Using the FMM plans

[MikaelSlevinsky]

This starts using the new binaries that incorporate MikaelSlevinsky/FastTransforms#83. Unfortunately, the code is structured somewhat differently, so it may take some thought to determine the best way forward. However, it seems to be significantly faster, which is great! CC @ioannisPApapadopoulos, @dlfivefifty

julia> using FastTransforms

julia> x = randn(10_000);

julia> @time p = plan_leg2cheb(x);
  0.584059 seconds (1 allocation: 48 bytes)

julia> @time p*x;
  0.008889 seconds (2 allocations: 78.172 KiB)

julia> @time pfmm = FastTransforms.plan_fmm_leg2cheb(x);
N 10000
Num levels 6
Num submatrices 360
Num blocks 120
Given max s 64 
Computed s 40 
Computed N 10240
Lagrange 0
Using exact binomial matrix
Initialization 1.4929e-03 s
  0.001504 seconds (1 allocation: 48 bytes)

julia> @time pfmm*x;
  0.000425 seconds (4 allocations: 156.344 KiB)

[mikaem]

Very nice to see this in Julia, thanks @MikaelSlevinsky!
Looking at the computation I was thinking perhaps the verbosity should be turned down to 0 by default? The planning is now printing a lot of different numbers that are perhaps only important for someone really interested in the method and not the actual transform?

[MikaelSlevinsky]

Yep, I was just curious about your diagnostic info (and checking that the ccall was correct!). That will most definitely be elided before a merge.

[ioannisPApapadopoulos]

Hi @MikaelSlevinsky, what work remains in this PR? Does ldiv work with FastTransforms.plan_fmm_leg2cheb or does FastTransforms.plan_fmm_cheb2leg also need to be implemented?

[MikaelSlevinsky]

While it could be merged, I have held off so far because it would be best if the API were the same as the existing schemes so that this code would be a drop-in replacement. This means allowing 2-normalized Chebyshev and Legendre polynomials. and also, since the connection coefficients are upper triangular, it would make sense for the C library to have the execute routines work in-place on a vector of coefficients instead of having input and output arrays. Both of these (relatively minor) issues would be best resolved in the C library itself.

[ioannisPApapadopoulos]

ok, understood! Thanks @MikaelSlevinsky