Orientation refinement produces rubbish results on some Windows installations

[hakonanes]

Histogram of scores before and after refinement:

Corresponding score maps:

Not sure of the reason yet, might be related to some incorrect use of data types. Tests on Windows don't catch this. Haven't experienced on Linux yet. Don't know about macOS.

A fix should be released as a 0.5.7 patch as soon as the cause is identified!

[hakonanes]

Identified the culprit:

kikuchipy/kikuchipy/_rotation/__init__.py

Lines 38 to 74 in cb54764

	@nb.jit("float64[:](float64, float64, float64)", nogil=True, nopython=True)
	def _rotation_from_euler(alpha: float, beta: float, gamma: float) -> np.ndarray:
	"""Convert three Euler angles (alpha, beta, gamma) to a unit
	quaternion.
	Taken from :meth:`orix.quaternion.Rotation.from_euler`.
	Parameters
	----------
	alpha, beta, gamma
	Euler angles in the Bunge convention in radians.
	Returns
	-------
	rotation
	Unit quaternion.
	Notes
	-----
	This function is optimized with Numba, so care must be taken with
	array shapes and data types.
	"""
	sigma = 0.5 * np.add(alpha, gamma)
	delta = 0.5 * np.subtract(alpha, gamma)
	c = np.cos(beta / 2)
	s = np.sin(beta / 2)
	rotation = np.zeros(4)
	rotation[0] = c * np.cos(sigma)
	rotation[1] = -s * np.cos(delta)
	rotation[2] = -s * np.sin(delta)
	rotation[3] = -c * np.sin(sigma)
	if rotation[0] < 0:
	rotation = -rotation
	return rotation

This Numba function is used by objective functions during refinement to obtain an updated Rotation quaternion from a Euler angle triplet, which is returned by SciPy after each iteration in the parameter search. The function returned a completely different quaternion on Windows and Ubuntu when passing the same Euler angles. Turns out that initializing a zero (4,) NumPy array and setting each element is the cause for the different results. I replaced this with creating a Numpy array from the computed quaternion components, and Windows and Ubuntu produces the same quaternion, as expected. This in turn gave the same orientation refinement results on Windows and Ubuntu.

Will be fixed in a PR, and a new patch release 0.5.7 will be made tomorrow Monday January 10th.

[hakonanes]

Solved in #495.