RdToRd.java
package org.drip.function.definition;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
* Copyright (C) 2015 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>RdToRd</i> provides the evaluation of the R<sup>d</sup> To R<sup>d</sup> objective function and its
* derivatives for a specified set of R<sup>d</sup> variates. Default implementation of the derivatives are
* for non-analytical black box objective functions.
*
* <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/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/definition/README.md">Function Implementation Ancillary Support Objects</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class RdToRd {
private static final int QUADRATURE_SAMPLING = 10000;
protected org.drip.numerical.differentiation.DerivativeControl _dc = null;
protected RdToRd (
final org.drip.numerical.differentiation.DerivativeControl dc)
{
if (null == (_dc = dc)) _dc = new org.drip.numerical.differentiation.DerivativeControl();
}
/**
* Evaluate for the given Input R^d Variates
*
* @param adblVariate Array of Input R^d Variates
*
* @return The Output R^d Variates
*/
public abstract double[] evaluate (
final double[] adblVariate);
/**
* Calculate the Array of Differentials
*
* @param adblVariate Variate Array at which the derivative is to be calculated
* @param iVariateIndex Index of the Variate whose Derivative is to be computed
* @param iOrder Order of the derivative to be computed
*
* @return The Array of Differentials
*/
public org.drip.numerical.differentiation.Differential[] differential (
final double[] adblVariate,
final int iVariateIndex,
final int iOrder)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (adblVariate) || 0 >= iOrder) return null;
int iOutputDimension = -1;
double[] adblDerivative = null;
int iNumVariate = adblVariate.length;
double dblOrderedVariateInfinitesimal = 1.;
double dblVariateInfinitesimal = java.lang.Double.NaN;
if (iNumVariate <= iVariateIndex) return null;
try {
dblVariateInfinitesimal = _dc.getVariateInfinitesimal (adblVariate[iVariateIndex]);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
for (int i = 0; i <= iOrder; ++i) {
if (0 != i) dblOrderedVariateInfinitesimal *= (2. * dblVariateInfinitesimal);
double[] adblVariateIncremental = new double[iNumVariate];
for (int j = 0; i < iNumVariate; ++j)
adblVariateIncremental[j] = j == iVariateIndex ? adblVariate[j] + dblVariateInfinitesimal *
(iOrder - 2. * i) : adblVariate[j];
double[] adblValue = evaluate (adblVariateIncremental);
if (null == adblValue || 0 == (iOutputDimension = adblValue.length)) return null;
if (null == adblDerivative) {
adblDerivative = new double[iOutputDimension];
for (int j = 0; j < iOutputDimension; ++j)
adblDerivative[j] = 0.;
}
try {
for (int j = 0; j < iOutputDimension; ++j)
adblDerivative[j] += (i % 2 == 0 ? 1 : -1) * org.drip.numerical.common.NumberUtil.NCK
(iOrder, i) * adblValue[j];
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
org.drip.numerical.differentiation.Differential[] aDiff = new
org.drip.numerical.differentiation.Differential[iOutputDimension];
try {
for (int j = 0; j < iOutputDimension; ++j)
aDiff[j] = new org.drip.numerical.differentiation.Differential (dblOrderedVariateInfinitesimal,
adblDerivative[j]);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
return aDiff;
}
/**
* Calculate the Derivative Array as a double
*
* @param adblVariate Variate Array at which the derivative is to be calculated
* @param iVariateIndex Index of the Variate whose Derivative is to be computed
* @param iOrder Order of the derivative to be computed
*
* @return The Derivative Array
*/
public double[] derivative (
final double[] adblVariate,
final int iVariateIndex,
final int iOrder)
{
org.drip.numerical.differentiation.Differential[] aDiff = differential (adblVariate, iVariateIndex, iOrder);
if (null == aDiff) return null;
int iOutputDimension = aDiff.length;
double[] adblDerivative = new double[iOutputDimension];
if (0 == iOutputDimension) return null;
for (int i = 0; i < iOutputDimension; ++i)
adblDerivative[i] = aDiff[i].calcSlope (true);
return adblDerivative;
}
/**
* Integrate over the given Input Range Using Uniform Monte-Carlo
*
* @param adblLeftEdge Array of Input Left Edge
* @param adblRightEdge Array of Input Right Edge
*
* @return The Array Containing the Result of the Integration over the specified Range
*/
public double[] integrate (
final double[] adblLeftEdge,
final double[] adblRightEdge)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (adblLeftEdge) ||
!org.drip.numerical.common.NumberUtil.IsValid (adblRightEdge))
return null;
int iOutputDimension = -1;
double[] adblIntegrand = null;
int iNumVariate = adblLeftEdge.length;
double[] adblVariate = new double[iNumVariate];
double[] adblVariateWidth = new double[iNumVariate];
if (adblRightEdge.length != iNumVariate) return null;
for (int j = 0; j < iNumVariate; ++j)
adblVariateWidth[j] = adblRightEdge[j] - adblLeftEdge[j];
for (int i = 0; i < QUADRATURE_SAMPLING; ++i) {
for (int j = 0; j < iNumVariate; ++j)
adblVariate[j] = adblLeftEdge[j] + java.lang.Math.random() * adblVariateWidth[j];
double[] adblValue = evaluate (adblVariate);
if (null == adblValue || 0 == (iOutputDimension = adblValue.length)) return null;
if (null == adblIntegrand) adblIntegrand = new double[iOutputDimension];
for (int j = 0; j < iOutputDimension; ++j)
adblIntegrand[j] += adblValue[j];
}
for (int i = 0; i < iOutputDimension; ++i) {
for (int j = 0; j < iNumVariate; ++j)
adblIntegrand[i] = adblIntegrand[i] * adblVariateWidth[j];
adblIntegrand[i] /= QUADRATURE_SAMPLING;
}
return adblIntegrand;
}
}