AbscissaTransform.java
package org.drip.numerical.integration;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>AbscissaTransform</i> transforms the Abscissa over into Corresponding Integrand Variable. The
* References are:
*
* <br><br>
* <ul>
* <li>
* Briol, F. X., C. J. Oates, M. Girolami, and M. A. Osborne (2015): <i>Frank-Wolfe Bayesian
* Quadrature: Probabilistic Integration with Theoretical Guarantees</i> <b>arXiv</b>
* </li>
* <li>
* Forsythe, G. E., M. A. Malcolm, and C. B. Moler (1977): <i>Computer Methods for Mathematical
* Computation</i> <b>Prentice Hall</b> Englewood Cliffs NJ
* </li>
* <li>
* Leader, J. J. (2004): <i>Numerical Analysis and Scientific Computation</i> <b>Addison Wesley</b>
* </li>
* <li>
* Stoer, J., and R. Bulirsch (1980): <i>Introduction to Numerical Analysis</i>
* <b>Springer-Verlag</b> New York
* </li>
* <li>
* Wikipedia (2019): Numerical Integration https://en.wikipedia.org/wiki/Numerical_integration
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/README.md">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/integration/README.md">R<sup>1</sup> R<sup>d</sup> Numerical Integration Schemes</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class AbscissaTransform
{
private double _quadratureScale = java.lang.Double.NaN;
private org.drip.function.definition.R1ToR1 _r1PointValueScale = null;
private org.drip.function.definition.R1ToR1 _r1ToR1VariateChange = null;
/**
* Generate the Scaled and Displaced Abscissa Transform from (left, right) To (0, +1)
*
* @param left Span Left
* @param right Span Right
*
* @return The Scaled and Displaced Abscissa Transform from (left, right) To (0, +1)
*/
public static final AbscissaTransform DisplaceAndScaleZero_PlusOne (
final double left,
final double right)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (left) ||
!org.drip.numerical.common.NumberUtil.IsValid (right))
{
return null;
}
try
{
return new AbscissaTransform (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return (right - left) * x + left;
}
},
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return 1.;
}
},
right - left
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Scaled and Displaced Abscissa Transform from (left, right) To (-1, +1)
*
* @param left Span Left
* @param right Span Right
*
* @return The Scaled and Displaced Abscissa Transform from (left, right) To (-1, +1)
*/
public static final AbscissaTransform DisplaceAndScaleMinusOne_PlusOne (
final double left,
final double right)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (left) ||
!org.drip.numerical.common.NumberUtil.IsValid (right))
{
return null;
}
final double scale = 0.5 * (right - left);
final double offset = 0.5 * (right + left);
try
{
return new AbscissaTransform (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return scale * x + offset;
}
},
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return 1.;
}
},
scale
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Gauss-Hermite Abscissa Transform
*
* @return The Gauss-Hermite Abscissa Transform
*/
public static final AbscissaTransform GaussHermite()
{
try
{
return new AbscissaTransform (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return x / (1. - x * x);
}
},
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
double xSquared = x * x;
return -1. == x || 1. == x ? 0. : (1. + xSquared) / (1. - xSquared) / (1. - xSquared);
}
},
1.
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Gauss-Laguerre Abscissa Transform for Integrals in [a, +Infinity]
*
* @param left Span Left
*
* @return The Gauss-Laguerre Abscissa Transform for Integrals in [a, +Infinity]
*/
public static final AbscissaTransform GaussLaguerreLeftDefinite (
final double left)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (left))
{
return null;
}
try
{
return new AbscissaTransform (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return left + (x / (1. - x));
}
},
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return -1. == x || 1. == x ? 0. : 1. / (1. - x) / (1. - x);
}
},
1.
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Gauss-Laguerre Abscissa Transform for Integrals in [-Infinity, a]
*
* @param right Span Right
*
* @return The Gauss-Laguerre Abscissa Transform for Integrals in [-Infinity, a]
*/
public static final AbscissaTransform GaussLaguerreRightDefinite (
final double right)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (right))
{
return null;
}
try
{
return new AbscissaTransform (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return right - ((1. - x) / x);
}
},
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
{
return 0. == x ? 0. : 1. / (x * x);
}
},
1.
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* AbscissaTransform Constructor
*
* @param r1ToR1VariateChange R<sup>1</sup> to R<sup>1</sup> Variate Change Function
* @param r1PointValueScale R<sup>1</sup> Point Value Scale Function
* @param quadratureScale Quadrature Scale
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public AbscissaTransform (
final org.drip.function.definition.R1ToR1 r1ToR1VariateChange,
final org.drip.function.definition.R1ToR1 r1PointValueScale,
final double quadratureScale)
throws java.lang.Exception
{
if (null == (_r1ToR1VariateChange = r1ToR1VariateChange) ||
null == (_r1PointValueScale = r1PointValueScale) ||
!org.drip.numerical.common.NumberUtil.IsValid (_quadratureScale = quadratureScale))
{
throw new java.lang.Exception ("AbscissaTransform Constructor => Invalid Inputs");
}
}
/**
* Retrieve the R<sup>1</sup> to R<sup>1</sup> Variate Change Function
*
* @return The R<sup>1</sup> to R<sup>1</sup> Variate Change Function
*/
public org.drip.function.definition.R1ToR1 variateChange()
{
return _r1ToR1VariateChange;
}
/**
* Retrieve the R<sup>1</sup> Point Value Scale Function
*
* @return The R<sup>1</sup> Point Value Scale Function
*/
public org.drip.function.definition.R1ToR1 pointValueScale()
{
return _r1PointValueScale;
}
/**
* Retrieve the Quadrature Scale
*
* @return The Quadrature Scale
*/
public double quadratureScale()
{
return _quadratureScale;
}
}