Contents

• Getting started with Non-Linear Least-Squares Fitting
• Downloading and Installation
  • Prerequisites
  • Downloads
  • Installation
  • Development Version
  • Testing
  • Acknowledgements
  • Copyright, Licensing, and Re-distribution
• Release Notes
  • Version 1.3.2 Release Notes (July 19, 2024)
  • Version 1.3.1 Release Notes (April 19, 2024)
  • Version 1.3.0 Release Notes (April 4, 2024)
  • Version 1.2.2 Release Notes (July 14, 2023)
  • Version 1.2.1 Release Notes (May 02, 2023)
  • Version 1.2.0 Release Notes (April 05, 2023)
  • Version 1.1.0 Release Notes (November 27, 2022)
  • Version 1.0.3 Release Notes (October 14, 2021)
  • Version 1.0.2 Release Notes (February 7, 2021)
  • Version 1.0.1 Release Notes
  • Version 1.0.0 Release Notes
  • Version 0.9.15 Release Notes
  • Version 0.9.14 Release Notes
  • Version 0.9.13 Release Notes
  • Version 0.9.12 Release Notes
  • Version 0.9.10 Release Notes
  • Version 0.9.9 Release Notes
  • Version 0.9.6 Release Notes
  • Version 0.9.5 Release Notes
  • Version 0.9.4 Release Notes
  • Version 0.9.3 Release Notes
  • Version 0.9.0 Release Notes
    • Summary
    • Impact
    • Discussion
• Getting Help
• Frequently Asked Questions
  • What’s the best way to ask for help or submit a bug report?
  • Why did my script break when upgrading from lmfit 0.8.3 to 0.9.0?
  • I get import errors from IPython
  • How can I fit multi-dimensional data?
  • How can I fit multiple data sets?
  • How can I fit complex data?
  • How should I cite LMFIT?
  • I get errors from NaN in my fit. What can I do?
    • nan_policy
    • Common sources of NaN
  • Why are Parameter values sometimes stuck at initial values?
  • Why are uncertainties in Parameters sometimes not determined?
  • Can Parameters be used for Array Indices or Discrete Values?
• Parameter and Parameters
  • The Parameter class
    • Parameter
  • The Parameters class
    • Parameters
  • The create_params() function
    • create_params()
  • Simple Example
• Performing Fits and Analyzing Outputs
  • The minimize() function
    • minimize()
  • Writing a Fitting Function
  • Types of Data to Use for Fitting
  • Choosing Different Fitting Methods
  • MinimizerResult – the optimization result
    • MinimizerResult
    • Goodness-of-Fit Statistics
    • Akaike and Bayesian Information Criteria
    • Uncertainties in Variable Parameters, and their Correlations
  • Getting and Printing Fit Reports
    • fit_report()
  • Using a Iteration Callback Function
  • Using the Minimizer class
    • Minimizer
    • Minimizer.minimize()
    • Minimizer.leastsq()
    • Minimizer.least_squares()
    • Minimizer.scalar_minimize()
    • Minimizer.prepare_fit()
    • Minimizer.brute()
    • Minimizer.basinhopping()
    • Minimizer.ampgo()
    • Minimizer.shgo()
    • Minimizer.dual_annealing()
    • Minimizer.emcee()
  • Minimizer.emcee() - calculating the posterior probability distribution of parameters
• Modeling Data and Curve Fitting
  • Motivation and simple example: Fit data to Gaussian profile
  • The Model class
    • Model
    • Model class Methods
    • Model class Attributes
    • Determining parameter names and independent variables for a function
    • Explicitly specifying independent_vars
    • Functions with keyword arguments
    • Defining a prefix for the Parameters
    • Initializing model parameter values
    • Using parameter hints
    • Data Types for data and independent data with Model
    • Saving and Loading Models
  • The ModelResult class
    • ModelResult
    • ModelResult methods
    • ModelResult attributes
    • Calculating uncertainties in the model function
    • Using uncertainties in the fitted parameters for post-fit calculations
    • Saving and Loading ModelResults
  • Composite Models : adding (or multiplying) Models
    • CompositeModel
• Built-in Fitting Models in the models module
  • Peak-like models
    • GaussianModel
    • LorentzianModel
    • SplitLorentzianModel
    • VoigtModel
    • PseudoVoigtModel
    • MoffatModel
    • Pearson4Model
    • Pearson7Model
    • StudentsTModel
    • BreitWignerModel
    • LognormalModel
    • DampedOscillatorModel
    • DampedHarmonicOscillatorModel
    • ExponentialGaussianModel
    • SkewedGaussianModel
    • SkewedVoigtModel
    • ThermalDistributionModel
    • DoniachModel
  • Linear and Polynomial Models
    • ConstantModel
    • LinearModel
    • QuadraticModel
    • PolynomialModel
    • SplinelModel
  • Periodic Models
    • SineModel
  • Step-like models
    • StepModel
    • RectangleModel
  • Exponential and Power law models
    • ExponentialModel
    • PowerLawModel
  • Two dimensional Peak-like models
    • Gaussian2dModel
  • User-defined Models
    • ExpressionModel
  • Example 1: Fit Peak data to Gaussian, Lorentzian, and Voigt profiles
  • Example 2: Fit data to a Composite Model with pre-defined models
  • Example 3: Fitting Multiple Peaks – and using Prefixes
  • Example 4: Using a Spline Model
• Calculation of confidence intervals
  • Method used for calculating confidence intervals
  • A basic example
  • Working without standard error estimates
  • Calculating and visualizing maps of \(\chi^2\)
  • An advanced example for evaluating confidence intervals
  • Confidence Interval Functions
    • conf_interval()
    • conf_interval2d()
    • ci_report()
• Bounds Implementation
• Using Mathematical Constraints
  • Overview
  • Supported Operators, Functions, and Constants
  • Using Inequality Constraints
  • Advanced usage of Expressions in lmfit
• Examples gallery
• Examples from the documentation