dlarmm()

double precision function dlarmm	(	double precision	anorm,
		double precision	bnorm,
		double precision	cnorm
	)

DLARMM

Purpose:

 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.

Parameters

[in]	ANORM	ANORM is DOUBLE PRECISION The infinity norm of A. ANORM >= 0. The number of rows of the matrix A. M >= 0.
[in]	BNORM	BNORM is DOUBLE PRECISION The infinity norm of B. BNORM >= 0.
[in]	CNORM	CNORM is DOUBLE PRECISION The infinity norm of C. CNORM >= 0. 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.

Definition at line 60 of file dlarmm.f.

      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 ====
*

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