API Reference

SparseConnectivityTracer uses ADTypes.jl's interface for sparsity detection. In fact, the functions jacobian_sparsity and hessian_sparsity are re-exported from ADTypes.

ADTypes.jacobian_sparsity — Function

jacobian_sparsity(f, x, sd::AbstractSparsityDetector)::AbstractMatrix{Bool}
jacobian_sparsity(f!, y, x, sd::AbstractSparsityDetector)::AbstractMatrix{Bool}

Use detector sd to construct a (typically sparse) matrix S describing the pattern of nonzeroes in the Jacobian of f (resp. f!) applied at x (resp. (y, x)).

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ADTypes.hessian_sparsity — Function

hessian_sparsity(f, x, sd::AbstractSparsityDetector)::AbstractMatrix{Bool}

Use detector sd to construct a (typically sparse) matrix S describing the pattern of nonzeroes in the Hessian of f applied at x.

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To compute global sparsity patterns of f(x) over the entire input domain x, use

SparseConnectivityTracer.TracerSparsityDetector — Type

TracerSparsityDetector <: ADTypes.AbstractSparsityDetector

Singleton struct for integration with the sparsity detection framework of ADTypes.jl.

Computes global sparsity patterns over the entire input domain. For local sparsity patterns at a specific input point, use TracerLocalSparsityDetector.

Example

julia> using SparseConnectivityTracer

julia> detector = TracerSparsityDetector()
TracerSparsityDetector()

julia> jacobian_sparsity(diff, rand(4), detector)
3×4 SparseArrays.SparseMatrixCSC{Bool, Int64} with 6 stored entries:
 1  1  ⋅  ⋅
 ⋅  1  1  ⋅
 ⋅  ⋅  1  1

julia> f(x) = x[1] + x[2]*x[3] + 1/x[4];

julia> hessian_sparsity(f, rand(4), detector)
4×4 SparseArrays.SparseMatrixCSC{Bool, Int64} with 3 stored entries:
 ⋅  ⋅  ⋅  ⋅
 ⋅  ⋅  1  ⋅
 ⋅  1  ⋅  ⋅
 ⋅  ⋅  ⋅  1

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To compute local sparsity patterns of f(x) at a specific input x, use

SparseConnectivityTracer.TracerLocalSparsityDetector — Type

TracerLocalSparsityDetector <: ADTypes.AbstractSparsityDetector

Singleton struct for integration with the sparsity detection framework of ADTypes.jl.

Computes local sparsity patterns at an input point x. For global sparsity patterns, use TracerSparsityDetector.

Example

Local sparsity patterns are less convervative than global patterns and need to be recomputed for each input x:

julia> using SparseConnectivityTracer

julia> detector = TracerLocalSparsityDetector()
TracerLocalSparsityDetector()

julia> f(x) = x[1] * x[2]; # J_f = [x[2], x[1]]

julia> jacobian_sparsity(f, [1, 0], detector)
1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 1 stored entry:
 ⋅  1

julia> jacobian_sparsity(f, [0, 1], detector)
1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 1 stored entry:
 1  ⋅

julia> jacobian_sparsity(f, [0, 0], detector)
1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 0 stored entries:
 ⋅  ⋅

julia> jacobian_sparsity(f, [1, 1], detector)
1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 2 stored entries:
 1  1

TracerLocalSparsityDetector can compute sparsity patterns of functions that contain comparisons and ifelse statements:

julia> f(x) = x[1] > x[2] ? x[1:3] : x[2:4];

julia> jacobian_sparsity(f, [1, 2, 3, 4], TracerLocalSparsityDetector())
3×4 SparseArrays.SparseMatrixCSC{Bool, Int64} with 3 stored entries:
 ⋅  1  ⋅  ⋅
 ⋅  ⋅  1  ⋅
 ⋅  ⋅  ⋅  1

julia> jacobian_sparsity(f, [2, 1, 3, 4], TracerLocalSparsityDetector())
3×4 SparseArrays.SparseMatrixCSC{Bool, Int64} with 3 stored entries:
 1  ⋅  ⋅  ⋅
 ⋅  1  ⋅  ⋅
 ⋅  ⋅  1  ⋅

julia> f(x) = x[1] + max(x[2], x[3]) * x[3] + 1/x[4];

julia> hessian_sparsity(f, [1.0, 2.0, 3.0, 4.0], TracerLocalSparsityDetector())
4×4 SparseArrays.SparseMatrixCSC{Bool, Int64} with 2 stored entries:
 ⋅  ⋅  ⋅  ⋅
 ⋅  ⋅  ⋅  ⋅
 ⋅  ⋅  1  ⋅
 ⋅  ⋅  ⋅  1

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