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



NAME
       DLAQSB

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



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




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

           KD        (input)
                     KD is 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)
                     AB is 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**T*U or A = L*L**T of the band
                     matrix A, in the same storage format as A.

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

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

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

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

           EQUED     (output)
                     EQUED is 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).



       Internal 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.



LAPACK routine                  31 October 2017                      DLAQSB(3)