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| # Callable parameters and interpolating data | ||
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| ModelingToolkit.jl allows creating parameters that represent functions to be called. This | ||
| is especially useful for including interpolants and/or lookup tables inside ODEs. In this | ||
| tutorial we will create an `ODESystem` which employs callable parameters to interpolate data | ||
| inside an ODE and go over the various syntax options and their implications. | ||
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| ## Callable parameter syntax | ||
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| The syntax for callable parameters declared via `@parameters` must be one of the following | ||
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| 1. `(fn::FType)(..)` | ||
| 2. `fn(::argType1, ::argType2, ...)` | ||
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| In the first case, the parameter is callable with any number/combination of arguments, and | ||
| has a type of `FType` (the callable must be a subtype of `FType`). In the second case, | ||
| the parameter is callable with as many arguments as declared, and all must match the | ||
| declared types. | ||
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| By default, the return type of the callable symbolic is inferred to be `Real`. To change | ||
| this, a `::retType` annotation can be added at the end. | ||
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| To declare a function that returns an array of values, the same array syntax can be used | ||
| as for normal variables: | ||
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| ```julia | ||
| @parameters (foo::FType)(..)[1:3]::retType | ||
| @parameters foo(::argType1, ::argType2)[1:3]::retType | ||
| ``` | ||
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| `retType` here is the `eltype` of the returned array. | ||
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| ## Storage of callable parameters | ||
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| Callable parameters declared with the `::FType` syntax will be stored in a `Vector{FType}`. | ||
| Thus, if `FType` is non-concrete, the buffer will also be non-concrete. This is sometimes | ||
| necessary to allow the value of the callable to be switched out for a different type without | ||
| rebuilding the model. Typically this syntax is preferable when `FType` is concrete or | ||
| a small union. | ||
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| Callable parameters declared with the `::argType1, ...` syntax will be stored in a | ||
| `Vector{FunctionWrappers.FunctionWrapper{retType, Tuple{argType1, ...}}}`. This suffers | ||
| the small overhead of a `FunctionWrapper` and restricts the signature of the callable, | ||
| symbolic, but allows storing the parameter in a type-stable manner and swapping it out. | ||
| This is preferable when the values that the callable can take do not share a common | ||
| subtype. For example, when a callable can represent the activation of a neural network | ||
| and can be `tanh`, `sigmoid`, etc. which have a common ancestor of `Function`. | ||
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| If both `::FType` and `::argType`s are specified, `::FType` takes priority. For example, | ||
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| ```julia | ||
| @parameters (p::LinearInterpolation)(::Real) | ||
| ``` | ||
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| `p` will be stored in a `Vector{LinearInterpolation}`. If `::LinearInterpolation` was not | ||
| specified, it would be stored in a `Vector{FunctionWrapper{Real, Tuple{Real}}}`. | ||
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| ## Example using interpolations | ||
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| ```@example callable | ||
| using ModelingToolkit | ||
| using OrdinaryDiffEq | ||
| using DataInterpolations | ||
| using ModelingToolkit: t_nounits as t, D_nounits as D | ||
| ts = collect(0.0:0.1:10.0) | ||
| spline = LinearInterpolation(ts .^ 2, ts) | ||
| Tspline = typeof(spline) | ||
| @variables x(t) | ||
| @parameters (interp::Tspline)(..) | ||
| @mtkbuild sys = ODESystem(D(x) ~ interp(t), t) | ||
| ``` | ||
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| The derivative of `x` is obtained via an interpolation from DataInterpolations.jl. Note | ||
| the parameter syntax. The `(..)` marks the parameter as callable. `(interp::Tspline)` | ||
| indicates that the parameter is of type `Tspline`. | ||
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| ```@example callable | ||
| prob = ODEProblem(sys, [x => 0.0], (0.0, 1.0), [interp => spline]) | ||
| solve(prob) | ||
| ``` | ||
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| Note that the the following will not work: | ||
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| ```julia | ||
| ODEProblem( | ||
| sys; [x => 0.0], (0.0, 1.0), [interp => LinearInterpolation(0.0:0.1:1.0, 0.0:0.1:1.0)]) | ||
| ``` | ||
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| Since the type of the spline doesn't match. |
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