initial commit

Project.toml

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+name = "ADelemtree"
+uuid = "06eadbd4-12ad-4cbc-ab6e-10f8370940a5"
+authors = ["Stuart Daines <stuart.daines@gmail.com>"]
+version = "0.1.0"
+
+[deps]
+DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+
+[extras]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Test", "Logging", "LinearAlgebra"]

README.md

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+# ADelemtree.jl
+
+Automatic Jacobian sparsity detection using minimal scalar tracing and autodifferentiation.
+
+## Installation
+
+The package is not yet registered, so add it using:
+
+```julia
+julia> ] add https://github.com/sjdaines/ADelemtree.jl
+```
+
+## Example
+```julia
+julia> import ADelemtree as AD
+
+julia> function rober(du,u,p)
+                   y₁,y₂,y₃ = u
+                   k₁,k₂,k₃ = p
+                   du[1] = -k₁*y₁+k₃*y₂*y₃
+                   du[2] =  k₁*y₁-k₂*y₂^2-k₃*y₂*y₃
+                   du[3] =  k₂*y₂^2
+                   nothing
+               end;
+
+julia> u = [1.0, 2.0, 3.0];
+
+julia> p = (0.04,3e7,1e4);
+
+julia> u_ad = AD.create_advec(u);
+
+julia> du_ad = similar(u_ad);
+
+julia> rober(du_ad, u_ad, p)
+
+julia> AD.deriv(du_ad[3])
+2-element SparseArrays.SparseVector{Float64, Int64} with 1 stored entry:
+  [2]  =  1.2e8
+
+julia> Jad = AD.jacobian(du_ad, length(du_ad))
+3×3 SparseArrays.SparseMatrixCSC{Float64, Int64} with 7 stored entries:
+ -0.04  30000.0        20000.0
+  0.04     -1.2003e8  -20000.0
+   ⋅        1.2e8           ⋅ 
+
+```
+
+## Implementation
+
+Implements a scalar type `ADelemtree.ADval{T<:Real}` that holds a value and a binary tree of scalar derivatives. The tree is initialised to a Vector of leaf nodes by `ADelemtree.create_advec`.  It is populated with derivatives calculated by `DiffRules` when a Julia function is called (eg a function `y = f(x)` calculating the RHS of an ODE). `ADelemtree.jacobian` then walks the tree and calculates the Jacobian as a sparse matrix.  This provides a robust way of detecting Jacobian sparsity (and for test purposes only, a very slow way of calculating the actual derivative).  The sparsity pattern may then be used to generate matrix colouring for a fast AD package eg `SparseDiffTools`.