FourierSeriesEvaluators.jl

A package implementing efficient, multi-dimensional Fourier interpolation that is more convenient than FFTs when using hierarchical grids and when the number of coefficients is small compared to the number of evaluation points.

Quickstart

As a first example, we evaluate cosine from its Fourier series coefficients:

julia> using FourierSeriesEvaluators

julia> cosine = FourierSeries([0.5, 0.0, 0.5], period=2pi, offset=-2)
3-element and (6.283185307179586,)-periodic FourierSeries with Float64 coefficients, (0,) derivative, (-2,) offset

julia> cosine(pi)
-1.0 + 0.0im

Notice that we can create a series object and interpolate with a function-like interface. For more examples, see the documentation.

Features

Generic Fourier series can be implemented with the AbstractFourierSeries interface and the following implementations are provided as building blocks for others:

• FourierSeries: (inplace) evaluation at real/complex arguments
• HermitianFourierSeries: series coefficients with Hermitian symmetry
• ManyFourierSeries: evaluation of multiple series
• DerivativeSeries: automatic evaluation of derivatives of series to any order

Additionally, memory management for parallel workloads is supported by FourierWorkspace.

Extended help

The package also provides the following low-level routines that are also useful

• fourier_contract: contracts 1 variable of a multidimensional Fourier series
• fourier_evaluate: evaluates N-dimensional Fourier series with no allocations

These routines have the following features

• Support for abstract (esp. offset) coefficient arrays and array-valued coefficients
• Support for evaluation in the complex plane
• Evaluation of derivatives of the Fourier series with Fourier multipliers