.TH ZGEEQU 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
ZGEEQU - row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
.SH SYNOPSIS
.TP 19
SUBROUTINE ZGEEQU(
M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
INFO )
.TP 19
.ti +4
INTEGER
INFO, LDA, M, N
.TP 19
.ti +4
DOUBLE
PRECISION AMAX, COLCND, ROWCND
.TP 19
.ti +4
DOUBLE
PRECISION C( * ), R( * )
.TP 19
.ti +4
COMPLEX*16
A( LDA, * )
.SH PURPOSE
ZGEEQU 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.
.br
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.
.br
.SH ARGUMENTS
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
.TP 8
A (input) COMPLEX*16 array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
.TP 8
R (output) DOUBLE PRECISION array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
.TP 8
C (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
.TP 8
ROWCND (output) DOUBLE PRECISION
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.
.TP 8
COLCND (output) DOUBLE PRECISION
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.
.TP 8
AMAX (output) DOUBLE PRECISION
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.br
> 0: if INFO = i, and i is
.br
<= M: the i-th row of A is exactly zero
.br
> M: the (i-M)-th column of A is exactly zero