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

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