["BayesicFitting"]

class ChebyshevPolynomialModel( LinearModel )	Source

Chebyshev polynomial model of arbitrary degree.

f( x:p ) = ∑ p_k * T_k( x )

where the sum is over k running from 0 to degree ( inclusive ).

The T( x ) are Chebyshev polynomials of the first kind which are defined recursively as

T₀( x ) = 1
T₁( x ) = x
T_n( x ) = 2 x T_n-1( x ) - T_n-2( x ) for n >= 2

These polynomials are orthogonal, when integrated over x in [-1,+1].

It is a linear model.

Attributes

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

Examples

poly = ChebyshevPolynomialModel( 3 )         # 3rd degree polynomial
print poly.getNumberOfParameters( )
4

ChebyshevPolynomialModel( degree, copy=None, **kwargs )

Chebyshev Polynomial of a certain degree.

The number of parameters is ( degree + 1 )

Parameters

degree : int
the degree of the polynomial.
copy : ChebyshevPolynomialModel
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

copy( )

Copy method.

basePartial( xdata, params, parlist=None )

Returns the partials at the xdata value.

The partials are calculated using the recurrence formula

f_n( x ) = 2 * x * f_n-1( x ) - f_n-2( x )

Parameters

baseDerivative( xdata, params )

Returns the derivative df/dx at the xdata value.

df_n = n * U_n-1
where
U₀ = 1
U₁ = 2x
U_n+1 = 2 * x * U_n - U_n-1

Parameters

baseName( )

Returns a string representation of the model.

baseParameterUnit( k )

Return the unit of the indicated parameter. It is always yUnit, as it cannot be otherwise. The xUnit must be dimensionless.

Parameters

Methods inherited from LinearModel

Methods inherited from Model

Methods inherited from FixedModel

Methods inherited from BaseModel