QuadraticResampler.java

package org.drip.measure.discrete;

/*
 * -*- 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
 * 
 *  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>QuadraticResampler</i> Quadratically Re-samples the Input Points to Convert it to a Standard Normal.
 *
 *  <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/discrete/README.md">Antithetic, Quadratically Re-sampled, De-biased Distribution</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class QuadraticResampler {
    private boolean _bDebias = false;
    private boolean _bMeanCenter = false;

    /**
     * QuadraticResampler Constructor
     * 
     * @param bMeanCenter TRUE - The Sequence is to be Mean Centered
     * @param bDebias TRUE - Remove the Sampling Bias
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public QuadraticResampler (
        final boolean bMeanCenter,
        final boolean bDebias)
        throws java.lang.Exception
    {
        _bDebias = bDebias;
        _bMeanCenter = bMeanCenter;
    }

    /**
     * Indicate if the Sequence is to be Mean Centered
     * 
     * @return TRUE - The Sequence is to be Mean Centered
     */

    public boolean meanCenter()
    {
        return _bMeanCenter;
    }

    /**
     * Indicate if the Sampling Bias needs to be Removed
     * 
     * @return TRUE - The Sampling Bias needs to be Removed
     */

    public boolean debias()
    {
        return _bDebias;
    }

    /**
     * Transform the Input R^1 Sequence by applying Quadratic Sampling
     * 
     * @param adblSequence The Input R^1 Sequence
     * 
     * @return The Transformed Sequence
     */

    public double[] transform (
        final double[] adblSequence)
    {
        if (null == adblSequence) return null;

        double dblMean = 0.;
        double dblVariance = 0.;
        int iSequenceSize = adblSequence.length;
        double[] adblTransfomedSequence = 0 == iSequenceSize ? null : new double[iSequenceSize];

        if (0 == iSequenceSize) return null;

        if (_bMeanCenter) {
            for (int i = 0; i < iSequenceSize; ++i)
                dblMean += adblSequence[i];

            dblMean = dblMean / iSequenceSize;
        }

        for (int i = 0; i < iSequenceSize; ++i) {
            double dblOffset = adblSequence[i] - dblMean;
            dblVariance += dblOffset * dblOffset;
        }

        double dblStandardDeviation = java.lang.Math.sqrt (dblVariance / (_bDebias ? iSequenceSize - 1 :
            iSequenceSize));

        for (int i = 0; i < iSequenceSize; ++i)
            adblTransfomedSequence[i] = adblSequence[i] / dblStandardDeviation;

        return adblTransfomedSequence;
    }

    /**
     * Transform the Input R^d Sequence by applying Quadratic Sampling
     * 
     * @param aadblSequence The Input R^d Sequence
     * 
     * @return The Transformed Sequence
     */

    public double[][] transform (
        final double[][] aadblSequence)
    {
        double[][] aadblFlippedSequence = org.drip.numerical.linearalgebra.Matrix.Transpose (aadblSequence);

        if (null == aadblFlippedSequence) return null;

        int iDimension = aadblFlippedSequence.length;
        double[][] aadblFlippedTransformedSequence = new double[iDimension][];

        for (int i = 0; i < iDimension; ++i)
            aadblFlippedTransformedSequence[i] = transform (aadblFlippedSequence[i]);
        
        return org.drip.numerical.linearalgebra.Matrix.Transpose (aadblFlippedTransformedSequence);
    }
}