# cla_porpvgrw.f

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

## SYNOPSIS

### Functions/Subroutines

real function cla_porpvgrw (UPLO, NCOLS, A, LDA, AF, LDAF, WORK)
CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

## Function/Subroutine Documentation

### real function cla_porpvgrw (character*1 UPLO, integer NCOLS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldaf, * ) AF, integer LDAF, real, dimension( * ) WORK)

CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Purpose:

``` CLA_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.
```

Parameters:

UPLO

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

NCOLS

```          NCOLS is INTEGER
The number of columns of the matrix A. NCOLS >= 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 triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, as computed by CPOTRF.
```

LDAF

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

WORK

```          WORK is REAL array, dimension (2*N)
```

Author:

Univ. of Tennessee

Univ. of California Berkeley