
SPTCON(l) ) SPTCON(l)
NAME
SPTCON  compute the reciprocal of the condition number (in the 1norm) of a real symmet
ric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A =
U**T*D*U computed by SPTTRF
SYNOPSIS
SUBROUTINE SPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
INTEGER INFO, N
REAL ANORM, RCOND
REAL D( * ), E( * ), WORK( * )
PURPOSE
SPTCON computes the reciprocal of the condition number (in the 1norm) 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
RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTS
N (input) INTEGER
The order of the matrix A. N >= 0.
D (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the factorization of A, as
computed by SPTTRF.
E (input) REAL array, dimension (N1)
The (n1) offdiagonal elements of the unit bidiagonal factor U or L from the fac
torization of A, as computed by SPTTRF.
ANORM (input) REAL
The 1norm of the original matrix A.
RCOND (output) REAL
The reciprocal of the condition number of the matrix A, computed as RCOND =
1/(ANORM * AINVNM), where AINVNM is the 1norm of inv(A) computed in this routine.
WORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
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.
LAPACK version 3.0 15 June 2000 SPTCON(l) 
