# cptcon (l) - Linux Man Pages

## NAME

CPTCON - computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF

## SYNOPSIS

SUBROUTINE CPTCON(
N, D, E, ANORM, RCOND, RWORK, INFO )

INTEGER INFO, N

REAL ANORM, RCOND

REAL D( * ), RWORK( * )

COMPLEX E( * )

## PURPOSE

CPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as

RCOND (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 CPTTRF.
E (input) COMPLEX 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 CPTTRF.
ANORM (input) REAL
The 1-norm 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 1-norm of inv(A) computed in this routine.
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th 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.