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la_gerpvgrw(3) LAPACK la_gerpvgrw(3)

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 '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.

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.

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.

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.

Author

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