Package org.drip.function.definition

Class RdToR1

java.lang.Object

org.drip.function.definition.RdToR1

Direct Known Subclasses:

AffineBoundMultivariate, AffineMultivariate, CovarianceEllipsoidMultivariate, LagrangianMultivariate, LinearExpression, MultivariateRandom, ObjectiveFunction, RdDecisionFunction, RiskObjectiveUtilityMultivariate

public abstract class RdToR1
extends java.lang.Object

RdToR1 provides the evaluation of the R^d To R¹ objective function and its derivatives for a specified set of R^d variates. Default implementation of the derivatives are for non-analytical lack box objective functions.

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d To R^d Function Analysis
• Package = Function Implementation Ancillary Support Objects

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	conditionNumber(double[] variateArray)	Retrieve the Default Condition Number for the Function at the Domain Value - this uses L2 Metric
double	conditionNumberL2(double[] variateArray)	Retrieve the L2 Condition Number for the Function at the Domain Value
double	conditionNumberLInfinity(double[] variateArray)	Retrieve the LInfinity Condition Number for the Function at the Domain Value
double	conditionNumberLp(double[] variateArray, int p)	Retrieve the Lp Condition Number for the Function at the Domain Value
double	derivative(double[] adblVariate, int iVariateIndex, int iOrder)	Calculate the derivative as a double
Differential	differential(double[] adblVariate, int iVariateIndex, int iOrder)	Calculate the Differential
abstract int	dimension()	Retrieve the Dimension of the Input Variate
abstract double	evaluate(double[] adblVariate)	Evaluate for the given Input Variates
UnitVector	gradient(double[] adblVariate)	Construct an Instance of the Unit Gradient Vector at the given Input Variates
double	gradientModulus(double[] adblVariate)	Compute the Modulus of the Gradient at the Specified Variate location
RdToR1	gradientModulusFunction()	Generate the Gradient Modulus Function
double[][]	hessian(double[] adblVariate)	Evaluate The Hessian for the given Input Variates
double	integrate(double[] adblLeftEdge, double[] adblRightEdge)	Integrate over the given Input Range Using Uniform Monte-Carlo
double[]	jacobian(double[] adblVariate)	Evaluate the Jacobian for the given Input Variates
VariateOutputPair	maxima(double[] adblVariateLeft, double[] adblVariateRight)	Compute the Maximum VOP within the Variate Array Range Using Uniform Monte-Carlo
VariateOutputPair	minima(double[] adblVariateLeft, double[] adblVariateRight)	Compute the Minimum VOP within the Variate Array Range Using Uniform Monte-Carlo
static boolean	ValidateInput(double[] adblVariate)	Validate the Input Double Array

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

ValidateInput

public static final boolean ValidateInput(double[] adblVariate)

Validate the Input Double Array

Parameters:

adblVariate - The Input Double Array

Returns:

The Input Double Array consists of valid Values

dimension

public abstract int dimension()

Retrieve the Dimension of the Input Variate

Returns:

The Dimension of the Input Variate

evaluate

public abstract double evaluate(double[] adblVariate)
                         throws java.lang.Exception

Evaluate for the given Input Variates

Parameters:

adblVariate - Array of Input Variates

Returns:

The Calculated Value

Throws:

java.lang.Exception - Thrown if the Evaluation cannot be done

differential

public Differential differential(double[] adblVariate,
int iVariateIndex,
int iOrder)

Calculate the Differential

Parameters:

adblVariate - Variate Array at which the derivative is to be calculated

iVariateIndex - Index of the Variate whose Derivative is to be computed

iOrder - Order of the derivative to be computed

Returns:

The Derivative

derivative

public double derivative(double[] adblVariate,
int iVariateIndex,
int iOrder)
                  throws java.lang.Exception

Calculate the derivative as a double

Parameters:

adblVariate - Variate Array at which the derivative is to be calculated

iVariateIndex - Index of the Variate whose Derivative is to be computed

iOrder - Order of the derivative to be computed

Returns:

The Derivative

Throws:

java.lang.Exception - Thrown if the Derivative cannot be calculated

jacobian

public double[] jacobian(double[] adblVariate)

Evaluate the Jacobian for the given Input Variates

Parameters:

adblVariate - Array of Input Variates

Returns:

The Jacobian Array

gradient

public UnitVector gradient(double[] adblVariate)

Construct an Instance of the Unit Gradient Vector at the given Input Variates

Parameters:

adblVariate - Array of Input Variates

Returns:

Instance of the Unit Gradient Vector Array

hessian

public double[][] hessian(double[] adblVariate)

Evaluate The Hessian for the given Input Variates

Parameters:

adblVariate - Array of Input Variates

Returns:

The Hessian Matrix

integrate

public double integrate(double[] adblLeftEdge,
double[] adblRightEdge)
                 throws java.lang.Exception

Integrate over the given Input Range Using Uniform Monte-Carlo

Parameters:

adblLeftEdge - Array of Input Left Edge

adblRightEdge - Array of Input Right Edge

Returns:

The Result of the Integration over the specified Range

Throws:

java.lang.Exception - Thrown if the Integration cannot be done

maxima

public VariateOutputPair maxima(double[] adblVariateLeft,
double[] adblVariateRight)

Compute the Maximum VOP within the Variate Array Range Using Uniform Monte-Carlo

Parameters:

adblVariateLeft - The Range Left End Array

adblVariateRight - The Range Right End Array

Returns:

The Maximum VOP

minima

public VariateOutputPair minima(double[] adblVariateLeft,
double[] adblVariateRight)

Compute the Minimum VOP within the Variate Array Range Using Uniform Monte-Carlo

Parameters:

adblVariateLeft - The Range Left End Array

adblVariateRight - The Range Right End Array

Returns:

The Minimum VOP

gradientModulus

public double gradientModulus(double[] adblVariate)
                       throws java.lang.Exception

Compute the Modulus of the Gradient at the Specified Variate location

Parameters:

adblVariate - The Variate Array location

Returns:

The Modulus of the Gradient at the Specified Variate location

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

gradientModulusFunction

public RdToR1 gradientModulusFunction()

Generate the Gradient Modulus Function

Returns:

The Gradient Modulus Function

conditionNumberL2

public double conditionNumberL2(double[] variateArray)
                         throws java.lang.Exception

Retrieve the L₂ Condition Number for the Function at the Domain Value

Parameters:

variateArray - Domain Variate Array

Returns:

Condition Number for the Function at the Domain Value

Throws:

java.lang.Exception - Thrown if the Condition Number for the Function at the Domain Value cannot be calculated

conditionNumberLp

public double conditionNumberLp(double[] variateArray,
int p)
                         throws java.lang.Exception

Retrieve the L_p Condition Number for the Function at the Domain Value

Parameters:

variateArray - Domain Variate Array

p - p-Norm

Returns:

Condition Number for the Function at the Domain Value

Throws:

java.lang.Exception - Thrown if the Condition Number for the Function at the Domain Value cannot be calculated

conditionNumberLInfinity

public double conditionNumberLInfinity(double[] variateArray)
                                throws java.lang.Exception

Retrieve the L_Infinity Condition Number for the Function at the Domain Value

Parameters:

variateArray - Domain Variate Array

Returns:

Condition Number for the Function at the Domain Value

Throws:

java.lang.Exception - Thrown if the Condition Number for the Function at the Domain Value cannot be calculated

conditionNumber

public double conditionNumber(double[] variateArray)
                       throws java.lang.Exception

Retrieve the Default Condition Number for the Function at the Domain Value - this uses L₂ Metric

Parameters:

variateArray - Domain Variate Array

Returns:

Condition Number for the Function at the Domain Value

Throws:

java.lang.Exception - Thrown if the Condition Number for the Function at the Domain Value cannot be calculated