gov.sandia.cognition.learning.function.scalar

Class PolynomialFunction.Quadratic

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.math.AbstractScalarFunction<java.lang.Double>

gov.sandia.cognition.math.AbstractUnivariateScalarFunction

gov.sandia.cognition.math.AbstractDifferentiableUnivariateScalarFunction

gov.sandia.cognition.learning.function.scalar.PolynomialFunction.Linear

gov.sandia.cognition.learning.function.scalar.PolynomialFunction.Quadratic

All Implemented Interfaces:

Evaluator<java.lang.Double,java.lang.Double>, PolynomialFunction.ClosedForm, DifferentiableEvaluator<java.lang.Double,java.lang.Double,java.lang.Double>, DifferentiableUnivariateScalarFunction, ScalarFunction<java.lang.Double>, UnivariateScalarFunction, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

PolynomialFunction.Cubic

Enclosing class:

PolynomialFunction

public static class PolynomialFunction.Quadratic
extends PolynomialFunction.Linear

Utilities for algebraic treatment of a quadratic polynomial of the form y(x) = q0 + q1*x + q2*x^2.

See Also:

Serialized Form

Field Summary

Fields inherited from class gov.sandia.cognition.learning.function.scalar.PolynomialFunction.Linear

COLLINEAR_TOLERANCE

Constructor Summary

Constructors

Constructor and Description
Quadratic(double q0, double q1, double q2) Creates a new instance of Quadratic
Quadratic(PolynomialFunction.Quadratic other) Copy constructor

Method Summary

Modifier and Type	Method and Description
PolynomialFunction.Quadratic	clone() This makes public the clone method on the Object class and removes the exception that it throws.
double	differentiate(double input) Differentiates the output of the function about the given input
double	evaluate(double input) Produces a double output for the given double input
static double	evaluate(double x, double q0, double q1, double q2) Evaluates a quadratic polynomial of the form y(x) = q0 + q1*x + q2*x^2 for a given value of "x"
static PolynomialFunction.Quadratic	fit(InputOutputPair<java.lang.Double,java.lang.Double> p0, InputOutputPair<java.lang.Double,java.lang.Double> p1, InputOutputPair<java.lang.Double,java.lang.Double> p2) Fits a quadratic to three points
static PolynomialFunction.Quadratic	fit(InputOutputSlopeTriplet p0, InputOutputPair<java.lang.Double,java.lang.Double> p1) Fits a quadratic to two points, one of which has slope information.
double	getQ2() Getter for q2
java.lang.Double[]	roots() Finds the roots (zero-crossings) of the quadratic, which has at most two, but possibly one or zero
static java.lang.Double[]	roots(double q0, double q1, double q2) Finds the roots of the quadratic equation using the quadratic formula.
void	setQ2(double q2) Setter for q2
java.lang.Double[]	stationaryPoints() Finds the real-valued stationary points (zero-derivatives) of the quadratic.
static java.lang.Double[]	stationaryPoints(double q0, double q1, double q2) Finds the stationary point of the quadratic equation.
java.lang.String	toString()

Methods inherited from class gov.sandia.cognition.learning.function.scalar.PolynomialFunction.Linear

fit, fit, getQ0, getQ1, setQ0, setQ1

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface gov.sandia.cognition.math.DifferentiableUnivariateScalarFunction

differentiate

Methods inherited from interface gov.sandia.cognition.math.UnivariateScalarFunction

evaluate, evaluateAsDouble

Constructor Detail

Quadratic

public Quadratic(double q0,
                 double q1,
                 double q2)

Creates a new instance of Quadratic

Parameters:

q0 - Constant (zeroth-order) coefficient

q1 - Linear (first-order) coefficient

q2 - Quadratic (second-order) coefficient

Quadratic

public Quadratic(PolynomialFunction.Quadratic other)

Copy constructor

Parameters:

other - Quadratic to copy

Method Detail

clone

public PolynomialFunction.Quadratic clone()

Description copied from class: AbstractCloneableSerializable

This makes public the clone method on the Object class and removes the exception that it throws. Its default behavior is to automatically create a clone of the exact type of object that the clone is called on and to copy all primitives but to keep all references, which means it is a shallow copy. Extensions of this class may want to override this method (but call super.clone() to implement a "smart copy". That is, to target the most common use case for creating a copy of the object. Because of the default behavior being a shallow copy, extending classes only need to handle fields that need to have a deeper copy (or those that need to be reset). Some of the methods in ObjectUtil may be helpful in implementing a custom clone method. Note: The contract of this method is that you must use super.clone() as the basis for your implementation.

Specified by:

clone in interface CloneableSerializable

Overrides:

clone in class PolynomialFunction.Linear

Returns:

A clone of this object.

toString

public java.lang.String toString()

Overrides:

toString in class PolynomialFunction.Linear

evaluate

public double evaluate(double input)

Description copied from interface: UnivariateScalarFunction

Produces a double output for the given double input

Specified by:

evaluate in interface UnivariateScalarFunction

Overrides:

evaluate in class PolynomialFunction.Linear

Parameters:

input - Input to the Evaluator

Returns:

output at the given input

differentiate

public double differentiate(double input)

Description copied from interface: DifferentiableUnivariateScalarFunction

Differentiates the output of the function about the given input

Specified by:

differentiate in interface DifferentiableUnivariateScalarFunction

Overrides:

differentiate in class PolynomialFunction.Linear

Parameters:

input - Input about which to compute the derivative of the function output

Returns:

Derivative of the output with respect to the input

roots

public java.lang.Double[] roots()

Finds the roots (zero-crossings) of the quadratic, which has at most two, but possibly one or zero

Specified by:

roots in interface PolynomialFunction.ClosedForm

Overrides:

roots in class PolynomialFunction.Linear

Returns:

Array of roots

stationaryPoints

public java.lang.Double[] stationaryPoints()

Finds the real-valued stationary points (zero-derivatives) of the quadratic. A quadratic has at most one stationary point, it may be a minimum or maximum.

Specified by:

stationaryPoints in interface PolynomialFunction.ClosedForm

Overrides:

stationaryPoints in class PolynomialFunction.Linear

Returns:

Zero- or One-length array of stationary points

evaluate

public static double evaluate(double x,
                              double q0,
                              double q1,
                              double q2)

Evaluates a quadratic polynomial of the form y(x) = q0 + q1*x + q2*x^2 for a given value of "x"

Parameters:

x - Value at which to evaluate the polynomial

q0 - Constant-term coefficient

q1 - Linear-term coefficient

q2 - Quadratic-term coefficient

Returns:

Value of the polynomial at "x"

fit

public static PolynomialFunction.Quadratic fit(InputOutputPair<java.lang.Double,java.lang.Double> p0,
                                               InputOutputPair<java.lang.Double,java.lang.Double> p1,
                                               InputOutputPair<java.lang.Double,java.lang.Double> p2)

Fits a quadratic to three points

Parameters:

p0 - First point

p1 - Second point

p2 - Third point

Returns:

Quadratic fitting the three points

fit

public static PolynomialFunction.Quadratic fit(InputOutputSlopeTriplet p0,
                                               InputOutputPair<java.lang.Double,java.lang.Double> p1)

Fits a quadratic to two points, one of which has slope information.

Parameters:

p0 -

p1 -

Returns:

The quadratic fit.

roots

@PublicationReference(author="Wikipedia",
                      title="Quadratic formula",
                      type=WebPage,
                      year=2008,
                      url="http://en.wikipedia.org/wiki/Quadratic_formula#Quadratic_formula")
public static java.lang.Double[] roots(double q0,
                                                                                                                                                                                                                                                                                                     double q1,
                                                                                                                                                                                                                                                                                                     double q2)

Finds the roots of the quadratic equation using the quadratic formula. That is, finding the values of "x" such that y(x) = q0 + q1*x + q2*x^2 = 0.0. There will be at most two roots, but there can also be a single root, or no roots. In the case of two roots, the return Pair will have the "x" value for value. In the case of a single root, the Pair will have an "x" value for the First, but null for the second. In the case when there are no REAL roots, the return value will be null.

Parameters:

q0 - Constant-term coefficient

q1 - Linear-term coefficient

q2 - Quadratic-term coefficient

Returns:

In the case of two roots, the return Pair will have the "x" value for value. In the case of a single root, the Pair will have an "x" value for the First, but null for the second. In the case when there are no REAL roots, the return value will be a zero-length array.

stationaryPoints

public static java.lang.Double[] stationaryPoints(double q0,
                                                  double q1,
                                                  double q2)

Finds the stationary point of the quadratic equation. That is, the point when the derivative f'(x)=0.0

Parameters:

q0 - Constant-term coefficient

q1 - Linear-term coefficient

q2 - Quadratic-term coefficient

Returns:

Value of "x" when the derivative is zero, null when none is found

getQ2

public double getQ2()

Getter for q2

Returns:

Second-order coefficient

setQ2

public void setQ2(double q2)

Setter for q2

Parameters:

q2 - Second-order coefficient