R1PiecewiseLinear.java
package org.drip.measure.lebesgue;
/*
* -*- 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
*
* 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>R1PiecewiseLinear</i> implements the Piecewise Linear R<sup>1</sup> Distributions. It exports the
* Methods corresponding to the R<sup>1</sup> Lebesgue Base Class.
*
* <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/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/lebesgue/README.md">Uniform Piece-wise Lebesgue Measure</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1PiecewiseLinear extends org.drip.measure.lebesgue.R1Uniform {
private double[] _adblPiecewiseDensity = null;
private double[] _adblPredictorOrdinate = null;
/**
* Calibrate an R1PiecewiseLinear Lebesgue Instance
*
* @param dblLeftPredictorOrdinateEdge Left Predictor Ordinate Edge
* @param dblRightPredictorOrdinateEdge Right Predictor Ordinate Edge
* @param adblPredictorOrdinate Array of Intermediate Predictor Ordinates
* @param adblCumulativeProbability Array of corresponding Cumulative Probabilities
*
* @return The R1PiecewiseLinearLebesgue Instance
*/
public static final R1PiecewiseLinear Standard (
final double dblLeftPredictorOrdinateEdge,
final double dblRightPredictorOrdinateEdge,
final double[] adblPredictorOrdinate,
final double[] adblCumulativeProbability)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblLeftPredictorOrdinateEdge) ||
!org.drip.numerical.common.NumberUtil.IsValid (dblRightPredictorOrdinateEdge) ||
dblLeftPredictorOrdinateEdge >= dblRightPredictorOrdinateEdge || null ==
adblPredictorOrdinate || null == adblCumulativeProbability)
return null;
int iNumPredictorOrdinate = adblPredictorOrdinate.length;
double[] adblPiecewiseDensity = new double[iNumPredictorOrdinate + 1];
if (0 == iNumPredictorOrdinate || iNumPredictorOrdinate != adblCumulativeProbability.length)
return null;
for (int i = 0; i <= iNumPredictorOrdinate; ++i) {
double dblLeftPredictorOrdinate = 0 == i ? dblLeftPredictorOrdinateEdge :
adblPredictorOrdinate[i - 1];
if (!org.drip.numerical.common.NumberUtil.IsValid (dblLeftPredictorOrdinate) ||
dblLeftPredictorOrdinate < dblLeftPredictorOrdinateEdge)
return null;
double dblRightPredictorOrdinate = iNumPredictorOrdinate == i ? dblRightPredictorOrdinateEdge :
adblPredictorOrdinate[i];
if (!org.drip.numerical.common.NumberUtil.IsValid (dblRightPredictorOrdinate) ||
dblRightPredictorOrdinate <= dblLeftPredictorOrdinate || dblRightPredictorOrdinate >
dblRightPredictorOrdinateEdge)
return null;
double dblLeftCumulativeProbability = 0 == i ? 0. : adblCumulativeProbability[i - 1];
double dblRightCumulativeProbability = iNumPredictorOrdinate == i ? 1. :
adblCumulativeProbability[i];
adblPiecewiseDensity[i] = 2. * (dblRightCumulativeProbability - dblLeftCumulativeProbability) /
(dblRightPredictorOrdinate * dblRightPredictorOrdinate - dblLeftPredictorOrdinate *
dblLeftPredictorOrdinate);
}
try {
return new R1PiecewiseLinear (dblLeftPredictorOrdinateEdge,
dblRightPredictorOrdinateEdge, adblPredictorOrdinate, adblPiecewiseDensity);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* R1PiecewiseLinear Constructor
*
* @param dblLeftPredictorOrdinateEdge Left Predictor Ordinate Edge
* @param dblRightPredictorOrdinateEdge Right Predictor Ordinate Edge
* @param adblPredictorOrdinate Array of Intermediate Predictor Ordinates
* @param adblPiecewiseDensity Array of corresponding Piece-wise Densities
*
* @throws java.lang.Exception Thrown if the Inputs are invalid
*/
public R1PiecewiseLinear (
final double dblLeftPredictorOrdinateEdge,
final double dblRightPredictorOrdinateEdge,
final double[] adblPredictorOrdinate,
final double[] adblPiecewiseDensity)
throws java.lang.Exception
{
super (dblLeftPredictorOrdinateEdge, dblRightPredictorOrdinateEdge);
if (null == (_adblPredictorOrdinate = adblPredictorOrdinate) || null == (_adblPiecewiseDensity =
adblPiecewiseDensity))
throw new java.lang.Exception ("R1PiecewiseLinear Constructor: Invalid Inputs");
int iNumPredictorOrdinate = _adblPredictorOrdinate.length;
if (0 == iNumPredictorOrdinate || iNumPredictorOrdinate + 1 != _adblPiecewiseDensity.length)
throw new java.lang.Exception ("R1PiecewiseLinear Constructor: Invalid Inputs");
}
/**
* Retrieve the Array of Predictor Ordinates
*
* @return The Array of Predictor Ordinates
*/
public double[] predictorOrdinates()
{
return _adblPredictorOrdinate;
}
/**
* Retrieve the Array of Piecewise Densities
*
* @return The Array of Piecewise Densities
*/
public double[] piecewiseDensities()
{
return _adblPiecewiseDensity;
}
@Override public double cumulative (
final double dblX)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
throw new java.lang.Exception ("R1PiecewiseLinear::cumulative => Invalid Inputs");
double dblLeftEdge = leftEdge();
double dblRightEdge = rightEdge();
if (dblX <= dblLeftEdge) return 0.;
if (dblX >= dblRightEdge) return 1.;
int iSegmentIndex = 0;
double dblSegmentLeft = dblLeftEdge;
double dblCumulativeProbability = 0.;
int iMaxSegmentIndex = _adblPiecewiseDensity.length - 1;
while (iSegmentIndex < iMaxSegmentIndex) {
double dblSegmentRight = _adblPredictorOrdinate[iSegmentIndex];
if (dblX >= dblSegmentLeft && dblX <= dblSegmentRight)
return dblCumulativeProbability + 0.5 * _adblPiecewiseDensity[iSegmentIndex] * (dblX * dblX -
dblSegmentLeft * dblSegmentLeft);
dblCumulativeProbability += 0.5 * _adblPiecewiseDensity[iSegmentIndex] * (dblSegmentRight *
dblSegmentRight - dblSegmentLeft * dblSegmentLeft);
dblSegmentLeft = dblSegmentRight;
++iSegmentIndex;
}
return dblCumulativeProbability + 0.5 * _adblPiecewiseDensity[iMaxSegmentIndex] * (dblX * dblX -
dblRightEdge * dblRightEdge);
}
@Override public double invCumulative (
final double dblY)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblY) || dblY < 0. || dblY > 1.)
throw new java.lang.Exception ("R1PiecewiseLinear::invCumulative => Invalid inputs");
org.drip.function.definition.R1ToR1 r1ToR1CumulativeProbability = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblX)
throws java.lang.Exception
{
return cumulative (dblX);
}
};
org.drip.function.r1tor1solver.FixedPointFinderOutput fpfo = new
org.drip.function.r1tor1solver.FixedPointFinderBracketing (dblY, r1ToR1CumulativeProbability,
null, org.drip.function.r1tor1solver.VariateIteratorPrimitive.BISECTION, true).findRoot();
if (null == fpfo || !fpfo.containsRoot())
throw new java.lang.Exception ("R1PiecewiseLinear::invCumulative => No roots");
return fpfo.getRoot();
}
@Override public double density (
final double dblX)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
throw new java.lang.Exception ("R1PiecewiseLinear::density => Invalid Inputs");
if (dblX <= leftEdge() || dblX >= rightEdge()) return 0.;
int iSegmentIndex = 0;
int iMaxSegmentIndex = _adblPiecewiseDensity.length - 1;
while (iSegmentIndex < iMaxSegmentIndex) {
if (dblX >= _adblPredictorOrdinate[iSegmentIndex] && dblX <=
_adblPredictorOrdinate[iSegmentIndex + 1])
break;
++iSegmentIndex;
}
return _adblPiecewiseDensity[iSegmentIndex] * dblX;
}
@Override public org.drip.numerical.common.Array2D histogram()
{
double dblLeftEdge = leftEdge();
double[] adblX = new double[GRID_WIDTH];
double[] adblY = new double[GRID_WIDTH];
double dblWidth = (rightEdge() - dblLeftEdge) / GRID_WIDTH;
for (int i = 0; i < GRID_WIDTH; ++i) {
adblX[i] = dblLeftEdge + (i + 1) * dblWidth;
try {
adblY[i] = incremental (adblX[i] - dblWidth, adblX[i]);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
return org.drip.numerical.common.Array2D.FromArray (adblX, adblY);
}
}