ZGEEQU(l)								 )								 ZGEEQU(l)

NAME

       ZGEEQU - compute row and column scalings intended to equilibrate 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 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.

       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 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 version 3.0						   15 June 2000 							 ZGEEQU(l)