fr.cnes.sirius.patrius.math.analysis.polynomials

Class ChebyshevDecompositionEngine

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.polynomials.ChebyshevDecompositionEngine

public final class ChebyshevDecompositionEngine
extends Object

Approximate a UnivariateFunction by a Chebyshev polynomial.

Important notice: two conventions exist for defining Chebyshev polynomials:

• Defining the first coefficient similarly to other coefficients. Chebyshev Polynomial is then Σc_iT_i (for i in [0, n])
• Adding a 0.5 multiplier to first coefficient. Chebyshev Polynomial is then c₀/2 + Σc_iT_i (for i in [1, n])

PATRIUS uses the first convention (convention used in SPICE library).

Author:

bonitt

Method Summary

Modifier and Type	Method and Description
static PolynomialChebyshevFunction	approximateChebyshevFunction(UnivariateFunction fct, int degree, double start, double end, int nbNodes) Approximate the given function by a Chebyshev polynomial of the given degree on the specified range [start ; end].
static PolynomialChebyshevFunction	interpolateChebyshevFunction(double start, double end, double[] values) Interpolate the values of a f function defined at the Chebyshev abscissas by a Chebyshev polynomial on the specified range [start ; end].
static PolynomialChebyshevFunction	interpolateChebyshevFunction(UnivariateFunction fct, int degree, double start, double end) Interpolate the given function by a Chebyshev polynomial on the specified range [start ; end].

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

approximateChebyshevFunction

public static PolynomialChebyshevFunction approximateChebyshevFunction(UnivariateFunction fct,
                                                                       int degree,
                                                                       double start,
                                                                       double end,
                                                                       int nbNodes)

Approximate the given function by a Chebyshev polynomial of the given degree on the specified range [start ; end]. The approximation is done by interpolation if the given number of nodes is smaller or equal to the degree+1 and by fitting otherwise.

Parameters:

fct - Function to interpolate

degree - Chebyshev polynomial degree

start - Start interval

end - End interval

nbNodes - Number of nodes

Returns:

the approximated Chebyshev polynomial

Throws:

NullArgumentException - if fct is null

NotPositiveException - if degree < 0

MathIllegalArgumentException - if start >= end

interpolateChebyshevFunction

public static PolynomialChebyshevFunction interpolateChebyshevFunction(UnivariateFunction fct,
                                                                       int degree,
                                                                       double start,
                                                                       double end)

Interpolate the given function by a Chebyshev polynomial on the specified range [start ; end].

Parameters:

fct - Function to interpolate

degree - Chebyshev polynomial degree

start - Start interval

end - End interval

Returns:

the interpolated Chebyshev polynomial

Throws:

NullArgumentException - if fct is null

NotPositiveException - if degree < 0

MathIllegalArgumentException - if start >= end

interpolateChebyshevFunction

public static PolynomialChebyshevFunction interpolateChebyshevFunction(double start,
                                                                       double end,
                                                                       double[] values)

Interpolate the values of a f function defined at the Chebyshev abscissas by a Chebyshev polynomial on the specified range [start ; end].

Parameters:

start - Start range

end - End range

values - Values of the function to interpolate defined at the Chebyshev abscissas

Returns:

the interpolated Chebyshev polynomial

Throws:

NullArgumentException - if values is null

NoDataException - if values is empty

MathIllegalArgumentException - if start >= end