## Overview

In fitting, we estimate the optimum parameters in a numerical model, specifically a scattering simulation, by minimizing the difference between simulated and reference data.

BornAgain supports

- a variety of minimization algorithms;
- choice of fitting parameters, their properties and correlations;
- full control over objective function calculations, including the use of different normalizations and assignments of different masks and weights to different areas of the reference data;
- possibility to fit simultaneously an arbitrary number of data sets.

In the following we will show how to fit using the BornAgain Python API. For fitting through the graphical user interface, see GUI > Fitting.

## Introductory example

In the following, a very simple example shows how to fit a parametric model to given data.

The model is a specular reflectometry scan, with a sample consisting of 20 alternating Ti and Ni layers on a Si substrate. Using this model, synthetic data have been generated with GenX. These data are part of the BornAgain sources, testdata/specular/genx_alternating_layers.dat.gz. To make them findable by the script, the environment variable `BA_DATA_DIR` must point to a local copy of directory testdata.

The fit model is identical to the model used for generating the data. There is just one fit parameter, namely the thickness of the Ti layers. The resulting fit is indistinguishable from the data:

#### Script

auto/Examples/fit/specular/Specular1Par.py

#### Explanations

The arrays (Python lists) `exp_x`, `exp_y` contain the data to be fitted.

The dictionary `P` contains the fit parameter.

An instance of class `FitObjective` defines the objective function in terms of data $y(x)$ and fit model $f(x;P)$. By default, it is a $\chi^2$ function, weighted with the inverse standard deviation.

The function call `initPrint(10)` means that values of $\chi^2$ and of all fit parameters are printed to the terminal every 10 fit iterations. To suppress the printing, set the function argument to 0.

Similarly, the function call `initPlot(10, ...)` means that data and fit are replotted every 10 fit iterations. In the `PlotterSpecular`, the argument `pause=0.5` means that after refreshing the plot the program is put to sleep for 0.5 s. This enables humans to observe the evolution of the plots in real time. With `pause=0`, the program executes so fast that one only sees the final plot.

The actual fit is controlled by class `Minimizer`, and launched by the function call `minimize(...)`.

- Introduction
  - Functionality overview
  - Architectural overview

- Install or build
  - Install Python
    - Python on Linux
    - Python on Windows
    - Python on Mac
    - Python modules
  - Install BornAgain
    - Linux
    - Windows
    - MacOS
    - Development snapshot
  - Build BornAgain
    - Unix
      - Install third-party software
      - Get the source
      - Build and install BornAgain
      - Run a first simulation
    - Windows

- Graphical user interface
  - Quick Start
  - GUI overview
  - Fitting in the GUI

- Python scripting
  - Run a script
  - Understand the syntax
  - Fitting
  - Upgrading

- Reference
  - Simulation model
    - Simulation classes
      - Specular
        - Example
      - Scattering
        - Examples
          - GISAS
          - without DWBA terms
          - with specular peak
          - SAS
          - Polarized SANS
          - Monte-Carlo
      - Off-specular
        - Off-specular
      - Depth probe
        - Examples
          - Thin film
          - Transmitted modulus
          - Resonator
    - Common settings
      - Background
      - Options
        - Monte-Carlo
        - # threads
        - Average materials
        - Include specular
      - Progress monitor
  - Instrument model
    - Beam
      - Footprint
      - Beam divergence
    - Scan
      - TOF reflectometry
      - TOF resolution
      - Beam Angular Spread
      - Beam Wavelength Spread
    - Detectors
      - SphericalDetector
      - 2d detector resolution
      - Offspec detector
    - Neutron polarization
      - Spin asymmetry example
    - Examples
      - 2D detector resolution
      - Neutron polarization
        - Magnetic layer
        - Ditto, realistic instrument
        - Polarized scattering
  - Sample model
    - Materials
      - Magnetization
    - Sample
      - Layer
      - LayerStack
      - Layout
    - Roughness
      - Interface model
      - Transient
      - Cross-correlation
      - Examples
        - GISAS
        - Reflectivity
    - Particles
      - Form factor
        - Hard particles
          - Bipyramid4
          - Box
          - CantellatedCube
          - Cone
          - Cylinder
          - Dodecahedron
          - EllipsoidalCylinder
          - HemiEllipsoid
          - HorizontalCylinder
          - Icosahedron
          - PlatonicOctahedron
          - PlatonicTetrahedron
          - Prism3
          - Prism6
          - Pyramid2
          - Pyramid3
          - Pyramid4
          - Pyramid6
          - Sphere
          - SphericalSegment
          - Spheroid
          - SpheroidalSegment
          - TruncatedCube
        - Ripples
          - Bar ripple
          - Cosine ripple
          - Sawtooth ripple
        - Soft particles
          - FuzzySphere
          - Gauss
        - Custom formfactor
      - Composite particles
        - Core and shell
        - Compound particle
        - Mesocrystal
      - Examples
        - Compound particle
        - Core and shell
        - Crossing an interface
        - Mesocrystal
        - Rotation example
        - Dense cylinders
        - Dense hemispheres
        - Uncorrelated mixture
        - Polydispersity
    - Particle assemblies
      - Grating
        - 1D lattice
        - Cosine ripples in a lattice
        - Triangular ripples in a lattice
      - 2D lattice
        - Square lattice
        - Lattice orientation distribution
        - Finite square lattice
        - Lattice with basis
        - Multi-layer lattice
        - Position variance
      - Radial paracrystal
      - 2D paracrystal
      - Others
        - Size-distribution model: decoupling approximation
        - Size-distribution model: local monodisperse approximation
        - Size-distribution model: size-spacing coupling approximation
  - Model modifiers
    - Rotation
    - Distributions
  - Data types
    - Class Datafield
      - Export
      - Find intensity peaks
    - SLD profile
      - SLD profile with rough interfaces
      - SLD profile with a sliced particle layer
  - Plotting
    - Functions
    - Configuration
    - Heat map
    - LaTeX markup
    - Export
    - Plot axes in different units
  - Fitting
    - Data import
      - TIFF
    - Minimizer settings
    - Multiple datasets
    - Examples
      - Fitting with masks
      - Custom objective function
      - Fitting along slices
      - GISAS 2D fits
      - Experiment at GALAXI
      - Find background
      - Minimizer settings
      - Bayesian Sampling
      - Consecutive fitting
      - Considering uncertainties
      - External minimizer
      - External minimizer: plotting
      - Simultaneous fit of two datasets
      - Spin asymmetry fit example
      - Reflectometry: Fit Pt layer
      - Reflectometry: Fit honeycomb

- Literature
  - Babonneau2010
  - Babonneau2013
  - Croset2021
  - Lazzari2002
  - Lazzari2006
  - Pospelov2020
  - Renaud2009
  - Sears1992
  - Wuttke2021

- How to
  - Get announcements
  - Solve known problems
    - Set Python environmental variables under Windows
  - Request help or report bugs
  - Cite BornAgain

- Developers' corner
  - Configure
    - Build
    - Pyenv
  - Develop
    - Manual checks
    - Debug
    - Webdoc
    - Code analyses
  - Release
    - Manual GUI test