BasicSplinesModel

BasicSplinesModel = class BasicSplinesModel(SplinesModel)

BasicSplinesModel(knots=None, order=3, nrknots=None, min=None, max=None, xrange=None, border=0, copy=None, **kwargs) Splines model consisting of a basis of spline blobs. The blobs have limited support. Each blob is a segment of polynomial order, between 2 knots. At the knots they are continuous (differentiable) upto order - 1. Similarly the edges of the blobs are smoothly connected to 0. order support behaviour between knots continuity at knots 0 1 piecewise constant not continuous at all 1 2 piecewise linear lines are continuous (connected) 2 3 parabolic pieces 1st derivatives are also continuous 3 4 cubic pieces 2nd derivatives are also continuous n>3 n+1 n-th order polynomials (n-1)-th derivatives are also continuous The function result is the sum over all spline blobs, multiplied with the parameters, the amplitudes of the spline blobs. The support of the knots defined the domain where the function is defined. They are hard edges. Consequently the function is not continuous or differentiable at the edges. The spline blobs at the edges may be different from the ones in the middle. From SplinesModel ----------------- 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. This model is NOT for (cubic) spline interpolation. Examples -------- >>> knots = numpy.arange( 17, dtype=float ) * 10 # make equidistant knots from 0 to 160 >>> csm = BasicSplinesModel( 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 = BasicSplinesModel( 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.

Method resolution order:: BasicSplinesModel; SplinesModel; LinearModel; Model; FixedModel; BaseModel; builtins.object

Constructor:

BasicSplinesModel( knots=None, order=3, nrknots=None, min=None, max=None,
xrange=None, border=0, 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] border : [0, 1, 2] defines what happens at the borders of the knot range. 0 : Just like de Boors b-splines. the model is NOT defined outside the knot range. 1 : periodic, make knot[0] the same as knot[-1] 2 : easy borders. the model is slightly extensable. min : float minimum of the knot range max : float maximum of the knot range xrange : array_like range of the xdata copy : BasicSplinesModel 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.

Methods defined here:

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.

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)

baseResult( xdata, params ): Returns the functional result at the input value. Parameters ---------- xdata : array_like value at which to calculate the partials params : array_like parameters to the model (ignored in LinearModels)

basicBlob( xdata, basis, x2k, poly ): Calculates a spline blob for all of xdata Parameters ---------- xdata : array_like value at which to calculate the spline basis : array_like splineParameters x2k : int_array pointing to the knot preceeding each xdata point poly : PolynomialModel model to calculate the splines

copy(): Return a copy.

findParameters( knotix, dist, kpar=0): Find the parameters by assuming (order-1) continuous differentials. At the edges it is less. Normalized to 1.0 Parameters ---------- knotix : int array knot indices involved in this spline blob dist : array_like distances between knots kpar : int index of parameter for which the spline-blob is constructed Returns ------- par : 2-d array sets of poly parameters.

makeBaseBasis(): Make a sets of polynomial bases for each of the parameters Return ------ basis : 3-d array-like parameters to the polynomials that make up the spline blobs

makeDist( knotix )

makeKnotIndices( xdata ): Return a list of indices of the knots immediately preceeding the xdata. Parameters ---------- xdata : array_like values at which to calculate the indices

makePeriodicBasis(): Make a sets of polynomial bases for each of the parameters Return ------ basis : 3-d array-like parameters to the polynomials that make up the spline blobs

normalizeBasis( basis ): Normalize the base splines such that a constant value of 1.0 is returned when all model parameters are 1. Parameters ---------- basis : array_like parameters to the polynomials that make up the spline blobs

Methods inherited from Model:

Overloaded operators and aliases

Other methods

Methods inherited from FixedModel:

Methods inherited from BaseModel: