Class FunctionExpander

java.lang.Object

com.github.gbenroscience.math.numericalmethods.FunctionExpander

public class FunctionExpander
extends Object

Uses Chebyshev Polynomials to expand, evaluate, differentiate and integrate functions

Author:

GBEMIRO

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	FunctionExpander.ChebyshevForest	High-precision Piecewise Chebyshev approximation engine.
static final class	FunctionExpander.ChebyshevForest1

Constructor Summary

Constructors

Constructor	Description
FunctionExpander(Function function, double lower, double upper, double tolerance)
FunctionExpander(Function function, double lower, double upper, int degree)
FunctionExpander(MethodHandle function, double lower, double upper, double tolerance)
FunctionExpander(MethodHandle function, double lower, double upper, int degree)

Method Summary

Modifier and Type	Method	Description
String	buildPolynomial()
double	derivative(double x)	Computes the derivative of the approximation at point x.
double	evaluate(double x)	Evaluate the approximated polynomial using Clenshaw's Algorithm.
double	getLower()
double	getTailError()	Estimates the truncation error of the current approximation.
double	getUpper()
double	integrateApproximation()	Integrates the approximated polynomial analytically using Kahan summation.
static void	main(String[] args)
void	setLower(double lower)
void	setUpper(double upper)

Methods inherited from class java.lang.Object

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

Constructor Details

FunctionExpander

public FunctionExpander(MethodHandle function,
 double lower,
 double upper,
 int degree)
                 throws Throwable

Throws:

Throwable

FunctionExpander

public FunctionExpander(MethodHandle function,
 double lower,
 double upper,
 double tolerance)
                 throws Throwable

Throws:

Throwable

FunctionExpander

public FunctionExpander(Function function,
 double lower,
 double upper,
 int degree)

FunctionExpander

public FunctionExpander(Function function,
 double lower,
 double upper,
 double tolerance)

Method Details

setLower

public void setLower(double lower)

getLower

public double getLower()

setUpper

public void setUpper(double upper)

getUpper

public double getUpper()

evaluate

public double evaluate(double x)

Evaluate the approximated polynomial using Clenshaw's Algorithm. This is O(N) and much more stable than evaluating a^n + b^n-1...

derivative

public double derivative(double x)

Computes the derivative of the approximation at point x. This is an exact derivative of the surrogate polynomial.

integrateApproximation

public double integrateApproximation()

Integrates the approximated polynomial analytically using Kahan summation. This preserves the precision of the high-frequency coefficients.

buildPolynomial

public String buildPolynomial()

getTailError

public double getTailError()

Estimates the truncation error of the current approximation. For 16dp accuracy, this should be invalid input: '<' 1e-16.

main

public static void main(String[] args)