*> \brief \b CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CLAQHB + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) * * .. Scalar Arguments .. * CHARACTER EQUED, UPLO * INTEGER KD, LDAB, N * REAL AMAX, SCOND * .. * .. Array Arguments .. * REAL S( * ) * COMPLEX AB( LDAB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CLAQHB equilibrates an Hermitian band matrix A using the scaling *> factors in the vector S. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> 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 *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] KD *> \verbatim *> 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. *> \endverbatim *> *> \param[in,out] AB *> \verbatim *> AB is COMPLEX 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**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> The leading dimension of the array AB. LDAB >= KD+1. *> \endverbatim *> *> \param[out] S *> \verbatim *> S is REAL array, dimension (N) *> The scale factors for A. *> \endverbatim *> *> \param[in] SCOND *> \verbatim *> SCOND is REAL *> Ratio of the smallest S(i) to the largest S(i). *> \endverbatim *> *> \param[in] AMAX *> \verbatim *> AMAX is REAL *> Absolute value of largest matrix entry. *> \endverbatim *> *> \param[out] EQUED *> \verbatim *> 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). *> \endverbatim * *> \par Internal Parameters: * ========================= *> *> \verbatim *> 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complexOTHERauxiliary * * ===================================================================== SUBROUTINE CLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) * * -- 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 REAL AMAX, SCOND * .. * .. Array Arguments .. REAL S( * ) COMPLEX AB( LDAB, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, THRESH PARAMETER ( ONE = 1.0E+0, THRESH = 0.1E+0 ) * .. * .. Local Scalars .. INTEGER I, J REAL CJ, LARGE, SMALL * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH EXTERNAL LSAME, SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) THEN EQUED = 'N' RETURN END IF * * Initialize LARGE and SMALL. * SMALL = SLAMCH( 'Safe minimum' ) / SLAMCH( '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 - 1 AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J ) 10 CONTINUE AB( KD+1, J ) = CJ*CJ*REAL( AB( KD+1, J ) ) 20 CONTINUE ELSE * * Lower triangle of A is stored. * DO 40 J = 1, N CJ = S( J ) AB( 1, J ) = CJ*CJ*REAL( AB( 1, J ) ) DO 30 I = J + 1, 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 CLAQHB * END