Unify diffusion modules into single dynamics.diffusion

Currently, the diffusion1d module provides a separate interface to diffusion that focuses on one dimensional processes. The rationale for implementing a separate diffusion1d module are

Integration schemes (particularly Euler-Maruyama) can directly use operator * instead of matrix multiplication @.
There are often specific integration methods or analytical solutions for 1D processes.
On a the development-side of things, it is very often easier to implement a method in the 1D case, before extending it to the n-D case.

However the module stochrare.dynamics.diffusion1d effectively greatly overlaps with the more general stochrare.dynamics.diffusion. For example, key methods trajectory and update do not depend on the dimension of the process. Moreover, it is expected that as stochrare grows, both modules will implement the same methods, with the exception of additional methods specific to the 1d case.

We could diffusion1d into the diffusion module, resulting in a single API covering both 1D and n-D processes.

For example:

# New API
from stochrare.dynamics import diffusion
model = diffusion.ConstantDiffusionProcess(lambda x: 2*x, 1)

Should be equivalent to

# Old API
from stochrare.dynamics import diffusion1d
model = diffusion1d.ConstantDiffusionProcess1D(lambda x: 2*x, 1)

For this to work, we must

make sure integration schemes are implemented suitably dependending on the dimension of the process. Example:

x = xn + self.drift(xn, tn)*dt + self.diffusion(xn, tn)*wn # 1d case
x = xn + self.drift(xn, tn)*dt+self.diffusion(xn, tn)@dw # n-d case

Prevent methods that are only relevant to the 1d case to be called if n>1

>>> from stochrare.dynamics import diffusion # Create 3D OU process
>>> model = diffusion.OrnsteinUlhenbeckProcess(0, 1, 1, 3)
>>> model.mean_first_passage_time(0, 5.0) # Try to evaluate mean first passage time
Traceback (most recent call last):
 File "<diffusion.py>", line 3, in <stochare.dynamics.diffusion.mean_first_passage>
NotImplementedError: Mean first passage time is not available for processes of dimension higher than 1

Implement the above point is a way that makes initial development of 1d-only method convenient.

This issues depends on

cbherbert / stochrare

Unify diffusion modules into single dynamics.diffusion #4