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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_SYRPVGRW(  UPLO,  N,  INFO,  A, LDA, AF,
LDAF, IPIV, WORK )

IMPLICIT     NONE

CHARACTER*1  UPLO

INTEGER      N, INFO, LDA, LDAF

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

DOUBLE       PRECISION WORK( * )

INTEGER      IPIV( * )

PURPOSE
ZLA_SYRPVGRW   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.

N       (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.

INFO    (input) INTEGER
The value of INFO returned from ZSYTRF, .i.e., the pivot in
column INFO is exactly 0.

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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZSYTRF.

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

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

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

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