Internals Reference

Internals may change

This part of the developer documentation exclusively refers to internals that may change without warning in a future release of SparseConnectivityTracer. Anything written on this page should be treated as if it was undocumented. Only functionality that is exported or part of the user documentation adheres to semantic versioning.

Tracer Types

SparseConnectivityTracer.AbstractTracer — Type

AbstractTracer

Abstract supertype of tracers.

Type hierarchy

AbstractTracer
├── GradientTracer
└── HessianTracer

Note that Dual is not an AbstractTracer.

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SparseConnectivityTracer.GradientTracer — Type

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.

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SparseConnectivityTracer.HessianTracer — Type

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.

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SparseConnectivityTracer.Dual — Type

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

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Traits

SparseConnectivityTracer.NotShared — Type

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.

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SparseConnectivityTracer.Shared — Type

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.

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SparseConnectivityTracer.shared — Function

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.

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Utilities

SparseConnectivityTracer.gradient — Function

gradient(pattern::AbstractTracer)

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

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SparseConnectivityTracer.hessian — Function

hessian(pattern::HessianTracer)

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

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SparseConnectivityTracer.myempty — Function

myempty(T)
myempty(tracer::AbstractTracer)

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

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