smith-garrett/uniformization.jl

A Julia package for solving continuous-time Markov chains using the uniformization/randomization method

uniformization.jl's Issues

Consider implementing uniformization-based first-passage time statistics

See Latouche & Ramaswami (1999), p. 58 and Yoon & Shanthikumar (1989). Even when the system is not absorbing, the FPT measures could still be interesting (e.g., first time to reach state X).

This might also be feature creep.

Make custom PMF for solution of CTMC

Implement e.g., mean, variance, etc. of custom Categorical distribution (?).

Document code

Set up package documentation with Documenter.jl

Create tests for different array types

CUArray, OffsetArrays

Look into avoiding allocations using similar()

Could especially help in the standard uniformization fn.: get rid of deepcopy() and swap in similar().

Make tests for automatic differentiation

Partially covered by #19 with Dual types, but probably need more. Look at tests for ExponentialAction for inspiration.

Implement first-passage time statistics

(log) PDF, mean, variance, moments in general.

Implement other methods of solution?

E.g., from Yoon & Shanthikumar (1989) or Fox & Glynn 1988.

Create method for sampling trajectories

Consider interface w/ JumpProcesses.jl/Catalyst.jl. Could also just write a quick Gillespie implementation.

Create tests for general correctness

Consider additional tests with stiff systems

Figure out where breakdown should and should not occur, write tests that test that.

Allow more types of matrices

Sparse is probably most important, but generality should be a goal. StaticArrays might be good to include for smaller matrices.

Make plotting recipes

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Implement first-passage infrastructure

Probably need types for:

• Transient and absorbing matrices
• p0 as Categorical distribution?

Need functions for converting TransitionRateMatrix to first-pasage type

• Function should detect whether there are already absorbing states
• If so, create FP object
• Else, return error with reference to method that requires specifying initial and absorbing states
  • This method should modify the transition rate matrix to be have correct entries/elements

Switch to passing a named tuple for params instead of positional arguments

Similar to SciML way.

Consider implementing AbstractArrays interface for uniformized matrix

https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-array

Create function for simulating whole trajectories

Simulate solution of master equation by applying uniformization incrementally, e.g., starting at time point 0 w/ initial conditions, solve for t=0.01. That solution is now the initial state for getting the solution at t=0.02, e.g. This avoids problems related to stiffness: When the (time * uniformization rate) gets large, uniformization becomes inefficient due to the many matrix multiplications that have to be performed.

It would be interesting to consider adaptive time stepping or adaptation of the uniformization rate, but that might be too much initially.

Get DOI for code

Make benchmarking tests

Comparisons: ExponentialAction, ExponentialUtilities, base exp(::Matrix).

Improve documentation

• Follow advice on main Julia documentation (basic formatting)
• Use $(SIGNATURES) from DocStringExtentions to automatically fill in function signatures

Create tests for different element types

SciML recommends Dual (AD), and BigFloat, along with Float{64, 32}. Complex isn't relevant here.

Create a problem type

Should contain at least a transition matrix and initial condition, maybe a solution method. Relates to #3 and maybe #4.

Write readme