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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes the reciprocal pivot growth factor norm(A)/norm(U)

```NAME
LAPACK-3 - computes the reciprocal pivot growth factor norm(A)/norm(U)

SYNOPSIS
DOUBLE PRECISION FUNCTION  ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, LDAF,
WORK )

IMPLICIT     NONE

CHARACTER*1  UPLO

INTEGER      NCOLS, LDA, LDAF

COMPLEX*16   A( LDA, * ), AF( LDAF, * )

DOUBLE       PRECISION WORK( * )

PURPOSE
ZLA_PORPVGRW   computes   the   reciprocal    pivot    growth    factor
norm(A)/norm(U). The "max absolute element" norm is used. If this is
much less than 1, the stability of the LU factorization of the
(equilibrated) matrix A could be poor. This also means that the
solution X, estimated condition numbers, and error bounds could be
unreliable.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

NCOLS   (input) INTEGER
The number of columns of the matrix A. NCOLS >= 0.

A       (input) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A.

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

AF      (input) COMPLEX*16 array, dimension (LDAF,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, as computed by ZPOTRF.

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

WORK    (input) COMPLEX*16 array, dimension (2*N)

LAPACK routine (version 3.2.2)March 2011                       LAPACK-3(3)
```