NAME

ZGECON - estimate 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 = 1 / ( 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:
= ’1’ or ’O’:  1-norm;
= ’I’:         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 = ’1’ or ’O’, the 1-norm of the original matrix A. If NORM = ’I’, 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

  —  LAPACK version 2.0  —  08 October 1994