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(double start, double end, double[] values) Approximate the values of a f function defined at the Chebyshev abscissas by a Chebyshev polynomial on the specified range [start ; end].
static PolynomialChebyshevFunction	approximateChebyshevFunction(UnivariateFunction fct, int maxDegree, double start, double end) Approximate 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 maxDegree,
                                                                       double start,
                                                                       double end)

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

Parameters:

fct - Function to approximate

maxDegree - Maximum Chebyshev polynomial degree (can be lower after the truncation of insignificant coefficients terms)

start - Start interval

end - End interval

Returns:

the approximate Chebyshev polynomial

Throws:

NullArgumentException - if values is null

NotPositiveException - if degree < 0

MathIllegalArgumentException - if start >= end

approximateChebyshevFunction

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

Approximate 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 approximate defined at the Chebyshev abscissas

Returns:

the approximate Chebyshev polynomial

Throws:

NullArgumentException - if values is null

NoDataException - if values is empty

MathIllegalArgumentException - if start >= end