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class SplinesModel( LinearModel )	Source

General splines model of arbitrary order and with arbitrary knot settings. 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 (connected)
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 also 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.

If the end knots are put in between the x-values in the dataset, a kind of extrapoling spline is obtained. It still works more or less. Dont push it.

This model is NOT for (cubic) spline interpolation.

Examples

knots = numpy.arange( 17, dtype=float ) * 10    # make equidistant knots from 0 to 160
csm = SplinesModel( knots=knots, order=2 )
print csm.getNumberOfParameters( )
18
# or alternatively
csm = SplinesModel( 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 = SplinesModel( nrknots=17, order=2, xrange=x )     # automatic layout of knots
print csm.getNumberOfParameters( )
18

Attributes

• knots : array_like
       positions of the spline knots
• order : int
       order of the spline. default: 3

Attributes from Model

     npchain, parameters, stdevs, xUnit, yUnit

Attributes from FixedModel

     npmax, fixed, parlist, mlist

Attributes from BaseModel

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

Limitations

Dont construct the knots so closely spaced, that there are no datapoints in between.

SplinesModel( knots=None, order=3, nrknots=None, min=None, max=None, xrange=None, copy=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 : SplinesModel
       model to be copied.
• fixed : None or dictionary of {int:float|Model}
       int index of parameter to fix permanently.
       float|Model values for the fixed parameters.
       Attribute fixed can only be set in the constructor.
       See: FixedModel

Raises

• ValueError : At least either (knots) or (nrknots, min, max) or
           (nrknots, xrange) must be provided to define a valid model.

Notes

The SplinesModel is only strictly valid inside the domain defined by the minmax of knots. It deteriorates fastly going outside the domain.

copy( )

Return a copy of the model.

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)

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 name of the parameter.

Parameters

• k : int
       index of the parameter.

Methods inherited from LinearModel

• baseResult( xdata, params )

Methods inherited from Model

• chainLength( )
• isNullModel( )
• isolateModel( k )
• addModel( model )
• subtractModel( model )
• multiplyModel( model )
• divideModel( model )
• pipeModel( model )
• appendModel( model, operation )
• correctParameters( params )
• result( xdata, param=None )
• operate( res, pars, next )
• derivative( xdata, param, useNum=False )
• partial( xdata, param, useNum=False )
• selectPipe( ndim, ninter, ndout )
• pipe_0( dGd, dHdG )
• pipe_1( dGd, dHdG )
• pipe_2( dGd, dHdG )
• pipe_3( dGd, dHdG )
• pipe_4( dGdx, dHdG )
• pipe_5( dGdx, dHdG )
• pipe_6( dGdx, dHdG )
• pipe_7( dGdx, dHdG )
• pipe_8( dGdx, dHdG )
• pipe_9( dGdx, dHdG )
• shortName( )
• getNumberOfParameters( )
• numDerivative( xdata, param )
• numPartial( xdata, param )
• isDynamic( )
• hasPriors( isBound=True )
• getPrior( kpar )
• setPrior( kpar, prior=None, **kwargs )
• getParameterName( kpar )
• getParameterUnit( kpar )
• getIntegralUnit( )
• setLimits( lowLimits=None, highLimits=None )
• getLimits( )
• hasLimits( fitindex=None )
• unit2Domain( uvalue, kpar=None )
• domain2Unit( dvalue, kpar=None )
• partialDomain2Unit( dvalue )
• nextPrior( )
• isMixed( )
• getLinearIndex( )
• testPartial( xdata, params, silent=True )
• strictNumericPartial( xdata, params, parlist=None )
• assignDF1( partial, i, dpi )
• assignDF2( partial, i, dpi )
• strictNumericDerivative( xdata, param )

Methods inherited from FixedModel

• select( params )
• selectNames( names )
• expand( xdata, param )

Methods inherited from BaseModel

• checkParameter( param )
• checkPositive( param )
• checkZeroParameter( param )
• isModifiable( )
• basePrior( kpar )
• baseParameterName( kpar )