Actual source code: ex8.c
slepc-3.18.2 2023-01-26
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;
43: SlepcInitialize(&argc,&argv,(char*)0,help);
45: PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
46: 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: MatCreate(PETSC_COMM_WORLD,&A);
53: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
54: MatSetFromOptions(A);
55: MatSetUp(A);
57: MatGetOwnershipRange(A,&Istart,&Iend);
58: for (i=Istart;i<Iend;i++) {
59: col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
60: if (i==0) MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES);
61: else MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
62: }
64: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
65: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
67: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
68: Create the singular value solver and set the solution method
69: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
71: /*
72: Create singular value context
73: */
74: SVDCreate(PETSC_COMM_WORLD,&svd);
76: /*
77: Set operator
78: */
79: SVDSetOperators(svd,A,NULL);
81: /*
82: Set solver parameters at runtime
83: */
84: SVDSetFromOptions(svd);
85: SVDSetDimensions(svd,1,PETSC_DEFAULT,PETSC_DEFAULT);
87: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88: Solve the singular value problem
89: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
91: /*
92: First request a singular value from one end of the spectrum
93: */
94: SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
95: SVDSolve(svd);
96: /*
97: Get number of converged singular values
98: */
99: SVDGetConverged(svd,&nconv1);
100: /*
101: Get converged singular values: largest singular value is stored in sigma_1.
102: In this example, we are not interested in the singular vectors
103: */
104: if (nconv1 > 0) SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL);
105: else PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
107: /*
108: Request a singular value from the other end of the spectrum
109: */
110: SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
111: SVDSolve(svd);
112: /*
113: Get number of converged singular triplets
114: */
115: SVDGetConverged(svd,&nconv2);
116: /*
117: Get converged singular values: smallest singular value is stored in sigma_n.
118: As before, we are not interested in the singular vectors
119: */
120: if (nconv2 > 0) SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL);
121: else PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
123: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124: Display solution and clean up
125: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126: if (nconv1 > 0 && nconv2 > 0) {
127: PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n);
128: PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n));
129: }
131: /*
132: Free work space
133: */
134: SVDDestroy(&svd);
135: MatDestroy(&A);
136: SlepcFinalize();
137: return 0;
138: }
140: /*TEST
142: test:
143: suffix: 1
145: TEST*/