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version 1.8, 2011/07/22 07:38:07 version 1.9, 2011/11/21 20:42:57
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   *> \brief \b DLAQSB
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLAQSB + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsb.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsb.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsb.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          EQUED, UPLO
   *       INTEGER            KD, LDAB, N
   *       DOUBLE PRECISION   AMAX, SCOND
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AB( LDAB, * ), S( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLAQSB equilibrates a symmetric 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 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.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KD+1.
   *> \endverbatim
   *>
   *> \param[in] S
   *> \verbatim
   *>          S is DOUBLE PRECISION array, dimension (N)
   *>          The scale factors for A.
   *> \endverbatim
   *>
   *> \param[in] SCOND
   *> \verbatim
   *>          SCOND is DOUBLE PRECISION
   *>          Ratio of the smallest S(i) to the largest S(i).
   *> \endverbatim
   *>
   *> \param[in] AMAX
   *> \verbatim
   *>          AMAX is DOUBLE PRECISION
   *>          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. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )        SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.1) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          EQUED, UPLO        CHARACTER          EQUED, UPLO
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       DOUBLE PRECISION   AB( LDAB, * ), S( * )        DOUBLE PRECISION   AB( LDAB, * ), S( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLAQSB equilibrates a symmetric band matrix A using the scaling  
 *  factors in the vector S.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) 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) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  KD      (input) 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) 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) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KD+1.  
 *  
 *  S       (input) DOUBLE PRECISION array, dimension (N)  
 *          The scale factors for A.  
 *  
 *  SCOND   (input) DOUBLE PRECISION  
 *          Ratio of the smallest S(i) to the largest S(i).  
 *  
 *  AMAX    (input) DOUBLE PRECISION  
 *          Absolute value of largest matrix entry.  
 *  
 *  EQUED   (output) 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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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