DLAQSB  -  equilibrate a symmetric band matrix A using the
       scaling factors in the vector S


SYNOPSIS

       SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND,  AMAX,
                          EQUED )

           CHARACTER      EQUED, UPLO

           INTEGER        KD, LDAB, N

           DOUBLE         PRECISION AMAX, SCOND

           DOUBLE         PRECISION AB( LDAB, * ), S( * )


PURPOSE

       DLAQSB  equilibrates  a  symmetric band matrix A using the
       scaling factors in the vector S.


ARGUMENTS

       UPLO    (input) CHARACTER*1
               Specifies whether the upper  or  lower  triangular
               part  of the symmetric matrix A is stored.  = 'U':
               Upper triangular
               = 'L':  Lower triangular

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

       KD      (input) INTEGER
               The number of super-diagonals of the matrix  A  if
               UPLO = 'U', or the number of sub-diagonals if UPLO
               = 'L'.  KD >= 0.

       AB      (input/output) DOUBLE PRECISION array, dimension
               (LDAB,N)
               On entry, the upper or lower triangle of the  sym­
               metric  band  matrix  A,  stored in the first KD+1
               rows of the array.  The j-th column of A is stored
               in  the j-th column of the array AB as follows: if
               UPLO = 'U', AB(kd+1+i-j,j) = A(i,j)  for  max(1,j-
               kd)<=i<=j;  if UPLO = 'L', AB(1+i-j,j)    = A(i,j)
               for j<=i<=min(n,j+kd).

               On exit, if INFO = 0, the triangular factor U or L
               from  the  Cholesky  factorization A = U'*U or A =
               L*L' of the band matrix A,  in  the  same  storage
               format as A.

       LDAB    (input) INTEGER
               The  leading  dimension  of the array AB.  LDAB >=
               KD+1.

               The scale factors for A.

       SCOND   (input) DOUBLE PRECISION
               Ratio of the smallest S(i) to the largest S(i).

       AMAX    (input) DOUBLE PRECISION
               Absolute value of largest matrix entry.

       EQUED   (output) CHARACTER*1
               Specifies whether or not equilibration  was  done.
               = 'N':  No equilibration.
               =  'Y':   Equilibration was done, i.e., A has been
               replaced by diag(S) * A * diag(S).


PARAMETERS

       THRESH is a threshold value  used  to  decide  if  scaling
       should  be done based on the ratio of the scaling factors.
       If SCOND < THRESH, scaling is done.

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


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