Incorrect docstrings for kernel functions

[thawes-rse]

Summary

This issue relates to the docstring of the kernel_f method in mogp_emulator.Kernel.KernelBase. The docstring says the params argument should be "1-D with length one greater than the last dimension of x1 and x2". This does not appear to match the current implementation, which I think expects params to be a 1-dim Numpy array with length equal to the last dimensions of x1 and x2.

Aside from this, the documentation should make clear what these params refer to mathematically. Having looked at the implementation of SquaredExponential, I think these are meant to be the 'raw' version of the correlation length scale parameters (as outlined in the docstring for GPParams), although it would be good to get a package maintainer to confirm this. This would also seem to indicate that the kernels assume that the covariance is equal to 1 (again using the terminology of the docstring for GPParams). If true, this again needs to be made clear in the documentation, because it differs from other mathematical treatments of kernel functions (see e.g. https://uk.mathworks.com/help/stats/kernel-covariance-function-options.html).

Versions used

Python 3.9.18
mogp-emulator 0.7.2
numpy 1.26.3
scipy 1.11.4
patsy 0.5.6

Reproducible example of error

We consider only SquaredExponential and Matern52 below, but similar problems arise for the other named kernels, ProductMat52, UniformSqExp and UniformMat52.

>>> import numpy as np
>>> from mogp_emulator.Kernel import Matern52, SquaredExponential
>>> x1 = np.random.random(3)
>>> x2 = np.random.random(3)
>>> params = np.array([1, 2, 3, 4])  # len = x1.shape[-1] + 1 = x2.shape[-1] + 1, as per documentation for kernel_f
>>> Matern52().kernel_f(x1, x2, params)
>>> SquaredExponential().kernel_f(x1, x2, params)

Expected behaviour

The expressions Matern52().kernel_f(x1, x2, params) and SquaredExponential().kernel_f(x1, x2, params) evaluate to a single-element Numpy array of shape (1, 1).

Actual behaviour

>>> Matern52().kernel_f(x1, x2, params)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "path/to/lib/python3.9/site-packages/mogp_emulator/Kernel.py", line 129, in kernel_f
    x1, n1, x2, n2, params, D = self._check_inputs(x1, x2, params)
  File "path/to/lib/python3.9/site-packages/mogp_emulator/Kernel.py", line 79, in _check_inputs
    x1 = np.reshape(x1, (1, D))
  File "path/to/lib/python3.9/site-packages/numpy/core/fromnumeric.py", line 285, in reshape
    return _wrapfunc(a, 'reshape', newshape, order=order)
  File "path/to/lib/python3.9/site-packages/numpy/core/fromnumeric.py", line 59, in _wrapfunc
    return bound(*args, **kwds)
ValueError: cannot reshape array of size 3 into shape (1,4)
>>> SquaredExponential().kernel_f(x1, x2, params)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "path/to/lib/python3.9/site-packages/mogp_emulator/Kernel.py", line 129, in kernel_f
    x1, n1, x2, n2, params, D = self._check_inputs(x1, x2, params)
  File "path/to/lib/python3.9/site-packages/mogp_emulator/Kernel.py", line 79, in _check_inputs
    x1 = np.reshape(x1, (1, D))
  File "path/to/lib/python3.9/site-packages/numpy/core/fromnumeric.py", line 285, in reshape
    return _wrapfunc(a, 'reshape', newshape, order=order)
  File "path/to/lib/python3.9/site-packages/numpy/core/fromnumeric.py", line 59, in _wrapfunc
    return bound(*args, **kwds)
ValueError: cannot reshape array of size 3 into shape (1,4)