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100 lines
2.4 KiB
100 lines
2.4 KiB
2 years ago
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*> \brief \b SLARMM
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*
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* Definition:
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* ===========
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*
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* REAL FUNCTION SLARMM( ANORM, BNORM, CNORM )
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*
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* .. Scalar Arguments ..
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* REAL ANORM, BNORM, CNORM
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* ..
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*
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*> \par Purpose:
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* =======
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*>
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*> \verbatim
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*>
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*> SLARMM returns a factor s in (0, 1] such that the linear updates
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*>
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*> (s * C) - A * (s * B) and (s * C) - (s * A) * B
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*>
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*> cannot overflow, where A, B, and C are matrices of conforming
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*> dimensions.
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*>
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*> This is an auxiliary routine so there is no argument checking.
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*> \endverbatim
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*
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* Arguments:
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* =========
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*
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*> \param[in] ANORM
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*> \verbatim
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*> ANORM is REAL
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*> The infinity norm of A. ANORM >= 0.
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] BNORM
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*> \verbatim
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*> BNORM is REAL
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*> The infinity norm of B. BNORM >= 0.
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*> \endverbatim
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*>
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*> \param[in] CNORM
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*> \verbatim
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*> CNORM is REAL
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*> The infinity norm of C. CNORM >= 0.
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*> \endverbatim
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*>
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*>
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* =====================================================================
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*> References:
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*> C. C. Kjelgaard Mikkelsen and L. Karlsson, Blocked Algorithms for
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*> Robust Solution of Triangular Linear Systems. In: International
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*> Conference on Parallel Processing and Applied Mathematics, pages
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*> 68--78. Springer, 2017.
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*>
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*> \ingroup OTHERauxiliary
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* =====================================================================
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REAL FUNCTION SLARMM( ANORM, BNORM, CNORM )
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IMPLICIT NONE
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* .. Scalar Arguments ..
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REAL ANORM, BNORM, CNORM
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* .. Parameters ..
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REAL ONE, HALF, FOUR
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PARAMETER ( ONE = 1.0E0, HALF = 0.5E+0, FOUR = 4.0E+0 )
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* ..
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* .. Local Scalars ..
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REAL BIGNUM, SMLNUM
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* ..
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* .. External Functions ..
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REAL SLAMCH
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EXTERNAL SLAMCH
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* ..
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* .. Executable Statements ..
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*
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*
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* Determine machine dependent parameters to control overflow.
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*
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SMLNUM = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' )
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BIGNUM = ( ONE / SMLNUM ) / FOUR
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*
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* Compute a scale factor.
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*
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SLARMM = ONE
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IF( BNORM .LE. ONE ) THEN
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IF( ANORM * BNORM .GT. BIGNUM - CNORM ) THEN
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SLARMM = HALF
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END IF
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ELSE
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IF( ANORM .GT. (BIGNUM - CNORM) / BNORM ) THEN
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SLARMM = HALF / BNORM
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END IF
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END IF
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RETURN
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*
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* ==== End of SLARMM ====
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*
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END
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