Used to flag which argument is being specified in x̄.

A Branch is a Node with parents (args).

Fields: val - the value of this node produced in the forward pass. f - the function used to generate this Node. args - Values indicating which elements in the tape will require updating by this node. tape - The Tape to which this Branch is assigned. pos - the location of this Branch in the tape to which it is assigned.

An element at the 'bottom' of the computational graph.

Fields: val - the value of the node. tape - The Tape to which this Leaf is assigned. pos - the location of this Leaf in the tape to which it is assigned.

Basic unit on the computational graph.

A topologically ordered collection of Nodes.

check_errs(
    f,
    ȳ::∇ArrayOrScalar,
    x::T,
    v::T,
    ε_abs::∇Scalar=1e-10,
    ε_rel::∇Scalar=1e-7
)::Bool where T

Check that the difference between finite differencing directional derivative estimation and RMAD directional derivative computation for function f at x in direction v, for both allocating and in-place modes, has absolute and relative errors of ε_abs and ε_rel respectively, when scaled by reverse-mode sensitivity ȳ.

domain1{T}(in_domain::Function, measure::Function, points::Vector{T})
domain1(f::Function)

Attempt to find a domain for a unary, scalar function f.

Arguments

• in_domain::Function: Function that takes a single argument x and returns whether x argument is in f's domain.
• measure::Function: Function that measures the size of a set of points for f.
• points::Vector{T}: Ordered set of test points to construct the domain from.

domain2(f::Function)

Attempt to find a rectangular domain for a binary, scalar function f.

in_domain(f::Function, x::Float64...)

Check whether an input x is in a scalar, real function f's domain.

preprocess(::Function, args...)

Default implementation of preprocess returns an empty Tuple. Individual sensitivity implementations should add methods specific to their use case. The output is passed in to ∇ as the 3rd or 4th argument in the new-x̄ and update-x̄ cases respectively.

∇(f; get_output::Bool=false)

Returns a function which, when evaluated with arguments that are accepted by f, will return the gradient w.r.t. each of the arguments. If get_output is true, the result of calling f on the given arguments is also returned.

∇(y::Node{<:∇Scalar})
∇(y::Node{T}, ȳ::T) where T

Return a Tape object which can be indexed using Nodes, each element of which contains the result of multiplying ȳ by the transpose of the Jacobian of the function specified by the Tape object in y. If y is a scalar and ȳ = 1 then this is equivalent to computing the gradient of y w.r.t. each of the elements in the Tape.

∇(f::Function, ::Type{Arg{N}}, p, y, ȳ, x...)
∇(x̄, f::Function, ::Type{Arg{N}}, p, y, ȳ, x...)

To implement a new reverse-mode sensitivity for the N^{th} argument of function f. p is the output of preprocess. x1, x2,... are the inputs to the function, y is its output and ȳ the reverse-mode sensitivity of y.

@explicit_intercepts(f::Symbol, type_tuple::Expr, is_node::Expr[, kwargs::Expr])
@explicit_intercepts(f::Symbol, type_tuple::Expr)

Create a collection of methods which intecept the function calls to f in which at least one argument is a Node. Types of arguments are specified by the type tuple expression in type_tuple. If there are arguments which are not differentiable, they can be specified by providing a boolean vector is_node which indicates those arguments that are differentiable with true values and those which are not as false. Keyword arguments to add to the function signature can be specified in kwargs, which must be a NamedTuple.

@union_intercepts f type_tuple invoke_type_tuple [kwargs]

Interception strategy based on adding a method to f which accepts the union of each of the types specified by type_tuple. If none of the arguments are Nodes then the method of f specified by invoke_type_tuple is invoked. If applicable, keyword arguments should be provided as a NamedTuple and be added to the generated function's signature.

@unionise code

Transform code such that each function definition accepts Node objects as arguments, without effecting dispatch in other ways.