NormedRxToNormedRd.java

  1. package org.drip.spaces.rxtord;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>NormedRxToNormedRd</i> is the Abstract Class that exposes f : Normed R<sup>x</sup> (x .gte. 1) To
  83.  * Normed R<sup>d</sup> Function Space. The Reference we've used is:
  84.  *
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and the Approximation of Operators</i>
  89.  *              <b>Cambridge University Press</b> Cambridge UK 
  90.  *      </li>
  91.  *  </ul>
  92.  *
  93.  * <br><br>
  94.  *  <ul>
  95.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  96.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
  97.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/README.md">R<sup>1</sup> and R<sup>d</sup> Vector/Tensor Spaces (Validated and/or Normed), and Function Classes</a></li>
  98.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/rxtord/README.md">R<sup>x</sup> To R<sup>d</sup> Normed Function Spaces</a></li>
  99.  *  </ul>
  100.  * <br><br>
  101.  *
  102.  * @author Lakshmi Krishnamurthy
  103.  */

  105. public abstract class NormedRxToNormedRd {

  107.     /**
  108.      * Retrieve the Input Metric Vector Space
  109.      * 
  110.      * @return The Input Metric Vector Space
  111.      */

  113.     public abstract org.drip.spaces.metric.GeneralizedMetricVectorSpace inputMetricVectorSpace();

  115.     /**
  116.      * Retrieve the Output Metric Vector Space
  117.      * 
  118.      * @return The Output Metric Vector Space
  119.      */

  121.     public abstract org.drip.spaces.metric.RdNormed outputMetricVectorSpace();

  123.     /**
  124.      * Retrieve the Sample Supremum Norm Array
  125.      * 
  126.      * @param gvvi The Validated Vector Space Instance
  127.      * 
  128.      * @return The Sample Supremum Norm Array
  129.      */

  131.     public abstract double[] sampleSupremumNorm (
  132.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi);

  134.     /**
  135.      * Retrieve the Sample Metric Norm Array
  136.      * 
  137.      * @param gvvi The Validated Vector Space Instance
  138.      * 
  139.      * @return The Sample Metric Norm Array
  140.      */

  142.     public abstract double[] sampleMetricNorm (
  143.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi);

  145.     /**
  146.      * Retrieve the Sample Covering Number Array
  147.      * 
  148.      * @param gvvi The Validated Vector Space Instance
  149.      * @param dblCover The Cover
  150.      * 
  151.      * @return The Sample Covering Number Array
  152.      */

  154.     public double[] sampleCoveringNumber (
  155.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
  156.         final double dblCover)
  157.     {
  158.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;

  160.         double[] adblSampleMetricNorm = sampleMetricNorm (gvvi);

  162.         if (null == adblSampleMetricNorm) return null;

  164.         int iOutputDimensionality = adblSampleMetricNorm.length;
  165.         double[] adblSampleCoveringNumber = new double[iOutputDimensionality];

  167.         if (0 == iOutputDimensionality) return null;

  169.         double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());

  171.         for (int i = 0; i < iOutputDimensionality; ++i)
  172.             adblSampleCoveringNumber[i] = adblSampleMetricNorm[i] / dblCoverBallVolume;

  174.         return adblSampleCoveringNumber;
  175.     }

  177.     /**
  178.      * Retrieve the Sample Supremum Covering Number Array
  179.      * 
  180.      * @param gvvi The Validated Vector Space Instance
  181.      * @param dblCover The Cover
  182.      * 
  183.      * @return The Sample Supremum Covering Number Array
  184.      */

  186.     public double[] sampleSupremumCoveringNumber (
  187.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
  188.         final double dblCover)
  189.     {
  190.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;

  192.         double[] adblSampleSupremumNorm = sampleSupremumNorm (gvvi);

  194.         if (null == adblSampleSupremumNorm) return null;

  196.         int iOutputDimensionality = adblSampleSupremumNorm.length;
  197.         double[] adblSampleSupremumCoveringNumber = new double[iOutputDimensionality];

  199.         if (0 == iOutputDimensionality) return null;

  201.         double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());

  203.         for (int i = 0; i < iOutputDimensionality; ++i)
  204.             adblSampleSupremumCoveringNumber[i] = adblSampleSupremumNorm[i] / dblCoverBallVolume;

  206.         return adblSampleSupremumCoveringNumber;
  207.     }

  209.     /**
  210.      * Retrieve the Population ESS (Essential Spectrum) Array
  211.      * 
  212.      * @return The Population ESS (Essential Spectrum) Array
  213.      */

  215.     public abstract double[] populationESS();

  217.     /**
  218.      * Retrieve the Population Metric Norm Array
  219.      * 
  220.      * @return The Population Metric Norm Array
  221.      */

  223.     public abstract double[] populationMetricNorm();

  225.     /**
  226.      * Retrieve the Population Supremum Norm Array
  227.      * 
  228.      * @return The Population Supremum Norm Array
  229.      */

  231.     public double[] populationSupremumNorm()
  232.     {
  233.         return populationMetricNorm();
  234.     }

  236.     /**
  237.      * Retrieve the Population Covering Number Array
  238.      * 
  239.      * @param dblCover The Cover
  240.      * 
  241.      * @return The Population Covering Number Array
  242.      */

  244.     public double[] populationCoveringNumber (
  245.         final double dblCover)
  246.     {
  247.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;

  249.         double[] adblPopulationMetricNorm = populationMetricNorm();

  251.         if (null == adblPopulationMetricNorm) return null;

  253.         int iOutputDimensionality = adblPopulationMetricNorm.length;
  254.         double[] adblPopulationCoveringNumber = new double[iOutputDimensionality];

  256.         if (0 == iOutputDimensionality) return null;

  258.         double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());

  260.         for (int i = 0; i < iOutputDimensionality; ++i)
  261.             adblPopulationCoveringNumber[i] = adblPopulationMetricNorm[i] / dblCoverBallVolume;

  263.         return adblPopulationCoveringNumber;
  264.     }

  266.     /**
  267.      * Retrieve the Population Supremum Covering Number Array
  268.      * 
  269.      * @param dblCover The Cover
  270.      * 
  271.      * @return The Population Supremum Covering Number Array
  272.      */

  274.     public double[] populationSupremumCoveringNumber (
  275.         final double dblCover)
  276.     {
  277.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover) return null;

  279.         double[] adblPopulationSupremumNorm = populationSupremumNorm();

  281.         if (null == adblPopulationSupremumNorm) return null;

  283.         int iOutputDimensionality = adblPopulationSupremumNorm.length;
  284.         double[] adblPopulationSupremumCoveringNumber = new double[iOutputDimensionality];

  286.         if (0 == iOutputDimensionality) return null;

  288.         double dblCoverBallVolume = java.lang.Math.pow (dblCover, outputMetricVectorSpace().pNorm());

  290.         for (int i = 0; i < iOutputDimensionality; ++i)
  291.             adblPopulationSupremumCoveringNumber[i] = adblPopulationSupremumNorm[i] / dblCoverBallVolume;

  293.         return adblPopulationSupremumCoveringNumber;
  294.     }
  295. }
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