Deprecated

Removed v2.0 names, re-introduced as throwing shims: calling one always raises a PreconditionError naming its v2.1.0-beta replacement, so a search for the old name lands on an explanation rather than nothing. See Migrating to v2.1 for the full picture.

⋅'s entry below is misleading

⋅ is LinearAlgebra.dot, re-exported unchanged — the docstring Documenter shows for it below is dot's own, generic one. What actually changed is a method on it: X ⋅ f for X::AbstractVectorField always throws, pointing at ad(X, f). That override has no separate docstring of its own to display here.

OptimalControl.Lie Function

Lie(X, f)

Removed in v2.1.0-beta. Always throws — use ad(X, f) for a Lie derivative or ad(X, Y) for a Lie bracket instead.

LinearAlgebra.:⋅ Function

dot(x, y)
x ⋅ y

Compute the dot product between two vectors. For complex vectors, the first vector is conjugated.

dot also works on arbitrary iterable objects, including arrays of any dimension, as long as dot is defined on the elements.

dot is semantically equivalent to sum(dot(vx,vy) for (vx,vy) in zip(x, y)), with the added restriction that the arguments must have equal lengths.

x ⋅ y (where ⋅ can be typed by tab-completing \cdot in the REPL) is a synonym for dot(x, y).

Examples

julia> dot([1; 1], [2; 3])
5

julia> dot([im; im], [1; 1])
0 - 2im

julia> dot(1:5, 2:6)
70

julia> x = fill(2., (5,5));

julia> y = fill(3., (5,5));

julia> dot(x, y)
150.0

OptimalControl.HamiltonianLift Function

HamiltonianLift(args...)

Removed in v2.1.0-beta. Always throws — use Lift(f) for a plain function, or CTLie.LiftedHamiltonianFunction directly, instead.