LevMar

class sherpa.optmethods.LevMar(name='levmar')[source] [edit on github]

Bases: OptMethod

Levenberg-Marquardt optimization method.

The Levenberg-Marquardt method is an interface to the MINPACK subroutine lmdif to find the local minimum of nonlinear least squares functions of several variables by a modification of the Levenberg-Marquardt algorithm [1].

ftol

The function tolerance to terminate the search for the minimum; the default is FLT_EPSILON ~ 1.19209289551e-07, where FLT_EPSILON is the smallest number x such that 1.0 != 1.0 + x. The conditions are satisfied when both the actual and predicted relative reductions in the sum of squares are, at most, ftol.

Type:: number

xtol

The relative error desired in the approximate solution; default is FLT_EPSILON ~ 1.19209289551e-07, where FLT_EPSILON is the smallest number x such that 1.0 != 1.0 + x. The conditions are satisfied when the relative error between two consecutive iterates is, at most, xtol.

Type:: number

gtol

The orthogonality desired between the function vector and the columns of the jacobian; default is FLT_EPSILON ~ 1.19209289551e-07, where FLT_EPSILON is the smallest number x such that 1.0 != 1.0 + x. The conditions are satisfied when the cosine of the angle between fvec and any column of the jacobian is, at most, gtol in absolute value.

Type:: number

maxfev

The maximum number of function evaluations; the default value of None means to use 1024 * n, where n is the number of free parameters.

Type:: int or None

epsfcn

This is used in determining a suitable step length for the forward-difference approximation; default is FLT_EPSILON ~ 1.19209289551e-07, where FLT_EPSILON is the smallest number x such that 1.0 != 1.0 + x. This approximation assumes that the relative errors in the functions are of the order of epsfcn. If epsfcn is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision.

Type:: number

factor

Used in determining the initial step bound; default is 100. The initial step bound is set to the product of factor and the euclidean norm of diag*x if nonzero, or else to factor itself. In most cases, factor should be from the interval (.1,100.).

Type:: int

numcores

The number of CPU cores to use. The default is 1.

Type:: int

verbose

The amount of information to print during the fit. The default is 0, which means no output.

Type:: int

References

Attributes Summary

default_config

The default settings for the optimiser.

Methods Summary

fit(statfunc, pars, parmins, parmaxes[, ...])

Run the optimiser.

Attributes Documentation

default_config: The default settings for the optimiser.

Methods Documentation

fit(statfunc, pars, parmins, parmaxes, statargs=(), statkwargs=None) [edit on github]

Run the optimiser.

Changed in version 4.16.0: The statkwargs argument now defaults to None rather than {}.

Parameters:

statfunc (function) – Given a list of parameter values as the first argument and, as the remaining positional arguments, statargs and statkwargs as keyword arguments, return the statistic value.
pars (sequence) – The start position of the model parameter values.
parmins (sequence) – The minimum allowed values for each model parameter. This must match the length of pars.
parmaxes (sequence) – The maximum allowed values for each model parameter. This must match the length of pars.
statargs (optional) – Additional positional arguments to send to statfunc.
statkwargs (dict, optional) – Additional keyword arguments to send to statfunc.

Returns:

newpars – The tuple contains: boolean indicating whether the optimization succeeded or not, the best fit parameters as a NumPy array, the statistic value at the best-fit location, a string message indicating the status, and a dictionary containing information about the optimisation (this depends on the optimiser).

Return type:

tuple