Internals Reference

AbstractTracer

Abstract supertype of tracers.

Type hierarchy

AbstractTracer
├── GradientTracer
└── HessianTracer

Note that Dual is not an AbstractTracer.

struct GradientTracer{I<:Integer, G<:AbstractSet{I<:Integer}} <: SparseConnectivityTracer.AbstractTracer

Real number type keeping track of non-zero gradient entries.

Fields

• gradient::AbstractSet{I} where I<:Integer: Set of indices $i$ of non-zero values $∇f(x)_i ≠ 0$ in the gradient.

• isempty::Bool: Indicator whether gradient in tracer contains only zeros.

struct HessianTracer{I<:Integer, G<:AbstractSet{I<:Integer}, H<:Union{AbstractDict{I<:Integer, G<:AbstractSet{I<:Integer}}, AbstractSet{Tuple{I<:Integer, I<:Integer}}}, S<:SparseConnectivityTracer.SharingBehavior} <: SparseConnectivityTracer.AbstractTracer

Real number type keeping track of non-zero gradient and Hessian entries.

Fields

• gradient::AbstractSet{I} where I<:Integer: Set of indices $i$ of non-zero values $∇f(x)_i ≠ 0$ in the gradient.

• hessian::Union{AbstractDict{I, G}, AbstractSet{Tuple{I, I}}} where {I<:Integer, G<:AbstractSet{I}}: Set of index-tuples $(i, j)$ of non-zero values $∇²f(x)_{ij} ≠ 0$ in the Hessian.

• isempty::Bool: Indicator whether gradient and Hessian in tracer both contain only zeros.

struct Dual{P<:Real, T<:SparseConnectivityTracer.AbstractTracer} <: Real

Dual Real number type keeping track of the results of a primal computation as well as a tracer.

Fields

• primal::Real

• tracer::SparseConnectivityTracer.AbstractTracer

Indicates that patterns can share memory and operators are prohibited from mutating HessianTracer arguments. In practice, memory sharing is limited to second-order information in HessianTracer.

Indicates that patterns always share memory and that operators are allowed to mutate their HessianTracer arguments. In practice, memory sharing is limited to second-order information in HessianTracer.

shared(pattern)

Indicates whether patterns always share memory and whether operators are allowed to mutate their HessianTracer arguments. Returns either the Shared() or NotShared() trait.

If NotShared(), patterns can share memory and operators are prohibited from mutating HessianTracer arguments.

Note

In practice, memory sharing is limited to second-order information in HessianTracer.

gradient(pattern::AbstractTracer)

Return a representation of non-zero values $∇f(x)_{i} ≠ 0$ in the gradient.

hessian(pattern::HessianTracer)

Return a representation of non-zero values $∇²f(x)_{ij} ≠ 0$ in the Hessian.

myempty(T)
myempty(tracer::AbstractTracer)

Constructor for an empty tracer or pattern of type T representing a new number (usually an empty pattern).