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*> \brief \b DLARMM
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLARMM( ANORM, BNORM, CNORM )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ANORM, BNORM, CNORM
* ..
*
*> \par Purpose:
* =======
*>
*> \verbatim
*>
*> DLARMM returns a factor s in (0, 1] such that the linear updates
*>
*> (s * C) - A * (s * B) and (s * C) - (s * A) * B
*>
*> cannot overflow, where A, B, and C are matrices of conforming
*> dimensions.
*>
*> This is an auxiliary routine so there is no argument checking.
*> \endverbatim
*
* Arguments:
* =========
*
*> \param[in] ANORM
*> \verbatim
*> ANORM is DOUBLE PRECISION
*> The infinity norm of A. ANORM >= 0.
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] BNORM
*> \verbatim
*> BNORM is DOUBLE PRECISION
*> The infinity norm of B. BNORM >= 0.
*> \endverbatim
*>
*> \param[in] CNORM
*> \verbatim
*> CNORM is DOUBLE PRECISION
*> The infinity norm of C. CNORM >= 0.
*> \endverbatim
*>
*>
* =====================================================================
*> References:
*> C. C. Kjelgaard Mikkelsen and L. Karlsson, Blocked Algorithms for
*> Robust Solution of Triangular Linear Systems. In: International
*> Conference on Parallel Processing and Applied Mathematics, pages
*> 68--78. Springer, 2017.
*>
*> \ingroup larmm
* =====================================================================
DOUBLE PRECISION FUNCTION DLARMM( ANORM, BNORM, CNORM )
IMPLICIT NONE
* .. Scalar Arguments ..
DOUBLE PRECISION ANORM, BNORM, CNORM
* .. Parameters ..
DOUBLE PRECISION ONE, HALF, FOUR
PARAMETER ( ONE = 1.0D0, HALF = 0.5D+0, FOUR = 4.0D0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION BIGNUM, SMLNUM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Executable Statements ..
*
*
* Determine machine dependent parameters to control overflow.
*
SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
BIGNUM = ( ONE / SMLNUM ) / FOUR
*
* Compute a scale factor.
*
DLARMM = ONE
IF( BNORM .LE. ONE ) THEN
IF( ANORM * BNORM .GT. BIGNUM - CNORM ) THEN
DLARMM = HALF
END IF
ELSE
IF( ANORM .GT. (BIGNUM - CNORM) / BNORM ) THEN
DLARMM = HALF / BNORM
END IF
END IF
RETURN
*
* ==== End of DLARMM ====
*
END
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