DerivableFunctionsBase

DerivableFunction(F::Function; ADmode::Union{Val,Symbol}=Val(:Symbolic))
DerivableFunction(F::Function, testinput::Union{Number,AbstractVector{<:Number}}; ADmode::Union{Val,Symbol}=Val(:Symbolic))
DerivableFunction(F::Function, dF::Function; ADmode::Union{Val,Symbol}=Val(:Symbolic))
DerivableFunction(F::Function, dF::Function, ddF::Function)

Stores derivatives of a given function (as well as input-output dimensions) for potentially faster computations when derivatives are known.

Builder(Fexpr::Union{<:AbstractVector{<:Num},<:Num}, args...; inplace::Bool=false, parallel::Bool=false, kwargs...)

Builds RuntimeGeneratedFunctions from expressions via build_function().

GetArgLength(F::Function; max::Int=100) -> Int

Attempts to determine input structure of F, i.e. whether it accepts Numbers or AbstractVectors and of what length. This is achieved by successively evaluating the function on rand(i) until the evaluation no longer throws errors. As a result, GetArgLength will be unable to determine the correct input structure if F errors on rand(i).

GetDeriv(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes the scalar derivative of F out-of-place via a backend specified by ADmode.

Example:

Derivative = GetDeriv(Val(:ForwardDiff), x->exp(-x^2))
Derivative(5.0)

For available backends, see diff_backends().

GetDoubleJac(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes the Jacobian of the Jacobian for a vector-valued function F out-of-place via a backend specified by ADmode.

Example:

DoubleJacobian = GetDoubleJac(Val(:ForwardDiff), x->[x[1]^2, x[1]*x[2]^3])
DoubleJacobian(rand(2))

For available backends, see diff_backends().

GetGrad!(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes gradients in-place via a backend specified by ADmode. The function returned by GetGrad! has argument structure (Y::AbstractVector, X::AbstractVector) where the gradient of F evaluated at X is saved into Y.

Example:

Gradient! = GetGrad!(Val(:ForwardDiff), x->x[1]^2 - x[2]^3)
Y = Vector{Float64}(undef, 2)
Gradient!(Y, rand(2))

For available backends, see diff_backends().

GetGrad(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes the gradient of F out-of-place via a backend specified by ADmode.

Example:

Gradient = GetGrad(Val(:ForwardDiff), x->x[1]^2 - x[2]^3)
Gradient(rand(2))

For available backends, see diff_backends().

GetHess!(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes Hessians in-place via a backend specified by ADmode. The function returned by GetHess! has argument structure (Y::AbstractMatrix, X::AbstractVector) where the Hessian of F evaluated at X is saved into Y.

Example:

Hessian! = GetHess!(Val(:ForwardDiff), x->x[1]^2 -x[2]^3 + x[1]*x[2])
Y = Matrix{Float64}(undef, 2, 2)
Hessian!(Y, rand(2))

For available backends, see diff_backends().

GetHess(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes the Hessian of F out-of-place via a backend specified by ADmode.

Example:

Hessian = GetHess(Val(:ForwardDiff), x->x[1]^2 -x[2]^3 + x[1]*x[2])
Hessian(rand(2))

For available backends, see diff_backends().

GetJac!(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes Jacobians in-place via a backend specified by ADmode. The function returned by GetJac! has argument structure (Y::AbstractMatrix, X::AbstractVector) where the Jacobian of F evaluated at X is saved into Y.

Example:

Jacobian! = GetJac!(Val(:ForwardDiff), x->[x[1]^2, -x[2]^3, x[1]*x[2]])
Y = Matrix{Float64}(undef, 3, 2)
Jacobian!(Y, rand(2))

For available backends, see diff_backends().

GetJac(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes the Jacobian of F out-of-place via a backend specified by ADmode.

Example:

Jacobian = GetJac(Val(:ForwardDiff), x->[x[1]^2, -x[2]^3, x[1]*x[2]])
Jacobian(rand(2))

For available backends, see diff_backends().

GetMatrixJac(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes the Jacobian of an array-valued function F out-of-place via a backend specified by ADmode.

Example:

Jacobian = GetMatrixJac(Val(:ForwardDiff), x->[x[1]^2 x[2]^3; x[1]*x[2] 2])
Jacobian(rand(2))

For available backends, see diff_backends().

GetMatrixJac!(ADmode::Val, F::Function; kwargs...) -> Function

Returns a function which computes Jacobians in-place for array-valued functions via a backend specified by ADmode. The function returned by GetMatrixJac! has argument structure (Y::AbstractArray, X::AbstractVector) where the Jacobian of F evaluated at X is saved into Y.

Example:

Jacobian! = GetMatrixJac!(Val(:ForwardDiff), x->[x[1]^2 x[2]^3; x[1]*x[2] 2])
Y = Array{Float64}(undef, 2, 2, 2)
Jacobian!(Y, rand(2))

For available backends, see diff_backends().

GetOutLength(F::Function, input::Union{Number,AbstractVector{<:Number}})

Returns output dimensions of given F. If it outputs arrays of more than one dimension, a tuple is returned. This can also be used to determine the approximate size of the input for mutating F which accept 2 arguments.

GetSymbolicDerivative(F::Function, inputdim::Int=GetArgLength(F), deriv::Symbol=:jacobian; timeout::Real=5, inplace::Bool=false, parallel::Bool=false)

Computes symbolic derivatives, including :jacobian, :gradient, :hessian and :derivative which are specified via deriv. Special care has to be taken that the correct inputdim is specified! Silent errors may occur otherwise.

KillAfter(F::Function, args...; timeout::Real=5, verbose::Bool=false, kwargs...)

Tries to evaluate a given function F before a set timeout limit is reached and interrupts the evaluation and returns nothing if necessary. NOTE: The given function is evaluated via F(args...; kwargs...).

MaximalNumberOfArguments(F::Function) -> Int

Infers argument structure of given function, i.e. whether it is of the form F(x) or F(x,y) or F(x,y,z) etc. and returns maximal number of accepted arguments of all overloads of F as integer.

Executes symbolic derivative as specified by deriv::Symbol.

_GetArgLength(F::Function; max::Int=100) -> Int

Shows the currently loaded differentation backends available for use with DerivableFunctions.jl.

suff(x) -> Type

If x stores BigFloats, suff returns BigFloat, else suff returns Float64.