AbstractFourierSeries interface

AbstractFourierSeries{N,T,iip}

A supertype for multidimensional Fourier series objects. Given a f::AbstractFourierSeries, you can evaluate it at a point x with f(x), where x is a vector (or scalar if f is 1d).

Fourier series are periodic maps $T^N \to V$ where T is a space of real numbers and $V$ is any vector space. Typically, a Fourier series can be represented by N-dimensional arrays whose elements belong to the vector space. If iip is true, then $V$ is assumed to have mutable elements and inplace array operations are used. Otherwise, $V$ is assumed to be immutable. The period of the series should be specified by values of type T, although no restriction is placed on the inputs to the series, e.g. arguments of type Complex{T} are OK. Additionally, if the caller wants to determine the floating-point precision of the Fourier coefficients, T and the arguments must both have that precision.

allocate(f::AbstractFourierSeries{N}, x, ::Val{d}) where {N,d}

Return a cache that can be used by contract! to store the result of contracting the coefficients of f along axis d using an input x.

contract!(cache, f::AbstractFourierSeries{N}, x, ::Val{d}) where {N,d}

Return another Fourier series of dimension N-1 by summing over dimension d of f with the phase factors evaluated at x and using the storage in cache created by a call to allocate

evaluate!(cache, f::AbstractFourierSeries{1}, x)

Evaluate the Fourier series at the point x using a cache for inplace evaluation created by a call to allocate. If the series is inplace, the cache storage may be used as the return value, and if the series is not inplace the cache may be unused.

frequency(f::AbstractFourierSeries, [dim]) == map(inv, period(f, [dim]))

Return a tuple containing the frequency, or inverse of the period, of f. Optionally you can specify a dimension to just get the frequency of that dimension.

nextderivative(f::AbstractFourierSeries, ::Val{d}) where {d}

This method returns a new series that evaluates the derivative of f with respect to its dth variable. This method is optional for normal evaluation, but DerivativeSeries requires it.

period(f::AbstractFourierSeries, [dim])

Return a tuple containing the periodicity of f. Optionally you can specify a dimension to just get the period of that dimension. This should have the floating-point precision of the input used for the Fourier series evaluation.