Package org.hipparchus.analysis.polynomials

Class FieldPolynomialFunction<T extends CalculusFieldElement<T>>

java.lang.Object
org.hipparchus.analysis.polynomials.FieldPolynomialFunction<T>
Type Parameters:
T - the type of the field elements
All Implemented Interfaces:
CalculusFieldUnivariateFunction<T>
Direct Known Subclasses:
SmoothStepFactory.FieldSmoothStepFunction
public class FieldPolynomialFunction<T extends CalculusFieldElement<T>> extends Object implements CalculusFieldUnivariateFunction<T>
Immutable representation of a real polynomial function with real coefficients.

Horner's Method is used to evaluate the function.

Since:
1.5

  • Constructor Details

    • FieldPolynomialFunction

      public FieldPolynomialFunction(T[] 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 Details

    • value

      public T 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]

      Parameters:
      x - Argument for which the function value should be computed.
      Returns:
      the value of the polynomial at the given point.
      See Also:

    • value

      public T value(T 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 CalculusFieldUnivariateFunction<T extends CalculusFieldElement<T>>
      Parameters:
      x - Argument for which the function value should be computed.
      Returns:
      the value of the polynomial at the given point.
      See Also:

    • getField

      public Field<T> getField()
      Get the Field to which the instance belongs.
      Returns:
      Field to which the instance belongs

    • degree

      public int degree()
      Returns the degree of the polynomial.
      Returns:
      the degree of the polynomial.

    • getCoefficients

      public T[] 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 <T extends CalculusFieldElement<T>> T evaluate(T[] coefficients, T argument) throws MathIllegalArgumentException, NullArgumentException
      Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
      Type Parameters:
      T - the type of the field elements
      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.

    • add

      public FieldPolynomialFunction<T> add(FieldPolynomialFunction<T> 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 FieldPolynomialFunction<T> subtract(FieldPolynomialFunction<T> p)
      Subtract a polynomial from the instance.
      Parameters:
      p - Polynomial to subtract.
      Returns:
      a new polynomial which is the instance minus p.

    • negate

      public FieldPolynomialFunction<T> negate()
      Negate the instance.
      Returns:
      a new polynomial with all coefficients negated

    • multiply

      public FieldPolynomialFunction<T> multiply(FieldPolynomialFunction<T> 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 <T extends CalculusFieldElement<T>> T[] differentiate(T[] coefficients) throws MathIllegalArgumentException, NullArgumentException
      Returns the coefficients of the derivative of the polynomial with the given coefficients.
      Type Parameters:
      T - the type of the field elements
      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 FieldPolynomialFunction<T> 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 T 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

    • integrate

      public T integrate(T lower, T 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 FieldPolynomialFunction<T> polynomialDerivative()
      Returns the derivative as a FieldPolynomialFunction.
      Returns:
      the derivative polynomial.