ScaleSensitiveFunction.java

package org.drip.sample.coveringnumber;

import org.drip.function.definition.R1ToR1;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.spaces.cover.ScaleSensitiveCoveringBounds;

/*
 * -*- 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
 * 
 *  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>ScaleSensitiveFunction</i> demonstrates Computation of the Restricted Covers, Restricted Probability
 * Bounds, the Lower Bounds, and the Upper Bounds for Functions that are absolutely Bounded.
 *  
 * <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/StatisticalLearningLibrary.md">Statistical Learning</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/coveringnumber/README.md">R<sup>d</sup>Agnostic Function Covering Number Bounds</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class ScaleSensitiveFunction {

    public static final void main (
        final String[] astrArgs)
        throws Exception
    {
        EnvManager.InitEnv ("");

        final int iSampleSize = 10;

        R1ToR1 auFatShatter = new R1ToR1 (null) {
            @Override public double evaluate (
                final double dblX)
                throws Exception
            {
                return iSampleSize;
            }
        };

        ScaleSensitiveCoveringBounds sscn = new ScaleSensitiveCoveringBounds (
            auFatShatter,
            iSampleSize
        );

        double[] adblCover = new double[] {
            500., 600., 700., 800., 900., 960.
        };

        System.out.println ("\n\t||------------------------------------------------||");

        System.out.println ("\t||    Scale    Sensitive    Covering   Numbers    ||");

        System.out.println ("\t||    -----    ---------    --------   -------    ||");

        System.out.println ("\t|| L -> R:                                        ||");

        System.out.println ("\t||   Sample Size Lower Bound                      ||");

        System.out.println ("\t||   Restricted Subset Cardinality                ||");

        System.out.println ("\t||   Probability of the Cover Weight Upper Bound  ||");

        System.out.println ("\t||   Log Log Covering Number Lower Bound          ||");

        System.out.println ("\t||   Log Log Covering Number Upper Bound          ||");

        System.out.println ("\t||------------------------------------------------||");

        for (double dblCover : adblCover)
            System.out.println ("\t|| [" + FormatUtil.FormatDouble (dblCover, 3, 0, 1.) + "] => " +
                FormatUtil.FormatDouble (sscn.sampleSizeLowerBound (dblCover), 1, 1, 1.) + " |" +
                FormatUtil.FormatDouble (sscn.restrictedSubsetCardinality (dblCover), 3, 0, 1.) + " | " +
                FormatUtil.FormatDouble (sscn.upperProbabilityBoundWeight (dblCover), 5, 0, 1.) + " | " +
                FormatUtil.FormatDouble (Math.log (sscn.logLowerBound (dblCover)), 1, 2, 1.) + " -> " +
                FormatUtil.FormatDouble (Math.log (sscn.logUpperBound (dblCover)), 1, 2, 1.) + " ||"
            );

        System.out.println ("\t||------------------------------------------------||");

        EnvManager.TerminateEnv();
    }
}