FourierSeries (patrius 4.3 API)

java.lang.Object
- fr.cnes.sirius.patrius.math.analysis.polynomials.FourierSeries

All Implemented Interfaces:

DifferentiableIntegrableUnivariateFunction, UnivariateDifferentiableFunction, IntegrableUnivariateFunction, UnivariateFunction, Serializable
```
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

Constructors
Constructor and Description

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

Constructors
Constructor and Description
`FourierSeries(double omega, double a0, double[] a, double[] b)` Constructor for the `FourierSeries`.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`UnivariateFunction`	`derivative()` Compute and return derivative of polynomial
`UnivariateFunction`	`derivative(int n)` Compute and return n^th derivative of polynomial
`double`	`derivativeValue(int n, double x)` Return value at x of n^th 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 n^th order derivative as a `TrigonometricPolynomialFunction`.
`FourierSeries`	`polynomialPrimitive()` Get primitive of `FourierSeries`. a0 constant is considered equal to 0.
`protected static FourierSeries`	`polynomialPrimitive(FourierSeries poly)` Get primitive of `FourierSeries`. a0 constant is considered equal to 0.
`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

Class FourierSeries

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

FourierSeries

Method Detail

scalarAdd

scalarMultiply

scalarSubtract

scalarDivide

negate

polynomialDerivative

polynomialDerivative

polynomialDerivative

polynomialPrimitive

polynomialPrimitive

value

derivativeValue

primitiveValue

evaluate

primitive

derivative

derivative

getAngularFrequency

getPeriod

getConstant

getCosArray

getSinArray

getOrder

toString

value