Allow to use custom jacobian implementation.

[lassepe]

For prototyping, ForwardDiff.jacobian is very good but it still allocates significantly more memory than a hand-written Jacobian.

GaussianFilters.jl/src/ekf.jl

Line 26 in bc24efe

F = ForwardDiff.jacobian(μ -> filter.d.f(μ, u), b0.μ)

GaussianFilters.jl/src/ekf.jl

Line 73 in bc24efe

H = ForwardDiff.jacobian(μ -> filter.o.h(μ, u), bp.μ)

I think the user should be allowed to overload these functions by implementing something like GaussianFilters.linear_obsmodel and GaussianFilters.linear_dynamics. You can provide a default implementation based in ForwardDiff.jacobian of these methods and for the linear cases, you can provide a simple identity. By this means, you can avoid the manual type checking and let dispatch do the magic.

[zsunberg]

@lassepe just out of curiosity, can the performance problems of ForwardDiff be avoided by the user by them implementing a method of jacobian? or does that not work because of the mu -> filter.d.f(mu, u) anonymous function?

[lassepe]

The latter is the case.

[lassepe]

Also, this would not be very desirable because the user might want to use another AD tool like Zygote. It would be very weird for the user to write a version of ForwardDiff.jacobian that just calls another AD.

[zsunberg]

right - that makes a lot of sense