to each eigenpair */
146: PetscCall(PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error));
147: #if defined(PETSC_USE_COMPLEX)
148: re = PetscRealPart(kr);
149: im = PetscImaginaryPart(kr);
150: #else
151: re = kr;
152: im = ki;
153: #endif
154: if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error));
155: else PetscCall(PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error));
156: }
157: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
158: PetscCall(VecDestroy(&xr));
159: PetscCall(VecDestroy(&xi));
160: }
161: }
162: PetscCall(PEPDestroy(&pep));
163: PetscCall(MatDestroy(&M));
164: PetscCall(MatDestroy(&C));
165: PetscCall(MatDestroy(&K));
166: PetscCall(SlepcFinalize());
167: return 0;
168: }
170: /*TEST
172: testset:
173: args: -pep_nev 4 -pep_ncv 21 -n 12 -terse
174: output_file: output/ex16_1.out
175: test:
176: suffix: 1
177: args: -pep_type {{toar qarnoldi}}
178: test:
179: suffix: 1_linear
180: args: -pep_type linear -pep_linear_explicitmatrix
181: requires: !single
182: test:
183: suffix: 1_linear_symm
184: args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_eps_gen_indefinite -pep_scale scalar -pep_linear_bv_definite_tol 1e-12
185: requires: !single
186: test:
187: suffix: 1_stoar
188: args: -pep_type stoar -pep_scale scalar
189: requires: double !cuda
190: test:
191: suffix: 1_stoar_t
192: args: -pep_type stoar -pep_scale scalar -st_transform
193: requires: double !cuda
195: TEST*/