This is for the "ll" function defined for quaternions and octonions. The function returns the 1-norm of its argument. Does anyone know what the "ll" name stands for? I finally figured out that "sup" (the infinity-norm) most likely stands for "supremum". (BTW, "abs" is the 2-norm. The "norm" function isn't actually in this system, despite the name!) -- Daryle Walker Mac, Internet, and Video Game Junkie darylew AT hotmail DOT com
Daryle Walker wrote:
This is for the "ll" function defined for quaternions and octonions. The function returns the 1-norm of its argument. Does anyone know what the "ll" name stands for? I finally figured out that "sup" (the infinity-norm) most likely stands for "supremum". (BTW, "abs" is the 2-norm. The "norm" function isn't actually in this system, despite the name!)
Hmmm... My guess from looking at the name 'll' would have been ll == length * length (frobenius norm), but it's not the 1-norm ;-(. Regards, Tobias
Somewhere in the E.U., le 11/08/2005 Bonjour Peeking back after vacations are over... In article <BAY104-DAV130A4664B11F6CDE9DB931BFD20@phx.gbl>, Daryle Walker <darylew@hotmail.com> wrote:
This is for the "ll" function defined for quaternions and octonions. The function returns the 1-norm of its argument. Does anyone know what the "ll" name stands for? I finally figured out that "sup" (the infinity-norm) most likely stands for "supremum". (BTW, "abs" is the 2-norm. The "norm" function isn't actually in this system, despite the name!)
it is actually the L1 (ell-one) norm (sum of the norm of the components, the lp norm would be the sum of the p-th power of the norm of the components, and the l-infinite norm is just the supremum of the norm of the components). This was to be consistent with the usual mathematical terminology (lower-case "l" for the norm of sequence spaces, upper-case "l" for other measured spaces, though in this case we only have a quadruple or an octuple). I agree the resemblance between the "l" and the "1" is quite unfortunate. I have no special love for that notation, but fear that changing it now would be more hassle than what it's worth. At the very least, I'll add a note to the documentation after the 1.33 release. Merci Hubert Holin
On 8/11/05 10:05 AM, "Hubert Holin" <Hubert.Holin@meteo.fr> wrote: [SNIP]
it is actually the L1 (ell-one) norm [...]
[Use "Font increase" a bunch of times on the web page....] Wow! It really is an "l" (ell) and "1" (one), and not two "l" (ell) characters.
[...] I agree the resemblance between the "l" and the "1" is quite unfortunate. [TRUNCATE]
[Uses the "View source" command, which uses a (programmer's) fixed-font that distinguishes between "l" (ell) and "1" (one), to reconfirm.] I better fix the name I have on a similar function in the Sandbox.... -- Daryle Walker Mac, Internet, and Video Game Junkie darylew AT hotmail DOT com
participants (5)
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Daryle Walker -
Hubert Holin -
Jonathan Turkanis -
Tobias Schwinger