Added docs

Author: RafaelArutjunjan

README.md

@@ -7,6 +7,10 @@
 
 This package provides a front-end for differentiation operations in Julia that allows for code which is agnostic with respect to many of the available automatic and symbolic differentiation tools available in Julia. Moreover, the differentiation operators provided by **DerivableFunctions.jl** are also overloaded to allow for passthrough of symbolic variables. That is, if symbolic types such as `Symbolics.Num` are detected, the differentiation operators automatically switch to symbolic differentiation.
 
+In addition to these operators, **DerivableFunctions.jl** also provides the `DFunction` type, which stores methods for the first and second derivatives to allow for more convenient and potentially more performant computations if the derivatives are known.
+
+For detailed examples, please see the [**documentation**](https://RafaelArutjunjan.github.io/DerivableFunctions.jl/dev).
+
 ```julia
 julia> D = DFunction(x->[exp(x[1]^2 - x[2]), log(sin(x[2]))])
 (::DerivableFunction) (generic function with 1 method)

docs/make.jl

@@ -15,6 +15,8 @@ makedocs(;
     ),
     pages=[
         "Home" => "index.md",
+        "Differentiation Operators" => "Operators.md",
+        "DFunctions" => "DFunctions.md"
     ],
 )
 

docs/src/DFunctions.md

@@ -0,0 +1,19 @@
+
+### DFunctions
+
+The `DFunction` type stores the first and second derivatives of a given input function which is not only convenient but can enhance performance significantly. At this point, the `DFunction` type requires the given function to be out-of-place, however, this will likely be extended to in-place functions in the future.
+
+Once constructed, a `DFunction` object `D` can be evaluated at `x` via the syntax `EvalF(D,x)`, `EvaldF(D,x)` and `EvalddF(D,x)`.
+
+In order to construct the appropriate derivatives, the input and output dimensions of a given function `F` are assessed and the appropriate operators (`GetGrad(), GetJac()` and so on) called.
+
+By default, `DFunction()` attempts to construct the derivatives symbolically, however, this can be specified via the `ADmode` keyword:
+```@example 2
+using DerivableFunctions
+
+D = DFunction(x->[x^7 - sin(x), tanh(x)]; ADmode=Val(:ReverseDiff))
+EvalF(D, 5.), EvaldF(D, 5.), EvalddF(D, 5.)
+
+using Symbolics;  @variables y
+EvalF(D, y), EvaldF(D, y), EvalddF(D, y)
+```

docs/src/Operators.md

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+
+### Differentiation Operators
+
+[**DerivableFunctions.jl**](https://github.com/RafaelArutjunjan/DerivableFunctions.jl) aims to provide a backend-agnostic interface for differentiation and currently allows the user to seamlessly switch between [**ForwardDiff.jl**](https://github.com/JuliaDiff/ForwardDiff.jl), [**ReverseDiff.jl**](https://github.com/JuliaDiff/ReverseDiff.jl), [**Zygote.jl**](https://github.com/FluxML/Zygote.jl), [**FiniteDifferences.jl**](https://github.com/JuliaDiff/FiniteDifferences.jl) and [**Symbolics.jl**](https://github.com/JuliaSymbolics/Symbolics.jl).
+
+The desired backend is optionally specified in the first argument (default is ForwardDiff) via a `Symbol` or `Val`. The available backends can be listed via `diff_backends()`.
+
+Next, the function that is to be differentiated is provided. We will illustrate this syntax using the `GetMatrixJac` method:
+```@example 1
+using DerivableFunctions
+Metric(x) = [exp(x[1]^3) sin(cosh(x[2])); log(sqrt(x[1])) x[1]^2*x[2]^5]
+Jac = GetMatrixJac(Val(:ForwardDiff), Metric)
+Jac([1,2.])
+```
+
+Moreover, these operators are overloaded to allow for passthrough of symbolic variables.
+```@example 1
+using Symbolics
+@variables z[1:2]
+Jac(z)
+```
+
+Since the function `Metric` in this example can be represented in terms of analytic expressions, it is also possible to construct its derivative symbolically:
+```@example 1
+SymJac = GetMatrixJac(Val(:Symbolic), Metric)
+SymJac([1,2.])
+```
+
+Currently, [**DerivableFunctions.jl**](https://github.com/RafaelArutjunjan/DerivableFunctions.jl) exports `GetDeriv(), GetGrad(), GetHess(), GetJac()` and `GetMatrixJac()`.