1SGTCON(1)                LAPACK routine (version 3.1)                SGTCON(1)
2
3
4

NAME

6       SGTCON  -  the reciprocal of the condition number of a real tridiagonal
7       matrix A using the LU factorization as computed by SGTTRF
8

SYNOPSIS

10       SUBROUTINE SGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM,  RCOND,  WORK,
11                          IWORK, INFO )
12
13           CHARACTER      NORM
14
15           INTEGER        INFO, N
16
17           REAL           ANORM, RCOND
18
19           INTEGER        IPIV( * ), IWORK( * )
20
21           REAL           D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
22

PURPOSE

24       SGTCON  estimates  the  reciprocal  of  the  condition number of a real
25       tridiagonal matrix A using the LU factorization as computed by SGTTRF.
26
27       An estimate is obtained for norm(inv(A)), and  the  reciprocal  of  the
28       condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
29
30

ARGUMENTS

32       NORM    (input) CHARACTER*1
33               Specifies  whether the 1-norm condition number or the infinity-
34               norm condition number is required:
35               = '1' or 'O':  1-norm;
36               = 'I':         Infinity-norm.
37
38       N       (input) INTEGER
39               The order of the matrix A.  N >= 0.
40
41       DL      (input) REAL array, dimension (N-1)
42               The (n-1) multipliers that define the matrix L from the LU fac‐
43               torization of A as computed by SGTTRF.
44
45       D       (input) REAL array, dimension (N)
46               The  n  diagonal elements of the upper triangular matrix U from
47               the LU factorization of A.
48
49       DU      (input) REAL array, dimension (N-1)
50               The (n-1) elements of the first superdiagonal of U.
51
52       DU2     (input) REAL array, dimension (N-2)
53               The (n-2) elements of the second superdiagonal of U.
54
55       IPIV    (input) INTEGER array, dimension (N)
56               The pivot indices; for 1 <= i <= n, row i  of  the  matrix  was
57               interchanged with row IPIV(i).  IPIV(i) will always be either i
58               or i+1; IPIV(i)  =  i  indicates  a  row  interchange  was  not
59               required.
60
61       ANORM   (input) REAL
62               If  NORM = '1' or 'O', the 1-norm of the original matrix A.  If
63               NORM = 'I', the infinity-norm of the original matrix A.
64
65       RCOND   (output) REAL
66               The reciprocal of the condition number of the  matrix  A,  com‐
67               puted  as  RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
68               mate of the 1-norm of inv(A) computed in this routine.
69
70       WORK    (workspace) REAL array, dimension (2*N)
71
72       IWORK   (workspace) INTEGER array, dimension (N)
73
74       INFO    (output) INTEGER
75               = 0:  successful exit
76               < 0:  if INFO = -i, the i-th argument had an illegal value
77
78
79
80 LAPACK routine (version 3.1)    November 2006                       SGTCON(1)
Impressum