Non-linear Least Squares Fitting in IDL with MPFIT

By C. Markwardt. 2009

748 citations recorded by the source corpus.

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 this http URL

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/2a64cd16e0b6a7348eeaa11eca41d9e96daee284

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Citations in the corpus

CONSTRAINING THE MILKY WAY POTENTIAL WITH A SIX-DIMENSIONAL PHASE-SPACE MAP OF THE GD-1 STELLAR STREAM (2009, methodology): “The minimization is performed using the MPFIT code (Markwardt 2009) implementing the LevenbergMarquardt technique (Marquardt 1963) translated into Python7.”
The Complete Transmission Spectrum of WASP-39b with a Precise Water Constraint (2017, methodology): “The SPARC/MITgcm couples the MITgcm, a finite-volume code that solves the 3D primitive equations on a staggered Arakawa C grid (Adcroft et al. 2004) with a two-stream adaptation of a multistream radiative transfer code for solar system planets (Marley & McKay 1999).”
Planetary Spectrum Generator: An accurate online radiative transfer suite for atmospheres, comets, small bodies and exoplanets (2018, methodology): “rg–Marquardt method being more robust, meaning that it finds a solution even if the initial conditions are far from the final solution. The Levenberg-Marquardt algorithm is based on the MPFIT program [91], which draws from the robust package called MINPACK-1. The user-provided file should be formatt”
Molecular gas kinematics within the central 250 pc of the Milky Way (2016, methodology): “(iv) The minimization algorithm, mpfit (Markwardt 2009),5 uses these input parameters to find the best-fitting solution to the following function: I(v) = n∑ i=0 Ipeak,i exp [− (v− v0,i)2)/(2σ2i )], (1) whereby Ipeak,i, v0,i, σi represent the peak intensity, centroid velocity, and velocity…”
THE SLOAN LENS ACS SURVEY. IX. COLORS, LENSING, AND STELLAR MASSES OF EARLY-TYPE GALAXIES (2009, methodology): “The model parameters (the Einstein radius and ellipticity parameters for the lens) are first adjusted by hand before optimization by MPFIT (Markwardt 2009).”
Survey of ion plasma parameters in Saturn's magnetosphere (2010, methodology): “For the core fitting routine, we make use of a publicly available IDL source code called MPFIT, available from NASA Goddard Space Flight Center [Markwardt, 2008] (MPFIT is available at http://purl.com/net/mpfit).”
Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions (2016, methodology): “It was converted into IDL and named mpfit by Markwardt (2009), with the important addition of the ability to set bounds or keep any of the variables fixed. mpfit was ported to Python by Mark Rivers and later adapted for use with Numpy by Sergey Koposov.”
The MiMeS survey of Magnetism in Massive Stars : magnetic analysis of the O-type stars (2016, methodology): “This was carried out using the Levenberg-Marquardt, non-linear least-squares algorithm from the mpfit library (Moré 1978; Markwardt 2009).”
Remote sensing of larch phenological cycle and analysis of relationships with climate in the Alpine region (2010, methodology): “This was accomplished through the use of a Levenberg–Marquardt curve-fitting algorithm (MPFIT – Markwardt, 2008).”