API reference

fht(A [, dims])

Performs a multidimensional Fast Hartley Transform (FHT) of the array A. The optional dims argument specifies an iterable subset of dimensions (e.g. an integer, range, tuple, or array) to transform along. Most efficient if the size of A along the transformed dimensions is a product of small primes; see Base.nextprod. See also plan_fht() for even greater efficiency.

A one-dimensional FHT computes the one-dimensional discrete Hartley transform (DHT) as defined by

\[\operatorname{DHT}(A)[k] = \sum_{n=1}^{\operatorname{length}(A)} \operatorname{cas} \left( \frac{2\pi(n-1)(k-1)}{\operatorname{length}(A)} \right) A[n],\]

where $\operatorname{cas}$ is the cosine-and-sine function, or alternatively called Hartley kernel, defined by

\[\operatorname{cas}(x) = \cos(x) + \sin(x).\]

For transformed axes dims, the phase is the sum of the per-axis phases inside one Hartley kernel. This differs from the separable product of one-dimensional DHTs. The optional FFTW backend setting use_r2r=true retains that separable convention. The inverse is scaled by the product of the lengths of the transformed axes.

fht!(A [, dims])

Same as fht, but operates in-place on A.

ifht(A [, dims])

Multidimensional inverse FHT.

A one-dimensional inverse FHT computes the one-dimensional inverse DHT (IDHT) defined as

\[\operatorname{IDHT}(A)[k] = \frac{1}{\operatorname{length}(A)} \operatorname{DHT}(A)[k]\]

A multidimensional inverse divides the corresponding forward transform by the product of the lengths of the transformed axes, excluding untransformed batch axes.

ifht!(A [, dims])

Same as ifht, but operates in-place on A.

plan_fht(A [, dims]; flags=FFTW.ESTIMATE, timelimit=Inf)

Pre-plan an optimized FHT along given dimensions (dims) of arrays matching the shape and type of A. (The first two arguments have the same meaning as for fht.) Returns an object P which represents the linear operator computed by the FHT, and which contains all of the information needed to compute fht(A, dims) quickly.

plan_fht!(A [, dims]; flags=FFTW.ESTIMATE, timelimit=Inf)

Same as plan_fht, but operates in-place on A.

plan_ifht(A [, dims]; flags=FFTW.ESTIMATE, timelimit=Inf)

Same as plan_fht, but produces a plan that performs inverse transforms ifht.

plan_ifht!(A [, dims]; flags=FFTW.ESTIMATE, timelimit=Inf)

Same as plan_ifht, but operates in-place on A.

size(p::DHTPlan, [dim])

Return the size of the input of a plan p, optionally at a specified dimension dim.