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.SizedAbstractArrayType
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.eigen_safeFunction
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_pvFunction
find_pv(x...)

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

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Manifolds.log_safeFunction
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.nzsignFunction
nzsign(z[, absz])

Compute a modified sign(z) that is always nonzero, i.e. where

\[\operatorname(nzsign)(z) = \begin{cases} 1 & \text{if } z = 0\\ \frac{z}{|z|} & \text{otherwise} \end{cases}\]
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Manifolds.size_to_tupleFunction
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_tupleFunction
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.usincFunction
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_cosFunction
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.ziptuplesFunction
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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