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# cptcon

```
NAME
CPTCON - compute the reciprocal of the condition number (in
the 1-norm) of a complex Hermitian positive definite tridi-
agonal matrix using the factorization A = L*D*L**T or A =
U**T*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 tridi-
agonal matrix using the factorization A = L*D*L**T or A =
U**T*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 = 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 CPTTRF.

E       (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiago-
nal 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 rou-
tine.

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, "Effi-
cient Algorithms for Computing the Condition Number of a
Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No.
1, January 1986.
```