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 num
ber. 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 = small
est safe number and BIGNUM = largest safe number. Use of
these scaling factors is not guaranteed to reduce the con
dition 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.
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 under
flow, 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
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