get_vectorsnot working on a (nested) Power manifold of a product manifold.

[kellertuer]

Consider

using Manifolds
S = Sphere(2) × ℝ^1
N = PowerManifold(S, NestedPowerRepresentation(), 2)
q = rand(N)
C = get_basis(N, q, DefaultOrthonormalBasis())
get_vectors(N, q, C)

This throws an error

ERROR: MethodError: no method matching iterate(::ProductBasisData{Tuple{CachedBasis{ℝ, DefaultOrthonormalBasis{…}, Vector{…}}, CachedBasis{ℝ, DefaultOrthonormalBasis{…}, Vector{…}}}})

Closest candidates are:
  iterate(::Core.Compiler.InstructionStream, ::Int64)
   @ Base show.jl:2778
  iterate(::Core.Compiler.InstructionStream)
   @ Base show.jl:2778
  iterate(::LazyString)
   @ Base strings/lazy.jl:94
  ...

Stacktrace:
 [1] _get_vectors(M::PowerManifold{ℝ, ProductManifold{…}, Tuple{…}, NestedPowerRepresentation}, p::Vector{ArrayPartition{…}}, B::CachedBasis{ℝ, DefaultOrthonormalBasis{…}, PowerBasisData{…}})
   @ ManifoldsBase ~/Repositories/Julia/ManifoldsBase.jl/src/PowerManifold.jl:828
 [2] get_vectors(M::PowerManifold{ℝ, ProductManifold{…}, Tuple{…}, NestedPowerRepresentation}, p::Vector{ArrayPartition{…}}, B::CachedBasis{ℝ, DefaultOrthonormalBasis{…}, PowerBasisData{…}})
   @ ManifoldsBase ~/Repositories/Julia/ManifoldsBase.jl/src/bases.jl:821
 [3] top-level scope
   @ REPL[7]:1
Some type information was truncated. Use `show(err)` to see complete types.

So in line

ManifoldsBase.jl/src/PowerManifold.jl

Line 827 in 1bf8149

for v in b_i.data

it seems that the ProdyctBasisData is not iterable. I could fix that with writing instead of

        for v in b_i.data

just

        for v in get_vectors(M.manifold, p_i, b_i)

but that materialises all vectors here. So what is the right fix for this?

[mateuszbaran]

My quick guess is than for v in get_vectors(M.manifold, p_i, b_i) is fine in this case. Anyway, if you are doing get_vectors on a power manifold, you're doing something extremely sub-optimally anyway.

[kellertuer]

Yes, we are on the way of debugging something and are generating a full matrix representation of some linear operator on a tangent space.

Sure that is not the reasonable final version, but it also should not error ;)

[mateuszbaran]

If for v in get_vectors(M.manifold, p_i, b_i) works fine then I'm fine with that fix in ManifoldsBase 🙂

[kellertuer]

Ok, I was just not sure about performance, but maybe if one wants all vectors on a power manifold, performance is nothing to worry about any longer anyways (we only needed about 200 vectors or such)

[mateuszbaran]

For debugging it should be fast enough. In the main computations it shouldn't be used so it being slow doesn't matter.

[kellertuer]

Ok, sure. Then I will do a PR soon with that fix.