NormedRxToNormedR1.java

  1. package org.drip.spaces.rxtor1;

  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>NormedRxToNormedR1</i> is the Abstract Class that exposes f : Normed R<sup>x</sup> (x .gte. 1) To
  83.  * Normed R<sup>1</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/rxtor1/README.md">R<sup>x</sup> To R<sup>1</sup> Normed Function Spaces</a></li>
  99.  *  </ul>
  100.  * <br><br>
  101.  *
  102.  * @author Lakshmi Krishnamurthy
  103.  */

  105. public abstract class NormedRxToNormedR1 {

  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.R1Normed outputMetricVectorSpace();

  123.     /**
  124.      * Retrieve the Sample Supremum Norm
  125.      * 
  126.      * @param gvvi The Validated Vector Space Instance
  127.      * 
  128.      * @return The Sample Supremum Norm
  129.      * 
  130.      * @throws java.lang.Exception Thrown if the Supremum Norm cannot be computed
  131.      */

  133.     public abstract double sampleSupremumNorm (
  134.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  135.         throws java.lang.Exception;

  137.     /**
  138.      * Retrieve the Sample Metric Norm
  139.      * 
  140.      * @param gvvi The Validated Vector Space Instance
  141.      * 
  142.      * @return The Sample Metric Norm
  143.      * 
  144.      * @throws java.lang.Exception Thrown if the Sample Metric Norm cannot be computed
  145.      */

  147.     public abstract double sampleMetricNorm (
  148.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  149.         throws java.lang.Exception;

  151.     /**
  152.      * Retrieve the Sample Covering Number
  153.      * 
  154.      * @param gvvi The Validated Vector Space Instance
  155.      * @param dblCover The Cover
  156.      * 
  157.      * @return The Sample Covering Number
  158.      * 
  159.      * @throws java.lang.Exception Thrown if the Sample Covering Number cannot be computed
  160.      */

  162.     public double sampleCoveringNumber (
  163.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
  164.         final double dblCover)
  165.         throws java.lang.Exception
  166.     {
  167.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover)
  168.             throw new java.lang.Exception ("NormedRxToNormedR1::sampleCoveringNumber => Invalid Inputs");

  170.         return sampleMetricNorm (gvvi) / dblCover;
  171.     }

  173.     /**
  174.      * Retrieve the Sample Supremum Covering Number
  175.      * 
  176.      * @param gvvi The Validated Vector Space Instance
  177.      * @param dblCover The Cover
  178.      * 
  179.      * @return The Sample Supremum Covering Number
  180.      * 
  181.      * @throws java.lang.Exception Thrown if the Sample Covering Number cannot be computed
  182.      */

  184.     public double sampleSupremumCoveringNumber (
  185.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
  186.         final double dblCover)
  187.         throws java.lang.Exception
  188.     {
  189.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover)
  190.             throw new java.lang.Exception
  191.                 ("NormedRxToNormedR1::sampleSupremumCoveringNumber => Invalid Inputs");

  193.         return sampleSupremumNorm (gvvi) / dblCover;
  194.     }

  196.     /**
  197.      * Retrieve the Population ESS (Essential Spectrum)
  198.      * 
  199.      * @return The Population ESS (Essential Spectrum)
  200.      * 
  201.      * @throws java.lang.Exception Thrown if the Population ESS (Essential Spectrum) cannot be computed
  202.      */

  204.     public abstract double populationESS()
  205.         throws java.lang.Exception;

  207.     /**
  208.      * Retrieve the Population Metric Norm
  209.      * 
  210.      * @return The Population Metric Norm
  211.      * 
  212.      * @throws java.lang.Exception Thrown if the Population Metric Norm cannot be computed
  213.      */

  215.     public abstract double populationMetricNorm()
  216.         throws java.lang.Exception;

  218.     /**
  219.      * Retrieve the Population Supremum Metric Norm
  220.      * 
  221.      * @return The Population Supremum Metric Norm
  222.      * 
  223.      * @throws java.lang.Exception Thrown if the Population Supremum Metric Norm cannot be computed
  224.      */

  226.     public double populationSupremumMetricNorm()
  227.         throws java.lang.Exception
  228.     {
  229.         return populationESS();
  230.     }

  232.     /**
  233.      * Retrieve the Population Covering Number
  234.      * 
  235.      * @param dblCover The Cover
  236.      * 
  237.      * @return The Population Covering Number
  238.      * 
  239.      * @throws java.lang.Exception Thrown if the Population Covering Number cannot be computed
  240.      */

  242.     public double populationCoveringNumber (
  243.         final double dblCover)
  244.         throws java.lang.Exception
  245.     {
  246.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover)
  247.             throw new java.lang.Exception ("NormedRxToNormedR1::populationCoveringNumber => Invalid Inputs");

  249.         return populationMetricNorm() / dblCover;
  250.     }

  252.     /**
  253.      * Retrieve the Population Supremum Covering Number
  254.      * 
  255.      * @param dblCover The Cover
  256.      * 
  257.      * @return The Population Supremum Covering Number
  258.      * 
  259.      * @throws java.lang.Exception Thrown if the Population Supremum Covering Number cannot be computed
  260.      */

  262.     public double populationSupremumCoveringNumber (
  263.         final double dblCover)
  264.         throws java.lang.Exception
  265.     {
  266.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblCover) || 0. >= dblCover)
  267.             throw new java.lang.Exception
  268.                 ("NormedRxToNormedR1::populationSupremumCoveringNumber => Invalid Inputs");

  270.         return populationSupremumMetricNorm() / dblCover;
  271.     }
  272. }
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