zlaqge(3F)

NAME
     ZLAQGE - equilibrate a general M by N matrix A using the row and scaling
     factors in the vectors R and C

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

         CHARACTER      EQUED

         INTEGER        LDA, M, N

         DOUBLE         PRECISION AMAX, COLCND, ROWCND

         DOUBLE         PRECISION C( * ), R( * )

         COMPLEX*16     A( LDA, * )

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


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/output) COMPLEX*16 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) INTEGER
             The leading dimension of the array A.  LDA >= max(M,1).

     R       (input) DOUBLE PRECISION array, dimension (M)
             The row scale factors for A.

     C       (input) DOUBLE PRECISION array, dimension (N)
             The column scale factors for A.

     ROWCND  (input) DOUBLE PRECISION
             Ratio of the smallest R(i) to the largest R(i).

     COLCND  (input) DOUBLE PRECISION
             Ratio of the smallest C(i) to the largest C(i).

     AMAX    (input) DOUBLE PRECISION
             Absolute value of largest matrix entry.
     EQUED   (output) 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             equilibration, i.e., A has been replaced by diag(R) * A *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).

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.