CGEEQU(3)                  MathKeisan LAPACK routine                 CGEEQU(3)



NAME
       CGEEQU  -  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 routine (version 3.1)    November 2006                       CGEEQU(3)