python-lmfit-doc - 1.1.0-1 main

The lmfit Python package provides a simple, flexible interface to
non-linear optimization or curve fitting problems. The package
extends the optimization capabilities of scipy.optimize by replacing
floating pointing values for the variables to be optimized with
Parameter objects. These Parameters can be fixed or varied, have
upper and/or lower bounds placed on its value, or written as an
algebraic expression of other Parameters.
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The principal advantage of using Parameters instead of simple
variables is that the objective function does not have to be
rewritten to reflect every change of what is varied in the fit, or
what relationships or constraints are placed on the Parameters. This
means a scientific programmer can write a general model that
encapsulates the phenomenon to be optimized, and then allow user of
that model to change what is varied and fixed, what range of values
is acceptable for Parameters, and what constraints are placed on the
model. The ease with which the model can be changed also allows one
to easily test the significance of certain Parameters in a fitting
model.
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The lmfit package allows a choice of several optimization methods
available from scipy.optimize. The default, and by far best tested
optimization method used is the Levenberg-Marquardt algorithm from
MINPACK-1 as implemented in scipy.optimize.leastsq. This method
is by far the most tested and best support method in lmfit, and much
of this document assumes this algorithm is used unless explicitly
stated. An important point for many scientific analysis is that this
is only method that automatically estimates uncertainties and
correlations between fitted variables from the covariance matrix
calculated during the fit.
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A few other optimization routines are also supported, including
Nelder-Mead simplex downhill, Powell's method, COBYLA, Sequential
Least Squares methods as implemented in scipy.optimize.fmin, and
several others from scipy.optimize. In their native form, some of
these methods setting allow upper or lower bounds on parameter
variables, or adding constraints on fitted variables. By using
Parameter objects, lmfit allows bounds and constraints for all of
these methods, and makes it easy to swap between methods without
hanging the objective function or set of Parameters.
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Finally, because the approach derived from MINPACK-1 usin the
covariance matrix to determine uncertainties is sometimes questioned
(and sometimes rightly so), lmfit supports methods to do a brute
force search of the confidence intervals and correlations for sets of
parameters.
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This is the common documentation package.