BayesicFitting

Model Fitting and Evidence Calculation

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class BSplinesModel( LinearModel )Source

General b-splines model of arbitrary order and with arbitrary knot settings.

It encapsulates the bspline package of John Foster and Juha Jeronen, at http://github.com/johnfoster/bspline.

B-splines have some advantages over natural splines as implemented in SplinesModel. Specificly the parameters are much more easily interpreted as the amplitudes of spline-like blobs. The disadvantage of BSplinesModel is that the x-values need to fall strictly within the range spanned by the knots.

It is a linear model.

order behaviour between knots continuity at knots
0 piecewise constant not continuous at all
1 piecewise linear lines are continuous
2 parabolic pieces 1st derivatives are also continuous
3 cubic pieces 2nd derivatives are also continuous
n>3 n-th order polynomials (n-1)th derivatives are continuous

The user lays out a number ( << datapoints ) of knots on the x-axis at arbitrary position, generally more knots where the curvature is higher. The knots need to be monotonuously increasing in x. Alternatively one can ask this class to do the lay-out which is then equidistant in x over the user-provided range. Through these knots a splines function is obtained which best fits the datapoints. One needs at least 2 knots, one smaller and one larger than the x-values in the dataset.

Contrary to the SplinesModel here the xdata need to be strictly inside the range spanned by the knots: knots[0] <= xdata < knots[-1]

This model is NOT for (cubic) spline interpolation.

Examples

knots = numpy.arange( 17, dtype=float ) * 10    # make equidistant knots from 0 to 160
csm = BSplinesModel( knots=knots, order=2 )
print csm.getNumberOfParameters( )
18
# or alternatively
csm = BSplinesModel( nrknots=17, order=2, min=0, max=160 )    # automatic layout of knots
print csm.getNumberOfParameters( )
18
# or alternatively
npt = 161                                               # to include both 0 and 160.
x = numpy.arange( npt, dtype=float )                    # x-values
csm = BSplinesModel( nrknots=17, order=2, xrange=x )     # automatic layout of knots
print csm.getNumberOfParameters( )
18

Attributes

  • knots : array_like
         a array of arbitrarily positioned knots
  • order : int
         order of the spline. Default 3 (cubic splines)
  • eps : float
         small number to enable inclusion of endpoints. Default 0.0.

Attributes from Model

     parameters, stdevs, xUnit, yUnit, npchain

Attributes from FixedModel

     npmax, fixed, parlist, mlist

Attributes from BaseModel

     npbase, ndim, priors, posIndex, nonZero, tiny, deltaP, parNames

Limitations

Dont put the knots too closely so that there are no datapoints in between.

BSplinesModel( knots=None, order=3, nrknots=None, min=None, max=None, xrange=None, copy=None, fixed=None, **kwargs )

Splines on a given set of knots and a given order.

The number of parameters is ( length( knots ) + order - 1 )

Parameters

  • knots : array_like
         a array of arbitrarily positioned knots
  • order : int
         order of the spline. Default 3 (cubic splines)
  • nrknots : int
         number of knots, equidistantly posited over xrange or [min,max]
  • min : float
         minimum of the knot range
  • max : float
         maximum of the knot range
  • xrange : array_like
         range of the xdata
  • copy : BSplinesModel
         model to be copied.
  • fixed : dict
         If not None, raise AttributeError.

Raises

  • ValueError : At least either ('knots') or ('nrnkots', 'min', 'max') or
             ('nrknots', 'xrange') must be provided to define a valid model.
  • AttributeErrr : When fixed is not None

Notes

The BSplinesModel is only strictly valid inside the domain defined by the minmax of knots. It does not exist outside that domain.

copy( )

basePartial( xdata, params, parlist=None )
Returns the partials at the input value.

The partials are the powers of x (input) from 0 to degree.

Parameters

  • xdata : array_like
         value at which to calculate the partials
  • params : array_like
         parameters to the model (ignored in LinearModels)
  • parlist : array_like
         list of indices active parameters (or None for all)

Raises

ValueError when xdata < knots[0] or xdata > knots[1]

baseDerivative( xdata, params )
Return the derivative df/dx at each xdata (=x).

Parameters

  • xdata : array_like
         value at which to calculate the partials
  • params : array_like
         parameters to the model

baseName( )

Returns a string representation of the model.

baseParameterUnit( k )
Return the units of the parameter.

Parameters

  • k : int
         index of the parameter.
Methods inherited from LinearModel
Methods inherited from Model
Methods inherited from FixedModel
Methods inherited from BaseModel