AbstractFFTs
FFTL is a backend of AbstractFFTs.jl. Which methods each plan type provides:
| method | complex plans | real plans (rfft, brfft, irfft) | real-to-real plans |
|---|---|---|---|
AbstractFFTs.Plan supertype | ✓ | ✓ | ✓ |
size, ndims | ✓ | ✓ | ✓ |
AbstractFFTs.fftdims | ✓ | ✓ | ✓ |
mul!(y, p, x) | ✓ | ✓ | ✓ |
p * x | ✓ | ✓ | ✓ |
AbstractFFTs.plan_inv (inv(p), p \ y) | ✓ (ScaledPlan) | ✓ | ✓ |
Real plans are RFFTLPlan (rfft) and BRFFTLPlan (brfft, irfft); the complex ones are FFTLPlan; real-to-real are R2RPlan.
The generic functions
FFTL's exported fft, plan_fft, … are its own functions, not AbstractFFTs's. For generic code, FFTL adds methods to AbstractFFTs's plan_fft, plan_bfft, plan_fft!, plan_bfft!, plan_rfft and plan_brfft for arrays of floating-point numbers; AbstractFFTs derives the transform functions, the normalised inverses and the promotion of real input from them. So AbstractFFTs.fft(x) runs on FFTL when no other backend is loaded.
These methods are less specific than FFTW.jl's, which take StridedArrays of Float32 and Float64 values. With FFTW.jl loaded, the generic functions therefore run on FFTW for those arrays and on FFTL for the others (other floating-point types, non-strided arrays). Code that wants FFTL calls FFTL's functions; see Coming from FFTW.jl.
Inverses
inv(p) of a forward complex plan is the normalised inverse, a ScaledPlan wrapping the backward plan. For a real-to-real plan, inv applies the partner kind and the normalisation of the kind; the factors are on Cosine, sine and Hartley transforms.