Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
6 : This file is part of SLEPc.
7 : SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 : */
10 :
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";
15 :
16 : #include <slepcsvd.h>
17 :
18 : /*
19 : This example computes the singular values of an nxn Grcar matrix,
20 : which is a nonsymmetric Toeplitz matrix:
21 :
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 |
31 :
32 : */
33 :
34 1 : int main(int argc,char **argv)
35 : {
36 1 : Mat A; /* Grcar matrix */
37 1 : SVD svd; /* singular value solver context */
38 1 : PetscInt N=30,Istart,Iend,i,col[5],nconv1,nconv2;
39 1 : PetscScalar value[] = { -1, 1, 1, 1, 1 };
40 1 : PetscReal sigma_1,sigma_n;
41 :
42 1 : PetscFunctionBeginUser;
43 1 : PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
44 :
45 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
46 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%" PetscInt_FMT "\n\n",N));
47 :
48 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49 : Generate the matrix
50 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
51 :
52 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
53 1 : PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
54 1 : PetscCall(MatSetFromOptions(A));
55 :
56 1 : PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
57 31 : for (i=Istart;i<Iend;i++) {
58 30 : col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
59 30 : if (i==0) PetscCall(MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES));
60 30 : else PetscCall(MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES));
61 : }
62 :
63 1 : PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
64 1 : PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
65 :
66 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67 : Create the singular value solver and set the solution method
68 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
69 :
70 : /*
71 : Create singular value context
72 : */
73 1 : PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));
74 :
75 : /*
76 : Set operator
77 : */
78 1 : PetscCall(SVDSetOperators(svd,A,NULL));
79 :
80 : /*
81 : Set solver parameters at runtime
82 : */
83 1 : PetscCall(SVDSetFromOptions(svd));
84 1 : PetscCall(SVDSetDimensions(svd,1,PETSC_DETERMINE,PETSC_DETERMINE));
85 :
86 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87 : Solve the singular value problem
88 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89 :
90 : /*
91 : First request a singular value from one end of the spectrum
92 : */
93 1 : PetscCall(SVDSetWhichSingularTriplets(svd,SVD_LARGEST));
94 1 : PetscCall(SVDSolve(svd));
95 : /*
96 : Get number of converged singular values
97 : */
98 1 : 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 1 : if (nconv1 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL));
104 0 : else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n"));
105 :
106 : /*
107 : Request a singular value from the other end of the spectrum
108 : */
109 1 : PetscCall(SVDSetWhichSingularTriplets(svd,SVD_SMALLEST));
110 1 : PetscCall(SVDSolve(svd));
111 : /*
112 : Get number of converged singular triplets
113 : */
114 1 : 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 1 : if (nconv2 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL));
120 0 : else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n"));
121 :
122 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123 : Display solution and clean up
124 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
125 1 : if (nconv1 > 0 && nconv2 > 0) {
126 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n));
127 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n)));
128 : }
129 :
130 : /*
131 : Free work space
132 : */
133 1 : PetscCall(SVDDestroy(&svd));
134 1 : PetscCall(MatDestroy(&A));
135 1 : PetscCall(SlepcFinalize());
136 : return 0;
137 : }
138 :
139 : /*TEST
140 :
141 : test:
142 : suffix: 1
143 :
144 : TEST*/
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