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sgeequ.f(3) LAPACK sgeequ.f(3)

NAME

sgeequ.f

SYNOPSIS

Functions/Subroutines


subroutine sgeequ (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)
SGEEQU

Function/Subroutine Documentation

subroutine sgeequ (integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) R, real, dimension( * ) C, real ROWCND, real COLCND, real AMAX, integer INFO)

SGEEQU

Purpose:


SGEEQU computes row and column scalings intended to equilibrate an
M-by-N matrix A and reduce its condition number. R returns the row
scale factors and C the column scale factors, chosen to try to make
the largest element in each row and column of the matrix B with
elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
R(i) and C(j) are restricted to be between SMLNUM = smallest safe
number and BIGNUM = largest safe number. Use of these scaling
factors is not guaranteed to reduce the condition number of A but
works well in practice.

Parameters:

M


M is INTEGER
The number of rows of the matrix A. M >= 0.

N


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

A


A is REAL array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.

LDA


LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

R


R is REAL array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.

C


C is REAL array, dimension (N)
If INFO = 0, C contains the column scale factors for A.

ROWCND


ROWCND is REAL
If INFO = 0 or INFO > M, ROWCND contains the ratio of the
smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
AMAX is neither too large nor too small, it is not worth
scaling by R.

COLCND


COLCND is REAL
If INFO = 0, COLCND contains the ratio of the smallest
C(i) to the largest C(i). If COLCND >= 0.1, it is not
worth scaling by C.

AMAX


AMAX is REAL
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 141 of file sgeequ.f.

Author

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Tue Nov 14 2017 Version 3.8.0