dlaqsb(3F)

NAME
     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 symmetric 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.

     S       (output) DOUBLE PRECISION array, dimension (N)
             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             = 'Y':  Equilibration was done, i.e., A has been replaced by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.