LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dlaqsb.f
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00001 *> \brief \b DLAQSB
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DLAQSB + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          EQUED, UPLO
00025 *       INTEGER            KD, LDAB, N
00026 *       DOUBLE PRECISION   AMAX, SCOND
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       DOUBLE PRECISION   AB( LDAB, * ), S( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> DLAQSB equilibrates a symmetric band matrix A using the scaling
00039 *> factors in the vector S.
00040 *> \endverbatim
00041 *
00042 *  Arguments:
00043 *  ==========
00044 *
00045 *> \param[in] UPLO
00046 *> \verbatim
00047 *>          UPLO is CHARACTER*1
00048 *>          Specifies whether the upper or lower triangular part of the
00049 *>          symmetric matrix A is stored.
00050 *>          = 'U':  Upper triangular
00051 *>          = 'L':  Lower triangular
00052 *> \endverbatim
00053 *>
00054 *> \param[in] N
00055 *> \verbatim
00056 *>          N is INTEGER
00057 *>          The order of the matrix A.  N >= 0.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] KD
00061 *> \verbatim
00062 *>          KD is INTEGER
00063 *>          The number of super-diagonals of the matrix A if UPLO = 'U',
00064 *>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
00065 *> \endverbatim
00066 *>
00067 *> \param[in,out] AB
00068 *> \verbatim
00069 *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
00070 *>          On entry, the upper or lower triangle of the symmetric band
00071 *>          matrix A, stored in the first KD+1 rows of the array.  The
00072 *>          j-th column of A is stored in the j-th column of the array AB
00073 *>          as follows:
00074 *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00075 *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00076 *>
00077 *>          On exit, if INFO = 0, the triangular factor U or L from the
00078 *>          Cholesky factorization A = U**T*U or A = L*L**T of the band
00079 *>          matrix A, in the same storage format as A.
00080 *> \endverbatim
00081 *>
00082 *> \param[in] LDAB
00083 *> \verbatim
00084 *>          LDAB is INTEGER
00085 *>          The leading dimension of the array AB.  LDAB >= KD+1.
00086 *> \endverbatim
00087 *>
00088 *> \param[in] S
00089 *> \verbatim
00090 *>          S is DOUBLE PRECISION array, dimension (N)
00091 *>          The scale factors for A.
00092 *> \endverbatim
00093 *>
00094 *> \param[in] SCOND
00095 *> \verbatim
00096 *>          SCOND is DOUBLE PRECISION
00097 *>          Ratio of the smallest S(i) to the largest S(i).
00098 *> \endverbatim
00099 *>
00100 *> \param[in] AMAX
00101 *> \verbatim
00102 *>          AMAX is DOUBLE PRECISION
00103 *>          Absolute value of largest matrix entry.
00104 *> \endverbatim
00105 *>
00106 *> \param[out] EQUED
00107 *> \verbatim
00108 *>          EQUED is CHARACTER*1
00109 *>          Specifies whether or not equilibration was done.
00110 *>          = 'N':  No equilibration.
00111 *>          = 'Y':  Equilibration was done, i.e., A has been replaced by
00112 *>                  diag(S) * A * diag(S).
00113 *> \endverbatim
00114 *
00115 *> \par Internal Parameters:
00116 *  =========================
00117 *>
00118 *> \verbatim
00119 *>  THRESH is a threshold value used to decide if scaling should be done
00120 *>  based on the ratio of the scaling factors.  If SCOND < THRESH,
00121 *>  scaling is done.
00122 *>
00123 *>  LARGE and SMALL are threshold values used to decide if scaling should
00124 *>  be done based on the absolute size of the largest matrix element.
00125 *>  If AMAX > LARGE or AMAX < SMALL, scaling is done.
00126 *> \endverbatim
00127 *
00128 *  Authors:
00129 *  ========
00130 *
00131 *> \author Univ. of Tennessee 
00132 *> \author Univ. of California Berkeley 
00133 *> \author Univ. of Colorado Denver 
00134 *> \author NAG Ltd. 
00135 *
00136 *> \date November 2011
00137 *
00138 *> \ingroup doubleOTHERauxiliary
00139 *
00140 *  =====================================================================
00141       SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
00142 *
00143 *  -- LAPACK auxiliary routine (version 3.4.0) --
00144 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00145 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00146 *     November 2011
00147 *
00148 *     .. Scalar Arguments ..
00149       CHARACTER          EQUED, UPLO
00150       INTEGER            KD, LDAB, N
00151       DOUBLE PRECISION   AMAX, SCOND
00152 *     ..
00153 *     .. Array Arguments ..
00154       DOUBLE PRECISION   AB( LDAB, * ), S( * )
00155 *     ..
00156 *
00157 *  =====================================================================
00158 *
00159 *     .. Parameters ..
00160       DOUBLE PRECISION   ONE, THRESH
00161       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
00162 *     ..
00163 *     .. Local Scalars ..
00164       INTEGER            I, J
00165       DOUBLE PRECISION   CJ, LARGE, SMALL
00166 *     ..
00167 *     .. External Functions ..
00168       LOGICAL            LSAME
00169       DOUBLE PRECISION   DLAMCH
00170       EXTERNAL           LSAME, DLAMCH
00171 *     ..
00172 *     .. Intrinsic Functions ..
00173       INTRINSIC          MAX, MIN
00174 *     ..
00175 *     .. Executable Statements ..
00176 *
00177 *     Quick return if possible
00178 *
00179       IF( N.LE.0 ) THEN
00180          EQUED = 'N'
00181          RETURN
00182       END IF
00183 *
00184 *     Initialize LARGE and SMALL.
00185 *
00186       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
00187       LARGE = ONE / SMALL
00188 *
00189       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
00190 *
00191 *        No equilibration
00192 *
00193          EQUED = 'N'
00194       ELSE
00195 *
00196 *        Replace A by diag(S) * A * diag(S).
00197 *
00198          IF( LSAME( UPLO, 'U' ) ) THEN
00199 *
00200 *           Upper triangle of A is stored in band format.
00201 *
00202             DO 20 J = 1, N
00203                CJ = S( J )
00204                DO 10 I = MAX( 1, J-KD ), J
00205                   AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
00206    10          CONTINUE
00207    20       CONTINUE
00208          ELSE
00209 *
00210 *           Lower triangle of A is stored.
00211 *
00212             DO 40 J = 1, N
00213                CJ = S( J )
00214                DO 30 I = J, MIN( N, J+KD )
00215                   AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
00216    30          CONTINUE
00217    40       CONTINUE
00218          END IF
00219          EQUED = 'Y'
00220       END IF
00221 *
00222       RETURN
00223 *
00224 *     End of DLAQSB
00225 *
00226       END
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