["BayesicFitting"]

Global	Documentation
Home	Manual
Readme	Glossary
Notes	Design
Examples	Classes
	Trouble
	Style

class QRFitter( BaseFitter )	Source

Fitter for linear models, using QR decomposition. The QRFitter class is to be used in conjunction with Model classes, linear in its parameters.

For Linear models the matrix equation

H * p = β

is solved for p. H is the Hessian matrix ( D * w * D^T ) and β is the inproduct of the data with the D, design matrix.

β = y * w * D^T

The QRFitter class use QR decomposition which effectively is an inversion of the hessian matrix such that

p = β * inverse( H )

It can be more efficient if similar ydata needs to be fitter to the same model and xdata. In that case it uses the same decomposition for all fits.

Examples

# assume x and y are numpy.asarray data arrays
x = numpy.asarray.range( 100 )
poly = PolynomialModel( 1 )                             # line
fitter = QRFitter( x, poly )
for k in range( 1, 4 ) 
    y = numpy.arange( 100 ) // k                        # digitization noise
    param = fitter.fit( y )                             # use same QR decomposition
    stdev = fitter.stdevs                               # stdevs on the parameters
    print( k, param )
    print( " ", stdev )

Category : Mathematics/Fitting

Attributes

needsNewDecomposition : bool
     True when starting. Thereafter False,
         i.e. the previous QR-decomposition is used, unless weights are used.
         Only for linear fitters, setting it to false might improve efficiency.
         It only works properly when the model, the x-data etc are exactly the
         same in the previous run.
         Whenever weights are used, it always needs a new decomposition.
qrmat : matrix
     matrix formed by q * inverse( r ), where q,r is the QR decomposition
     of the design matrix.
     qrmat is to be multiplied with the data vector to get the solution.

QRFitter( xdata, model, map=False, keep=None )

Create a new Fitter, providing xdatas and model.

A Fitter class is defined by its model and the input vector (the independent variable). When a fit to another model and/or another input vector is needed a new object should be created.

Parameters

xdata : array_like
array of independent input values
model : Model
the model function to be fitted
map : bool (False)
     When true, the xdata should be interpreted as a map.
     The fitting is done on the pixel indices of the map,
     using ImageAssistant
keep : dict of {int:float}
     dictionary of indices (int) to be kept at a fixed value (float)
     The values of keep will be used by the Fitter as long as the Fitter exists.
     See also fit( ..., keep=dict )

fit( ydata, weights=None, accuracy=None, keep=None )

Return model parameters fitted to the data, including weights.

Parameters

ydata : array_like
the data vector to be fitted
weights : array_like
weights pertaining to the data ( = 1.0 / sigma^2 )
accuracy : float or array_like
accuracy of (individual) data
keep : dict of {int:float}
     dictionary of indices (int) to be kept at a fixed value (float)
     The values will override those at initialization.
     They are only used in this call of fit. Raises

ValueError when ydata or weights contain a NaN

Methods inherited from BaseFitter