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



NAME
       DLAQGB

SYNOPSIS
       SUBROUTINE DLAQGB (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
           EQUED)



PURPOSE
            DLAQGB equilibrates a general M by N band matrix A with KL
            subdiagonals and KU superdiagonals using the row and 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.

           KL        (input)
                     KL is INTEGER
                     The number of subdiagonals within the band of A.  KL >= 0.

           KU        (input)
                     KU is INTEGER
                     The number of superdiagonals within the band of A.  KU >= 0.

           AB        (input/output)
                     AB is DOUBLE PRECISION array, dimension (LDAB,N)
                     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
                     The j-th column of A is stored in the j-th column of the
                     array AB as follows:
                     AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

                     On exit, the equilibrated matrix, in the same storage format
                     as A.  See EQUED for the form of the equilibrated matrix.

           LDAB      (input)
                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDA >= KL+KU+1.

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

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

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

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

           AMAX      (input)
                     AMAX is DOUBLE PRECISION
                     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                      DLAQGB(3)