The Simulation Model

Usage

• Setters to be used to configure the lens and the simulator
  • setLens() - lens parameters are set in the lens object
  • setCentred()
  • setMaskMode()
  • setBGColour()
  • setXY()
  • setPolar()
  • setCHI()
  • setNterms()
  • setSource()
• update() has to be called to recalculate the image
• getDistorted() returns the distorted image
• Other image getters
  • getSource()
  • getActual()
  • getApparent()
• Other parameter getters (used in CosmoSimPy)
  • getXi()
  • getTrueXi()
  • getNu()

Attributes

• Private variables in SimulatorModel
  • eta ($\eta$) is the actual position of the source in the source plane.
    • setters SimulatorModel::setXY or SimulatorModel::setPolar
      • these should be called by the user interface
    • RaytraceModel uses a local $\eta$ corresponding to the pixel currently being evaluated, but this is local to that single method.
  • nu ($\nu$) is the apparent position of the source in the source plane.
    • setter SimulatorModel::setNu($\nu$)
      • this also sets referenceXi and etaOffset
    • updateApparentAbs() calculates $\nu$ and calls setNu($\nu$).
    • To calculate $\nu$ for a given $\eta$, Lens::getXi($\chi\eta$) is used.
  • xi ($\xi$) refers to a reference point in the lens plane. It appears in many local scopes, typically referring to the point being calculated. In the Roulette Model, we use referenceXi to refer to the reference point around which the roulettes are expanded.
    • This is updated by SimulatorModel::setNu, as $\xi=\chi\nu$.
    • setter setXi()
      • this also sets etaOffset
• etaOffset ($\Delta\eta$) is so that $\xi$ is the image of $\eta+\Delta\eta$; i.e. $\Delta\eta=\xi/\chi-\eta$
  • This is protected and accessed in RouletteRegenerator

Consistency

It is important to note that the setters do not ensure a consistent state. Hence, after setting parameters, the model must be updated to ensure consistency.

• updateApparentAbs (protected) calculates inferred variables to ensure a consistent state.
  • First it calls lens->updatePsi(im.size()) to make sure the lens is consistent
  • Then it sets the apparent position $\nu$ using $\xi$ as calculated by lens->getXi( $\chi\eta$ )
  • Overriding subclasses:
    • RotatedModel where the image is rotated for calculation
    • RouletteRegenerator where it does nothing
  • updateApparentAbs is only called by update() below.
• update recalculates the distorted image
• calculateAlphaBeta calculates the roulete amplitudes if required.
  • In most classes, this is empty and does nothing.
  • In RouletteModel (but not RouletteRegenerator) it calls lens->calculateAlphaBeta to compute the amplitudes.
  • It is called only from the distort() method which is never overridden.

The Update Procedure

• The update() function is non-virtual; there are two update procedures that need to be overridden
  • updateApparentAbs() which is called by update()
  • calculateAlphaBeta() which is called by distort()
• getDistorted() calculates the distorted image. It is also non-virtual, and there are two approaches to override its behaviour.
  • distort() calculates the distorted image. By default it uses getDistortedPos() which works in the local co-ordinate system of the roulette formalism. The RaytraceModel overrides it, because it relies on global positioning.
  • getDistortedPos() is provided by the subclasses of RotatedModel() and by RouletteModel(). All of these classes have been designed using the roulette co-ordinate system.
    • getDistortedPos(r,theta) calculates the source plane position $\eta’$ in the local co-ordinate system centred at eta, given a polar co-ordinates $(r,\theta)$ centred on \xi in the lens plane.
    • etaOffset is added to the output to compensate if $\xi$ is not the apparent position

This could possibly be simplified

SimulatorModel flowchart

Technical Design

Components

C++ components

• Simulation Models
  • SimulatorModel.cpp is the abstract base class.
  • Modular Lens Models
    • RouletteModel.cpp
    • Raytrace.cpp
  • Semi-Modular Models using RotatedModel.cpp as a superclass. It overrides functions to rotate the image and make all calculations assuming the source placed on the $x$-axis. The subclasses override getDistortedPos() to hardcode the actual distortion, and thus assume a specific lens model, but they still delegate getXi() to a Lens Object.
    • PointMassExact.cpp simulates the point mass model using the exact formulation
    • PointMassRoulette.cpp simulates the point mass model using the Roulette formalism
  • Monolithic Lens/Simulation Models
  • RouletteRegenerator.cpp is for simulation from roulette amplitudes without any concrete lens model.
• Lens Models
  • SIS.cpp
  • SIE.cpp
  • PointMass.cpp is incomplete and so far used only with the RotateModel models.
• Source Models
  • Source.cpp is the abstract base class.
  • SphericalSource.cpp is standard Guassian model
  • EllipsoidSource.cpp is an ellipsoid Guassian model
  • TriangleSource.cpp is a three colour triangle source, intended for debugging
• simaux.cpp is auxiliary functions
• CosmoSim.cpp defines the CosmoSimPy class with python bindigs. This class operates as a facade to the library, and does not expose the individual classes.

Python Components

• CosmoSim is a wrapper around CosmoSimPy from CosmoSim.cpp, defining the CosmoSim class.
• CosmoGUI is a tkinter desktop application, providing a GUI to the simulator
• CosmoSim.View is a tkinter widget displaying the source and distorted image for CosmoGUI.
• CosmoSim.Controller is a tkinter widget to interactively set the simulator parameters for CosmoGUI.
• CosmoSim.Image provides post-processing functions for the images.
• datagen.py is a batch script to generate distorted images.

Simulator Model Class

Virtual Functions

The following virtual functions have to be overridden by most subclasses. They are called from the main update function and overriding them, the entire lens model changes.

• calculateAlphaBeta() pre-calculates $\alpha$ and $\beta$ in the distortion equation.
• getDistortedPos() calculates the distortion equation for a give pixel.

The constructor typically has to be overridden as well, to load the formulæ for $\alpha$ and $\beta$.

Getters

Getters are provided for the three images.

• getActual()
• getApparent()
• getDistorted()

Update

The main routine of the Simulator is update() which recalculates the three images: actual, apparent, and distorted. This is called by the setters.

In addition to the virtual functions mentioned above, it depends on

• parallelDistort() and distort() which runs the main steps in parallel.
• drawParallel() and drawSource() which draws the source image.