org.hipparchus.analysis.polynomials

## Class PolynomialFunction

• ### Nested Class Summary

Nested Classes
Modifier and Type Class and Description
static class  PolynomialFunction.Parametric
Dedicated parametric polynomial class.
• ### Constructor Summary

Constructors
Constructor and Description
PolynomialFunction(double[] c)
Construct a polynomial with the given coefficients.
• ### Method Summary

All Methods
Modifier and Type Method and Description
PolynomialFunction add(PolynomialFunction p)
Add a polynomial to the instance.
PolynomialFunction antiDerivative()
Returns an anti-derivative of this polynomial, with 0 constant term.
int degree()
Returns the degree of the polynomial.
protected static double[] differentiate(double[] coefficients)
Returns the coefficients of the derivative of the polynomial with the given coefficients.
boolean equals(Object obj)
protected static double evaluate(double[] coefficients, double argument)
Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
double[] getCoefficients()
Returns a copy of the coefficients array.
int hashCode()
double integrate(double lower, double upper)
Returns the definite integral of this polymomial over the given interval.
PolynomialFunction multiply(PolynomialFunction p)
Multiply the instance by a polynomial.
PolynomialFunction negate()
Negate the instance.
PolynomialFunction polynomialDerivative()
Returns the derivative as a PolynomialFunction.
PolynomialFunction subtract(PolynomialFunction p)
Subtract a polynomial from the instance.
String toString()
Returns a string representation of the polynomial.
DerivativeStructure value(DerivativeStructure t)
Simple mathematical function.
double value(double x)
Compute the value of the function for the given argument.
• ### Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait
• ### Constructor Detail

• #### PolynomialFunction

public PolynomialFunction(double[] c)
throws MathIllegalArgumentException,
NullArgumentException
Construct a polynomial with the given coefficients. The first element of the coefficients array is the constant term. Higher degree coefficients follow in sequence. The degree of the resulting polynomial is the index of the last non-null element of the array, or 0 if all elements are null.

The constructor makes a copy of the input array and assigns the copy to the coefficients property.

Parameters:
c - Polynomial coefficients.
Throws:
NullArgumentException - if c is null.
MathIllegalArgumentException - if c is empty.
• ### Method Detail

• #### value

public double value(double x)
Compute the value of the function for the given argument.

The value returned is

coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]

Specified by:
value in interface UnivariateFunction
Parameters:
x - Argument for which the function value should be computed.
Returns:
the value of the polynomial at the given point.
UnivariateFunction.value(double)
• #### degree

public int degree()
Returns the degree of the polynomial.
Returns:
the degree of the polynomial.
• #### getCoefficients

public double[] getCoefficients()
Returns a copy of the coefficients array.

Changes made to the returned copy will not affect the coefficients of the polynomial.

Returns:
a fresh copy of the coefficients array.
• #### evaluate

protected static double evaluate(double[] coefficients,
double argument)
throws MathIllegalArgumentException,
NullArgumentException
Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
Parameters:
coefficients - Coefficients of the polynomial to evaluate.
argument - Input value.
Returns:
the value of the polynomial.
Throws:
MathIllegalArgumentException - if coefficients is empty.
NullArgumentException - if coefficients is null.
• #### value

public DerivativeStructure value(DerivativeStructure t)
throws MathIllegalArgumentException,
NullArgumentException
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
Throws:
MathIllegalArgumentException - if coefficients is empty.
NullArgumentException - if coefficients is null.

public PolynomialFunction add(PolynomialFunction p)
Add a polynomial to the instance.
Parameters:
p - Polynomial to add.
Returns:
a new polynomial which is the sum of the instance and p.
• #### subtract

public PolynomialFunction subtract(PolynomialFunction p)
Subtract a polynomial from the instance.
Parameters:
p - Polynomial to subtract.
Returns:
a new polynomial which is the instance minus p.
• #### negate

public PolynomialFunction negate()
Negate the instance.
Returns:
a new polynomial with all coefficients negated
• #### multiply

public PolynomialFunction multiply(PolynomialFunction p)
Multiply the instance by a polynomial.
Parameters:
p - Polynomial to multiply by.
Returns:
a new polynomial equal to this times p
• #### differentiate

protected static double[] differentiate(double[] coefficients)
throws MathIllegalArgumentException,
NullArgumentException
Returns the coefficients of the derivative of the polynomial with the given coefficients.
Parameters:
coefficients - Coefficients of the polynomial to differentiate.
Returns:
the coefficients of the derivative or null if coefficients has length 1.
Throws:
MathIllegalArgumentException - if coefficients is empty.
NullArgumentException - if coefficients is null.
• #### antiDerivative

public PolynomialFunction antiDerivative()
Returns an anti-derivative of this polynomial, with 0 constant term.
Returns:
a polynomial whose derivative has the same coefficients as this polynomial
• #### integrate

public double integrate(double lower,
double upper)
Returns the definite integral of this polymomial over the given interval.

[lower, upper] must describe a finite interval (neither can be infinite and lower must be less than or equal to upper).

Parameters:
lower - lower bound for the integration
upper - upper bound for the integration
Returns:
the integral of this polymomial over the given interval
Throws:
MathIllegalArgumentException - if the bounds do not describe a finite interval
• #### polynomialDerivative

public PolynomialFunction polynomialDerivative()
Returns the derivative as a PolynomialFunction.
Returns:
the derivative polynomial.
• #### toString

public String toString()
Returns a string representation of the polynomial.

The representation is user oriented. Terms are displayed lowest degrees first. The multiplications signs, coefficients equals to one and null terms are not displayed (except if the polynomial is 0, in which case the 0 constant term is displayed). Addition of terms with negative coefficients are replaced by subtraction of terms with positive coefficients except for the first displayed term (i.e. we display -3 for a constant negative polynomial, but 1 - 3 x + x^2 if the negative coefficient is not the first one displayed).

Overrides:
toString in class Object
Returns:
a string representation of the polynomial.
• #### hashCode

public int hashCode()
Overrides:
hashCode in class Object
• #### equals

public boolean equals(Object obj)
Overrides:
equals in class Object