
ZPTCON(l) ) ZPTCON(l)
NAME
ZPTCON  compute the reciprocal of the condition number (in the 1norm) of a complex Her
mitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A =
U**H*D*U computed by ZPTTRF
SYNOPSIS
SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION D( * ), RWORK( * )
COMPLEX*16 E( * )
PURPOSE
ZPTCON computes the reciprocal of the condition number (in the 1norm) of a complex Her
mitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A =
U**H*D*U computed by ZPTTRF. Norm(inv(A)) is computed by a direct method, and the recip
rocal 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) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the factorization of A, as
computed by ZPTTRF.
E (input) COMPLEX*16 array, dimension (N1)
The (n1) offdiagonal elements of the unit bidiagonal factor U or L from the fac
torization of A, as computed by ZPTTRF.
ANORM (input) DOUBLE PRECISION
The 1norm of the original matrix A.
RCOND (output) DOUBLE PRECISION
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.
RWORK (workspace) DOUBLE PRECISION 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 ZPTCON(l) 
