org.apache.commons.math3.analysis.polynomials
Class FourierSeries

java.lang.Object
  org.apache.commons.math3.analysis.polynomials.FourierSeries

All Implemented Interfaces:

Serializable, DifferentiableIntegrableUnivariateFunction, UnivariateDifferentiableFunction, IntegrableUnivariateFunction, UnivariateFunction

public final class FourierSeries
extends Object
implements DifferentiableIntegrableUnivariateFunction, Serializable

This class represents a finite Fourier Series

Since:

1.2

Version:

$Id: FourierSeries.java 17603 2017-05-18 08:28:32Z bignon $

Author:

Rami Houdroge

See Also:

FourierDecompositionEngine, Serialized Form

Concurrency :

immutable

Constructor Summary

FourierSeries(double omega, double a0, double[] a, double[] b)
Constructor for the FourierSeries.

Method Summary

UnivariateFunction	derivative() Compute and return derivative of polynomial
UnivariateFunction	derivative(int n) Compute and return nth derivative of polynomial
double	derivativeValue(int n, double x) Return value at x of nth order derivative
protected static double	evaluate(FourierSeries poly, double x) Compute value at x of trigonometric polynomial P : P(x) = a0 + a(k) * cos(kx) + b(k) * sin(kx)
double	getAngularFrequency()
double	getConstant()
double[]	getCosArray()
int	getOrder()
double	getPeriod()
double[]	getSinArray()
FourierSeries	negate() Negate polynomial
FourierSeries	polynomialDerivative() Returns the first order derivative as a TrigonometricPolynomialFunction.
protected static FourierSeries	polynomialDerivative(FourierSeries poly) Returns the derivative as a TrigonometricPolynomialFunction.
FourierSeries	polynomialDerivative(int order) Returns the nth order derivative as a TrigonometricPolynomialFunction.
FourierSeries	polynomialPrimitive() Get primitive of FourierSeries.
protected static FourierSeries	polynomialPrimitive(FourierSeries poly) Get primitive of FourierSeries.
UnivariateFunction	primitive() Get primitive of TrigonometricPolynomialFunction
double	primitiveValue(double x) Return value at x of the function primitive
FourierSeries	scalarAdd(double scalar) Add a scalar
FourierSeries	scalarDivide(double scalar) Divide by a scalar
FourierSeries	scalarMultiply(double scalar) Multiply by a scalar
FourierSeries	scalarSubtract(double scalar) Subtract a scalar
String	toString() Get String representation of polynomial
DerivativeStructure	value(DerivativeStructure t) Simple mathematical function.
double	value(double x) Return value at x of polynomial.

Methods inherited from class java.lang.Object

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

Constructor Detail

FourierSeries

public FourierSeries(double omega,
                     double a0,
                     double[] a,
                     double[] b)

Constructor for the FourierSeries. This constructor creates the following trigonometric polynomial :
P(X) = a0 + a(k) * cos(k * omega * X) + b(k) * sin(k * omega * X)
where omega = 2 * pi / period

Parameters:

omega - angular frequency

a0 - a0 coefficient

a - cosine coefficients array

b - sine coefficients array

Throws:

MathIllegalArgumentException - if arrays a and b are of different lengths

Method Detail

scalarAdd

public FourierSeries scalarAdd(double scalar)

Add a scalar

Parameters:

scalar - to add

Returns:

new TrigonometricPolynomialFunction

scalarMultiply

public FourierSeries scalarMultiply(double scalar)

Multiply by a scalar

Parameters:

scalar - to multiply polynomial by

Returns:

polynomial multiplied by scalar

scalarSubtract

public FourierSeries scalarSubtract(double scalar)

Subtract a scalar

Parameters:

scalar - to subtract

Returns:

new TrigonometricPolynomialFunction

scalarDivide

public FourierSeries scalarDivide(double scalar)

Divide by a scalar

Parameters:

scalar - to divide polynomial by

Returns:

polynomial divide by scalar

negate

public FourierSeries negate()

Negate polynomial

Returns:

negated polynomial

polynomialDerivative

public FourierSeries polynomialDerivative()

Returns the first order derivative as a TrigonometricPolynomialFunction.

Returns:

the derivative polynomial.

polynomialDerivative

public FourierSeries polynomialDerivative(int order)

Returns the n^th order derivative as a TrigonometricPolynomialFunction.

Parameters:

order - order of derivative (must be > 0)

Returns:

the derivative polynomial.

polynomialDerivative

protected static FourierSeries polynomialDerivative(FourierSeries poly)

Returns the derivative as a TrigonometricPolynomialFunction.

Parameters:

poly - polynomial to derivate

Returns:

the derivative polynomial.

polynomialPrimitive

public FourierSeries polynomialPrimitive()

Get primitive of FourierSeries. a0 constant is considered equal to 0.

Returns:

the primitive as a FourierSeries

polynomialPrimitive

protected static FourierSeries polynomialPrimitive(FourierSeries poly)

Get primitive of FourierSeries. a0 constant is considered equal to 0.

Parameters:

poly - polynomial for primitive computation

Returns:

the primitive as a FourierSeries

value

public double value(double x)

Return value at x of polynomial.

Specified by:

value in interface UnivariateFunction

Parameters:

x - desired abscissa

Returns:

value of polynomial function

derivativeValue

public double derivativeValue(int n,
                              double x)

Return value at x of n^th order derivative

Parameters:

n - order of derivative

x - desired abscissa

Returns:

value of derivative

primitiveValue

public double primitiveValue(double x)

Return value at x of the function primitive

Parameters:

x - desired abscissa

Returns:

value of derivative

evaluate

protected static double evaluate(FourierSeries poly,
                                 double x)

Compute value at x of trigonometric polynomial P :
P(x) = a0 + a(k) * cos(kx) + b(k) * sin(kx)

Parameters:

poly - polynomial to evaluate

x - abscissa of desired value

Returns:

value of poly at x

primitive

public UnivariateFunction primitive()

Get primitive of TrigonometricPolynomialFunction

Specified by:

primitive in interface IntegrableUnivariateFunction

Returns:

the primitive as a UnivariateFunction

derivative

public UnivariateFunction derivative()

Compute and return derivative of polynomial

Returns:

derivative of polynomial function

derivative

public UnivariateFunction derivative(int n)

Compute and return n^th derivative of polynomial

Parameters:

n - order of derivative

Returns:

n^th derivative of polynomial function

getAngularFrequency

public double getAngularFrequency()

Returns:

the angularFrequency

getPeriod

public double getPeriod()

Returns:

the period

getConstant

public double getConstant()

Returns:

the constant

getCosArray

public double[] getCosArray()

Returns:

the cosArray

getSinArray

public double[] getSinArray()

Returns:

the sinArray

getOrder

public int getOrder()

Returns:

the order of the Fourier Decomposition

toString

public String toString()

Get String representation of polynomial

Overrides:

toString in class Object

Returns:

string

value

public DerivativeStructure value(DerivativeStructure t)

Simple mathematical function.

UnivariateDifferentiableFunction classes compute both the value and the first derivative of the function.

Specified by:

value in interface UnivariateDifferentiableFunction

Parameters:

t - function input value

Returns:

function result