1d transforms with multi-dimensional regions are slow

[MikaelSlevinsky]

Using the v0.15 default, I'm getting:

julia> using FastTransforms, LinearAlgebra

julia> X = randn(1024, 1024);

julia> @time leg2cheb(X);
  4.387465 seconds (218 allocations: 3.476 GiB, 4.53% gc time)

julia> @time leg2cheb(X);
  3.772526 seconds (218 allocations: 3.476 GiB, 5.03% gc time)

Is this defaulting to Toeplitz-dot-Hankel?
This is equivalent to the library call (plans included):

julia> @time begin
           p = plan_leg2cheb(X)
           lmul!(p, Matrix(lmul!(p, Matrix(X'))'))
       end;
  0.069058 seconds (7 allocations: 16.000 MiB)

julia> @time begin
           p = plan_leg2cheb(X)
           lmul!(p, Matrix(lmul!(p, Matrix(X'))'))
       end;
  0.071369 seconds (7 allocations: 16.000 MiB)

@dlfivefifty

[MikaelSlevinsky]

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

[dlfivefifty]

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)

[dlfivefifty]

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?