LevenbergMarquardtFitter

LevenbergMarquardtFitter = class LevenbergMarquardtFitter(IterativeFitter)

LevenbergMarquardtFitter(xdata, model, **kwargs) Non-linear fitter using the Levenberg-Marquardt method. Implementation of the Levenberg-Marquardt algorithm to fit the parameters of a non-linear model. It is a gradient fitter which uses partial derivatives to find the downhill gradient. Consequently it ends in the first minimum it finds. The original C-version stems from Numerical Recipes with some additions of my own. This might be the third or fourth transcription of it. Author Do Kester. Examples -------- # assume x and y are Double1d data arrays: >>> x = numpy.arange( 100, dtype=float ) / 10 >>> y = numpy.arange( 100, dtype=float ) / 122 # make slope >>> rg = RandomGauss( seed=12345L ) # Gaussian random number generator >>> y += rg( numpy.asarray( 100, dtype=float ) ) * 0.2 # add noise >>> y[Range( 9,12 )] += numpy.asarray( [5,10,7], dtype=float ) # make some peak # define a model: GaussModel + background polynomial >>> gauss = GaussModel( ) # Gaussian >>> gauss += PolynomialModel( 1 ) # add linear background >>> gauss.setParameters( numpy.asarray( [1,1,0.1,0,0], dtype=float ) ) # initial parameter guess >>> print gauss.getNumberOfParameters( ) # 5 ( = 3 for Gauss + 2 for line ) >>> gauss.keepFixed( numpy.asarray( [2] ), numpy.asarray( [0.1], dtype=float ) ) # keep width fixed at 0.1 >>> lmfit = LevenbergMarquardtFitter( x, gauss ) >>> param = lmfit.fit( y ) >>> print param.length( ) # 4 ( = 5 - 1 fixed ) >>> stdev = lmfit.getStandardDeviation( ) # stdevs on the parameters >>> chisq = lmfit.getChiSquared( ) >>> scale = lmfit.getScale( ) # noise scale >>> yfit = lmfit.getResult( ) # fitted values >>> yband = lmfit.monteCarloError( ) # 1 sigma confidence region # for diagnostics ( or just for fun ) >>> lmfit = LevenbergMarquardtFitter( x, gauss ) >>> lmfit.setVerbose( 2 ) # report every 100th iteration >>> plotter = IterationPlotter( ) # from BayesicFitting >>> lmfit.setPlotter( plotter, 20 ) # make a plot every 20th iteration >>> param = lmfit.fit( y ) Notes ----- In case of problems look at the "Troubles" page in the documentation area. Limitations ----------- 1. LMF is <b>not</b> guaranteed to find the global minimum. 2. The calculation of the evidence is an Gaussian approximation which is only exact for linear models with a fixed scale. Attributes ---------- xdata : array_like vector of numbers as input for model model : Model the model to be fitted lamda : float to balance the curvature matrix (see Numerical Recipes)

Method resolution order:: LevenbergMarquardtFitter; IterativeFitter; BaseFitter; builtins.object

Constructor:

LevenbergMarquardtFitter( xdata, model, **kwargs ): Create a class, providing xdata and model. Parameters ---------- xdata : array_like vector of independent input values model : Model a model function to be fitted kwargs : dict Possibly includes keywords from IterativeFitter : maxIter, tolerance, verbose BaseFitter : map, keep, fixedScale

Methods defined here:

checkLimits( fitpar, fitindex )

chiSquaredExtra( data, params, weights=None ): Add normalizing data to chisq.

fit( data, weights=None, par0=None, keep=None, limits=None,
maxiter=None, tolerance=None, verbose=None, plot=False, accuracy=None,
callback=None): Return Model fitted to the data arrays. It will calculate the hessian matrix and chisq. Parameters ---------- data : array_like the data vector to be fitted weights : array_like weights pertaining to the data accuracy : float or array_like accuracy of (individual) data par0 : array_like initial values for the parameters of the model default: from model keep : dict of {int : float} dictionary of indices (int) of parameters to be kept at fixed value (float) The values of `keep` are only valid for *this* fit see also `LevenbergMarquardtFitter( ..., keep=dict ) limits : None or list of 2 floats or list of 2 array_like None : no limits applied [lo,hi] : low and high limits for all values of the parameters [la,ha] : arrays of low and high limits for all values of the parameters maxiter : int max number of iterations. default=1000, tolerance : float absolute and relative tolrance. default=0.0001, verbose : int 0 : silent >0 : more output default=1 plot : bool plot the results callback : callable is called each iteration as `val = callback( val )` where val is the parameter list. Raises ------ ConvergenceError if it stops when the tolerance has not yet been reached.

getParameters(): Return status of the fitter: parameters ( for debugging ). Only for debugging; use Model.getParameters( ) otherwise

trialfit( params, fi, data, weights, verbose, maxiter ): # *************************************************************************

Methods inherited from IterativeFitter:

Methods inherited from BaseFitter: