---
name: "zgecon"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zgecon/3lapack"
---

# zgecon(3lapack)

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

## 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 = 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