LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
claqsb.f
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00001 *> \brief \b CLAQSB
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLAQSB + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claqsb.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claqsb.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          EQUED, UPLO
00025 *       INTEGER            KD, LDAB, N
00026 *       REAL               AMAX, SCOND
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       REAL               S( * )
00030 *       COMPLEX            AB( LDAB, * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> CLAQSB equilibrates a symmetric band matrix A using the scaling
00040 *> factors in the vector S.
00041 *> \endverbatim
00042 *
00043 *  Arguments:
00044 *  ==========
00045 *
00046 *> \param[in] UPLO
00047 *> \verbatim
00048 *>          UPLO is CHARACTER*1
00049 *>          Specifies whether the upper or lower triangular part of the
00050 *>          symmetric matrix A is stored.
00051 *>          = 'U':  Upper triangular
00052 *>          = 'L':  Lower triangular
00053 *> \endverbatim
00054 *>
00055 *> \param[in] N
00056 *> \verbatim
00057 *>          N is INTEGER
00058 *>          The order of the matrix A.  N >= 0.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] KD
00062 *> \verbatim
00063 *>          KD is INTEGER
00064 *>          The number of super-diagonals of the matrix A if UPLO = 'U',
00065 *>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
00066 *> \endverbatim
00067 *>
00068 *> \param[in,out] AB
00069 *> \verbatim
00070 *>          AB is COMPLEX array, dimension (LDAB,N)
00071 *>          On entry, the upper or lower triangle of the symmetric band
00072 *>          matrix A, stored in the first KD+1 rows of the array.  The
00073 *>          j-th column of A is stored in the j-th column of the array AB
00074 *>          as follows:
00075 *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00076 *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00077 *>
00078 *>          On exit, if INFO = 0, the triangular factor U or L from the
00079 *>          Cholesky factorization A = U**H *U or A = L*L**H of the band
00080 *>          matrix A, in the same storage format as A.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDAB
00084 *> \verbatim
00085 *>          LDAB is INTEGER
00086 *>          The leading dimension of the array AB.  LDAB >= KD+1.
00087 *> \endverbatim
00088 *>
00089 *> \param[in] S
00090 *> \verbatim
00091 *>          S is REAL array, dimension (N)
00092 *>          The scale factors for A.
00093 *> \endverbatim
00094 *>
00095 *> \param[in] SCOND
00096 *> \verbatim
00097 *>          SCOND is REAL
00098 *>          Ratio of the smallest S(i) to the largest S(i).
00099 *> \endverbatim
00100 *>
00101 *> \param[in] AMAX
00102 *> \verbatim
00103 *>          AMAX is REAL
00104 *>          Absolute value of largest matrix entry.
00105 *> \endverbatim
00106 *>
00107 *> \param[out] EQUED
00108 *> \verbatim
00109 *>          EQUED is CHARACTER*1
00110 *>          Specifies whether or not equilibration was done.
00111 *>          = 'N':  No equilibration.
00112 *>          = 'Y':  Equilibration was done, i.e., A has been replaced by
00113 *>                  diag(S) * A * diag(S).
00114 *> \endverbatim
00115 *
00116 *> \par Internal Parameters:
00117 *  =========================
00118 *>
00119 *> \verbatim
00120 *>  THRESH is a threshold value used to decide if scaling should be done
00121 *>  based on the ratio of the scaling factors.  If SCOND < THRESH,
00122 *>  scaling is done.
00123 *>
00124 *>  LARGE and SMALL are threshold values used to decide if scaling should
00125 *>  be done based on the absolute size of the largest matrix element.
00126 *>  If AMAX > LARGE or AMAX < SMALL, scaling is done.
00127 *> \endverbatim
00128 *
00129 *  Authors:
00130 *  ========
00131 *
00132 *> \author Univ. of Tennessee 
00133 *> \author Univ. of California Berkeley 
00134 *> \author Univ. of Colorado Denver 
00135 *> \author NAG Ltd. 
00136 *
00137 *> \date November 2011
00138 *
00139 *> \ingroup complexOTHERauxiliary
00140 *
00141 *  =====================================================================
00142       SUBROUTINE CLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
00143 *
00144 *  -- LAPACK auxiliary routine (version 3.4.0) --
00145 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00146 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00147 *     November 2011
00148 *
00149 *     .. Scalar Arguments ..
00150       CHARACTER          EQUED, UPLO
00151       INTEGER            KD, LDAB, N
00152       REAL               AMAX, SCOND
00153 *     ..
00154 *     .. Array Arguments ..
00155       REAL               S( * )
00156       COMPLEX            AB( LDAB, * )
00157 *     ..
00158 *
00159 *  =====================================================================
00160 *
00161 *     .. Parameters ..
00162       REAL               ONE, THRESH
00163       PARAMETER          ( ONE = 1.0E+0, THRESH = 0.1E+0 )
00164 *     ..
00165 *     .. Local Scalars ..
00166       INTEGER            I, J
00167       REAL               CJ, LARGE, SMALL
00168 *     ..
00169 *     .. External Functions ..
00170       LOGICAL            LSAME
00171       REAL               SLAMCH
00172       EXTERNAL           LSAME, SLAMCH
00173 *     ..
00174 *     .. Intrinsic Functions ..
00175       INTRINSIC          MAX, MIN
00176 *     ..
00177 *     .. Executable Statements ..
00178 *
00179 *     Quick return if possible
00180 *
00181       IF( N.LE.0 ) THEN
00182          EQUED = 'N'
00183          RETURN
00184       END IF
00185 *
00186 *     Initialize LARGE and SMALL.
00187 *
00188       SMALL = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' )
00189       LARGE = ONE / SMALL
00190 *
00191       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
00192 *
00193 *        No equilibration
00194 *
00195          EQUED = 'N'
00196       ELSE
00197 *
00198 *        Replace A by diag(S) * A * diag(S).
00199 *
00200          IF( LSAME( UPLO, 'U' ) ) THEN
00201 *
00202 *           Upper triangle of A is stored in band format.
00203 *
00204             DO 20 J = 1, N
00205                CJ = S( J )
00206                DO 10 I = MAX( 1, J-KD ), J
00207                   AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
00208    10          CONTINUE
00209    20       CONTINUE
00210          ELSE
00211 *
00212 *           Lower triangle of A is stored.
00213 *
00214             DO 40 J = 1, N
00215                CJ = S( J )
00216                DO 30 I = J, MIN( N, J+KD )
00217                   AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
00218    30          CONTINUE
00219    40       CONTINUE
00220          END IF
00221          EQUED = 'Y'
00222       END IF
00223 *
00224       RETURN
00225 *
00226 *     End of CLAQSB
00227 *
00228       END
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