Package org.drip.numerical.integration

Class R1ToR1Integrator

java.lang.Object

org.drip.numerical.integration.R1ToR1Integrator

public class R1ToR1Integrator
extends java.lang.Object

R1ToR1Integrator implements the following routines for integrating the R¹ To R¹ objective Function.

• Linear Quadrature
• Mid-Point Scheme
• Trapezoidal Scheme
• Simpson/Simpson38 schemes
• Boole Scheme

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = R¹ R^d Numerical Integration Schemes

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1ToR1Integrator()

Method Summary

Modifier and Type	Method	Description
static double	Boole(R1ToR1 funcR1ToR1, double dblLeft, double dblRight)	Compute the function's integral within the specified limits using the Boole rule.
static double	LeftInfinite(R1ToR1 funcR1ToR1, double dblRight)	Integrate the specified Function Numerically from -infinity to the specified Right Limit
static double	LeftInfiniteRightInfinite(R1ToR1 funcR1ToR1)	Integrate Numerically over [-infinity, +infinity] using a Change of Variables
static double	LinearQuadrature(R1ToR1 funcR1ToR1, double dblLeft, double dblRight)	Compute the function's integral within the specified limits using the LinearQuadrature technique.
static double	MidPoint(R1ToR1 funcR1ToR1, double dblLeft, double dblRight)	Compute the function's integral within the specified limits using the Mid-point rule.
static double	RightInfinite(R1ToR1 funcR1ToR1, double dblLeft)	Integrate the specified Function Numerically from the specified Left Limit to +infinity
static double	Simpson(R1ToR1 funcR1ToR1, double dblLeft, double dblRight)	Compute the function's integral within the specified limits using the Simpson rule.
static double	Simpson38(R1ToR1 funcR1ToR1, double dblLeft, double dblRight)	Compute the function's integral within the specified limits using the Simpson 3/8 rule.
static double	Trapezoidal(R1ToR1 funcR1ToR1, double dblLeft, double dblRight)	Compute the function's integral within the specified limits using the Trapezoidal rule.

Methods inherited from class java.lang.Object

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

Constructor Details

R1ToR1Integrator

public R1ToR1Integrator()

Method Details

LinearQuadrature

public static final double LinearQuadrature(R1ToR1 funcR1ToR1,
double dblLeft,
double dblRight)
                                     throws java.lang.Exception

Compute the function's integral within the specified limits using the LinearQuadrature technique.

Parameters:

funcR1ToR1 - R1ToR1 Function

dblLeft - Left Variate

dblRight - Right Variate

Returns:

The Integral

Throws:

java.lang.Exception - Thrown if the error cannot be computed

MidPoint

public static final double MidPoint(R1ToR1 funcR1ToR1,
double dblLeft,
double dblRight)
                             throws java.lang.Exception

Compute the function's integral within the specified limits using the Mid-point rule.

Parameters:

funcR1ToR1 - R1ToR1 Function

dblLeft - Left Variate

dblRight - Right Variate

Returns:

The Integral

Throws:

java.lang.Exception - Thrown if the error cannot be computed

Trapezoidal

public static final double Trapezoidal(R1ToR1 funcR1ToR1,
double dblLeft,
double dblRight)
                                throws java.lang.Exception

Compute the function's integral within the specified limits using the Trapezoidal rule.

Parameters:

funcR1ToR1 - R1ToR1 Function

dblLeft - Left Variate

dblRight - Right Variate

Returns:

The Integral

Throws:

java.lang.Exception - Thrown if the error cannot be computed

Simpson

public static final double Simpson(R1ToR1 funcR1ToR1,
double dblLeft,
double dblRight)
                            throws java.lang.Exception

Compute the function's integral within the specified limits using the Simpson rule.

Parameters:

funcR1ToR1 - R1ToR1 Function

dblLeft - Left Variate

dblRight - Right Variate

Returns:

The Integral

Throws:

java.lang.Exception - Thrown if the error cannot be computed

Simpson38

public static final double Simpson38(R1ToR1 funcR1ToR1,
double dblLeft,
double dblRight)
                              throws java.lang.Exception

Compute the function's integral within the specified limits using the Simpson 3/8 rule.

Parameters:

funcR1ToR1 - R1ToR1 Function

dblLeft - Left Variate

dblRight - Right Variate

Returns:

The Integral

Throws:

java.lang.Exception - Thrown if the error cannot be computed

Boole

public static final double Boole(R1ToR1 funcR1ToR1,
double dblLeft,
double dblRight)
                          throws java.lang.Exception

Compute the function's integral within the specified limits using the Boole rule.

Parameters:

funcR1ToR1 - R1ToR1 Function

dblLeft - Left Variate

dblRight - Right Variate

Returns:

The Integral

Throws:

java.lang.Exception - Thrown if the error cannot be computed

LeftInfiniteRightInfinite

public static final double LeftInfiniteRightInfinite(R1ToR1 funcR1ToR1)
                                              throws java.lang.Exception

Integrate Numerically over [-infinity, +infinity] using a Change of Variables

Parameters:

funcR1ToR1 - The R1ToR1 Function

Returns:

The Numerical Integrand

Throws:

java.lang.Exception - Thrown if the Integral cannot be computed

LeftInfinite

public static final double LeftInfinite(R1ToR1 funcR1ToR1,
double dblRight)
                                 throws java.lang.Exception

Integrate the specified Function Numerically from -infinity to the specified Right Limit

Parameters:

funcR1ToR1 - The Input R1ToR1 Function

dblRight - The Right Integration Limit

Returns:

The Results of the Integration

Throws:

java.lang.Exception - Thrown if the Integrand cannot be evaluated

RightInfinite

public static final double RightInfinite(R1ToR1 funcR1ToR1,
double dblLeft)
                                  throws java.lang.Exception

Integrate the specified Function Numerically from the specified Left Limit to +infinity

Parameters:

funcR1ToR1 - The Input R1ToR1 Function

dblLeft - The Left Integration Limit

Returns:

The Results of the Integration

Throws:

java.lang.Exception - Thrown if the Integrand cannot be evaluated