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

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

All Implemented Interfaces:

Serializable, DifferentiableIntegrableUnivariateFunction, UnivariateDifferentiableFunction, IntegrableUnivariateFunction, UnivariateFunction

public final class TrigonometricPolynomialFunction
extends Object
implements DifferentiableIntegrableUnivariateFunction, Serializable

This class is the Trigonometric Polynomial Function class. Given a constant a0, and two arrays of same lengths a and b, the corresponding trigonometric polynomial function p is given by the following expression :
p(x) = a0 + sum( a(k) * cos(k*x) + b(k) * sin(k*x) , k, 1, n )
where a(k) (resp . b(k)) is the k^th coefficient of the array a (resp. b).

Since:

1.1

Version:

$Id: TrigonometricPolynomialFunction.java 16755 2016-10-07 15:47:40Z bignon $

Author:

Rami Houdroge

See Also:

Serialized Form

Concurrency :

immutable

Constructor Summary

TrigonometricPolynomialFunction(double coefA0, double[] coefA, double[] coefB)
Constructor for the TrigonometricPolynomialFunction.

Method Summary

TrigonometricPolynomialFunction	add(TrigonometricPolynomialFunction newPol) Add two TrigonometricPolynomialFunction
UnivariateFunction	derivative() Compute and return derivative of polynomial
UnivariateFunction	derivative(int n) Compute and return nth derivative of polynomial
protected static TrigonometricPolynomialFunction	elementaryMultiplication(TrigonometricPolynomialFunction poly, ElementaryMultiplicationTypes.ElementaryType type, int j) Multiply TrigonometricPolynomialFunction by an ElementaryMultiplicationTypes
protected static double	evaluate(TrigonometricPolynomialFunction poly, double x) Compute value at x of trigonometric polynomial P : P(x) = a0 + a(k) * cos(kx) + b(k) * sin(kx)
double[]	getA() Get array of cosine coefficients
double	getA0() Get value of order zero coefficient
double[]	getB() Get array of sine coefficients
int	getDegree() Get polynomial degree
TrigonometricPolynomialFunction	multiply(TrigonometricPolynomialFunction polynomial) Multiply this polynomial by another polynomial
TrigonometricPolynomialFunction	negate() Negate polynomial
TrigonometricPolynomialFunction	polynomialDerivative() Returns the first order derivative as a TrigonometricPolynomialFunction.
TrigonometricPolynomialFunction	polynomialDerivative(int order) Returns the nth order derivative as a TrigonometricPolynomialFunction.
protected static TrigonometricPolynomialFunction	polynomialDerivative(TrigonometricPolynomialFunction poly) Returns the derivative as a TrigonometricPolynomialFunction.
TrigonometricPolynomialPrimitive	polynomialPrimitive(double constant) Get primitive of TrigonometricPolynomialFunction
protected static TrigonometricPolynomialPrimitive	polynomialPrimitive(TrigonometricPolynomialFunction poly, double constant) Get primitive of TrigonometricPolynomialFunction
UnivariateFunction	primitive() Get primitive of TrigonometricPolynomialFunction
TrigonometricPolynomialFunction	scalarAdd(double scalar) Add a scalar
TrigonometricPolynomialFunction	scalarDivide(double scalar) Divide by a scalar
TrigonometricPolynomialFunction	scalarMultiply(double scalar) Multiply by a scalar
TrigonometricPolynomialFunction	scalarSubtract(double scalar) Subtract a scalar
TrigonometricPolynomialFunction	subtract(TrigonometricPolynomialFunction polynomial) Subtract a polynomial to the current polynomial :
String	toString() Get String representation of polynomial
DerivativeStructure	value(DerivativeStructure t) Simple mathematical function.
double	value(double x) Return value at x of polynomial
double	value(int n, double x) Return value at x of nth order derivative

Methods inherited from class java.lang.Object

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

Constructor Detail

TrigonometricPolynomialFunction

public TrigonometricPolynomialFunction(double coefA0,
                                       double[] coefA,
                                       double[] coefB)

Constructor for the TrigonometricPolynomialFunction. This constructor creates the following trigonometric polynomial :
P(X) = a0 + a(k) * cos(kX) + b(k) * sin(kX)

Parameters:

coefA0 - a0 coefficient

coefA - cosine coefficients array

coefB - sine coefficients array

Throws:

MathIllegalArgumentException - if arrays a and b are of different lengths

Method Detail

add

public TrigonometricPolynomialFunction add(TrigonometricPolynomialFunction newPol)

Add two TrigonometricPolynomialFunction

Parameters:

newPol - polynomial to add to current

Returns:

resulting TrigonometricPolynomialFunction

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

elementaryMultiplication

protected static TrigonometricPolynomialFunction elementaryMultiplication(TrigonometricPolynomialFunction poly,
                                                                          ElementaryMultiplicationTypes.ElementaryType type,
                                                                          int j)

Multiply TrigonometricPolynomialFunction by an ElementaryMultiplicationTypes

Parameters:

poly - polynomial

type - of elementary polynomial

j - order of elementary polynomial

Returns:

resulting polynomial

evaluate

protected static double evaluate(TrigonometricPolynomialFunction 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

getA

public double[] getA()

Get array of cosine coefficients

Returns:

a

getA0

public double getA0()

Get value of order zero coefficient

Returns:

a0

getB

public double[] getB()

Get array of sine coefficients

Returns:

b

getDegree

public int getDegree()

Get polynomial degree

Returns:

n

multiply

public TrigonometricPolynomialFunction multiply(TrigonometricPolynomialFunction polynomial)

Multiply this polynomial by another polynomial

Parameters:

polynomial - polynomial to multiply instance by

Returns:

multiplied polynomials in a new instance

negate

public TrigonometricPolynomialFunction negate()

Negate polynomial

Returns:

negated polynomial

polynomialDerivative

public TrigonometricPolynomialFunction polynomialDerivative()

Returns the first order derivative as a TrigonometricPolynomialFunction.

Returns:

the derivative polynomial.

polynomialDerivative

public TrigonometricPolynomialFunction 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 TrigonometricPolynomialFunction polynomialDerivative(TrigonometricPolynomialFunction poly)

Returns the derivative as a TrigonometricPolynomialFunction.

Parameters:

poly - polynomial to derivate

Returns:

the derivative polynomial.

polynomialPrimitive

public TrigonometricPolynomialPrimitive polynomialPrimitive(double constant)

Get primitive of TrigonometricPolynomialFunction

Parameters:

constant - integration constant

Returns:

the primitive as a TrigonometricPolynomialPrimitive

polynomialPrimitive

protected static TrigonometricPolynomialPrimitive polynomialPrimitive(TrigonometricPolynomialFunction poly,
                                                                      double constant)

Get primitive of TrigonometricPolynomialFunction

Parameters:

poly - polynomial for primitive computation

constant - integration constant

Returns:

the primitive as a TrigonometricPolynomialPrimitive

primitive

public UnivariateFunction primitive()

Get primitive of TrigonometricPolynomialFunction

Specified by:

primitive in interface IntegrableUnivariateFunction

Returns:

the primitive as a UnivariateFunction

scalarAdd

public TrigonometricPolynomialFunction scalarAdd(double scalar)

Add a scalar

Parameters:

scalar - to add

Returns:

new TrigonometricPolynomialFunction

scalarMultiply

public TrigonometricPolynomialFunction scalarMultiply(double scalar)

Multiply by a scalar

Parameters:

scalar - to multiply polynomial by

Returns:

polynomial multiplied by scalar

scalarSubtract

public TrigonometricPolynomialFunction scalarSubtract(double scalar)

Subtract a scalar

Parameters:

scalar - to subtract

Returns:

new TrigonometricPolynomialFunction

scalarDivide

public TrigonometricPolynomialFunction scalarDivide(double scalar)

Divide by a scalar

Parameters:

scalar - to divide polynomial by

Returns:

polynomial divide by scalar

subtract

public TrigonometricPolynomialFunction subtract(TrigonometricPolynomialFunction polynomial)

Subtract a polynomial to the current polynomial :

Parameters:

polynomial - to perform subtraction

Returns:

this - polynomial

toString

public String toString()

Get String representation of polynomial

Overrides:

toString in class Object

Returns:

string

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

value

public double value(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

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