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Preliminary work on complex derivatives complete, everything should a…
…t least work.
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,62 +1,90 @@ | ||
| function finite_difference!(df::AbstractArray{<:Real}, f, x::AbstractArray{<:Real}, | ||
| fdtype::DataType, ::Type{Val{:Real}}, ::Type{Val{:DiffEqDerivativeWrapper}}, | ||
| fx::Union{Void,AbstractArray{<:Real}}=nothing, epsilon::Union{Void,AbstractArray{<:Real}}=nothing, return_type::DataType=eltype(x)) | ||
| function finite_difference!(df::AbstractArray{<:Number}, f, x::Union{Number,AbstractArray{<:Number}}, | ||
| fdtype::DataType, funtype::DataType, ::Type{Val{:DiffEqDerivativeWrapper}}, | ||
| fx::Union{Void,AbstractArray{<:Number}}=nothing, epsilon::Union{Void,AbstractArray{<:Real}}=nothing, return_type::DataType=eltype(x)) | ||
|
|
||
| # TODO: test this one, and figure out what happens with epsilon | ||
| fx1 = f.fx1 | ||
| if fdtype == Val{:forward} | ||
| epsilon = compute_epsilon(Val{:forward}, x) | ||
| f(fx, x) | ||
| f(fx1, x+epsilon) | ||
| @. df = (fx1 - fx) / epsilon | ||
| elseif fdtype == Val{:central} | ||
| epsilon = compute_epsilon(Val{:central}, x) | ||
| f(fx, x-epsilon) | ||
| f(fx1, x+epsilon) | ||
| @. df = (fx1 - fx) / (2 * epsilon) | ||
| elseif fdtype == Val{:complex} | ||
| epsilon = eps(eltype(x)) | ||
| f(fx, f(x+im*epsilon)) | ||
| @. df = imag(fx) / epsilon | ||
| end | ||
| # TODO: optimized implementations for specific wrappers using the added DiffEq caching where appopriate | ||
|
|
||
| finite_difference!(df, f, x, fdtype, funtype, Val{:Default}, fx, epsilon, return_type) | ||
| df | ||
| end | ||
|
|
||
| # AbstractArray{T} should be OK if JacobianWrapper is provided | ||
| function finite_difference_jacobian!(J::AbstractArray{T}, f, x::StridedArray{T}, ::Type{Val{:forward}}, fx::StridedArray{T}, ::Type{Val{:JacobianWrapper}}) where T<:Real | ||
| function finite_difference_jacobian!(J::AbstractMatrix{<:Real}, f, x::AbstractArray{<:Real}, | ||
| fdtype::DataType, ::Type{Val{:Real}}, ::Type{Val{:JacobianWrapper}}, | ||
| fx::AbstractArray{<:Real}, epsilon::Union{Void,AbstractArray{<:Real}}=nothing, return_type::DataType=eltype(x)) | ||
|
|
||
| m, n = size(J) | ||
| epsilon_factor = compute_epsilon_factor(Val{:forward}, T) | ||
| epsilon_elemtype = compute_epsilon_elemtype(epsilon, x) | ||
| x1, fx1 = f.x1, f.fx1 | ||
| copy!(x1, x) | ||
| copy!(fx1, fx) | ||
| @inbounds for i in 1:n | ||
| epsilon = compute_epsilon(Val{:forward}, x[i], epsilon_factor) | ||
| epsilon_inv = one(T) / epsilon | ||
| x1[i] += epsilon | ||
| f(fx, x) | ||
| f(fx1, x1) | ||
| @. J[:,i] = (fx-fx1) * epsilon_inv | ||
| x1[i] -= epsilon | ||
| if fdtype == Val{:forward} | ||
| epsilon_factor = compute_epsilon_factor(Val{:forward}, epsilon_elemtype) | ||
| @inbounds for i ∈ 1:n | ||
| epsilon = compute_epsilon(Val{:forward}, x[i], epsilon_factor) | ||
| x1[i] += epsilon | ||
| f(fx1, x1) | ||
| f(fx, x) | ||
| @. J[:,i] = (fx1 - fx) / epsilon | ||
| x1[i] -= epsilon | ||
| end | ||
| elseif fdtype == Val{:central} | ||
| epsilon_factor = compute_epsilon_factor(Val{:central}, epsilon_elemtype) | ||
| @inbounds for i ∈ 1:n | ||
| epsilon = compute_epsilon(Val{:central}, x[i], epsilon_factor) | ||
| x1[i] += epsilon | ||
| x[i] -= epsilon | ||
| f(fx1, x1) | ||
| f(fx, x) | ||
| @. J[:,i] = (fx1 - fx) / (2*epsilon) | ||
| x1[i] -= epsilon | ||
| x[i] += epsilon | ||
| end | ||
| elseif fdtype == Val{:complex} | ||
| x0 = Complex{eltype(x)}(x) | ||
| epsilon = eps(eltype(x)) | ||
| @inbounds for i ∈ 1:n | ||
| x0[i] += im * epsilon | ||
| @. J[:,i] = imag(f(x0)) / epsilon | ||
| x0[i] -= im * epsilon | ||
| end | ||
| else | ||
| fdtype_error(Val{:Real}) | ||
| end | ||
| J | ||
| end | ||
|
|
||
| function finite_difference_jacobian!(J::AbstractArray{T}, f, x::StridedArray{T}, ::Type{Val{:central}}, fx::StridedArray{T}, ::Type{Val{:JacobianWrapper}}) where T<:Real | ||
| function finite_difference_jacobian!(J::AbstractMatrix{<:Number}, f, x::AbstractArray{<:Number}, | ||
| fdtype::DataType, ::Type{Val{:Complex}}, ::Type{Val{:JacobianWrapper}}, | ||
| fx::AbstractArray{<:Number}, epsilon::Union{Void,AbstractArray{<:Real}}=nothing, return_type::DataType=eltype(x)) | ||
|
|
||
| # TODO: test this | ||
| m, n = size(J) | ||
| epsilon_factor = compute_epsilon_factor(Val{:central}, T) | ||
| epsilon_elemtype = compute_epsilon_elemtype(epsilon, x) | ||
| x1, fx1 = f.x1, f.fx1 | ||
| copy!(x1, x) | ||
| copy!(fx1, fx) | ||
| @inbounds for i in 1:n | ||
| epsilon = compute_epsilon(Val{:central}, x[i], epsilon_factor) | ||
| epsilon_double_inv = one(T) / (2 * epsilon) | ||
| x[i] += epsilon | ||
| x1[i] -= epsilon | ||
| f(fx, x) | ||
| f(fx1, x1) | ||
| @. J[:,i] = (fx-fx1) * epsilon_double_inv | ||
| x[i] -= epsilon | ||
| x1[i] += epsilon | ||
| if fdtype == Val{:forward} | ||
| epsilon_factor = compute_epsilon_factor(Val{:forward}, epsilon_elemtype) | ||
| @inbounds for i ∈ 1:n | ||
| epsilon = compute_epsilon(Val{:forward}, real(x[i]), epsilon_factor) | ||
| x1[i] += epsilon | ||
| f(fx1, x1) | ||
| f(fx, x) | ||
| @. J[:,i] = ( real( (fx1 - fx) ) + im*imag( (fx1 - fx) ) ) / epsilon | ||
| x1[i] -= epsilon | ||
| end | ||
| elseif fdtype == Val{:central} | ||
| epsilon_factor = compute_epsilon_factor(Val{:central}, epsilon_elemtype) | ||
| @inbounds for i ∈ 1:n | ||
| epsilon = compute_epsilon(Val{:central}, real(x[i]), epsilon_factor) | ||
| x1[i] += epsilon | ||
| x[i] -= epsilon | ||
| f(fx1, x1) | ||
| f(fx, x) | ||
| @. J[:,i] = ( real( (fx1 - fx) ) + im*imag( fx1 - fx ) ) / (2*epsilon) | ||
| x1[i] -= epsilon | ||
| x[i] += epsilon | ||
| end | ||
| else | ||
| fdtype_error(Val{:Complex}) | ||
| end | ||
| J | ||
| end |
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