Polynomial.java
package org.drip.function.r1tor1;
/*
* -*- 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>Polynomial</i> provides the evaluation of the n<sup>th</sup> order Polynomial and its derivatives for a
* specified variate.
*
* <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/r1tor1/README.md">Built-in R<sup>1</sup> To R<sup>1</sup> Functions</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class Polynomial extends org.drip.function.definition.R1ToR1 {
private int _iDegree = -1;
/**
* Polynomial constructor
*
* @param iDegree Degree of the Polynomial
*
* @throws java.lang.Exception Thrown if the input is invalid
*/
public Polynomial (
final int iDegree)
throws java.lang.Exception
{
super (null);
if (0 > (_iDegree = iDegree)) throw new java.lang.Exception ("Polynomial ctr: Invalid Inputs");
}
@Override public double evaluate (
final double dblVariate)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblVariate))
throw new java.lang.Exception ("Polynomial::evaluate => Invalid Inputs");
return java.lang.Math.pow (dblVariate, _iDegree);
}
@Override public double derivative (
final double dblVariate,
final int iOrder)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblVariate) || 0 > iOrder)
throw new java.lang.Exception ("Polynomial::derivative => Invalid Inputs");
return iOrder > _iDegree ? 0. : java.lang.Math.pow (dblVariate, _iDegree - iOrder) *
org.drip.numerical.common.NumberUtil.NPK (_iDegree, _iDegree - iOrder);
}
@Override public double integrate (
final double dblBegin,
final double dblEnd)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblBegin) || !org.drip.numerical.common.NumberUtil.IsValid
(dblEnd))
throw new java.lang.Exception ("Polynomial::integrate => Invalid Inputs");
return (java.lang.Math.pow (dblEnd, _iDegree + 1) - java.lang.Math.pow (dblBegin, _iDegree + 1)) /
(_iDegree + 1);
}
/**
* Retrieve the degree of the polynomial
*
* @return Degree of the polynomial
*/
public double getDegree()
{
return _iDegree;
}
public static final void main (
final java.lang.String[] astrArgs)
throws java.lang.Exception
{
Polynomial poly = new Polynomial (4);
System.out.println ("Poly[0.0] = " + poly.evaluate (0.0));
System.out.println ("Poly[0.5] = " + poly.evaluate (0.5));
System.out.println ("Poly[1.0] = " + poly.evaluate (1.0));
System.out.println ("Deriv[0.0] = " + poly.derivative (0.0, 3));
System.out.println ("Deriv[0.5] = " + poly.derivative (0.5, 3));
System.out.println ("Deriv[1.0] = " + poly.derivative (1.0, 3));
}
}