Implement Perrichon2022 McStas TOSCA function as lookup table

[ajjackson]

This scheme is a "scaled" lookup table:

• At each energy-transfer a Gaussian fit was performed to determine a nominal width parameter "sigma". The relationship between sigma and energy-transfer is in turn described by a fitted polynomial.
• Each row in the lookup table corresponds to a different energy-transfer.
• The columns correspond to a zero-centered energy mesh (i.e. these are kernels) as a multiple of sigma.
• This scaling keeps the overall widths in the table fairly consistent, allowing clean linear interpolation of the shape.
• x-values are shifted and scaled appropriately in order to produce interpolated peak functions at their true locations and scales.

The table is quite compact but still a bit chunky to include in the .yaml files. Instead we store all the model parameters in a .npz file and point to this from the .yaml.

Some pre-processing was performed on the original data:

• smoothing with a Scipy "smoothing spline"
• truncation to 10σ with a smooth Tukey window function
• normalisation to constant area

[ajjackson]

Results in usage are visually pretty similar to the AbINS model but we do see some divergence especially at high energy transfer.

[RastislavTuranyi]

Some comments, mostly to do with the most recent changes from #39, but there are two major things that stick out:

1. No docstrings for get_kernel and get_peak
2. No unit tests

Could you add these? That said, tho, not sure how viable unit tests are in this case, ig they'll just have to be reference values to test for regression.

[RastislavTuranyi]

I am not sure i like this circular import (i'm surprised it works) - should we move it elsewhere?

[RastislavTuranyi]

Is there a reason to import these here instead of the top of the file?

[RastislavTuranyi]

Not sure how nitpicky to be, but this is not aligned... 😅

[RastislavTuranyi]

Suggested change

	def get_kernel(self,
	omega_q: Float[np.ndarray, 'sample dimension=1'],
	mesh: Float[np.ndarray, 'mesh'],
	) -> Float[np.ndarray, 'sample mesh']:
	def get_kernel(self,
	points: Float[np.ndarray, 'sample dimension=1'],
	mesh: Float[np.ndarray, 'mesh'],
	) -> Float[np.ndarray, 'sample mesh']:

Also, could you add a docstring?

[RastislavTuranyi]

Suggested change

	assert len(omega_q.shape) == 2 and omega_q.shape[1] == 1
	energy = omega_q
	assert points.ndim == 2 and points.shape[1] == 1
	energy = points

First, related to the discussion #39, is this check necessary? Secondly, are you sure you want to keep it as a 2D array?

[RastislavTuranyi]

Suggested change

	def get_peak(self,
	omega_q: Float[np.ndarray, 'sample dimension=1'],
	mesh: Float[np.ndarray, 'mesh'],
	) -> Float[np.ndarray, 'sample mesh']:
	def get_peak(self,
	points: Float[np.ndarray, 'sample dimension=1'],
	mesh: Float[np.ndarray, 'mesh'],
	) -> Float[np.ndarray, 'sample mesh']:

Again, could you add a docstring please?

[RastislavTuranyi]

Suggested change

	shifted_meshes = [mesh - energy for energy in omega_q[:, 0]]
	try:
	points = points[:, 0]
	except IndexError as e:
	raise InvalidPointsError(
	f'The provided array of points (shape={points.shape}) is not valid. The points '
	f'array must be a Nx1 2D array where N is the number of energy transfers.'
	) from e
	shifted_meshes = [mesh - energy for energy in points]

[RastislavTuranyi]

Suggested change

	shifted_kernels = [
	self.get_kernel(np.array([omega_q]), shifted_mesh)
	for omega_q, shifted_mesh in zip(omega_q, shifted_meshes)
	]
	shifted_kernels = [
	self.get_kernel(np.array([[point]]), shifted_mesh)
	for point, shifted_mesh in zip(points, shifted_meshes)
	]