Support direction `tdir` change in `reinit!`

[ivborissov]

Is your feature request related to a problem? Please describe.

Currently reinit! supports tspan change. However changing the endpoint to a negative (reverse) direction doesn't work. An artificial MWE of a problem, which arises when integrating a profile of a likelihood function:

using OrdinaryDiffEq

prob = ODEProblem((du, u, p, t) -> du[1] = 1.0, [0.], (0.,1.))

# right direction
integrator = init(prob, Tsit5())
reinit!(integrator; t0=0., tf=5.0)
solve!(integrator)
integrator.sol.t[end] 
# 5.0 correct

# left direction
integrator = init(prob, Tsit5())
reinit!(integrator; t0=0., tf=-5.0)
solve!(integrator)
integrator.sol.t[end] 
# 5.0 wrong

A trick, which seems to makes the code work is to change tdir, dtmax manualy:

integrator = init(prob, Tsit5())
integrator.tdir = -1.0
integrator.opts.dtmax *= -1.0
reinit!(integrator; t0=0., tf=-5.0)
solve!(integrator)
integrator.sol.t[end] 
# -5.0 correct

Describe the solution you’d like

Can we add support for integration direction change to reinit! if it is just about checking and changing tdir and dtmax?

Describe alternatives you’ve considered

An alternative solution is to remake the problem.