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*> \brief \b SLARMM
*
* Definition:
* ===========
*
* REAL FUNCTION SLARMM( ANORM, BNORM, CNORM )
*
* .. Scalar Arguments ..
* REAL ANORM, BNORM, CNORM
* ..
*
*> \par Purpose:
* =======
*>
*> \verbatim
*>
*> SLARMM 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 REAL
*> The infinity norm of A. ANORM >= 0.
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] BNORM
*> \verbatim
*> BNORM is REAL
*> The infinity norm of B. BNORM >= 0.
*> \endverbatim
*>
*> \param[in] CNORM
*> \verbatim
*> CNORM is REAL
*> 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 OTHERauxiliary
* =====================================================================
REAL FUNCTION SLARMM( ANORM, BNORM, CNORM )
IMPLICIT NONE
* .. Scalar Arguments ..
REAL ANORM, BNORM, CNORM
* .. Parameters ..
REAL ONE, HALF, FOUR
PARAMETER ( ONE = 1.0E0, HALF = 0.5E+0, FOUR = 4.0E+0 )
* ..
* .. Local Scalars ..
REAL BIGNUM, SMLNUM
* ..
* .. External Functions ..
REAL SLAMCH
EXTERNAL SLAMCH
* ..
* .. Executable Statements ..
*
*
* Determine machine dependent parameters to control overflow.
*
SMLNUM = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' )
BIGNUM = ( ONE / SMLNUM ) / FOUR
*
* Compute a scale factor.
*
SLARMM = ONE
IF( BNORM .LE. ONE ) THEN
IF( ANORM * BNORM .GT. BIGNUM - CNORM ) THEN
SLARMM = HALF
END IF
ELSE
IF( ANORM .GT. (BIGNUM - CNORM) / BNORM ) THEN
SLARMM = HALF / BNORM
END IF
END IF
RETURN
*
* ==== End of SLARMM ====
*
END
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