slaqgb(3F)

NAME
     SLAQGB - equilibrate 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

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

         CHARACTER      EQUED

         INTEGER        KL, KU, LDAB, M, N

         REAL           AMAX, COLCND, ROWCND

         REAL           AB( LDAB, * ), C( * ), R( * )

PURPOSE
     SLAQGB 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) INTEGER
             The number of rows of the matrix A.  M >= 0.

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

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

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

     AB      (input/output) REAL 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) INTEGER
             The leading dimension of the array AB.  LDA >= KL+KU+1.

     R       (output) REAL array, dimension (M)
             The row scale factors for A.
     C       (output) REAL array, dimension (N)
             The column scale factors for A.

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

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

     AMAX    (input) REAL
             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             equilibration, i.e., A has been replaced by diag(R) * A *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.