LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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.

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*
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function dlarmm(anorm, bnorm, cnorm)
DLARMM
Definition dlarmm.f:61
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