Actual source code: ex8.c
slepc-main 2024-11-15
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[] = "Estimates the 2-norm condition number of a matrix A, that is, the ratio of the largest to the smallest singular values of A. "
12: "The matrix is a Grcar matrix.\n\n"
13: "The command line options are:\n"
14: " -n <n>, where <n> = matrix dimension.\n\n";
16: #include <slepcsvd.h>
18: /*
19: This example computes the singular values of an nxn Grcar matrix,
20: which is a nonsymmetric Toeplitz matrix:
22: | 1 1 1 1 |
23: | -1 1 1 1 1 |
24: | -1 1 1 1 1 |
25: | . . . . . |
26: A = | . . . . . |
27: | -1 1 1 1 1 |
28: | -1 1 1 1 |
29: | -1 1 1 |
30: | -1 1 |
32: */
34: int main(int argc,char **argv)
35: {
36: Mat A; /* Grcar matrix */
37: SVD svd; /* singular value solver context */
38: PetscInt N=30,Istart,Iend,i,col[5],nconv1,nconv2;
39: PetscScalar value[] = { -1, 1, 1, 1, 1 };
40: PetscReal sigma_1,sigma_n;
42: PetscFunctionBeginUser;
43: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
45: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
46: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%" PetscInt_FMT "\n\n",N));
48: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: Generate the matrix
50: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
52: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
53: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
54: PetscCall(MatSetFromOptions(A));
56: PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
57: for (i=Istart;i<Iend;i++) {
58: col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
59: if (i==0) PetscCall(MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES));
60: else PetscCall(MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES));
61: }
63: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
64: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
66: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: Create the singular value solver and set the solution method
68: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
70: /*
71: Create singular value context
72: */
73: PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));
75: /*
76: Set operator
77: */
78: PetscCall(SVDSetOperators(svd,A,NULL));
80: /*
81: Set solver parameters at runtime
82: */
83: PetscCall(SVDSetFromOptions(svd));
84: PetscCall(SVDSetDimensions(svd,1,PETSC_DETERMINE,PETSC_DETERMINE));
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: Solve the singular value problem
88: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
90: /*
91: First request a singular value from one end of the spectrum
92: */
93: PetscCall(SVDSetWhichSingularTriplets(svd,SVD_LARGEST));
94: PetscCall(SVDSolve(svd));
95: /*
96: Get number of converged singular values
97: */
98: PetscCall(SVDGetConverged(svd,&nconv1));
99: /*
100: Get converged singular values: largest singular value is stored in sigma_1.
101: In this example, we are not interested in the singular vectors
102: */
103: if (nconv1 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL));
104: else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n"));
106: /*
107: Request a singular value from the other end of the spectrum
108: */
109: PetscCall(SVDSetWhichSingularTriplets(svd,SVD_SMALLEST));
110: PetscCall(SVDSolve(svd));
111: /*
112: Get number of converged singular triplets
113: */
114: PetscCall(SVDGetConverged(svd,&nconv2));
115: /*
116: Get converged singular values: smallest singular value is stored in sigma_n.
117: As before, we are not interested in the singular vectors
118: */
119: if (nconv2 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL));
120: else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n"));
122: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123: Display solution and clean up
124: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
125: if (nconv1 > 0 && nconv2 > 0) {
126: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n));
127: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n)));
128: }
130: /*
131: Free work space
132: */
133: PetscCall(SVDDestroy(&svd));
134: PetscCall(MatDestroy(&A));
135: PetscCall(SlepcFinalize());
136: return 0;
137: }
139: /*TEST
141: test:
142: suffix: 1
144: TEST*/