1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
|
.TH SPTCON l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
SPTCON - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF
.SH SYNOPSIS
.TP 19
SUBROUTINE SPTCON(
N, D, E, ANORM, RCOND, WORK, INFO )
.TP 19
.ti +4
INTEGER
INFO, N
.TP 19
.ti +4
REAL
ANORM, RCOND
.TP 19
.ti +4
REAL
D( * ), E( * ), WORK( * )
.SH PURPOSE
SPTCON computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF.
Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
.br
RCOND = 1 / (ANORM * norm(inv(A))).
.br
.SH ARGUMENTS
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
D (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by SPTTRF.
.TP 8
E (input) REAL array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization of A, as computed by SPTTRF.
.TP 8
ANORM (input) REAL
The 1-norm of the original matrix A.
.TP 8
RCOND (output) REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
1-norm of inv(A) computed in this routine.
.TP 8
WORK (workspace) REAL array, dimension (N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.SH FURTHER DETAILS
The method used is described in Nicholas J. Higham, "Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
|
