BatchedTransformations

Composed{Outer<:Transformation,Inner<:Transformation}

A Composed contains two transformations outer and inner that are composed, where inner gets applied first, and then outer.. It can be constructed with compose(outer, inner) or outer ∘ inner, unless the compose function is overloaded for the specific types.

Identity <: Transformation

Inverse{T<:Transformation} <: Transformation

An Inverse represents a lazy inverse of a Transformation t.

inverse(t) is a lazy inverse that defaults to inv(t) when evaluated. transform(inverse(t), x) is equivalent to inverse_transform(t, x). This allows for specialized inverse transform implementations that don't require the inverse to be computed explicitly.

Transformation

An abstract type whose concrete subtypes contain batches of transformations that can be applied to an array. A Transformation t can be applied to x with transform(t, x), t * x, and t(x).

compose(t2, t1)
t2 ∘ t1

imaginary_to_quaternion_rotations(bcd::AbstractArray, a²=1)

Convert a batch of imaginary vectors represented as an array of size 3xB to a batch of unit quaternions.

Taken from Algorithm 23 of AlphaFold 2 supplementary information.

transform(t, x)
t * x
t(x)