# zgecon (l) - Linux Manuals

## NAME

ZGECON - estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF

## SYNOPSIS

SUBROUTINE ZGECON(
NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO )

CHARACTER NORM

INTEGER INFO, LDA, N

DOUBLE PRECISION ANORM, RCOND

DOUBLE PRECISION RWORK( * )

COMPLEX*16 A( LDA, * ), WORK( * )

## PURPOSE

ZGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as

RCOND norm(A) norm(inv(A)) ).

## ARGUMENTS

NORM (input) CHARACTER*1
Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
= aq1aq or aqOaq: 1-norm;
= aqIaq: Infinity-norm.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U as computed by ZGETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM (input) DOUBLE PRECISION
If NORM = aq1aq or aqOaq, the 1-norm of the original matrix A. If NORM = aqIaq, the infinity-norm of the original matrix A.
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value