TrigonometricPolynomialFunction (patrius 4.3 API)

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

All Implemented Interfaces:

DifferentiableIntegrableUnivariateFunction, UnivariateDifferentiableFunction, IntegrableUnivariateFunction, UnivariateFunction, Serializable
```
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 17603 2017-05-18 08:28:32Z bignon $

Author:

Rami Houdroge

See Also:

Serialized Form

Concurrency :

immutable

Constructor Summary

Constructors
Constructor and Description
`TrigonometricPolynomialFunction(double coefA0, double[] coefA, double[] coefB)` Constructor for the `TrigonometricPolynomialFunction`.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`TrigonometricPolynomialFunction`	`add(TrigonometricPolynomialFunction newPol)` Add two `TrigonometricPolynomialFunction`
`UnivariateFunction`	`derivative()` Compute and return derivative of polynomial
`UnivariateFunction`	`derivative(int n)` Compute and return n^th 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 n^th 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 n^th 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

Class TrigonometricPolynomialFunction

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

TrigonometricPolynomialFunction

Method Detail

add

derivative

derivative

elementaryMultiplication

evaluate

getA

getA0

getB

getDegree

multiply

negate

polynomialDerivative

polynomialDerivative

polynomialDerivative

polynomialPrimitive

polynomialPrimitive

primitive

scalarAdd

scalarMultiply

scalarSubtract

scalarDivide

subtract

toString

value

value

value