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unify all DIscrete DS (PR #23) from JuliaDynamics/new_discrete
unify all DIscrete DS amazing changes. so much wow.
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CHANGELOG.md

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# v0.5.2
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# v0.6
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## Massively Breaking
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* Complete overhaul of Discrete Systems: all systems are now one, there is
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no longer `DDS` and `BigDDS`. Everything is `DDS`!
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* `variational_integrator` renamed to `tangent_integrator`.
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* `DDS` is made up of 2 fundamental parts: a DiscreteProblem and a
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TangentEvolver.
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## Non-breaking
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* Massive performance boost of up to 8x in system evolution.
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* Massive performance boost of up to 8x in system evolution of continuous systems.
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* `ParallelEvolver`
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* `TangentEvolver`
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# v0.5.0
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deps/build.jl

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infomsg = """
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~~~ DynamicalSystemsBase.jl update message ~~~
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We have changed the fundamental way users define
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equations of motion and Jacobians
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for all subtypes of `DynamicalSystem`!
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In short, parameters are now directly passed
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into the equations of motion function, e.g.
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`f(du, u, p, t)`. These updates are in-line
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with DifferentialEquations v4.0 release.
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Notice that the same changes happened for
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discrete systems as well. For example, the
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e.o.m. for `DiscreteDS` are now expected
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in the form `eom(x, p)`.
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Please see the documentation strings of the system types you are using!
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Also, be sure to visit the updated documentation here:
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https://juliadynamics.github.io/DynamicalSystems.jl/latest/
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"""
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info(infomsg)
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# infomsg = """
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# ~~~ DynamicalSystemsBase.jl update message ~~~
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#
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# We have changed the fundamental way users define
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# equations of motion and Jacobians
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# for all subtypes of `DynamicalSystem`!
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# In short, parameters are now directly passed
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# into the equations of motion function, e.g.
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# `f(du, u, p, t)`. These updates are in-line
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# with DifferentialEquations v4.0 release.
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#
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# Notice that the same changes happened for
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# discrete systems as well. For example, the
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# e.o.m. for `DDS` are now expected
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# in the form `eom(x, p)`.
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#
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# Please see the documentation strings of the system types you are using!
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#
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# Also, be sure to visit the updated documentation here:
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# https://juliadynamics.github.io/DynamicalSystems.jl/latest/
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#
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# """
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#
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# info(infomsg)

src/DynamicalSystemsBase.jl

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"""
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module DynamicalSystemsBase
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abstract type DynamicalSystem end
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export DynamicalSystem, Systems
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include("dataset.jl")
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include("reconstruction.jl")
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include("various.jl")
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include("continuous.jl")
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include("famous_systems.jl")
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export Systems
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end

src/continuous.jl

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import OrdinaryDiffEq.ODEProblem
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import OrdinaryDiffEq.ODEIntegrator
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export ContinuousDS, variational_integrator, ODEIntegrator, ODEProblem
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export ContinuousDS, tangent_integrator, ODEIntegrator, ODEProblem
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export ContinuousDynamicalSystem, DEFAULT_DIFFEQ_KWARGS, get_sol
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export parallel_integrator
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"""
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variational_integrator(ds::ContinuousDS, S::Matrix, [, t]; diff_eq_kwargs)
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tangent_integrator(ds::ContinuousDS, S::Matrix, [, t]; diff_eq_kwargs)
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Return an `ODEIntegrator` that represents the variational equations
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of motion for the system. `t` makes the `tspan` and if it is `Real`
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instead of `Tuple`, initial time is assumed zero.
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The only keyword argument for this funcion is `diff_eq_kwargs` (see
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[`trajectory`](@ref)).
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"""
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function variational_integrator(ds::ContinuousDS, S::Matrix, T = ds.prob.tspan;
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function tangent_integrator(ds::ContinuousDS, S::Matrix, T = ds.prob.tspan;
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diff_eq_kwargs = DEFAULT_DIFFEQ_KWARGS)
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f! = ds.prob.f

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