.TH CPTCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
CPTCON - 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
.SH SYNOPSIS
.TP 19
SUBROUTINE CPTCON(
N, D, E, ANORM, RCOND, RWORK, INFO )
.TP 19
.ti +4
INTEGER
INFO, N
.TP 19
.ti +4
REAL
ANORM, RCOND
.TP 19
.ti +4
REAL
D( * ), RWORK( * )
.TP 19
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COMPLEX
E( * )
.SH 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
.br
RCOND = 1 / (ANORM * norm(inv(A))).
.br
.SH ARGUMENTS
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
D (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by CPTTRF.
.TP 8
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.
.TP 8
ANORM (input) REAL
The 1-norm of the original matrix A.
.TP 8
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.
.TP 8
RWORK (workspace) REAL array, dimension (N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.SH 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.