AkimaLocalC1Generator.java
package org.drip.spline.pchip;
/*
* -*- 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
* Copyright (C) 2014 Lakshmi Krishnamurthy
* Copyright (C) 2013 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>AkimaLocalC1Generator</i> generates the local control C1 Slope using the Akima Cubic Algorithm.
*
* <br><br>
* <ul>
* <li>
* Akima (1970): A New Method of Interpolation and Smooth Curve Fitting based on Local Procedures
* <i>Journal of the Association for the Computing Machinery</i> <b>17 (4)</b> 589-602
* </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/SplineBuilderLibrary.md">Spline Builder Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/README.md">Basis Splines and Linear Compounders across a Broad Family of Spline Basis Functions</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/pchip/README.md">Monotone Convex Themed PCHIP Splines</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class AkimaLocalC1Generator {
private double[] _adblResponseValue = null;
private double[] _adblPredictorOrdinate = null;
private double[] _adblExtendedResponseValue = null;
private double[] _adblExtendedPredictorOrdinate = null;
/**
* Construct an Instance of AkimaLocalC1Generator from the Array of the supplied Predictor Ordinates
* and the Response Values
*
* @param adblPredictorOrdinate Array of the Predictor Ordinates
* @param adblResponseValue Array of the Response Values
*
* @return Instance of AkimaLocalC1Generator
*/
public static final AkimaLocalC1Generator Create (
final double[] adblPredictorOrdinate,
final double[] adblResponseValue)
{
AkimaLocalC1Generator alcr = null;
try {
alcr = new AkimaLocalC1Generator (adblPredictorOrdinate, adblResponseValue);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
return alcr.extendPredictorOrdinate() && alcr.extendResponseValue() ? alcr : null;
}
private AkimaLocalC1Generator (
final double[] adblPredictorOrdinate,
final double[] adblResponseValue)
throws java.lang.Exception
{
if (null == (_adblPredictorOrdinate = adblPredictorOrdinate) || null == (_adblResponseValue =
adblResponseValue))
throw new java.lang.Exception ("AkimaLocalC1Generator ctr: Invalid Inputs");
int iNumPredictorOrdinate = _adblPredictorOrdinate.length;
if (2 >= iNumPredictorOrdinate || iNumPredictorOrdinate != _adblResponseValue.length)
throw new java.lang.Exception ("AkimaLocalC1Generator ctr: Invalid Inputs");
}
private boolean extendPredictorOrdinate()
{
int iNumPredictorOrdinate = _adblPredictorOrdinate.length;
int iNumExtendedPredictorOrdinate = iNumPredictorOrdinate + 4;
_adblExtendedPredictorOrdinate = new double[iNumExtendedPredictorOrdinate];
for (int i = 0; i < iNumExtendedPredictorOrdinate; ++i) {
if (2 <= i && iNumExtendedPredictorOrdinate - 3 >= i)
_adblExtendedPredictorOrdinate[i] = _adblPredictorOrdinate[i - 2];
}
double dblSkippedLeftPredictorWidth = _adblPredictorOrdinate[2] - _adblPredictorOrdinate[0];
_adblExtendedPredictorOrdinate[0] = _adblPredictorOrdinate[0] - dblSkippedLeftPredictorWidth;
_adblExtendedPredictorOrdinate[1] = _adblPredictorOrdinate[1] - dblSkippedLeftPredictorWidth;
double dblSkippedRightPredictorWidth = _adblPredictorOrdinate[iNumPredictorOrdinate - 1] -
_adblPredictorOrdinate[iNumPredictorOrdinate - 3];
_adblExtendedPredictorOrdinate[iNumExtendedPredictorOrdinate - 2] =
_adblPredictorOrdinate[iNumPredictorOrdinate - 2] + dblSkippedRightPredictorWidth;
_adblExtendedPredictorOrdinate[iNumExtendedPredictorOrdinate - 1] =
_adblPredictorOrdinate[iNumPredictorOrdinate - 1] + dblSkippedRightPredictorWidth;
return true;
}
private boolean setExtendedResponseValue (
final int i,
final boolean bRight)
{
if (bRight) {
_adblExtendedResponseValue[i] = 2. * (_adblExtendedResponseValue[i - 1] -
_adblExtendedResponseValue[i - 2]) / (_adblExtendedPredictorOrdinate[i - 1] -
_adblExtendedPredictorOrdinate[i - 2]) - ((_adblExtendedResponseValue[i - 2] -
_adblExtendedResponseValue[i - 3]) / (_adblExtendedPredictorOrdinate[i - 2] -
_adblExtendedPredictorOrdinate[i - 3]));
_adblExtendedResponseValue[i] = _adblExtendedResponseValue[i] * (_adblExtendedResponseValue[i] -
_adblExtendedResponseValue[i - 1]) + _adblExtendedResponseValue[i - 1];
} else {
_adblExtendedResponseValue[i] = 2. * (_adblExtendedResponseValue[i + 2] -
_adblExtendedResponseValue[i + 1]) / (_adblExtendedPredictorOrdinate[i + 2] -
_adblExtendedPredictorOrdinate[i + 1]) - ((_adblExtendedResponseValue[i + 3] -
_adblExtendedResponseValue[i + 2]) / (_adblExtendedPredictorOrdinate[i + 3] -
_adblExtendedPredictorOrdinate[i + 2]));
_adblExtendedResponseValue[i] = _adblExtendedResponseValue[i + 1] - _adblExtendedResponseValue[i]
* (_adblExtendedResponseValue[i + 1] - _adblExtendedResponseValue[i]);
}
return true;
}
private boolean extendResponseValue()
{
int iNumResponseValue = _adblResponseValue.length;
int iNumExtendedResponseValue = iNumResponseValue + 4;
_adblExtendedResponseValue = new double[iNumExtendedResponseValue];
for (int i = 0; i < iNumExtendedResponseValue; ++i) {
if (2 <= i && iNumExtendedResponseValue - 3 >= i)
_adblExtendedResponseValue[i] = _adblResponseValue[i - 2];
}
return setExtendedResponseValue (1, false) && setExtendedResponseValue (0, false) &&
setExtendedResponseValue (iNumExtendedResponseValue - 2, true) && setExtendedResponseValue
(iNumExtendedResponseValue - 1, true) ? true : false;
}
public double[] C1()
{
int iNumPredictorOrdinate = _adblPredictorOrdinate.length;
double[] adblC1 = new double[iNumPredictorOrdinate];
double[] adblExtendedSlope = new double[iNumPredictorOrdinate + 3];
for (int i = 0; i < iNumPredictorOrdinate + 3; ++i)
adblExtendedSlope[i] = (_adblExtendedResponseValue[i + 1] - _adblExtendedResponseValue[i]) /
(_adblExtendedPredictorOrdinate[i + 1] - _adblExtendedPredictorOrdinate[i]);
for (int i = 0; i < iNumPredictorOrdinate; ++i) {
double dblSlope10 = java.lang.Math.abs (adblExtendedSlope[i + 1] - adblExtendedSlope[i]);
double dblSlope32 = java.lang.Math.abs (adblExtendedSlope[i + 3] - adblExtendedSlope[i + 2]);
if (0. == dblSlope10 && 0. == dblSlope32)
adblC1[i] = 0.5 * (adblExtendedSlope[i + 1] + adblExtendedSlope[i + 2]);
else
adblC1[i] = (dblSlope32 * adblExtendedSlope[i + 1] + dblSlope10 * adblExtendedSlope[i + 2]) /
(dblSlope10 + dblSlope32);
}
return adblC1;
}
}