ChebyshevPolynomialModel = class ChebyshevPolynomialModel(LinearModel) |
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ChebyshevPolynomialModel(degree, copy=None, **kwargs)
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:
T_0( x ) = 1
T_1( x ) = x
T_n( x ) = 2 x T_{n-1}( x ) - T_{n-2}( x ) for n >= 2
These polynomials are orthogonal, only when x is in [-1,+1].
It is a linear model.
Attributes
----------
degree : int
degree of the polynomial
Attributes from Model
--------------------------
npchain, parameters, stdevs, xUnit, yUnit
Attributes from FixedModel
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npmax, fixed, parlist, mlist
Attributes from BaseModel
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npbase, ndim, priors, posIndex, nonZero,
tiny, deltaP, parNames
Examples
--------
>>> poly = ChebyshevPolynomialModel( 3 ) # 3rd degree polynomial
>>> print poly.getNumberOfParameters( )
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- Method resolution order:
- ChebyshevPolynomialModel
- LinearModel
- Model
- FixedModel
- BaseModel
- builtins.object
Constructor:
- 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
Methods defined here:
- baseDerivative( xdata, params )
- Returns the derivative df/dx at the xdata value.
df_n = n * U_{n-1}
where
U_0 = 1
U_1 = 2x
U_{n+1} = 2 * x * U_n - U_{n-1}
Parameters
----------
xdata : array_like
value at which to calculate the partials
params : array_like
parameters of the model
- 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
----------
k : int
parameter number.
- 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
----------
xdata : array_like
value at which to calculate the partials
params : array_like
parameters of the model (ignored for linear models)
parlist : array_like
list of indices of active parameters
- copy()
- Copy method.
Methods inherited from LinearModel:
Methods inherited from Model:
Overloaded operators and aliases
Other methods
- addModel( model )
- appendModel( model, operation )
- assignDF1( partial, i, dpi )
- assignDF2( partial, i, dpi )
- chainLength()
- correctParameters( params )
- derivative( xdata, param, useNum=False )
- divideModel( model )
- domain2Unit( dvalue, kpar=None )
- getIntegralUnit()
- getLimits()
- getLinearIndex()
- getNumberOfParameters()
- getParameterName( k )
- getParameterUnit( k )
- getPrior( k )
- hasLimits( fitindex=None )
- hasPriors( isBound=True )
- isDynamic()
- isMixed()
- isNullModel()
- isolateModel( k )
- multiplyModel( model )
- nextPrior()
- numDerivative( xdata, param )
- numPartial( xdata, param )
- operate( res, pars, next )
- partial( xdata, param, useNum=False )
- partialDomain2Unit( dvalue )
- pipeModel( model )
- 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)
- result( xdata, param=None )
- selectPipe( ndim, ninter, ndout )
- setLimits( lowLimits=None, highLimits=None )
- setPrior( k, prior=None, **kwargs )
- shortName()
- strictNumericDerivative( xdata, param )
- strictNumericPartial( xdata, params, parlist=None )
- subtractModel( model )
- testPartial( xdata, params, silent=True )
- unit2Domain( uvalue, kpar=None )
Methods inherited from FixedModel:
Methods inherited from BaseModel:
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