Actual source code: ex16.c
slepc-3.16.1 2021-11-17
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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;
31: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
33: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
34: PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
35: if (!flag) m=n;
36: N = n*m;
37: PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%D (%Dx%D 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: MatCreate(PETSC_COMM_WORLD,&K);
45: MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N);
46: MatSetFromOptions(K);
47: MatSetUp(K);
48: MatGetOwnershipRange(K,&Istart,&Iend);
49: for (II=Istart;II<Iend;II++) {
50: i = II/n; j = II-i*n;
51: if (i>0) { MatSetValue(K,II,II-n,-1.0,INSERT_VALUES); }
52: if (i<m-1) { MatSetValue(K,II,II+n,-1.0,INSERT_VALUES); }
53: if (j>0) { MatSetValue(K,II,II-1,-1.0,INSERT_VALUES); }
54: if (j<n-1) { MatSetValue(K,II,II+1,-1.0,INSERT_VALUES); }
55: MatSetValue(K,II,II,4.0,INSERT_VALUES);
56: }
57: MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);
58: MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);
60: /* C is the 1-D Laplacian on horizontal lines */
61: MatCreate(PETSC_COMM_WORLD,&C);
62: MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
63: MatSetFromOptions(C);
64: MatSetUp(C);
65: MatGetOwnershipRange(C,&Istart,&Iend);
66: for (II=Istart;II<Iend;II++) {
67: i = II/n; j = II-i*n;
68: if (j>0) { MatSetValue(C,II,II-1,-1.0,INSERT_VALUES); }
69: if (j<n-1) { MatSetValue(C,II,II+1,-1.0,INSERT_VALUES); }
70: MatSetValue(C,II,II,2.0,INSERT_VALUES);
71: }
72: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
73: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
75: /* M is a diagonal matrix */
76: MatCreate(PETSC_COMM_WORLD,&M);
77: MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N);
78: MatSetFromOptions(M);
79: MatSetUp(M);
80: MatGetOwnershipRange(M,&Istart,&Iend);
81: for (II=Istart;II<Iend;II++) {
82: MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES);
83: }
84: MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
85: MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
87: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88: Create the eigensolver and set various options
89: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
91: /*
92: Create eigensolver context
93: */
94: PEPCreate(PETSC_COMM_WORLD,&pep);
96: /*
97: Set matrices and problem type
98: */
99: A[0] = K; A[1] = C; A[2] = M;
100: PEPSetOperators(pep,3,A);
101: PEPSetProblemType(pep,PEP_HERMITIAN);
103: /*
104: In complex scalars, use a real initial vector since in this example
105: the matrices are all real, then all vectors generated by the solver
106: will have a zero imaginary part. This is not really necessary.
107: */
108: PEPGetBV(pep,&V);
109: BVGetRandomContext(V,&rand);
110: PetscRandomSetInterval(rand,-1,1);
112: /*
113: Set solver parameters at runtime
114: */
115: PEPSetFromOptions(pep);
117: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118: Solve the eigensystem
119: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
121: PEPSolve(pep);
123: /*
124: Optional: Get some information from the solver and display it
125: */
126: PEPGetDimensions(pep,&nev,NULL,NULL);
127: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Display solution and clean up
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133: /* show detailed info unless -terse option is given by user */
134: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
135: if (terse) {
136: PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
137: } else {
138: PEPGetConverged(pep,&nconv);
139: if (nconv>0) {
140: MatCreateVecs(M,&xr,&xi);
141: /* display eigenvalues and relative errors */
142: PetscPrintf(PETSC_COMM_WORLD,
143: "\n k ||P(k)x||/||kx||\n"
144: " ----------------- ------------------\n");
145: for (i=0;i<nconv;i++) {
146: /* get converged eigenpairs */
147: PEPGetEigenpair(pep,i,&kr,&ki,xr,xi);
148: /* compute the relative error associated to each eigenpair */
149: PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error);
150: #if defined(PETSC_USE_COMPLEX)
151: re = PetscRealPart(kr);
152: im = PetscImaginaryPart(kr);
153: #else
154: re = kr;
155: im = ki;
156: #endif
157: if (im!=0.0) {
158: PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error);
159: } else {
160: PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error);
161: }
162: }
163: PetscPrintf(PETSC_COMM_WORLD,"\n");
164: VecDestroy(&xr);
165: VecDestroy(&xi);
166: }
167: }
168: PEPDestroy(&pep);
169: MatDestroy(&M);
170: MatDestroy(&C);
171: MatDestroy(&K);
172: SlepcFinalize();
173: return ierr;
174: }
176: /*TEST
178: testset:
179: args: -pep_nev 4 -pep_ncv 21 -n 12 -terse
180: output_file: output/ex16_1.out
181: test:
182: suffix: 1
183: args: -pep_type {{toar qarnoldi}}
184: test:
185: suffix: 1_linear
186: args: -pep_type linear -pep_linear_explicitmatrix
187: requires: !single
188: test:
189: suffix: 1_linear_symm
190: args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_eps_gen_indefinite -pep_scale scalar -pep_linear_bv_definite_tol 1e-12
191: requires: !single
192: test:
193: suffix: 1_stoar
194: args: -pep_type stoar -pep_scale scalar
195: requires: double !cuda
196: test:
197: suffix: 1_stoar_t
198: args: -pep_type stoar -pep_scale scalar -st_transform
199: requires: double !cuda
201: TEST*/