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    1: *> \brief \b DLARMM
    2: *
    3: * Definition:
    4: * ===========
    5: *
    6: *      DOUBLE PRECISION FUNCTION DLARMM( ANORM, BNORM, CNORM )
    7: *
    8: *     .. Scalar Arguments ..
    9: *      DOUBLE PRECISION   ANORM, BNORM, CNORM
   10: *     ..
   11: *
   12: *>  \par Purpose:
   13: *  =======
   14: *>
   15: *> \verbatim
   16: *>
   17: *> DLARMM returns a factor s in (0, 1] such that the linear updates
   18: *>
   19: *>    (s * C) - A * (s * B)  and  (s * C) - (s * A) * B
   20: *>
   21: *> cannot overflow, where A, B, and C are matrices of conforming
   22: *> dimensions.
   23: *>
   24: *> This is an auxiliary routine so there is no argument checking.
   25: *> \endverbatim
   26: *
   27: *  Arguments:
   28: *  =========
   29: *
   30: *> \param[in] ANORM
   31: *> \verbatim
   32: *>          ANORM is DOUBLE PRECISION
   33: *>          The infinity norm of A. ANORM >= 0.
   34: *>          The number of rows of the matrix A.  M >= 0.
   35: *> \endverbatim
   36: *>
   37: *> \param[in] BNORM
   38: *> \verbatim
   39: *>          BNORM is DOUBLE PRECISION
   40: *>          The infinity norm of B. BNORM >= 0.
   41: *> \endverbatim
   42: *>
   43: *> \param[in] CNORM
   44: *> \verbatim
   45: *>          CNORM is DOUBLE PRECISION
   46: *>          The infinity norm of C. CNORM >= 0.
   47: *> \endverbatim
   48: *>
   49: *>
   50: *  =====================================================================
   51: *>  References:
   52: *>    C. C. Kjelgaard Mikkelsen and L. Karlsson, Blocked Algorithms for
   53: *>    Robust Solution of Triangular Linear Systems. In: International
   54: *>    Conference on Parallel Processing and Applied Mathematics, pages
   55: *>    68--78. Springer, 2017.
   56: *>
   57: *> \ingroup OTHERauxiliary
   58: *  =====================================================================
   59: 
   60:       DOUBLE PRECISION FUNCTION DLARMM( ANORM, BNORM, CNORM )
   61:       IMPLICIT NONE
   62: *     .. Scalar Arguments ..
   63:       DOUBLE PRECISION   ANORM, BNORM, CNORM
   64: *     .. Parameters ..
   65:       DOUBLE PRECISION   ONE, HALF, FOUR
   66:       PARAMETER          ( ONE = 1.0D0, HALF = 0.5D+0, FOUR = 4.0D0 )
   67: *     ..
   68: *     .. Local Scalars ..
   69:        DOUBLE PRECISION   BIGNUM, SMLNUM
   70: *     ..
   71: *     .. External Functions ..
   72:       DOUBLE PRECISION   DLAMCH
   73:       EXTERNAL           DLAMCH
   74: *     ..
   75: *     .. Executable Statements ..
   76: *
   77: *
   78: *     Determine machine dependent parameters to control overflow.
   79: *
   80:       SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
   81:       BIGNUM = ( ONE / SMLNUM ) / FOUR
   82: *
   83: *     Compute a scale factor.
   84: *
   85:       DLARMM = ONE
   86:       IF( BNORM .LE. ONE ) THEN
   87:          IF( ANORM * BNORM .GT. BIGNUM - CNORM ) THEN
   88:             DLARMM = HALF
   89:          END IF
   90:       ELSE
   91:          IF( ANORM .GT. (BIGNUM - CNORM) / BNORM ) THEN
   92:             DLARMM = HALF / BNORM
   93:          END IF
   94:       END IF
   95:       RETURN
   96: *
   97: *     ==== End of DLARMM ====
   98: *
   99:       END