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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H

```NAME
LAPACK-3  -  estimates  the  reciprocal  of  the  condition number of a
complex Hermitian matrix A using the factorization A = U*D*U**H or A  =
L*D*L**H computed by ZHETRF

SYNOPSIS
SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO )

CHARACTER      UPLO

INTEGER        INFO, LDA, N

DOUBLE         PRECISION ANORM, RCOND

INTEGER        IPIV( * )

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

PURPOSE
ZHECON  estimates  the  reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
computed by ZHETRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS
UPLO    (input) CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**H;
= 'L':  Lower triangular, form is A = L*D*L**H.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

A       (input) COMPLEX*16 array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

IPIV    (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF.

ANORM   (input) DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND   (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK    (workspace) COMPLEX*16 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)
```