# dla_syrpvgrw.f

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

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### double precision function dla_syrpvgrw (character*1 UPLO, integer N, integer INFO, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, double precision, dimension( * ) WORK)

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

Purpose:

``` DLA_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 DSYTRF, .i.e., the pivot in
column INFO is exactly 0.
```

A

```          A is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAF,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by DSYTRF.
```

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 DSYTRF.
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (2*N)
```

Author:

Univ. of Tennessee

Univ. of California Berkeley