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[![Travis](https://travis-ci.org/JuliaDiffEq/ParameterizedFunctions.jl.svg?branch=master)](https://travis-ci.org/JuliaDiffEq/ParameterizedFunctions.jl) [![AppVeyor](https://ci.appveyor.com/api/projects/status/k6b7d86ddbas1ajk?svg=true)](https://ci.appveyor.com/project/ChrisRackauckas/parameterizedfunctions-jl)
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[![codecov](https://codecov.io/gh/JuliaDiffEq/ParameterizedFunctions.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaDiffEq/ParameterizedFunctions.jl)
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## Note that this library is deprecated in favor of [ModelingToolkit.jl](https://github.com/JuliaDiffEq/ModelingToolkit.jl). ParameterizedFunctions.jl will continue to work but is in maitanance mode.
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ParameterizedFunctions.jl is a component of the JuliaDiffEq ecosystem which allows
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for parameters to be explicitly present within functions. The interface which
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ParameterizedFunctions describes allows for functionality which requires parameters,
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such as parameter sensitivity analysis and parameter estimation, to be added to
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the differential equation solvers of [DifferentialEquations.jl](https://github.com/JuliaDiffEq/DifferentialEquations.jl).
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While the interface itself is of importance to ecosystem developers,
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ParameterizedFunctions.jl provides user-facing macros which make a
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`ParameterizedFunction` easy to define, and automatically
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include optimizations like explicit Jacobian functions and explicit inverse Jacobian
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functions for the differential equation solvers to take advantage of. The result
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is an easy to use API which allows for more functionality and more performance
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optimizations than could traditionally be offered.
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test
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## The Basic Idea
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`ParameterizedFunction` is a type which can be used in various JuliaDiffEq solvers where
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the parameters must be accessible by the solver function. These use call overloading
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generate a type which acts like a function `f(t,u,du)` but has access to many more
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features. For example, a `ParameterizedFunction` can contain a function for the Jacobian
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or Inverse Jacobian. If such functions exist, the solvers can use them to increase
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the speed of computations. If they don't exist, the solvers will ignore them. Since
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`ParameterizedFunction` is a subtype of `Function`, these can be used anywhere that
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a function can be used, just with the extra functionality ignored.
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ParameterizedFunctions.jl is a component of the SciML ecosystem which allows
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for easily defining parameterized ODE models in a simple syntax.
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## Basic Usage
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