neutronpy.kmpfit.Fitter¶

class neutronpy.kmpfit.Fitter(residuals, deriv=None, params0=None, parinfo=None, ftol=None, xtol=None, gtol=None, epsfcn=None, stepfactor=None, covtol=None, maxiter=None, maxfev=None, nofinitecheck=None, data=None)¶

Uses the implementation in C of MPFIT, Craig Markwardt’s non-linear least squares curve fitting routines for IDL. MPFIT uses the Levenberg-Marquardt technique to solve the least-squares problem, which is a particular strategy for iteratively searching for the best fit. In its typical use, MPFIT will be used to fit a user-supplied function (the “model”) to user-supplied data points (the “data”) by adjusting a set of parameters. MPFIT is based upon the robust routine MINPACK-1 (LMDIF.F) by Moré and collaborators.

Parameters:

residuals : func

the residuals function, see description below.

deriv : func

optional derivatives function, see description below. If a derivatives function is given, user-computed explicit derivatives are automatically set for all parameters in the attribute parinfo, but this can be changed by the user.

kwargs :

other parameters, each corresponding with one of the configuration attributes described below. They can be defined here, when the Fitter object is created, or later. The attributes params0 and data must be defined before the method fit is called.

Notes

Objects of this class are callable and return the fitted parameters when called.

Residuals function The residuals function must return a NumPy (dtype=’d’) array with weighted deviations between the model and the data. It takes two arguments: a NumPy array containing the parameter values and a reference to the attribute data which can be any object containing information about the data to be fitted. E.g., a tuple like (xvalues, yvalues, errors).

In a typical scientific problem the residuals should be weighted so that each deviate has a Gaussian sigma of 1.0. If x represents values of the independent variable, y represents a measurement for each value of x, and err represents the error in the measurements, then the deviates could be calculated as follows:

$deviates = (y - f(x)) / err$

where f is the analytical function representing the model. If err are the 1-sigma uncertainties in y, then

$\sum deviates^2$

will be the total chi-squared value. Fitter will minimize this value. As described above, the values of x, y and err are passed through Fitter to the residuals function via the attribute data.

Derivatives function The optional derivates function can be used to compute weighted function derivatives, which are used in the minimization process. This can be useful to save time, or when the derivative is tricky to evaluate numerically.

The function takes three arguments: a NumPy array containing the parameter values, a reference to the attribute data and a list with boolean values corresponding with the parameters. If a boolean in the list is True, the derivative with respect to the corresponding parameter should be computed, otherwise it may be ignored. Fitter determines these flags depending on how derivatives are specified in item side of the attribute parinfo, or whether the parameter is fixed.

The function must return a NumPy array with partial derivatives with respect to each parameter. It must have shape (n,m), where n is the number of parameters and m the number of data points.

Configuration attributes The following attributes can be set by the user to specify a Fitter object’s behavior.

Attributes

`parinfo`	A list of dicts with parameter contraints, one dict per parameter, or None if not given.
`params0`	Required attribute.
`data`	Required attribute.
`ftol`	Relative $\chi^2$ convergence criterium.
`xtol`	Relative parameter convergence criterium.
`gtol`	Orthogonality convergence criterium.
`epsfcn`	Finite derivative step size.
`stepfactor`	Initial step bound.
`covtol`	Range tolerance for covariance calculation.
`maxiter`	Maximum number of iterations.
`maxfev`	Maximum number of function evaluations.
`params`	A NumPy array, list or tuple with the fitted parameters.
`xerror`	Final parameter uncertainties ( $1 \sigma$ )
`covar`	Final parameter covariance (NumPy-) matrix.
`chi2_min`	Final $\chi^2$ .
`orignorm`	Starting value of $\chi^2$ .
`rchi2_min`	Minimum reduced $\chi^2$ .
`stderr`	Standard errors.
`npar`	Number of parameters.
`nfree`	Number of free parameters.
`npegged`	Number of pegged parameters.
`dof`	Number of degrees of freedom.
`resid`	Final residuals.
`niter`	Number of iterations.
`nfev`	Number of function evaluations.
`version`	mpfit.c’s version string.
`status`	Fitting status code.
`message`	Message string.
`residuals`	residuals: object
`nofinitecheck`	Does not check for finite values.

Methods

`fit`(self[, params0])	Perform a fit with the current values of parameters and other attributes.
`confidence_band`(self, x, dfdp, confprob, f)	After the method `fit` has been called, this method calculates the upper and lower value of the confidence interval for all elements of the NumPy array x.