Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3 - computes row and column scalings intended to equilibrate an M-by-N matrix A and
reduce its condition number

SYNOPSIS

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

IMPLICIT        NONE

INTEGER         INFO, LDA, M, N

DOUBLE          PRECISION AMAX, COLCND, ROWCND

DOUBLE          PRECISION A( LDA, * ), C( * ), R( * )

PURPOSE

DGEEQUB 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 an absolute value of at most
R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from DGEEQU by restricting the scaling factors
to a power of the radix.  Baring over- and underflow, scaling by
these factors introduces no additional rounding errors.  However, the
scaled entries' magnitured are no longer approximately 1 but lie

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) DOUBLE PRECISION 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 smallest
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 underflow, 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

LAPACK routine (version 3.2)            April 2011                           DGEEQUB(3lapack)