dlaqsb()

subroutine dlaqsb	(	character	uplo,
		integer	n,
		integer	kd,
		double precision, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( * )	s,
		double precision	scond,
		double precision	amax,
		character	equed )

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

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Purpose:

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

Parameters

[in]	UPLO	!> 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 !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	KD	!> 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. !>
[in,out]	AB	!> 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. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
[in]	S	!> S is DOUBLE PRECISION array, dimension (N) !> The scale factors for A. !>
[in]	SCOND	!> SCOND is DOUBLE PRECISION !> Ratio of the smallest S(i) to the largest S(i). !>
[in]	AMAX	!> AMAX is DOUBLE PRECISION !> Absolute value of largest matrix entry. !>
[out]	EQUED	!> 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 = 'Y': Equilibration was done, i.e., A has been replaced by !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.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 137 of file dlaqsb.f.

*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          EQUED, UPLO
      INTEGER            KD, LDAB, N
      DOUBLE PRECISION   AMAX, SCOND
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * ), S( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, THRESH
      parameter( one = 1.0d+0, thresh = 0.1d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      DOUBLE PRECISION   CJ, LARGE, SMALL
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           lsame, dlamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.LE.0 ) THEN
         equed = 'N'
         RETURN
      END IF
*
*     Initialize LARGE and SMALL.
*
      small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
      large = one / small
*
      IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
*
*        No equilibration
*
         equed = 'N'
      ELSE
*
*        Replace A by diag(S) * A * diag(S).
*
         IF( lsame( uplo, 'U' ) ) THEN
*
*           Upper triangle of A is stored in band format.
*
            DO 20 j = 1, n
               cj = s( j )
               DO 10 i = max( 1, j-kd ), j
                  ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
   10          CONTINUE
   20       CONTINUE
         ELSE
*
*           Lower triangle of A is stored.
*
            DO 40 j = 1, n
               cj = s( j )
               DO 30 i = j, min( n, j+kd )
                  ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
   30          CONTINUE
   40       CONTINUE
         END IF
         equed = 'Y'
      END IF
*
      RETURN
*
*     End of DLAQSB
*

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