SLAQGE(3)      LAPACK routine of NEC Numeric Library Collection      SLAQGE(3)



NAME
       SLAQGE

SYNOPSIS
       SUBROUTINE SLAQGE (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED)



PURPOSE
            SLAQGE equilibrates a general M by N matrix A using the row and
            column scaling factors in the vectors R and C.




ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           A         (input/output)
                     A is REAL array, dimension (LDA,N)
                     On entry, the M by N matrix A.
                     On exit, the equilibrated matrix.  See EQUED for the form of
                     the equilibrated matrix.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(M,1).

           R         (input)
                     R is REAL array, dimension (M)
                     The row scale factors for A.

           C         (input)
                     C is REAL array, dimension (N)
                     The column scale factors for A.

           ROWCND    (input)
                     ROWCND is REAL
                     Ratio of the smallest R(i) to the largest R(i).

           COLCND    (input)
                     COLCND is REAL
                     Ratio of the smallest C(i) to the largest C(i).

           AMAX      (input)
                     AMAX is REAL
                     Absolute value of largest matrix entry.

           EQUED     (output)
                     EQUED is CHARACTER*1
                     Specifies the form of equilibration that was done.
                     = 'N':  No equilibration
                     = 'R':  Row equilibration, i.e., A has been premultiplied by
                             diag(R).
                     = 'C':  Column equilibration, i.e., A has been postmultiplied
                             by diag(C).
                     = 'B':  Both row and column equilibration, i.e., A has been
                             replaced by diag(R) * A * diag(C).



       Internal Parameters:


             THRESH is a threshold value used to decide if row or column scaling
             should be done based on the ratio of the row or column scaling
             factors.  If ROWCND < THRESH, row scaling is done, and if
             COLCND < THRESH, column scaling is done.

             LARGE and SMALL are threshold values used to decide if row scaling
             should be done based on the absolute size of the largest matrix
             element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.



LAPACK routine                  31 October 2017                      SLAQGE(3)