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I plan to bring some oder into the zoo of integrators by introducing the following interface. Currently I am thinking of

For ODEs

solve!(method::ODESolver, X::SamplePath, x0, F::Function)
solve(method::ODESolver, x0, F::Function)

where for example method=BS3() and for SDEs

solve!(method, X::SamplePath, x0, W, P)
solve!(method, X::SamplePath, x0, W, b, σ)
solve(method, x0, W, P)
solve(method, x0, W, b, σ)
bridge!(method, X::SamplePath, W, P)
bridge(method, W, P)

where for example method=Euler() which should cover all cases needed in Bridge.

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Release notes:

Fix build and add #40 "fix reference to internal Zip2 for julia 1.1"

The tag name "v0.4.0-pre" is not of the appropriate SemVer form (vX.Y.Z).
cc: @mschauer

• various instances of 'type piracy', e.g. chol
• remove randn(T) is defined in base
• propose logdet(::Number) for base and add to compat
• dot is defined for numbers in base
• avoid dubious dot product for linear scalings
• use ellipsisnotation.jl
• remove Compat dependency

I am getting rid of the bi(i, x, P) variants of the generic drift function b(t, x, P) which take an index i instead of a time t. In future SDE solver will call
b((i,t), x, P) with fallback b((i,t), x, P) = b(t, x, P) and models which need the corresponding index and not only the time point t to compute the drift should use dispatch to overwrite that fallback.

@ChrisRackauckas

Real OU bridge was implemented in 7397f01

For the vector valued OU bridge some matrix algebra is missing, but the one-dimensional formulas give a good idea how the answer should look like.

JuliaMath/SpecialFunctions.jl#236 should replace the version in src/expint.jl (once a new version of SpecialFunctions is tagged).

For exponential integrals with n>1, expint(n, 0.0) returns NaN, instead of 1/(n-1). Compare the behavior to scipy.special.expn, which returns the appropriate value.

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Hi, Thanks for all your work in making Bridge.jl available.
I'm new to Julia, and feeling my way in terms of leading/best-of-breed packages and idioms.

It seems to me that Bridge.jl is the best of breed diffusion simulating package - closely followed by the DiffEqNoiseProcess.jl, to my mind the BridgeDiffEq,jl supports that conclusion.

I am planning a package that likely would take as input an array such as that generated by Bridge.jl.
In that context I hoped you might share your thoughts on the usefulness of adopting JuliaDiffEq/LabelledArrays.jl.

I am getting the following error when trying to precompile Bridge (Julia v1.1 on Mac)

[ Info: Precompiling Bridge [2d3116d5-4b8f-5680-861c-71f149790274]
ERROR: LoadError: LoadError: UndefVarError: Zip2 not defined
Stacktrace:
 [1] getproperty(::Module, ::Symbol) at ./sysimg.jl:13
 [2] top-level scope at none:0
 [3] include at ./boot.jl:326 [inlined]
 [4] include_relative(::Module, ::String) at ./loading.jl:1038
 [5] include at ./sysimg.jl:29 [inlined]
 [6] include(::String) at /Users/antonio/.julia/packages/Bridge/s3VsI/src/Bridge.jl:1
 [7] top-level scope at none:0
 [8] include at ./boot.jl:326 [inlined]
 [9] include_relative(::Module, ::String) at ./loading.jl:1038
 [10] include(::Module, ::String) at ./sysimg.jl:29
 [11] top-level scope at none:2
 [12] eval at ./boot.jl:328 [inlined]
 [13] eval(::Expr) at ./client.jl:404
 [14] top-level scope at ./none:3
in expression starting at /Users/antonio/.julia/packages/Bridge/s3VsI/src/types.jl:127
in expression starting at /Users/antonio/.julia/packages/Bridge/s3VsI/src/Bridge.jl:101
ERROR: Failed to precompile Bridge [2d3116d5-4b8f-5680-861c-71f149790274] to /Users/antonio/.julia/compiled/v1.1/Bridge/cfWTr.ji.
Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] compilecache(::Base.PkgId, ::String) at ./loading.jl:1197
 [3] _require(::Base.PkgId) at ./loading.jl:960
 [4] require(::Base.PkgId) at ./loading.jl:858
 [5] require(::Module, ::Symbol) at ./loading.jl:853```

This issue is held open for general feedback, feature requests and to coordinate contributions to the package; or just to say "hello".

Trying to run the examples on Julia 1.2, I encouter linspace deprecated and replaced by range and some problem with SArray here:

S = 9.0:0.05:11.0
Ρ = 26.0:0.05:30.0
Β = 2.0:0.02:4.0
θref = s0, Ρ[end÷2], Β[end÷2]
@show θref;

θref = (10.0, 27.95, 2.98)

llsurface = [loglikelihood((s0, ρ, β), θref, X) for ρ in Ρ, β in Β];

gives:

The size of type SArray{Tuple{S},T,1,S} where T where S is not known.

If you were trying to construct (or convert to) a StaticArray you
may need to add the size explicitly as a type parameter so its size is
inferrable to the Julia compiler (or performance would be terrible). For
example, you might try

m = zeros(3,3)
SMatrix(m)      # this error
SMatrix{3,3}(m) # correct - size is inferrable

Stacktrace:
[1] error(::String) at .\error.jl:33
[2] missing_size_error(::Type{SArray{Tuple{S},T,1,S} where T where S}) at C:\Users\Denis.julia\packages\StaticArrays\DBECI\src\traits.jl:72
[3] Size(::Type{SArray{Tuple{S},T,1,S} where T where S}) at C:\Users\Denis.julia\packages\StaticArrays\DBECI\src\traits.jl:88
[4] length(::Type{SArray{Tuple{S},T,1,S} where T where S}) at C:\Users\Denis.julia\packages\StaticArrays\DBECI\src\abstractarray.jl:2
[5] convert at C:\Users\Denis.julia\packages\StaticArrays\DBECI\src\convert.jl:22 [inlined]
[6] Type at C:\Users\Denis.julia\packages\StaticArrays\DBECI\src\convert.jl:7 [inlined]
[7] Diagonal{T,SArray{Tuple{N},T,1,N}} where T where N(::Diagonal{Float64,SArray{Tuple{3},Float64,1,3}}) at C:\Users\Denis.julia\packages\StaticArrays\DBECI\src\SDiagonal.jl:7
[8] σ at C:\Users\Denis.julia\packages\Bridge\vPofv\src\Models.jl:57 [inlined]
[9] a(::Float64, ::SArray{Tuple{3},Float64,1,3}, ::Lorenz) at C:\Users\Denis.julia\packages\Bridge\vPofv\src\types.jl:32
[10] Γ(::Float64, ::SArray{Tuple{3},Float64,1,3}, ::Lorenz) at C:\Users\Denis.julia\packages\Bridge\vPofv\src\types.jl:33
[11] girsanov(::SamplePath{SArray{Tuple{3},Float64,1,3}}, ::Lorenz, ::Lorenz) at C:\Users\Denis.julia\packages\Bridge\vPofv\src\diffusion.jl:119
[12] loglikelihood(::Tuple{Float64,Float64,Float64}, ::Tuple{Float64,Float64,Float64}, ::SamplePath{SArray{Tuple{3},Float64,1,3}}) at .\In[36]:4
[13] (::getfield(Main, Symbol("##17#18")))(::Tuple{Float64,Float64}) at .\none:0
[14] iterate at .\generator.jl:47 [inlined]
[15] collect(::Base.Generator{Base.Iterators.ProductIterator{Tuple{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}},StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}},getfield(Main, Symbol("##17#18"))}) at .\array.jl:606
[16] top-level scope at In[38]:1

I am looking to run experiments to calculate first exits across a boundary using Levy-driven SDE. Does this package have a quick and dirty way to simulate $\alpha$-stable distribution based jump SDEs using Bridge.jl?

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I am working on a more flexible implementation of SamplePath. I hope you appreciate renaming tt and yy fields t and x.
You can follow design here:

https://github.com/mschauer/Trajectories.jl