GaussMLE.GaussModel

GaussModel

The GaussModel module offers a unified framework for defining, manipulating, and fitting Gaussian models to data. It prescribes a set of abstract types, concrete model types, and function signatures that are expected for fitting and simulation codes.

Abstract Types Hierarchy

1. GaussMLEParams{T}: An abstract type for the parameters of a Gaussian model.
2. GaussMLEArgs{T}: An abstract type for model-specific arguments, such as non-fitted parameters.
3. GaussMLEΣ{T}: An abstract type for representing the uncertainty associated with a Gaussian model.

Required Methods

Each concrete Gaussian model, such as :xynb, must implement the following methods:

• model(θ, args, i, j): Calculates the model's predicted intensity at pixel locations (i, j) based on the parameters θ and additional arguments args.
• gradient!(θ, args, out, i, j): Computes and stores the gradient of the model with respect to its parameters at pixel locations (i, j) in the out array.
• curvature!(θ, args, out, i, j): Computes and stores the diagonal elements of the model's Hessian matrix (curvature) at pixel locations (i, j) in the out array.
• initialize_parameters!(θ, data, boxsize, args): Initializes the parameters of the model type based on the provided 2D data matrix, box size, and additional arguments args.
• update!(θ, numerator, denominator): Updates the model parameters based on provided numerator and denominator arrays, typically sums of gradients and curvatures over data points.
• genargs(::Type{θ}, args): Returns an instance of the model-specific GaussMLEArgs type.
• genθ(::Type{θ}, boxsize): Returns an instance of the θ_xynbs type, initialized based on the given boxsize.
• genΣ(::Type{θ}): Returns an instance of theΣ_xynbs` type, initialized with default values.

Notes

• All function are Parametric in the type T, which is expected to be a subtype of Real.

Concrete Models

• xynb: A 2D Gaussian model that includes parameters for the x and y coordinates, sum intensity, and background.
• xynbs: An extended version of xynb that also includes an additional term for the PSF width, σ_PSF.

Internal Constants

• MODEL_MAP: A dictionary that associates model symbols with their corresponding concrete types, facilitating internal model selection and mapping.