FFTLoggin.jl

Julia port of the fftloggin Python package — a vectorized FFTLog implementation for fast Hankel transforms.

Documentation

Sample-axis convention. The transform/sample axis is the first axis (Julia is column-major). This is the opposite of the Python package, which uses the last axis.

Installation

Until the package is registered, install it from the package subdirectory:

using Pkg
Pkg.add(url="https://github.com/binado/FFTLoggin.jl", subdir="FFTLoggin")

For local development from the repository root:

using Pkg
Pkg.activate("FFTLoggin")
Pkg.instantiate()

Quickstart

using FFTLoggin

r = 10 .^ range(-2, 2; length=128)
fftlog = FFTLog(BesselJKernel(0), r; kr=1.0)

a = @. exp(-(r/1.0)^2)
A = forward(fftlog, a)

g = loggrid(fftlog; r=r)        # NamedTuple (r=..., k=...)
a_back = inverse(fftlog, A)     # roundtrip

Shapes and batching

Axis 1 is reserved for FFTLog samples. Every remaining axis participates in Julia-style broadcasting across signal batches, array-valued kernel parameters, and array-valued grid centers (kr).

n = 128
r = 10 .^ range(-2, 2; length=n)
a = @. exp(-r^2)

# Vector input, scalar kernel: output is a vector.
f0 = FFTLog(BesselJKernel(0), r)
size(forward(f0, a)) == (n,)

# Matrix input: columns are independent signal batches.
signals = hcat(a, 2a, 0.5a)
size(forward(f0, signals)) == (n, 3)

# Array-valued kernel parameters add trailing output axes.
orders = reshape([0.0, 1.0, 2.0], 1, :)
forders = FFTLog(BesselJKernel(orders); n=n, dlog=infer_dlog(r), lowring=false)
size(forward(forders, a)) == (n, 3)

# Grid centers are batched the same way; axis 1 is the r <-> k correspondence.
fkr = FFTLog(BesselJKernel(0); n=n, dlog=infer_dlog(r), kr=[0.8, 1.0, 1.2], lowring=false)
size(loggrid(fkr; r=r).k) == (n, 3)

Inputs whose trailing axes are not mutually broadcast-compatible throw DimensionMismatch.

Workspaces

Use FFTLogWorkspace when repeatedly transforming arrays with the same FFTLog and shape pattern.

ws = FFTLogWorkspace(f0, signals)
out = similar(signals)

forward!(out, f0, signals, ws)
inverse!(out, f0, out, ws)

A workspace caches FFT plans for a representative input shape and the corresponding broadcast output shape. Later inputs must match one of those cached shapes, and mutating outputs must match the workspace output shape.

Advanced utilities

Advanced helper functions are available with qualified names, for example FFTLoggin.infer_logc, FFTLoggin.optimal_logcenter, FFTLoggin.isindomain, and FFTLoggin.mellin.

Status (Phase 1)

• BesselJKernel, SphericalBesselJKernel, ShiftedKernel, DerivativeKernel
• forward/inverse for Vector and column-batched Matrix
• loggrid, infer_dlog
• Fortran-reference benchmark agreement (216 cases at rtol = 1e-5)