# cla_syrpvgrw.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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cla_syrpvgrw.f

## SYNOPSIS

### Functions/Subroutines

real function cla_syrpvgrw (UPLO, N, INFO, A, LDA, AF, LDAF, IPIV, WORK)
CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

## Function/Subroutine Documentation

### real function cla_syrpvgrw (character*1 UPLO, integer N, integer INFO, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, real, dimension( * ) WORK)

CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

Purpose:

CLA_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.

Parameters:

UPLO

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

N

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

INFO

INFO is INTEGER
The value of INFO returned from CSYTRF, .i.e., the pivot in
column INFO is exactly 0.

A

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

LDA

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

AF

AF is COMPLEX array, dimension (LDAF,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CSYTRF.

LDAF

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

IPIV

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

WORK

WORK is REAL array, dimension (2*N)

Author:

Univ. of Tennessee

Univ. of California Berkeley