StationaryRandomFields.jl API

Index

• StationaryRandomFields.AbstractContinuousNoiseSignal
• StationaryRandomFields.AbstractNoiseSignal
• StationaryRandomFields.AbstractPowerSpectrumModel
• StationaryRandomFields.ContinuousNoiseSignal
• StationaryRandomFields.DensityAnalytic
• StationaryRandomFields.IsAnalytic
• StationaryRandomFields.ModelModifier
• StationaryRandomFields.ModifiedPowerSpectrumModel
• StationaryRandomFields.NoiseSignal
• StationaryRandomFields.NotAnalytic
• StationaryRandomFields.PowerSpectrumNoiseGenerator
• StationaryRandomFields.Renormalize
• StationaryRandomFields.Rotate
• StationaryRandomFields.SaturatedPowerLaw
• StationaryRandomFields.SinglePowerLaw
• StationaryRandomFields.Stretch
• StationaryRandomFields.amplitude_map
• StationaryRandomFields.amplitude_point
• StationaryRandomFields.basemodel
• StationaryRandomFields.fourieranalytic
• StationaryRandomFields.generate_gaussian_noise
• StationaryRandomFields.generate_signal_noise
• StationaryRandomFields.get_fourier_noise
• StationaryRandomFields.get_power_spectrum
• StationaryRandomFields.modify
• StationaryRandomFields.posangle
• StationaryRandomFields.power_map
• StationaryRandomFields.power_point
• StationaryRandomFields.renormed
• StationaryRandomFields.rfftsize
• StationaryRandomFields.rotated
• StationaryRandomFields.scale_fourier
• StationaryRandomFields.stretched
• StationaryRandomFields.transform_ν
• StationaryRandomFields.unmodified

Docstrings

StationaryRandomFields.AbstractContinuousNoiseSignal Type

AbstractContinuousNoiseSignal

This is an abstract data type for N dimensional continuous signal data on which signal noise will be generated. The data type extends the AbstractNoiseSignal data type for use in PowerSpectrumNoiseGenerator methods.

Mandatory fields

• noisesignal::AbstractNoiseSignal: noise signal object

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StationaryRandomFields.AbstractNoiseSignal Type

AbstractNoiseSignal

This is an abstract data type for signal data on which powerspectrum noises will be created. The data type contains information to define the dimensions and sizes of data, and provides various methods.

Mandatory fields

• dims::Tuple: dimension of data

Mandatory methods

• size: returns the size of the signal

• sizeof: returns product of signal dimensions

• ndims: returns the number of the dimension

• rfftsize: returns the size of the signal in the Fourier plane (for rfft)

• rfftfreq: returns the frequency grid along each dimension in the Fourier plane (for rfft)

• generate_gaussian_noise: returns Gaussian noises in Fourier domain with the size of rfftsize(data)

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StationaryRandomFields.AbstractPowerSpectrumModel Type

AbstractPowerSpectrumModel{N}

The abstract model type for a PowerSpectrum at N dimension. To instantiate your own model type you should subtype from this model. Additionally you need to implement the following methods to satify the interface:

Mandatory Methods

• fourieranalytic: Defines whether the model fourier coefficients can be computed analytically. If yes then this should return IsAnalytic() and the user must to define visibility_point. If not analytic then fourieranalytic should return NotAnalytic().

• power_point: Defines how to compute model power of fourier coefficients pointwise. Note this must be defined if fourieranalytic(::Type{YourModel})==IsAnalytic().

• power_map: Maps the fourier power spectrum for a set of frequencies.

Optional Methods

• amplitude_point: Defines how to compute model amplitudes of fourier coefficients pointwise. Note this must be defined if fourieranalytic(::Type{YourModel})==IsAnalytic(). It should be defined as √(power_point(model, ν...)).

• amplitude_map: Maps the fourier amplitude spectrum for a grid of frequencies.

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StationaryRandomFields.ContinuousNoiseSignal Type

struct ContinuousNoiseSignal{T, N<:AbstractNoiseSignal, D<:Tuple, P, PI} <: AbstractContinuousNoiseSignal

Data type for continuous noise signals. Input an AbstractNoiseSignal and the corresponding dimensions, RFFT plan, and inverse RFFT plan will automatically be defined. The type of data (default Float64) may also be specified.

Fields

• noisesignal

• dims

• plan

• invplan

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StationaryRandomFields.DensityAnalytic Type

DensityAnalytic

Internal type for specifying the nature of the model functions. Whether they can be easily evaluated pointwise analytic. This is an internal type that may change.

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StationaryRandomFields.IsAnalytic Type

struct IsAnalytic <: StationaryRandomFields.DensityAnalytic

Defines a trait that a states that a model is analytic. This is usually used with an abstract model where we use it to specify whether a model has a analytic fourier transform and/or image.

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StationaryRandomFields.ModelModifier Type

abstract type ModelModifier{T}

General type for a model modifier. These transform any model using simple Fourier transform properties. To modify a model you can use the ModifiedPowerSpectrumModel{N} constructor or the modify function.

julia> visanalytic(stretched(Disk(), 2.0, 2.0)) == visanalytic(Disk())
true

To implement a model transform you need to specify the following methods:

• transform_ν

• scale_fourier

See the docstrings of those methods for guidance on implementation details.

Additionally these methods assume the modifiers are of the form

I(x,y) -> fᵢ(x,y)I(gᵢ(x,y)) V(u,v) -> fᵥ(u,v)V(gᵥ(u,v))

where g are the transform_image/uv functions and f are the scale_image/uv function.

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StationaryRandomFields.ModifiedPowerSpectrumModel Type

struct ModifiedPowerSpectrumModel{N, M<:AbstractPowerSpectrumModel{N}, T<:Tuple} <: AbstractPowerSpectrumModel{N}

Container type for models that have been transformed in some way. For a list of potential modifiers or transforms see subtypes(ModelModifiers).

Fields

• model: base model

• transform: model transforms

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StationaryRandomFields.NoiseSignal Type

struct NoiseSignal{T<:Tuple} <: AbstractNoiseSignal

This is a data type for noise signals of any dimension.

Fields

• dims

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StationaryRandomFields.NotAnalytic Type

struct NotAnalytic <: StationaryRandomFields.DensityAnalytic

Defines a trait that a states that a model is analytic. This is usually used with an abstract model where we use it to specify whether a model has does not have a easy analytic fourier transform and/or intensity function.

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StationaryRandomFields.PowerSpectrumNoiseGenerator Type

PowerSpectrumNoiseGenerator

This is an abstract data type for power spectrum noise generators.

Mandatory methods

• generate_signal_noise: Transforms fourier noise to signal noise in position plane for given power spectrum model

• get_fourier_noise: Computes fourier noise for given signal domain noise

• get_power_spectrum: Returns power spectrum model retrieved from given signal domain noise

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StationaryRandomFields.Renormalize Type

struct Renormalize{T} <: StationaryRandomFields.ModelModifier{T}

Renormalizes the flux of the model to the new value scale*flux(model). We have also overloaded the Base.😗 operator as syntactic sugar although I may get rid of this.

Example

julia> modify(Gaussian(), Renormalize(2.0)) == 2.0*Gaussian()
true

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StationaryRandomFields.Rotate Type

Rotate(ξ)

Type for the rotated model. This is more fine grained control of rotated model.

Example

julia> modify(Gaussian(), Rotate(2.0)) == rotated(Gaussian(), 2.0)
true

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StationaryRandomFields.SaturatedPowerLaw Type

$(TYPEDEF)

Type for power law with input dimension {N} and profile: $\text{P(nu) = |nu| ^{beta} end{cases}}$ when inscale < |ν| < outscale. When |ν| > outscale: P(ν) = 0. When |ν| < inscale: $$\begin{gathered} P( \\ nu)=(inscale{)}^{ \\ beta} \\ endcases. \end{gathered}$$

β refers to the input index. Can be renormalized, stretched, and rotated via ModelModifier.

Fields

FIELDS

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StationaryRandomFields.SinglePowerLaw Type

$(TYPEDEF)

Type for single power law with input dimension {N} and profile $\text{P(nu) = |nu| ^{beta} end{cases}}$ where β is the input index and ν is frequency. Can be renormalized, stretched, and rotated via ModelModifier.

Fields

FIELDS

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StationaryRandomFields.Stretch Type

Stretch(α, β)
Stretch(r)

Stretched the model in the x and y directions, i.e. the new intensity is Iₛ(x,y) = 1/(αβ) I(x/α, y/β), where were renormalize the intensity to preserve the models flux.

Example

julia> modify(Gaussian(), Stretch(2.0)) == stretched(Gaussian(), 2.0, 1.0)
true

If only a single argument is given it assumes the same stretch is applied in both direction.

julia> Stretch(2.0) == Stretch(2.0, 2.0)
true

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StationaryRandomFields.amplitude_map Method

amplitude_map(model::AbstractPowerSpectrumModel, data)

Function that maps the amplitude function of a signal data frequency grid. The intended input "data" is the frequency grid output by FFTW.rfftfreq. Alternatively a SignalNoise or ContinuousSignalNoise object can be input, and the corresponding frequency grid will be computed and mapped.

In default, it should be defined as .√(power_point(model, data)).

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StationaryRandomFields.amplitude_point Method

amplitude_point(model::AbstractPowerSpectrumModel, ν...)

Function that computes the pointwise amplitude of fourier component at a set of frequencies ν. This must be implemented in the model interface if fourieranalytic(::Type{MyModel}) == IsAnalytic().

In default, it should be defined as √(power_point(model, ν...)).

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StationaryRandomFields.basemodel Method

basemodel(model::ModifiedPowerSpectrumModel)

Returns the ModifiedPowerSpectrumModel with the last transformation stripped.

Example

julia> basemodel(stretched(Disk(), 1.0, 2.0)) == Disk()
true

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StationaryRandomFields.fourieranalytic Method

fourieranalytic(::Type{<:AbstractPowerSpectrumModel})

Determines whether the model is pointwise analytic in Fourier domain, i.e. we can evaluate its fourier transform at an arbritrary point.

If IsAnalytic() then it will try to call visibility_point to calculate the complex visibilities. Otherwise it fallback to using the FFT that works for all models that can compute an image.

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StationaryRandomFields.generate_gaussian_noise Method

generate_gaussian_noise(data::AbstractNoiseSignal; rng=Random.default_rng())

Generate complex gausisian noises on Fourier space over the frequency space expected for Real FFT. This return a complex array, which is consistent with Fourier-domain representation of a real uncorrelated Gaussian noise with the zero mean and variance of sizeof(data) in signal-domain. The size of the output array is given by rfftsize(data).

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StationaryRandomFields.generate_signal_noise Function

generate_signal_noise(psgen::PowerSpectrumNoiseGenerator)

Converts fourier domain gaussian noise to signal noise, corresponding to the continuous noise signal and power spectrum contained in psgen. Scaling the gaussian fourier noise by the power law function and then transforming to the signal domain with an inverse rfft generates the signal noise.

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StationaryRandomFields.get_fourier_noise Method

get_fourier_noise(psgen::PowerSpectrumNoiseGenerator, signoise::AbstractArray)

Retrieve power-spectrum-scaled fourier noise from given signal noise by transforming to fourier space.

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StationaryRandomFields.get_power_spectrum Method

get_power_spectrum(psgen::PowerSpectrumNoiseGenerator, signoise::AbstractArray)

Retrieve power spectrum from given signal noise.

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StationaryRandomFields.modify Method

modify(m::AbstractPowerSpectrumModel, transforms...)

Modify a given model using the set of transforms. This is the most general function that allows you to apply a sequence of model transformation for example

modify(Gaussian(), Stretch(2.0, 1.0), Rotate(π/4), Shift(1.0, 2.0), Renorm(2.0))

will create a asymmetric Gaussian with position angle π/4 shifted to the position (1.0, 2.0) with a flux of 2 Jy. This is similar to Flux's chain.

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StationaryRandomFields.posangle Method

posangle(model)

Returns the rotation angle of the rotated model

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StationaryRandomFields.power_map Method

power_map(model, gridofν)

Function that maps the power law function of a signal data frequency grid. The intended input "data" is the frequency grid output by FFTW.rfftfreq. Alternatively a SignalNoise or ContinuousSignalNoise object can be input, and the corresponding frequency grid will be computed and mapped.

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StationaryRandomFields.power_point Function

power_point(model::AbstractPowerSpectrumModel, ν...)

Function that computes the pointwise amplitude of fourier component at a set of frequencies ν. This must be implemented in the model interface if fourieranalytic(::Type{MyModel}) == IsAnalytic()

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StationaryRandomFields.renormed Method

renormed(model, f)

Renormalizes the model m to have total flux f*flux(m). This can also be done directly by calling Base.:* i.e.,

julia> renormed(m, f) == f*M
true

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StationaryRandomFields.rfftsize Method

rfftsize(data::AbstractNoiseSignal)::Tuple

Returns the size of the Fourier-domain signal

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StationaryRandomFields.rotated Method

rotated(model, ξ)

Rotates the model by an amount ξ in radians in the clockwise direction.

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StationaryRandomFields.scale_fourier Function

scale_fourier(model::AbstractModifier, ν...)

Returns a number on how to scale the fourier coefficients at the frequency coordinate ν for an modified model

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StationaryRandomFields.stretched Method

stretched(model, α)

Stretches the model m according to the formula Vₛ(u) = V(u1/α1, u2/α2, ...), where were renormalize the intensity to preserve the models flux.

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StationaryRandomFields.transform_ν Function

transform_ν(model::AbstractModifier, ν...)

Returns a transformed frequency coordinate ν according to the model modifier

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StationaryRandomFields.unmodified Method

unmodified(model::ModifiedPowerSpectrumModel)

Returns the un-modified model

Example

julia> m = stretched(rotated(Gaussian(), π/4), 2.0, 1.0)
julia> umodified(m) == Gaussian()
true

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