Inverse not defined for MBlade?

[Erik Schnetter]

I'm trying to calculate the inverse of a blade with Grassmann v0.1.3:

julia> basis"3"
(⟨+++⟩, v, v₁, v₂, v₃, v₁₂, v₁₃, v₂₃, v₁₂₃)
julia> inv(v1+v2)
ERROR: MethodError: no method matching inv(::MBlade{Int64,⟨+++⟩,1,3})

Is this function missing, or am I looking in the wrong place?

[Dream Scatter]

Currently, the implementation of inv is only for single Basis and SValue elements. It can be extended to MBlade elements but not for mixed-grade MultiVector elements, I believe.

[Dream Scatter]

A naive implementation would be the following formula

julia> using Grassmann; basis"3"
(⟨+++⟩, v, v₁, v₂, v₃, v₁₂, v₁₃, v₂₃, v₁₂₃)

julia> Base.inv(a::TensorAlgebra) = (A=~a; A/(A⋅a))

julia> inv(v1+v2)
0.0 + 0.5v₁ + 0.5v₂

However, a more optimized method could also be defined, similar to the other operations.

[Dream Scatter]

The MBlade should now be invertible with the inv method on master branch, which will be on v0.1.4

[Dream Scatter]

The inv method has now been fully generalized to arbitrary MultiVector elements, provided that the it is defined for the given input value.

julia> 1/(0v+2v1)
0.0 + 0.5v₁

julia> @btime inv(0v+2v1)
  5.677 μs (80 allocations: 4.81 KiB)
0.0 + 0.5v₁

julia> @btime inv(2v1)
  62.522 ns (4 allocations: 64 bytes)
0.5v₁

julia> @btime inv(0v2+2v1)
  136.415 ns (6 allocations: 128 bytes)
0.5v₁ + 0.0v₂ + 0.0v₃

However, it is much slower for an arbitrary MultiVector input at the moment, due to type instability.

This may be improved in the future with the MultiGrade type, when it is further implemented.