Nested and Inner Type Summary

Modifier and Type	Class and Description
public static class	PolynomialFunction.Parametric Dedicated parametric polynomial class.

Field Summary

Modifier and Type	Field and Description
private final double[]	coefficients The coefficients of the polynomial, ordered by degree -- i.e., coefficients[0] is the constant term and coefficients[n] is the coefficient of x^n where n is the degree of the polynomial.
private static final long	serialVersionUID Serialization identifier

Constructor Summary

Access	Constructor and Description
public	PolynomialFunction(double[] Polynomial coefficients. c) Construct a polynomial with the given coefficients.

Method Summary

Modifier and Type	Method and Description
public PolynomialFunction	Returns: a new polynomial which is the sum of the instance and `p`. add(final PolynomialFunction Polynomial to add. p) Deprecated as a consequence of `PolynomialFunction` being deprecated. Add a polynomial to the instance.
public int	Returns: the degree of the polynomial. degree() Returns the degree of the polynomial.
public UnivariateFunction	Returns: the derivative function. derivative() Implements org.apache.commons.math3.analysis.DifferentiableUnivariateFunction.derivative. Returns the derivative as a `UnivariateFunction`.
protected static double[]	Returns: the coefficients of the derivative or `null` if coefficients has length 1. differentiate(double[] Coefficients of the polynomial to differentiate. coefficients) Returns the coefficients of the derivative of the polynomial with the given coefficients.
public boolean	equals(Object the reference object with which to compare. obj) Overrides java.lang.Object.equals. Indicates whether some other object is "equal to" this one.
protected static double	Returns: the value of the polynomial. evaluate(double[] Coefficients of the polynomial to evaluate. coefficients, double Input value. argument) Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
public double[]	Returns: a fresh copy of the coefficients array. getCoefficients() Returns a copy of the coefficients array.
public int	hashCode() Overrides java.lang.Object.hashCode. Returns a hash code value for this object.
public PolynomialFunction	Returns: a new polynomial equal to this times `p` multiply(final PolynomialFunction Polynomial to multiply by. p) Deprecated as a consequence of `PolynomialFunction` being deprecated. Multiply the instance by a polynomial.
public PolynomialFunction	Returns: a new polynomial with all coefficients negated negate() Deprecated as a consequence of `PolynomialFunction` being deprecated. Negate the instance.
public PolynomialFunction	Returns: the derivative polynomial. polynomialDerivative() Deprecated as a consequence of `PolynomialFunction` being deprecated. Returns the derivative as a `PolynomialFunction`.
public PolynomialFunction	Returns: a new polynomial which is the instance minus `p`. subtract(final PolynomialFunction Polynomial to subtract. p) Deprecated as a consequence of `PolynomialFunction` being deprecated. Subtract a polynomial from the instance.
public String	Returns: a string representation of the polynomial. toString() Overrides java.lang.Object.toString. Returns a string representation of the polynomial.
private static String	Returns: a string representation of `coeff`. toString(double Coefficient. coeff) Creates a string representing a coefficient, removing ".0" endings.
public double	Returns: the value of the polynomial at the given point. value(double Argument for which the function value should be computed. x) Implements org.apache.commons.math3.analysis.UnivariateFunction.value. Compute the value of the function for the given argument.
public DerivativeStructure	value(final DerivativeStructure function input value t) Implements org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction.value. Simple mathematical function.

Inherited from java.lang.Object:: clone finalize getClass notify notifyAll wait wait wait

Field Detail

coefficients	back to summary
private final double[] coefficients The coefficients of the polynomial, ordered by degree -- i.e., coefficients[0] is the constant term and coefficients[n] is the coefficient of x^n where n is the degree of the polynomial.

serialVersionUID	back to summary
private static final long serialVersionUID Serialization identifier

Constructor Detail

PolynomialFunction back to summary

PolynomialFunction	back to summary
public PolynomialFunction(double[] c) throws NullArgumentException, NoDataException 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:double[] Polynomial coefficients. Exceptions NullArgumentException: if `c` is `null`. NoDataException: if `c` is empty.

public PolynomialFunction(double[] c) throws NullArgumentException, NoDataException

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:double[]: Polynomial coefficients.

Exceptions

NullArgumentException:: if c is null.
NoDataException:: if c is empty.

Method Detail

add back to summary

add	back to summary
public PolynomialFunction add(final PolynomialFunction p) Deprecated as a consequence of `PolynomialFunction` being deprecated. See corresponding docs for further information. Add a polynomial to the instance. Parameters p:PolynomialFunction Polynomial to add. Returns:PolynomialFunction a new polynomial which is the sum of the instance and `p`.

public PolynomialFunction add(final PolynomialFunction p)

Deprecated

as a consequence of PolynomialFunction being deprecated. See corresponding docs for further information.

Add a polynomial to the instance.

Parameters

p:PolynomialFunction: Polynomial to add.

Returns:PolynomialFunction

a new polynomial which is the sum of the instance and p.

degree	back to summary
public int degree() Returns the degree of the polynomial. Returns:int the degree of the polynomial.

degree

back to summary

public int degree()

Returns the degree of the polynomial.

Returns:int: the degree of the polynomial.

derivative back to summary

derivative	back to summary
public UnivariateFunction derivative() Implements org.apache.commons.math3.analysis.DifferentiableUnivariateFunction.derivative. Returns the derivative as a `UnivariateFunction`. Returns:UnivariateFunction the derivative function.

public UnivariateFunction derivative()

Implements org.apache.commons.math3.analysis.DifferentiableUnivariateFunction.derivative.

Returns the derivative as a UnivariateFunction.

Returns:UnivariateFunction: the derivative function.

differentiate back to summary

differentiate	back to summary
protected static double[] differentiate(double[] coefficients) throws NullArgumentException, NoDataException Returns the coefficients of the derivative of the polynomial with the given coefficients. Parameters coefficients:double[] Coefficients of the polynomial to differentiate. Returns:double[] the coefficients of the derivative or `null` if coefficients has length 1. Exceptions NullArgumentException: if `coefficients` is `null`. NoDataException: if `coefficients` is empty.

protected static double[] differentiate(double[] coefficients) throws NullArgumentException, NoDataException

Returns the coefficients of the derivative of the polynomial with the given coefficients.

Parameters

coefficients:double[]: Coefficients of the polynomial to differentiate.

Returns:double[]

the coefficients of the derivative or null if coefficients has length 1.

Exceptions

NullArgumentException:: if coefficients is null.
NoDataException:: if coefficients is empty.

equals back to summary

equals	back to summary
public boolean equals(Object obj) Overrides java.lang.Object.equals. Doc from java.lang.Object.equals. Indicates whether some other object is "equal to" this one. The `equals` method implements an equivalence relation on non-null object references: It is reflexive: for any non-null reference value `x`, `x.equals(x)` should return `true`. It is symmetric: for any non-null reference values `x` and `y`, `x.equals(y)` should return `true` if and only if `y.equals(x)` returns `true`. It is transitive: for any non-null reference values `x`, `y`, and `z`, if `x.equals(y)` returns `true` and `y.equals(z)` returns `true`, then `x.equals(z)` should return `true`. It is consistent: for any non-null reference values `x` and `y`, multiple invocations of `x.equals(y)` consistently return `true` or consistently return `false`, provided no information used in `equals` comparisons on the objects is modified. For any non-null reference value `x`, `x.equals(null)` should return `false`. An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes. Parameters obj:Object the reference object with which to compare. Returns:boolean `true` if this object is the same as the obj argument; `false` otherwise. Annotations @Override

public boolean equals(Object obj)

Overrides java.lang.Object.equals.

Doc from java.lang.Object.equals.

Indicates whether some other object is "equal to" this one.

The equals method implements an equivalence relation on non-null object references:

It is reflexive: for any non-null reference value x, x.equals(x) should return true.
It is symmetric: for any non-null reference values x and y, x.equals(y) should return true if and only if y.equals(x) returns true.
It is transitive: for any non-null reference values x, y, and z, if x.equals(y) returns true and y.equals(z) returns true, then x.equals(z) should return true.
It is consistent: for any non-null reference values x and y, multiple invocations of x.equals(y) consistently return true or consistently return false, provided no information used in equals comparisons on the objects is modified.
For any non-null reference value x, x.equals(null) should return false.

An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes.

Parameters

obj:Object: the reference object with which to compare.

Returns:boolean

true if this object is the same as the obj argument; false otherwise.

Annotations

@Override

evaluate back to summary

evaluate	back to summary
protected static double evaluate(double[] coefficients, double argument) throws NullArgumentException, NoDataException Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument. Parameters coefficients:double[] Coefficients of the polynomial to evaluate. argument:double Input value. Returns:double the value of the polynomial. Exceptions NullArgumentException: if `coefficients` is `null`. NoDataException: if `coefficients` is empty.

protected static double evaluate(double[] coefficients, double argument) throws NullArgumentException, NoDataException

Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.

Parameters

coefficients:double[]: Coefficients of the polynomial to evaluate.
argument:double: Input value.

Returns:double

the value of the polynomial.

Exceptions

NullArgumentException:: if coefficients is null.
NoDataException:: if coefficients is empty.

getCoefficients	back to summary
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:double[] a fresh copy of the coefficients array.

getCoefficients

back to summary

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:double[]: a fresh copy of the coefficients array.

hashCode back to summary

hashCode	back to summary
public int hashCode() Overrides java.lang.Object.hashCode. Doc from java.lang.Object.hashCode. Returns a hash code value for this object. This method is supported for the benefit of hash tables such as those provided by `java.util.HashMap`. The general contract of `hashCode` is: Whenever it is invoked on the same object more than once during an execution of a Java application, the `hashCode` method must consistently return the same integer, provided no information used in `equals` comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application. If two objects are equal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce the same integer result. It is not required that if two objects are unequal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables. Returns:int a hash code value for this object Annotations @Override

public int hashCode()

Overrides java.lang.Object.hashCode.

Doc from java.lang.Object.hashCode.

Returns a hash code value for this object. This method is supported for the benefit of hash tables such as those provided by java.util.HashMap.

The general contract of hashCode is:

Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.
If two objects are equal according to the equals method, then calling the hashCode method on each of the two objects must produce the same integer result.
It is not required that if two objects are unequal according to the equals method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables.

Returns:int

a hash code value for this object

Annotations

@Override

multiply back to summary

multiply	back to summary
public PolynomialFunction multiply(final PolynomialFunction p) Deprecated as a consequence of `PolynomialFunction` being deprecated. See corresponding docs for further information. Multiply the instance by a polynomial. Parameters p:PolynomialFunction Polynomial to multiply by. Returns:PolynomialFunction a new polynomial equal to this times `p`

public PolynomialFunction multiply(final PolynomialFunction p)

Deprecated

as a consequence of PolynomialFunction being deprecated. See corresponding docs for further information.

Multiply the instance by a polynomial.

Parameters

p:PolynomialFunction: Polynomial to multiply by.

Returns:PolynomialFunction

a new polynomial equal to this times p

negate back to summary

negate	back to summary
public PolynomialFunction negate() Deprecated as a consequence of `PolynomialFunction` being deprecated. See corresponding docs for further information. Negate the instance. Returns:PolynomialFunction a new polynomial with all coefficients negated

public PolynomialFunction negate()

Deprecated

as a consequence of PolynomialFunction being deprecated. See corresponding docs for further information.

Negate the instance.

Returns:PolynomialFunction: a new polynomial with all coefficients negated

polynomialDerivative back to summary

polynomialDerivative	back to summary
public PolynomialFunction polynomialDerivative() Deprecated as a consequence of `PolynomialFunction` being deprecated. See corresponding docs for further information. Returns the derivative as a `PolynomialFunction`. Returns:PolynomialFunction the derivative polynomial.

public PolynomialFunction polynomialDerivative()

Deprecated

as a consequence of PolynomialFunction being deprecated. See corresponding docs for further information.

Returns the derivative as a PolynomialFunction.

Returns:PolynomialFunction: the derivative polynomial.

subtract back to summary

subtract	back to summary
public PolynomialFunction subtract(final PolynomialFunction p) Deprecated as a consequence of `PolynomialFunction` being deprecated. See corresponding docs for further information. Subtract a polynomial from the instance. Parameters p:PolynomialFunction Polynomial to subtract. Returns:PolynomialFunction a new polynomial which is the instance minus `p`.

public PolynomialFunction subtract(final PolynomialFunction p)

Deprecated

as a consequence of PolynomialFunction being deprecated. See corresponding docs for further information.

Subtract a polynomial from the instance.

Parameters

p:PolynomialFunction: Polynomial to subtract.

Returns:PolynomialFunction

a new polynomial which is the instance minus p.

toString back to summary

toString	back to summary
public String toString() Overrides java.lang.Object.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). Returns:String a string representation of the polynomial. Annotations @Override

public String toString()

Overrides java.lang.Object.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).

Returns:String

a string representation of the polynomial.

Annotations

@Override

toString back to summary

toString	back to summary
private static String toString(double coeff) Creates a string representing a coefficient, removing ".0" endings. Parameters coeff:double Coefficient. Returns:String a string representation of `coeff`.

private static String toString(double coeff)

Creates a string representing a coefficient, removing ".0" endings.

Parameters

coeff:double: Coefficient.

Returns:String

a string representation of coeff.

value back to summary

value	back to summary
public double value(double x) Implements org.apache.commons.math3.analysis.UnivariateFunction.value. 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:double Argument for which the function value should be computed. Returns:double the value of the polynomial at the given point. See Also `UnivariateFunction#value(double)`

public double value(double x)

Implements org.apache.commons.math3.analysis.UnivariateFunction.value.

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:double: Argument for which the function value should be computed.

Returns:double

the value of the polynomial at the given point.

See Also

UnivariateFunction#value(double)

value back to summary

value	back to summary
public DerivativeStructure value(final DerivativeStructure t) throws NullArgumentException, NoDataException Implements org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction.value. Doc from org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction.value. Simple mathematical function. `UnivariateDifferentiableFunction` classes compute both the value and the first derivative of the function. Parameters t:DerivativeStructure function input value Returns:DerivativeStructure function result Exceptions NullArgumentException: if `coefficients` is `null`. NoDataException: if `coefficients` is empty. Since 3.1

public DerivativeStructure value(final DerivativeStructure t) throws NullArgumentException, NoDataException

Implements org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction.value.

Doc from org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction.value.

Simple mathematical function.

UnivariateDifferentiableFunction classes compute both the value and the first derivative of the function.

Parameters

t:DerivativeStructure: function input value

Returns:DerivativeStructure

function result

Exceptions

NullArgumentException:: if coefficients is null.
NoDataException:: if coefficients is empty.

Since

3.1

org.apache.commons.math3.analysis.polynomials back to summary

public Class PolynomialFunction.Parametric

Class Inheritance

extends Object
implements ParametricUnivariateFunction

java.lang.Object
org.apache.commons.math3.analysis.polynomials.PolynomialFunction.Parametric

All Implemented Interfaces

org.apache.commons.math3.analysis.ParametricUnivariateFunction

Dedicated parametric polynomial class.

Since: 3.0

Constructor Summary

Access	Constructor and Description
public	Parametric()

Method Summary

Modifier and Type	Method and Description
public double[]	gradient(double Point for which the function value should be computed. x, double... Function parameters. parameters) Implements org.apache.commons.math3.analysis.ParametricUnivariateFunction.gradient. Compute the gradient of the function with respect to its parameters.
public double	value(final double Point for which the function value should be computed. x, final double... Function parameters. parameters) Implements org.apache.commons.math3.analysis.ParametricUnivariateFunction.value. Compute the value of the function.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Constructor Detail

Parametric	back to summary
public Parametric()

Method Detail

gradient	back to summary
public double[] gradient(double x, double... parameters) Implements org.apache.commons.math3.analysis.ParametricUnivariateFunction.gradient. Doc from org.apache.commons.math3.analysis.ParametricUnivariateFunction.gradient. Compute the gradient of the function with respect to its parameters. Parameters x:double Point for which the function value should be computed. parameters:double[] Function parameters. Returns:double[] the value.

gradient

back to summary

public double[] gradient(double x, double... parameters)

Implements org.apache.commons.math3.analysis.ParametricUnivariateFunction.gradient.

Doc from org.apache.commons.math3.analysis.ParametricUnivariateFunction.gradient.

Compute the gradient of the function with respect to its parameters.

Parameters

x:double: Point for which the function value should be computed.
parameters:double[]: Function parameters.

Returns:double[]

the value.

value	back to summary
public double value(final double x, final double... parameters) throws NoDataException Implements org.apache.commons.math3.analysis.ParametricUnivariateFunction.value. Doc from org.apache.commons.math3.analysis.ParametricUnivariateFunction.value. Compute the value of the function. Parameters x:double Point for which the function value should be computed. parameters:double[] Function parameters. Returns:double the value.

value

back to summary

public double value(final double x, final double... parameters) throws NoDataException

Implements org.apache.commons.math3.analysis.ParametricUnivariateFunction.value.

Doc from org.apache.commons.math3.analysis.ParametricUnivariateFunction.value.

Compute the value of the function.

Parameters

x:double: Point for which the function value should be computed.
parameters:double[]: Function parameters.

Returns:double

the value.