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Annotation of rpl/lapack/lapack/zlaqhe.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
        !             2: *
        !             3: *  -- LAPACK auxiliary routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       CHARACTER          EQUED, UPLO
        !            10:       INTEGER            LDA, N
        !            11:       DOUBLE PRECISION   AMAX, SCOND
        !            12: *     ..
        !            13: *     .. Array Arguments ..
        !            14:       DOUBLE PRECISION   S( * )
        !            15:       COMPLEX*16         A( LDA, * )
        !            16: *     ..
        !            17: *
        !            18: *  Purpose
        !            19: *  =======
        !            20: *
        !            21: *  ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
        !            22: *  in the vector S.
        !            23: *
        !            24: *  Arguments
        !            25: *  =========
        !            26: *
        !            27: *  UPLO    (input) CHARACTER*1
        !            28: *          Specifies whether the upper or lower triangular part of the
        !            29: *          Hermitian matrix A is stored.
        !            30: *          = 'U':  Upper triangular
        !            31: *          = 'L':  Lower triangular
        !            32: *
        !            33: *  N       (input) INTEGER
        !            34: *          The order of the matrix A.  N >= 0.
        !            35: *
        !            36: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
        !            37: *          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
        !            38: *          n by n upper triangular part of A contains the upper
        !            39: *          triangular part of the matrix A, and the strictly lower
        !            40: *          triangular part of A is not referenced.  If UPLO = 'L', the
        !            41: *          leading n by n lower triangular part of A contains the lower
        !            42: *          triangular part of the matrix A, and the strictly upper
        !            43: *          triangular part of A is not referenced.
        !            44: *
        !            45: *          On exit, if EQUED = 'Y', the equilibrated matrix:
        !            46: *          diag(S) * A * diag(S).
        !            47: *
        !            48: *  LDA     (input) INTEGER
        !            49: *          The leading dimension of the array A.  LDA >= max(N,1).
        !            50: *
        !            51: *  S       (input) DOUBLE PRECISION array, dimension (N)
        !            52: *          The scale factors for A.
        !            53: *
        !            54: *  SCOND   (input) DOUBLE PRECISION
        !            55: *          Ratio of the smallest S(i) to the largest S(i).
        !            56: *
        !            57: *  AMAX    (input) DOUBLE PRECISION
        !            58: *          Absolute value of largest matrix entry.
        !            59: *
        !            60: *  EQUED   (output) CHARACTER*1
        !            61: *          Specifies whether or not equilibration was done.
        !            62: *          = 'N':  No equilibration.
        !            63: *          = 'Y':  Equilibration was done, i.e., A has been replaced by
        !            64: *                  diag(S) * A * diag(S).
        !            65: *
        !            66: *  Internal Parameters
        !            67: *  ===================
        !            68: *
        !            69: *  THRESH is a threshold value used to decide if scaling should be done
        !            70: *  based on the ratio of the scaling factors.  If SCOND < THRESH,
        !            71: *  scaling is done.
        !            72: *
        !            73: *  LARGE and SMALL are threshold values used to decide if scaling should
        !            74: *  be done based on the absolute size of the largest matrix element.
        !            75: *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
        !            76: *
        !            77: *  =====================================================================
        !            78: *
        !            79: *     .. Parameters ..
        !            80:       DOUBLE PRECISION   ONE, THRESH
        !            81:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
        !            82: *     ..
        !            83: *     .. Local Scalars ..
        !            84:       INTEGER            I, J
        !            85:       DOUBLE PRECISION   CJ, LARGE, SMALL
        !            86: *     ..
        !            87: *     .. External Functions ..
        !            88:       LOGICAL            LSAME
        !            89:       DOUBLE PRECISION   DLAMCH
        !            90:       EXTERNAL           LSAME, DLAMCH
        !            91: *     ..
        !            92: *     .. Intrinsic Functions ..
        !            93:       INTRINSIC          DBLE
        !            94: *     ..
        !            95: *     .. Executable Statements ..
        !            96: *
        !            97: *     Quick return if possible
        !            98: *
        !            99:       IF( N.LE.0 ) THEN
        !           100:          EQUED = 'N'
        !           101:          RETURN
        !           102:       END IF
        !           103: *
        !           104: *     Initialize LARGE and SMALL.
        !           105: *
        !           106:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
        !           107:       LARGE = ONE / SMALL
        !           108: *
        !           109:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
        !           110: *
        !           111: *        No equilibration
        !           112: *
        !           113:          EQUED = 'N'
        !           114:       ELSE
        !           115: *
        !           116: *        Replace A by diag(S) * A * diag(S).
        !           117: *
        !           118:          IF( LSAME( UPLO, 'U' ) ) THEN
        !           119: *
        !           120: *           Upper triangle of A is stored.
        !           121: *
        !           122:             DO 20 J = 1, N
        !           123:                CJ = S( J )
        !           124:                DO 10 I = 1, J - 1
        !           125:                   A( I, J ) = CJ*S( I )*A( I, J )
        !           126:    10          CONTINUE
        !           127:                A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
        !           128:    20       CONTINUE
        !           129:          ELSE
        !           130: *
        !           131: *           Lower triangle of A is stored.
        !           132: *
        !           133:             DO 40 J = 1, N
        !           134:                CJ = S( J )
        !           135:                A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
        !           136:                DO 30 I = J + 1, N
        !           137:                   A( I, J ) = CJ*S( I )*A( I, J )
        !           138:    30          CONTINUE
        !           139:    40       CONTINUE
        !           140:          END IF
        !           141:          EQUED = 'Y'
        !           142:       END IF
        !           143: *
        !           144:       RETURN
        !           145: *
        !           146: *     End of ZLAQHE
        !           147: *
        !           148:       END