# 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.

## 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 '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

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 '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

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 '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

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 '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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **98** of file **zla_gerpvgrw.f**.

## Author

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