Internal documentation

This page documents the internal types and methods of Manifolds.jl's that might be of use for writing your own manifold.

Types

Manifolds.SizedAbstractArray — Type

SizedAbstractArray{Tuple{dims...}}(array)

Wraps an AbstractArray with a static size, so to take advantage of the (faster) methods defined by the static array package. The size is checked once upon construction to determine if the number of elements (length) match, but the array may be reshaped.

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Functions

Manifolds._gradient — Function

_gradient(f, p::Number, backend = adbackend()) -> Number
_gradient(f, p::Array, backend = adbackend()) -> Array

Compute gradient of function f at x using AD backend backend.

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Manifolds._jacobian — Function

_jacobian(f, p, backend = adbackend()) -> Array

Compute Jacobian matrix of function f at p using AD backend backend. Inputs and outputs of f are vectorized.

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Manifolds.eigen_safe — Function

eigen_safe(x)

Compute the eigendecomposition of x. If x is a StaticMatrix, it is converted to a Matrix before the decomposition.

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Manifolds.find_pv — Function

find_pv(x...)

A = find_pv(x...) returns the first ProductArray among the arguments.

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Manifolds.log_safe — Function

log_safe(x)

Compute the matrix logarithm of x. If x is a StaticMatrix, it is converted to a Matrix before computing the log.

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Manifolds.size_to_tuple — Function

size_to_tuple(::Type{S}) where S<:Tuple

Converts a size given by Tuple{N, M, ...} into a tuple (N, M, ...).

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Manifolds.select_from_tuple — Function

select_from_tuple(t::NTuple{N, Any}, positions::Val{P})

Selects elements of tuple t at positions specified by the second argument. For example select_from_tuple(("a", "b", "c"), Val((3, 1, 1))) returns ("c", "a", "a").

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Manifolds.usinc — Function

usinc(θ::Real)

Unnormalized version of sinc function, i.e. $\operatorname{usinc}(θ) = \frac{\sin(θ)}{θ}$. This is equivalent to sinc(θ/π).

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Manifolds.usinc_from_cos — Function

usinc_from_cos(x::Real)

Unnormalized version of sinc function, i.e. $\operatorname{usinc}(θ) = \frac{\sin(θ)}{θ}$, computed from $x = cos(θ)$.

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Manifolds.ziptuples — Function

ziptuples(a, b[, c[, d[, e]]])

Zips tuples a, b, and remaining in a fast, type-stable way. If they have different lengths, the result is trimmed to the length of the shorter tuple.

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