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# zgeequ

```
NAME
ZGEEQU - compute row and column scalings intended to equili-
brate an M by N matrix A and reduce its condition number

SYNOPSIS
SUBROUTINE ZGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
INFO )

INTEGER        INFO, LDA, M, N

DOUBLE         PRECISION AMAX, COLCND, ROWCND

DOUBLE         PRECISION C( * ), R( * )

COMPLEX*16     A( LDA, * )

PURPOSE
ZGEEQU computes row and column scalings intended to equili-
brate an M by N matrix A and reduce its condition number.  R
returns the row scale factors and C the column scale fac-
tors, chosen to try to make the largest entry 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.

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*16 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) DOUBLE PRECISION array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale
factors for A.

C       (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0,  C contains the column scale factors
for A.

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.

COLCND  (output) DOUBLE PRECISION
If INFO = 0, COLCND contains the ratio of the smal-
lest C(i) to the largest C(i).  If COLCND >= 0.1, it
is not worth scaling by C.

AMAX    (output) DOUBLE PRECISION
Absolute value of largest matrix element.  If AMAX
is very close to overflow or very close to under-
flow, the matrix should be scaled.

INFO    (output) 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
```