224 lines
6.2 KiB
Fortran
224 lines
6.2 KiB
Fortran
*> \brief \b DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLAQSB + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsb.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsb.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsb.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
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*
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* .. Scalar Arguments ..
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* CHARACTER EQUED, UPLO
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* INTEGER KD, LDAB, N
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* DOUBLE PRECISION AMAX, SCOND
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION AB( LDAB, * ), S( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DLAQSB equilibrates a symmetric band matrix A using the scaling
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*> factors in the vector S.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> symmetric matrix A is stored.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KD
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*> \verbatim
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*> KD is INTEGER
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*> The number of super-diagonals of the matrix A if UPLO = 'U',
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*> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] AB
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*> \verbatim
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*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
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*> On entry, the upper or lower triangle of the symmetric band
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*> matrix A, stored in the first KD+1 rows of the array. The
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*> j-th column of A is stored in the j-th column of the array AB
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*> as follows:
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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*>
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*> On exit, if INFO = 0, the triangular factor U or L from the
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*> Cholesky factorization A = U**T*U or A = L*L**T of the band
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*> matrix A, in the same storage format as A.
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= KD+1.
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*> \endverbatim
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*>
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*> \param[in] S
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*> \verbatim
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*> S is DOUBLE PRECISION array, dimension (N)
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*> The scale factors for A.
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*> \endverbatim
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*>
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*> \param[in] SCOND
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*> \verbatim
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*> SCOND is DOUBLE PRECISION
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*> Ratio of the smallest S(i) to the largest S(i).
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*> \endverbatim
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*>
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*> \param[in] AMAX
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*> \verbatim
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*> AMAX is DOUBLE PRECISION
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*> Absolute value of largest matrix entry.
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*> \endverbatim
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*>
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*> \param[out] EQUED
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*> \verbatim
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*> EQUED is CHARACTER*1
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*> Specifies whether or not equilibration was done.
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*> = 'N': No equilibration.
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*> = 'Y': Equilibration was done, i.e., A has been replaced by
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*> diag(S) * A * diag(S).
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*> \endverbatim
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*
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*> \par Internal Parameters:
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* =========================
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*>
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*> \verbatim
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*> THRESH is a threshold value used to decide if scaling should be done
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*> based on the ratio of the scaling factors. If SCOND < THRESH,
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*> scaling is done.
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*>
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*> LARGE and SMALL are threshold values used to decide if scaling should
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*> be done based on the absolute size of the largest matrix element.
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*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doubleOTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER EQUED, UPLO
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INTEGER KD, LDAB, N
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DOUBLE PRECISION AMAX, SCOND
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AB( LDAB, * ), S( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, THRESH
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PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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DOUBLE PRECISION CJ, LARGE, SMALL
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH
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EXTERNAL LSAME, DLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.LE.0 ) THEN
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EQUED = 'N'
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RETURN
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END IF
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*
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* Initialize LARGE and SMALL.
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*
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SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
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LARGE = ONE / SMALL
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*
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IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
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*
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* No equilibration
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*
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EQUED = 'N'
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ELSE
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*
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* Replace A by diag(S) * A * diag(S).
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* Upper triangle of A is stored in band format.
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*
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DO 20 J = 1, N
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CJ = S( J )
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DO 10 I = MAX( 1, J-KD ), J
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AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
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10 CONTINUE
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20 CONTINUE
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ELSE
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*
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* Lower triangle of A is stored.
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*
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DO 40 J = 1, N
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CJ = S( J )
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DO 30 I = J, MIN( N, J+KD )
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AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
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30 CONTINUE
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40 CONTINUE
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END IF
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EQUED = 'Y'
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END IF
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*
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RETURN
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*
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* End of DLAQSB
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*
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END
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