type s = mats is the type of the state (and thus also of the initial condition) provided to Owl_ode.Ode.odeint. For example Owl.Mat.mat.
type t = matt is type of the output of the evolution function f: s-> float ->t. For example, in the case of sympletic solvers, type s = Owl.Mat.(mat*mat) and type t = Owl.Mat.mat.
type step_output = mat * floatstep_output defines the type of the output of Owl_ode.Ode.step. For example, in the case of native adaptive solvers, type output = Owl.Mat.(mat * float * float * bool), corresponds to matrices and floats that contain respectively the y1, t1, dt, and whether this step was valid
output defines the type of the output of Owl_ode.Ode.odeint. For example, in the case of sympletc solvers, type output = Owl.Mat.(mat * mat * mat), corresponds to matrices that contain respectively the time, position, and momentum coordinates of the integrated solution
val step : (s -> float -> t) -> dt:float -> s -> float -> step_outputstep f dt y0 t0 () solves for one step given dt, y0, t0 and the evolution function. Several such functions have already been implemented in this library and can be used as reference.
val solve : (s -> float -> t) -> s -> Types.tspec_t -> unit -> outputsolve f y0 tspec () solves the initial value problem
∂ₜ y = f(y, t) y(t₀) = y₀
with the given evolution function f, initial condition y0, and temporal specification tspec, and returns the desired outputs of type output. Several such functions have already been implemented in this library and can be used as reference.