1d transforms with multi-dimensional regions are slow about fasttransforms.jl HOT 3 CLOSED

Moreover, the partial interface change was bad because now similar functions don't behave similarly:

julia> jac2jac(X, 0, 0, -0.5, -0.5)[:,2] == jac2jac(X[:,2], 0, 0, -0.5, -0.5)
true

julia> leg2cheb(X)[:,2] == leg2cheb(X[:,2])
false

from fasttransforms.jl.

We could change it to use lib_leg2cheb if the dimensions are very small. But when the dimensions are large the plan_leg2cheb is so slow its unusable:

julia> n = 100_000; x = randn(n); @time cheb2leg(x);
  1.184869 seconds (50.38 k allocations: 74.845 GiB, 22.38% gc time, 5.08% compilation time)

julia> n = 100_000; x = randn(n); @time (p = plan_cheb2leg(x); p*x)
 44.783364 seconds (53.23 k allocations: 3.302 MiB, 0.06% compilation time)

from fasttransforms.jl.

Maybe for now with matrices we default to libfasttransforms since we aren't going to make it to n = 100k and leave the 1D transforms as Toeplitz dot Hankel?

from fasttransforms.jl.