---
name: "la_gerpvgrw"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/la_gerpvgrw"
---

# la\_gerpvgrw(3)

la\_gerpvgrw: reciprocal pivot growth

## NAME

la\_gerpvgrw - 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.

## Detailed Description

## 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  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

Univ. of Colorado Denver

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  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

Univ. of Colorado Denver

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  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

Univ. of Colorado Denver

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  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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **98** of file **zla\_gerpvgrw.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.