The ode_def macro

@ode_def name begin
    differential equation
end parameters :: ODEFunction

Definition of the Domain-Specific Language (DSL)

A helper macro is provided to make it easier to define a ParameterizedFunction, and it will symbolically compute a bunch of extra functions to make the differential equation solvers run faster. For example, to define the previous LotkaVolterra, you can use the following command:

f = @ode_def LotkaVolterra begin
    dx = a*x - b*x*y
    dy = -c*y + d*x*y
end a b c d

or you can define it anonymously:

f = @ode_def begin
    dx = a*x - b*x*y
    dy = -c*y + d*x*y
end a b c d

@ode_def uses ModelingToolkit.jl internally and returns an ODEFunction with the extra definitions (Jacobian, parameter Jacobian, etc.) defined through the MTK symbolic tools.

@ode_def_bare name begin
    differential equation
end parameters :: ODEFunction

Like @ode_def but the opts options are set so that no symbolic functions are generated. See the @ode_def docstring for more details.

@ode_def_all name begin
    differential equation
end parameters :: ODEFunction

Like @ode_def but the opts options are set so that all possible symbolic functions are generated. See the @ode_def docstring for more details.

ode_def_opts(name::Symbol,opts::Dict{Symbol,Bool},curmod,ex::Expr,params...;depvar=:t)

The core internal. Users should only interact with this through the @ode_def_* macros.

Options are self-explanatory by name mapping to ODEFunction:

• build_tgrad
• build_jac
• build_expjac
• build_invjac
• build_invW
• buildinvWt
• build_hes
• build_invhes
• build_dpfuncs

depvar sets the symbol for the dependent variable.

Example:

opts = Dict{Symbol,Bool}(
      :build_tgrad => true,
      :build_jac => true,
      :build_expjac => false,
      :build_invjac => true,
      :build_invW => true,
      :build_invW_t => true,
      :build_hes => false,
      :build_invhes => false,
      :build_dpfuncs => true)