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SUBROUTINE <a name="DLAQSB.1"></a><a href="dlaqsb.f.html#DLAQSB.1">DLAQSB</a>( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
DOUBLE PRECISION AMAX, SCOND
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION AB( LDAB, * ), S( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DLAQSB.19"></a><a href="dlaqsb.f.html#DLAQSB.1">DLAQSB</a> equilibrates a symmetric band matrix A using the scaling
</span><span class="comment">*</span><span class="comment"> factors in the vector S.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment"> symmetric matrix A is stored.
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KD (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of super-diagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the symmetric band
</span><span class="comment">*</span><span class="comment"> matrix A, stored in the first KD+1 rows of the array. The
</span><span class="comment">*</span><span class="comment"> j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, the triangular factor U or L from the
</span><span class="comment">*</span><span class="comment"> Cholesky factorization A = U'*U or A = L*L' of the band
</span><span class="comment">*</span><span class="comment"> matrix A, in the same storage format as A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KD+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> S (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The scale factors for A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SCOND (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> Ratio of the smallest S(i) to the largest S(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AMAX (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> Absolute value of largest matrix entry.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> EQUED (output) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether or not equilibration was done.
</span><span class="comment">*</span><span class="comment"> = 'N': No equilibration.
</span><span class="comment">*</span><span class="comment"> = 'Y': Equilibration was done, i.e., A has been replaced by
</span><span class="comment">*</span><span class="comment"> diag(S) * A * diag(S).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Internal Parameters
</span><span class="comment">*</span><span class="comment"> ===================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> THRESH is a threshold value used to decide if scaling should be done
</span><span class="comment">*</span><span class="comment"> based on the ratio of the scaling factors. If SCOND < THRESH,
</span><span class="comment">*</span><span class="comment"> scaling is done.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LARGE and SMALL are threshold values used to decide if scaling should
</span><span class="comment">*</span><span class="comment"> be done based on the absolute size of the largest matrix element.
</span><span class="comment">*</span><span class="comment"> If AMAX > LARGE or AMAX < SMALL, scaling is done.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE, THRESH
PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, J
DOUBLE PRECISION CJ, LARGE, SMALL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.90"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
DOUBLE PRECISION <a name="DLAMCH.91"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
EXTERNAL <a name="LSAME.92"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="DLAMCH.92"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, MIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.LE.0 ) THEN
EQUED = <span class="string">'N'</span>
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Initialize LARGE and SMALL.
</span><span class="comment">*</span><span class="comment">
</span> SMALL = <a name="DLAMCH.108"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'Safe minimum'</span> ) / <a name="DLAMCH.108"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'Precision'</span> )
LARGE = ONE / SMALL
<span class="comment">*</span><span class="comment">
</span> IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> No equilibration
</span><span class="comment">*</span><span class="comment">
</span> EQUED = <span class="string">'N'</span>
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Replace A by diag(S) * A * diag(S).
</span><span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.120"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Upper triangle of A is stored in band format.
</span><span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span> 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 = <span class="string">'Y'</span>
END IF
<span class="comment">*</span><span class="comment">
</span> RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="DLAQSB.146"></a><a href="dlaqsb.f.html#DLAQSB.1">DLAQSB</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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