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