Homepage > Man Pages > Category > Subroutines
Homepage > Man Pages > Name > L

# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the

```NAME
LAPACK-3  -  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 = 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 routine (version 3.2)     March 2011                       LAPACK-3(3)
```