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CGEEQU(l)			       )			     CGEEQU(l)

NAME
       CGEEQU  - compute row and column scalings intended to equilibrate 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 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  num‐
       ber  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 com‐
	       puted.

       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 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			     CGEEQU(l)
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