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NAME
     dgeequ - compute row and column scalings intended to equili-
     brate an M-by-N matrix A and reduce its condition number

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

     INTEGER INFO, LDA, M, N

     DOUBLE PRECISION AMAX, COLCND, ROWCND

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



     #include <sunperf.h>

     void dgeequ(int m, int n, double *da, int  lda,  double  *r,
               double  *dc, double *rowcnd, double * colcnd, dou-
               ble *amax, int *info) ;

PURPOSE
     DGEEQU computes row and column scalings intended to  equili-
     brate an M-by-N matrix A and reduce its condition number.  R
     returns the row scale factors and C the  column  scale  fac-
     tors,  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) 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 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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