Actual source code: ex8.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2011, Universitat 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[] = "Estimates the 2-norm condition number of a matrix A, that is, the ratio of the largest to the smallest singular values of A. "
23: "The matrix is a Grcar matrix.\n\n"
24: "The command line options are:\n"
25: " -n <n>, where <n> = matrix dimension.\n\n";
27: #include <slepcsvd.h>
29: /*
30: This example computes the singular values of an nxn Grcar matrix,
31: which is a nonsymmetric Toeplitz matrix:
33: | 1 1 1 1 |
34: | -1 1 1 1 1 |
35: | -1 1 1 1 1 |
36: | . . . . . |
37: A = | . . . . . |
38: | -1 1 1 1 1 |
39: | -1 1 1 1 |
40: | -1 1 1 |
41: | -1 1 |
43: */
47: int main(int argc,char **argv)
48: {
49: Mat A; /* Grcar matrix */
50: SVD svd; /* singular value solver context */
51: PetscInt N=30,Istart,Iend,i,col[5],nconv1,nconv2;
52: PetscScalar value[] = { -1, 1, 1, 1, 1 };
53: PetscReal sigma_1,sigma_n;
56: SlepcInitialize(&argc,&argv,(char*)0,help);
58: PetscOptionsGetInt(PETSC_NULL,"-n",&N,PETSC_NULL);
59: PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%D\n\n",N);
61: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
62: Generate the matrix
63: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
65: MatCreate(PETSC_COMM_WORLD,&A);
66: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
67: MatSetFromOptions(A);
69: MatGetOwnershipRange(A,&Istart,&Iend);
70: for (i=Istart;i<Iend;i++) {
71: col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
72: if (i==0) {
73: MatSetValues(A,1,&i,4,col+1,value+1,INSERT_VALUES);
74: } else {
75: MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
76: }
77: }
79: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
80: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Create the singular value solver and set the solution method
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: /*
87: Create singular value context
88: */
89: SVDCreate(PETSC_COMM_WORLD,&svd);
91: /*
92: Set operator
93: */
94: SVDSetOperator(svd,A);
96: /*
97: Set solver parameters at runtime
98: */
99: SVDSetFromOptions(svd);
100: SVDSetDimensions(svd,1,PETSC_IGNORE,PETSC_IGNORE);
102: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: Solve the singular value problem
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
106: /*
107: First request a singular value from one end of the spectrum
108: */
109: SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
110: SVDSolve(svd);
111: /*
112: Get number of converged singular values
113: */
114: SVDGetConverged(svd,&nconv1);
115: /*
116: Get converged singular values: largest singular value is stored in sigma_1.
117: In this example, we are not interested in the singular vectors
118: */
119: if (nconv1 > 0) {
120: SVDGetSingularTriplet(svd,0,&sigma_1,PETSC_NULL,PETSC_NULL);
121: } else {
122: PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
123: }
125: /*
126: Request a singular value from the other end of the spectrum
127: */
128: SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
129: SVDSolve(svd);
130: /*
131: Get number of converged eigenpairs
132: */
133: SVDGetConverged(svd,&nconv2);
134: /*
135: Get converged singular values: smallest singular value is stored in sigma_n.
136: As before, we are not interested in the singular vectors
137: */
138: if (nconv2 > 0) {
139: SVDGetSingularTriplet(svd,0,&sigma_n,PETSC_NULL,PETSC_NULL);
140: } else {
141: PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
142: }
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Display solution and clean up
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: if (nconv1 > 0 && nconv2 > 0) {
148: PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%6F, sigma_n=%6F\n",sigma_1,sigma_n);
149: PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%6F\n\n",sigma_1/sigma_n);
150: }
151:
152: /*
153: Free work space
154: */
155: SVDDestroy(&svd);
156: MatDestroy(&A);
157: SlepcFinalize();
158: return 0;
159: }