Simulations

Gravity.jl allows one to carry out simulations using the same format of the YAML configuration file normally used for model fitting.

Simulations are activated with scheme: simulation. All other parts of the configuration file can be kept. The simulation mode is, in many respects, very similar to the scheme: extended-imageplane: that is, all source parameters are considered and included in the parameter vector. Additionally, since in a simulation one generally does not know a-priori the positions of the images associated to each source, it is a good idea to explicitly include a grid.

Two new commands control the generation of simulated images. They are Main.model.make_simulations and the related Main.model.flat_simulations. They respectively return a dictionary or a list of images produced by the gravitational lensing configuration associated with the provided parameters. One important point, is that these commands generate observations with random statistical errors: therefore, multiple successive calls of these functions with the same arguments will return different results.

The errors are distributed accordingly to the specified image section. More specifically, the functions produce errors that will follow, in sequence for each source, the error distributions specified in the various images: therefore, if four images are indicated in the configuration file, but only two images are predicted, the errors will be distributed using the errors of the two images. In case more images are predicted than the ones listed in the configuration file, the distribution of the last image is used for the exceeding ones.

Example

parameters:
    angular_unit: 1
    z_lens: 0.6423
    wcs_origin: (0.0, 0.0)
lens-inversion:
    failsafe: always
    grid: (-10:0.01:10, -10:0.01:10)
    methods:
        newton: 
            maxiters: 100
            xtol: 1e-4
            ftol: null
        success:
sampling:
    scheme: simulation
    algorithm: pt
    random-seed: 1
lenses:
    - NIS:
        name: L1
        z: z_lens
        x: (-1.0, -1.0)
        s: 0.02
        σ: 200
    - NIS:
        name: L2
        z: z_lens
        x: (1.0, -1.0)
        s: 0.02
        σ: 200
    - NIS:
        name: L3
        z: z_lens
        x: (1.0, 1.0)
        s: 0.02
        σ: 200
    - NIS:
        name: L4
        z: z_lens
        x: (-1.0, 1.0)
        s: 0.02
        σ: 200
sources:
    - Point:
        z: 1.689
        x: (0.0, 0.0) ± 0.2
        images:
            - Point:
                x: (0.0, 0.0) ± 0.01

The model above has free parameters only associated with the source (the $x$ and $y$ coordinates of the source position), but in general one might also include parameters associated with the lenses or the cosmological model, as in any other configuration file.

If one runs then

julia> model = gravitymodel("examples/simulation/simulation.yml")
Main.GravityModel

julia> model.flat_simulations([0.1, 0.1])
OrderedCollections.OrderedDict{String, PointImageMeasurement{Float64}} with 11 entries:
  "sources_1_Point_simulations_1"  => PointImageMeasurement{Float64}([0.410292, 0.41101], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_2"  => PointImageMeasurement{Float64}([1.05161, -1.65546], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_3"  => PointImageMeasurement{Float64}([-1.3494, -1.35027], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_4"  => PointImageMeasurement{Float64}([-1.00726, -0.99563], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_5"  => PointImageMeasurement{Float64}([0.993632, -1.0095], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_6"  => PointImageMeasurement{Float64}([2.0003, 0.410325], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_7"  => PointImageMeasurement{Float64}([-1.00409, 1.00108], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_8"  => PointImageMeasurement{Float64}([1.00434, 0.999732], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_9"  => PointImageMeasurement{Float64}([-1.68338, 1.03757], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_10" => PointImageMeasurement{Float64}([1.59038, 1.60052], [10000.0 0.0; 0.0 10000.0], 7.37246)
  "sources_1_Point_simulations_11" => PointImageMeasurement{Float64}([0.423186, 2.00879], [10000.0 0.0; 0.0 10000.0], 7.37246)

Note how several (11) images are produced, all with the same error distribution, taken from the only image present in the configuration file.

With the usual Makie visual interface we can display the lensing configuration:

julia> using CairoMakie

julia> fig = Makie.Figure(size=(800, 400));

julia> ax1 = Makie.Axis(fig[1, 1]; aspect=Makie.DataAspect(), xgridvisible=false, ygridvisible=false, title="Image plane")

julia> plotmodel!(ax1, model, [0.1, 0.1])

julia> ax2 = Makie.Axis(fig[1, 2]; aspect=Makie.DataAspect(), xgridvisible=false, ygridvisible=false, title="Source plane")

julia> plotcaustics!(ax2, model, [0.1, 0.1])

julia> plotsources!(ax2, model, [0.1, 0.1])

julia> fig

API Interface

make_simulations([rng=default_rng(),] x [, options, sys])

flat_simulations([rng=default_rng(),] x [, prop1, prop2...]; matches=:best, tolerant=false)