Internals Reference

AbstractTracer

Abstract supertype of tracers.

Type hierarchy

AbstractTracer
├── GradientTracer
└── HessianTracer

Note that Dual is not an AbstractTracer.

struct GradientTracer{P<:SparseConnectivityTracer.AbstractGradientPattern} <: SparseConnectivityTracer.AbstractTracer{P<:SparseConnectivityTracer.AbstractGradientPattern}

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

Fields

• pattern::SparseConnectivityTracer.AbstractGradientPattern: Sparse representation of non-zero entries in the gradient.

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

struct HessianTracer{P<:SparseConnectivityTracer.AbstractHessianPattern} <: SparseConnectivityTracer.AbstractTracer{P<:SparseConnectivityTracer.AbstractHessianPattern}

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

Fields

• pattern::SparseConnectivityTracer.AbstractHessianPattern: Sparse representation of non-zero entries in the gradient and 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

AbstractPattern

Abstract supertype of all sparsity pattern representations.

Type hierarchy

AbstractPattern
├── AbstractGradientPattern: used in GradientTracer
│   └── IndexSetGradientPattern
└── AbstractHessianPattern: used in HessianTracer
    └── IndexSetHessianPattern

AbstractGradientPattern <: AbstractPattern

Abstract supertype of sparsity patterns representing a vector. For use with GradientTracer.

Expected interface

• myempty
• create_patterns
• gradient
• shared

struct IndexSetGradientPattern{I<:Integer, S<:AbstractSet{I<:Integer}} <: SparseConnectivityTracer.AbstractGradientPattern

Gradient sparsity pattern represented by a set.

Fields

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

AbstractHessianPattern <: AbstractPattern

Abstract supertype of sparsity patterns representing both gradient and Hessian sparsity. For use with HessianTracer.

Expected interface

• myempty
• create_patterns
• gradient
• hessian
• shared

struct IndexSetHessianPattern{I<:Integer, G<:AbstractSet{I<:Integer}, H<:AbstractSet{Tuple{I<:Integer, I<:Integer}}, SB<:SparseConnectivityTracer.SharingBehavior} <: SparseConnectivityTracer.AbstractHessianPattern

Hessian sparsity pattern represented by two sets.

Fields

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

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

Internals

The last type parameter shared is a Bool indicating whether the hessian field of this object should be shared among all intermediate scalar quantities involved in a function.

struct DictHessianPattern{I<:Integer, S<:AbstractSet{I<:Integer}, D<:AbstractDict{I<:Integer, S<:AbstractSet{I<:Integer}}, shared<:SparseConnectivityTracer.SharingBehavior} <: SparseConnectivityTracer.AbstractHessianPattern

Hessian sparsity pattern represented by a set and a dictionary.

Fields

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

• hessian::AbstractDict{I, S} where {I<:Integer, S<:AbstractSet{I}}: Dictionary representing index-tuples $(i, j)$ of non-zero values $∇²f(x)_{ij} ≠ 0$ in the Hessian. For a given key $i$, values in the set ${j}$ represent index-tuples ${i, j}$.

Internals

The last type parameter shared is a Bool indicating whether the hessian field of this object should be shared among all intermediate scalar quantities involved in a function.

shared(pattern)

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

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

Note

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

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)
myempty(pattern::AbstractPattern)

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

create_patterns(P, xs, is)

Convenience constructor for patterns of type P for multiple inputs xs and their indices is.