# la_gerpvgrw - Man Page

la_gerpvgrw: reciprocal pivot growth

## Synopsis

### Functions

real function cla_gerpvgrw (n, ncols, a, lda, af, ldaf)
CLA_GERPVGRW multiplies a square real matrix by a complex matrix.
double precision function dla_gerpvgrw (n, ncols, a, lda, af, ldaf)
DLA_GERPVGRW
real function sla_gerpvgrw (n, ncols, a, lda, af, ldaf)
SLA_GERPVGRW
double precision function zla_gerpvgrw (n, ncols, a, lda, af, ldaf)
ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.

## Function Documentation

### real function cla_gerpvgrw (integer n, integer ncols, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf)

CLA_GERPVGRW multiplies a square real matrix by a complex matrix.

Purpose:

``` CLA_GERPVGRW 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

N

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

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 factors L and U from the factorization
A = P*L*U as computed by CGETRF.```

LDAF

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 97 of file cla_gerpvgrw.f.

### double precision function dla_gerpvgrw (integer n, integer ncols, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf)

DLA_GERPVGRW

Purpose:

``` DLA_GERPVGRW 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

N

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

NCOLS

```          NCOLS is INTEGER
The number of columns of the matrix A. NCOLS >= 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 factors L and U from the factorization
A = P*L*U as computed by DGETRF.```

LDAF

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 98 of file dla_gerpvgrw.f.

### real function sla_gerpvgrw (integer n, integer ncols, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf)

SLA_GERPVGRW

Purpose:

``` SLA_GERPVGRW 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

N

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

NCOLS

```          NCOLS is INTEGER
The number of columns of the matrix A. NCOLS >= 0.```

A

```          A is REAL 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 REAL array, dimension (LDAF,N)
The factors L and U from the factorization
A = P*L*U as computed by SGETRF.```

LDAF

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 96 of file sla_gerpvgrw.f.

### double precision function zla_gerpvgrw (integer n, integer ncols, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf)

ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.

Purpose:

``` ZLA_GERPVGRW 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

N

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

NCOLS

```          NCOLS is INTEGER
The number of columns of the matrix A. NCOLS >= 0.```

A

```          A is COMPLEX*16 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*16 array, dimension (LDAF,N)
The factors L and U from the factorization
A = P*L*U as computed by ZGETRF.```

LDAF

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

Univ. of Tennessee

Univ. of California Berkeley