PrincipalFactorSequenceGenerator.java

package org.drip.sequence.random;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * 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 risk, transaction costs, exposure, margin
 *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
 *      FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three main modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning Library
 *  - Numerical Optimizer Library
 *  - Machine Learning Library
 *  - Spline Builder Library
 * 
 *  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
 *  - 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>PrincipalFactorSequenceGenerator</i> implements the Principal Factors Based Multivariate Random
 * Sequence Generator Functionality.
 * 
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence">Sequence</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence/random">Random</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class PrincipalFactorSequenceGenerator extends org.drip.sequence.random.MultivariateSequenceGenerator
{
    private double[][] _aadblFactor = null;
    private double[] _adblFactorWeight = null;

    /**
     * PrincipalFactorSequenceGenerator Constructor
     * 
     * @param aUSG Array of Univariate Sequence Generators
     * @param aadblCorrelation The Correlation Matrix
     * @param iNumFactor Number of Factors
     * 
     * @throws java.lang.Exception Thrown if the Inputs are invalid
     */

    public PrincipalFactorSequenceGenerator (
        final org.drip.sequence.random.UnivariateSequenceGenerator[] aUSG,
        final double[][] aadblCorrelation,
        final int iNumFactor)
        throws java.lang.Exception
    {
        super (aUSG, aadblCorrelation);

        int iNumVariate = aUSG.length;

        if (0 >= iNumFactor || iNumFactor > iNumVariate)
            throw new java.lang.Exception ("PrincipalFactorSequenceGenerator ctr: Invalid Inputs");

        org.drip.numerical.eigen.QREigenComponentExtractor qrece = new
            org.drip.numerical.eigen.QREigenComponentExtractor (80, 0.00001);

        org.drip.numerical.eigen.EigenComponent[] aEC = qrece.orderedEigenComponentArray (aadblCorrelation);

        if (null == aEC || 0 == aEC.length)
            throw new java.lang.Exception ("PrincipalFactorSequenceGenerator ctr: Invalid Inputs");

        double dblNormalizer = 0.;
        _adblFactorWeight = new double[iNumFactor];
        _aadblFactor = new double[iNumFactor][iNumVariate];

        for (int i = 0; i < iNumFactor; ++i) {
            for (int j = 0; j < iNumVariate; ++j)
                _aadblFactor[i] = aEC[i].eigenVector();

            _adblFactorWeight[i] = aEC[i].eigenValue();

            dblNormalizer += _adblFactorWeight[i] * _adblFactorWeight[i];
        }

        dblNormalizer = java.lang.Math.sqrt (dblNormalizer);

        for (int i = 0; i < iNumFactor; ++i)
            _adblFactorWeight[i] /= dblNormalizer;
    }

    /**
     * Retrieve the Number of Factors
     * 
     * @return The Number of Factors
     */

    public int numFactor()
    {
        return _adblFactorWeight.length;
    }

    /**
     * Retrieve the Principal Component Factor Array
     * 
     * @return The Principal Component Factor Array
     */

    public double[][] factors()
    {
        return _aadblFactor;
    }

    /**
     * Retrieve the Array of Factor Weights
     * 
     * @return The Array of Factor Weights
     */

    public double[] factorWeight()
    {
        return _adblFactorWeight;
    }

    @Override public double[] random()
    {
        double[] adblBaseRandom = super.random();

        int iNumVariate = _aadblFactor[0].length;
        int iNumFactor = _adblFactorWeight.length;
        double[] adblRandom = new double[iNumFactor];

        if (iNumFactor == iNumVariate) return adblBaseRandom;

        for (int i = 0; i < iNumFactor; ++i) {
            adblRandom[i] = 0.;

            for (int j = 0; j < iNumVariate; ++j)
                adblRandom[i] += _aadblFactor[i][j] * adblBaseRandom[j];
        }

        return adblRandom;
    }
}