    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 (J.J. More, "The Levenberg Marquardt algorithm: implementation and theory," in Lecture Notes in Mathematics 630: Numerical Analysis, G.A. Watson (Ed.), Springer-Verlag: Berlin, 1978, pp.105-116).

Method Options
ftol - the relative error desired in the sum of squares; default is sqrt( DBL_EPSILON ) ~ 1.19209289551e-07, where DBL_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.
xtol - the relative error desired in the approximate solution; default is sqrt( DBL_EPSILON ) ~ 1.19209289551e-07, where DBL_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
gtol - the orthogonality desired between the function vector and the columns of the jacobian; default is sqrt( DBL_EPSILON ) ~ 1.19209289551e-07, where DBL_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.
maxfev - the maximum number of function evaluation; default is 1024 * n (number of free parameters).
epsfcn - used in determining a suitable step length for the forward-difference approximation; default is sqrt( DBL_EPSILON ) ~ 1.19209289551e-07, where DBL_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.
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.).
verbose - the amount of information to print about the fit progress. Default is 0 (no output).
sherpa> set_method("levmar")
sherpa> get_method_name()
'levmar'

Set the optimization method and then confirm the new value.

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.

December 2013