lambertw, all branches

[Albert Chan]

(02-01-2024 04:16 PM)Albert Chan Wrote:  Previous post customized LN and ability to enter W guess also included.

Python W nudge imag part from inside LN, because it is free.
Customized LN need to fix ±0j effect to phase angle anyway.

Lua I.W (post 14) work differently, by forcing positive x imag part, with "flips"
The reason is signed-zero arithmetic preferred +0. It is much easier to maintain +0 than -0.

If I were to implement equivalent safe feature, I would just force this for each iteration.
This is a safe patch, since it is what is assumed. Just place it before Newton correction.

Code:

x = I(I.real(x), abs(I.imag(x)))

For the ability to user to enter W guess, add this before Newton loops.

Code:

if verbal and verbal~=true then x = flip(verbal) end

With these patches to post 14, this is Lua I.W version 4

The patch does not mean we can use any guess.
The problem is again ±0*I, with negative real part.

We get phase angle of ±pi, difference of ±2*pi, exactly matched branch ±1
This is why branch 0, ±1 with small imag parts *must* have good guess.