Actual source code: ex13.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7:
8: SLEPc is free software: you can redistribute it and/or modify it under the
9: terms of version 3 of the GNU Lesser General Public License as published by
10: the Free Software Foundation.
12: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
13: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
14: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
15: more details.
17: You should have received a copy of the GNU Lesser General Public License
18: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
19: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
20: */
22: static char help[] = "Generalized Symmetric eigenproblem.\n\n"
23: "The problem is Ax = lambda Bx, with:\n"
24: " A = Laplacian operator in 2-D\n"
25: " B = diagonal matrix with all values equal to 4 except nulldim zeros\n\n"
26: "The command line options are:\n"
27: " -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
28: " -m <m>, where <m> = number of grid subdivisions in y dimension.\n"
29: " -nulldim <k>, where <k> = dimension of the nullspace of B.\n\n";
31: #include slepceps.h
35: int main( int argc, char **argv )
36: {
37: Mat A, B; /* matrices */
38: EPS eps; /* eigenproblem solver context */
39: ST st; /* spectral transformation context */
40: const EPSType type;
41: PetscReal error, tol, re, im;
42: PetscScalar kr, ki;
44: PetscInt N, n=10, m, Istart, Iend, II, nev, maxit, i, j, its, nconv, nulldim=0;
45: PetscTruth flag;
47: SlepcInitialize(&argc,&argv,(char*)0,help);
49: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
50: PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);
51: if(!flag) m=n;
52: N = n*m;
53: PetscOptionsGetInt(PETSC_NULL,"-nulldim",&nulldim,PETSC_NULL);
54: PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%d (%dx%d grid), null(B)=%d\n\n",N,n,m,nulldim);
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Compute the matrices that define the eigensystem, Ax=kBx
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: MatCreate(PETSC_COMM_WORLD,&A);
61: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
62: MatSetFromOptions(A);
63:
64: MatCreate(PETSC_COMM_WORLD,&B);
65: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
66: MatSetFromOptions(B);
68: MatGetOwnershipRange(A,&Istart,&Iend);
69: for( II=Istart; II<Iend; II++ ) {
70: i = II/n; j = II-i*n;
71: if(i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
72: if(i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
73: if(j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
74: if(j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
75: MatSetValue(A,II,II,4.0,INSERT_VALUES);
76: if (II>=nulldim) { MatSetValue(B,II,II,4.0,INSERT_VALUES); }
77: }
79: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
80: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
81: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
82: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Create the eigensolver and set various options
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: /*
89: Create eigensolver context
90: */
91: EPSCreate(PETSC_COMM_WORLD,&eps);
93: /*
94: Set operators. In this case, it is a generalized eigenvalue problem
95: */
96: EPSSetOperators(eps,A,B);
97: EPSSetProblemType(eps,EPS_GHEP);
99: /*
100: Use shift-and-invert to avoid solving linear systems with a singular B
101: in case nulldim>0
102: */
103: EPSGetST(eps,&st);
104: EPSSetTarget(eps,0.0);
105: EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
106: STSetType(st,STSINVERT);
108: /*
109: Set solver parameters at runtime
110: */
111: EPSSetFromOptions(eps);
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Solve the eigensystem
115: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
117: EPSSolve(eps);
118: EPSGetIterationNumber(eps, &its);
119: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);
121: /*
122: Optional: Get some information from the solver and display it
123: */
124: EPSGetType(eps,&type);
125: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
126: EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);
127: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
128: EPSGetTolerances(eps,&tol,&maxit);
129: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: Display solution and clean up
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: /*
136: Get number of converged approximate eigenpairs
137: */
138: EPSGetConverged(eps,&nconv);
139: PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);
140:
142: if (nconv>0) {
143: /*
144: Display eigenvalues and relative errors
145: */
146: PetscPrintf(PETSC_COMM_WORLD,
147: " k ||Ax-kBx||/||kx||\n"
148: " ----------------- ------------------\n" );
150: for( i=0; i<nconv; i++ ) {
151: /*
152: Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
153: ki (imaginary part)
154: */
155: EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
156: /*
157: Compute the relative error associated to each eigenpair
158: */
159: EPSComputeRelativeError(eps,i,&error);
161: #ifdef PETSC_USE_COMPLEX
162: re = PetscRealPart(kr);
163: im = PetscImaginaryPart(kr);
164: #else
165: re = kr;
166: im = ki;
167: #endif
168: if (im!=0.0) {
169: PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);
170: } else {
171: PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",re,error);
172: }
173: }
174: PetscPrintf(PETSC_COMM_WORLD,"\n" );
175: }
176:
177: /*
178: Free work space
179: */
180: EPSDestroy(eps);
181: MatDestroy(A);
182: MatDestroy(B);
183: SlepcFinalize();
184: return 0;
185: }