cgeequ(3)

NAME

CGEEQU - compute row and column scalings intended to equi

librate an M-by-N matrix A and reduce its condition number

SYNOPSIS

SUBROUTINE  CGEEQU(  M,  N,  A, LDA, R, C, ROWCND, COLCND,
AMAX, INFO )
    INTEGER        INFO, LDA, M, N
    REAL           AMAX, COLCND, ROWCND
    REAL           C( * ), R( * )
    COMPLEX        A( LDA, * )

PURPOSE

CGEEQU computes row and column scalings intended to equi

librate an M-by-N matrix A and reduce its condition number. R re

turns the row scale factors and C the column scale factors, cho

sen 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 = small

est 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.

ARGUMENTS

M (input) INTEGER

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

N (input) INTEGER

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

A (input) COMPLEX array, dimension (LDA,N)

The M-by-N matrix whose equilibration factors are

to be computed.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,M).

R (output) REAL array, dimension (M)

If INFO = 0 or INFO > M, R contains the row scale

factors for A.

C (output) REAL array, dimension (N)

If INFO = 0, C contains the column scale factors

for A.

ROWCND (output) 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 (output) 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 (output) 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 (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal 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

LAPACK version 3.0 15 June 2000

CGEEQU(3)