Allow pure python Fq for beta approximation.

[pkienzle]

Allow pure python F(q) functions such as the following:

def Fq(q, sld, sld_solvent, radius):
    """Calculate F(q), F^2(q) for sphere"""
    qr = q * radius
    sn, cn = sin(qr), cos(qr)
    with np.errstate(all='ignore'):
        bes = 3 * (sn - qr * cn) / qr ** 3 # may be 0/0 but we fix that next line
        bes[qr == 0] = 1
    fq = bes * (1e-2 * (sld - sld_solvent) * form_volume(radius))
    return fq, fq**2
Fq.vectorized = vectorized  # Fq accepts an array of q value

Test using:

python -m sasmodels.compare -pars -midq sphere@hardsphere,_spherepy@hardsphere radius_pd=0.1 structure_factor_mode=1

[butlerpd]

@yunliu01 and @smalex-z to speak with @pkienzle about this

[butlerpd]

Looks like it needs some unit tests.

[wpotrzebowski]

Not a priority for 6.0 but will be good to have

[lucas-wilkins]

This looks OK and it looks like it will do what it is supposed to do, but there does seem to be a lot of mordernisation to be done on these files. If assessed it more consistency with existing code, rather than something approximating best practice.

[lucas-wilkins]

I take it you're using callable here because model_info.compiled isn't exactly what you want. If it is, consider being consistent with the other changes.

[pkienzle]

info.compiled is for info.Fq and info.Iq jointly. Only one of them will be defined, and it may be defined using C source or using a callable python function.

It occurs to me that we could use some numba transforms here so that the code runs as fast as a C model on the CPU (or faster since loop parallelization can run over multiple cores). Python models get much easier to write when we don't have to vectorize across if statements.

[lucas-wilkins]

I'm not certain, but slicing a numpy array might be considerably faster than zip(*)

[pkienzle]

Surprisingly, the zip version is faster:

In [15]: %timeit x,y = [np.array(v) for v in zip(*(((i, i) for i in np.arange(1000))))]
242 μs ± 7.15 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)

In [16]: %timeit x,y = (a:=np.array(list((i, i) for i in np.arange(1000))))[:,0],a[:,1]
389 μs ± 4.75 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)

But in any case, this cost is small compared to evaluating the function at each q.

[lucas-wilkins]

It might make sense to make this a dataclass and avoid having variables initialised to values outside their type

[lucas-wilkins]

If they were for prototyping, consider removing them, if they're for testing, they and their dependents should be settable after loading the file.

[pkienzle]

prototyping. It could be moved to the explore directory.

[lucas-wilkins]

I think @butlerpd said he would try writing some python models to check with.

[butlerpd]

yes @lucas-wilkins that bit is now on me.