["BayesicFitting"]

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class LevenbergMarquardtFitter( IterativeFitter )	Source

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

LMF is not guaranteed to find the global minimum.
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)

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

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.

chiSquaredExtra( data, params, weights=None )

Add normalizing data to chisq.

trialfit( params, fi, data, weights, verbose, maxiter )

getParameters( )

Return status of the fitter: parameters ( for debugging ).

Only for debugging; use Model.getParameters( ) otherwise

checkLimits( fitpar, fitindex )

Methods inherited from IterativeFitter

Methods inherited from BaseFitter