Package org.hipparchus.analysis.polynomials

Class PolynomialFunction

java.lang.Object
org.hipparchus.analysis.polynomials.PolynomialFunction
All Implemented Interfaces:
Serializable, UnivariateDifferentiableFunction, FieldUnivariateFunction, UnivariateFunction
Direct Known Subclasses:
SmoothStepFactory.SmoothStepFunction
public class PolynomialFunction extends Object implements UnivariateDifferentiableFunction, FieldUnivariateFunction, Serializable
Immutable representation of a real polynomial function with real coefficients.

Horner's Method is used to evaluate the function.

See Also:

  • Constructor Details

    • 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 Details

    • 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.
      See Also:

    • 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 <T extends Derivative<T>> T value(T t) throws MathIllegalArgumentException, NullArgumentException
      Compute the value for the function.
      Specified by:
      value in interface UnivariateDifferentiableFunction
      Type Parameters:
      T - the type of the field elements
      Parameters:
      t - the point for which the function value should be computed
      Returns:
      the value
      Throws:
      MathIllegalArgumentException - if coefficients is empty.
      NullArgumentException - if coefficients is null.

    • value

      public <T extends CalculusFieldElement<T>> T value(T t) throws MathIllegalArgumentException, NullArgumentException
      Compute the value of the function.
      Specified by:
      value in interface FieldUnivariateFunction
      Type Parameters:
      T - the type of the field elements
      Parameters:
      t - Point at which the function value should be computed.
      Returns:
      the value of the function.
      Throws:
      MathIllegalArgumentException - if coefficients is empty.
      NullArgumentException - if coefficients is null.
      Since:
      1.3

    • add

      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