Non-linear Least Squares Fitting in IDL with MPFIT

TL;DR

MPFIT is an IDL implementation of the robust non-linear least squares fitting program MINPACK-1, optimized for performance, with extensive features for various data fitting tasks and diagnostics.

Contribution

This paper introduces MPFIT, a versatile IDL package for non-linear least squares fitting, including new specialized functions, constraints, and diagnostic tools, with translations to C and Python.

Findings

Robust fitting performance comparable to MINPACK-1

Supports multiple data types and constraints

Provides extensive diagnostic capabilities

Abstract

MPFIT is a port to IDL of the non-linear least squares fitting program MINPACK-1. MPFIT inherits the robustness of the original FORTRAN version of MINPACK-1, but is optimized for performance and convenience in IDL. In addition to the main fitting engine, MPFIT, several specialized functions are provided to fit 1-D curves and 2-D images; 1-D and 2-D peaks; and interactive fitting from the IDL command line. Several constraints can be applied to model parameters, including fixed constraints, simple bounding constraints, and "tying" the value to another parameter. Several data weighting methods are allowed, and the parameter covariance matrix is computed. Extensive diagnostic capabilities are available during the fit, via a call-back subroutine, and after the fit is complete. Several different forms of documentation are provided, including a tutorial, reference pages, and frequently asked questions. The package has been translated to C and Python as well. The full IDL and C packages can be found at http://purl.com/net/mpfit