Improve mixmode

[d7919]

There are several possible modifications to the mixmode modifier that might be helpful in some scenarios.

1. There are some precision issues with the logistic map used (see fix test-initial to allow more precise calculation #555), could we replace this with something better behaved (but avoiding library code which code change from version to version).
2. User configurable index for the location of the peak amplitude -- currently always a fixed mode index that gets the largest amplitude (I think it may be 4) but this means the conditions are z resolution dependent (i.e. different n will be the peak depending on mz).
3. User configurable cutoff -- currently always initialises up to the first 14 modes and then the rest are zero. Would be nice to be able to change this so that we could initialise all modes (for example) or just a larger subset, can avoid sharp boundaries in the spectrum, which might help some cases.

Maybe we should introduce a new modifier for this so we can maintain the existing behaviour for compatibility?

Any other suggestions?

[bendudson]

Functions like mixmode can take an arbitrary number of optional inputs. The constructor is just given a list, so any which are not set can default to current settings.

https://github.com/boutproject/BOUT-dev/blob/master/src/field/fieldgenerators.cxx#L199

1. Yes, a better PRNG seems like a definite

2. the n=4 mode is currently the maximum, but this should not be mz dependent: The 4th harmonic depends on the length in z, not the resolution. Agree though that it would be good to make this configurable

3. Yes, also a good idea

Currently the second (optional) parameter to mixmode is the random seed, so we could have

mixmode(z, [seed, [npeak, [nmax]]] )

to be backward compatible, or rearrange the arguments if desired. Unfortunately the parser doesn't support keywords at the moment. Maybe not too hard to add, but more mission creep.

[d7919]

On 2. -- Ah yes, I thought it was operating in Fourier space but it's not, thanks.

[dschwoerer]

I am not quite sure, but is there a good reason the amplitude (in fft space) has to have the form 1/(1+|n-n_i|)^2 ?
Something along the line of
mixmode(z[, f(n)[,seed]])
would be far more flexible.
Where the legacy mixmode would be reproduced as something like:
mixmode(z, "1/((1+abs(n-4))*(1+abs(n-4)))*h(14-n)",seed)