NormedRxToNormedRxFinite.java

  1. package org.drip.spaces.functionclass;

  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>NormedRxToNormedRxFinite</i> exposes the Space of Functions that are a Transform from the Normed
  83.  * R<sup>x</sup> To Normed R<sup>d</sup> Spaces. The References are:
  84.  *
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of
  89.  *              Operators in Banach Spaces <i>Annals of the Fourier Institute</i> <b>35 (3)</b> 79-118
  90.  *      </li>
  91.  *      <li>
  92.  *          Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and the Approximation of Operators</i>
  93.  *              <b>Cambridge University Press</b> Cambridge UK 
  94.  *      </li>
  95.  *      <li>
  96.  *          Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function
  97.  *              Classes, in: <i>Proceedings of the 13th Annual Conference on Computational Learning
  98.  *                  Theory</i> <b>ACM</b> New York
  99.  *      </li>
  100.  *  </ul>
  101.  *
  102.  * <br><br>
  103.  *  <ul>
  104.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  105.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
  106.  *      <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>
  107.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/functionclass/README.md">Normed Finite Spaces Function Class</a></li>
  108.  *  </ul>
  109.  * <br><br>
  110.  *
  111.  * @author Lakshmi Krishnamurthy
  112.  */

  114. public abstract class NormedRxToNormedRxFinite {
  115.     private double _dblMaureyConstant = java.lang.Double.NaN;

  117.     protected NormedRxToNormedRxFinite (
  118.         final double dblMaureyConstant)
  119.         throws java.lang.Exception
  120.     {
  121.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblMaureyConstant = dblMaureyConstant) || 0. >=
  122.             _dblMaureyConstant)
  123.             throw new java.lang.Exception ("NormedRxToNormedRxFinite ctr => Invalid Inputs");
  124.     }

  126.     /**
  127.      * Retrieve the Input Vector Space
  128.      * 
  129.      * @return The Input Vector Space
  130.      */

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

  134.     /**
  135.      * Retrieve the Output Vector Space
  136.      * 
  137.      * @return The Output Vector Space
  138.      */

  140.     public abstract org.drip.spaces.metric.GeneralizedMetricVectorSpace outputMetricVectorSpace();

  142.     /**
  143.      * Compute the Operator Population Metric Norm
  144.      * 
  145.      * @return The Operator Population Metric Norm
  146.      * 
  147.      * @throws java.lang.Exception Thrown if the Operator Norm cannot be computed
  148.      */

  150.     public abstract double operatorPopulationMetricNorm()
  151.         throws java.lang.Exception;

  153.     /**
  154.      * Compute the Operator Population Supremum Norm
  155.      * 
  156.      * @return The Operator Population Supremum Norm
  157.      * 
  158.      * @throws java.lang.Exception Thrown if the Operator Population Supremum Norm cannot be computed
  159.      */

  161.     public abstract double operatorPopulationSupremumNorm()
  162.         throws java.lang.Exception;

  164.     /**
  165.      * Compute the Operator Sample Metric Norm
  166.      * 
  167.      * @param gvvi The Validated Vector Space Instance
  168.      * 
  169.      * @return The Operator Sample Metric Norm
  170.      * 
  171.      * @throws java.lang.Exception Thrown if the Operator Norm cannot be computed
  172.      */

  174.     public abstract double operatorSampleMetricNorm (
  175.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  176.         throws java.lang.Exception;

  178.     /**
  179.      * Compute the Operator Sample Supremum Norm
  180.      * 
  181.      * @param gvvi The Validated Vector Space Instance
  182.      * 
  183.      * @return The Operator Sample Supremum Norm
  184.      * 
  185.      * @throws java.lang.Exception Thrown if the Operator Sample Supremum Norm cannot be computed
  186.      */

  188.     public abstract double operatorSampleSupremumNorm (
  189.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  190.         throws java.lang.Exception;

  192.     /**
  193.      * Retrieve the Agnostic Covering Number Upper/Lower Bounds for the Function Class
  194.      * 
  195.      * @return The Agnostic Covering Number Upper/Lower Bounds for the Function Class
  196.      */

  198.     public abstract org.drip.spaces.cover.FunctionClassCoveringBounds agnosticCoveringNumberBounds();

  200.     /**
  201.      * Retrieve the Maurey Constant
  202.      * 
  203.      * @return The Maurey Constant
  204.      */

  206.     public double maureyConstant()
  207.     {
  208.         return _dblMaureyConstant;
  209.     }

  211.     /**
  212.      * Retrieve the Scale-Sensitive Covering Number Upper/Lower Bounds given the Specified Sample for the
  213.      *  Function Class
  214.      * 
  215.      * @param gvvi The Validated Instance Vector Sequence
  216.      * @param funcR1ToR1FatShatter The Cover Fat Shattering Coefficient R^1 To R^1
  217.      * 
  218.      * @return The Scale-Sensitive Covering Number Upper/Lower Bounds given the Specified Sample for the
  219.      *  Function Class
  220.      */

  222.     public org.drip.spaces.cover.FunctionClassCoveringBounds scaleSensitiveCoveringBounds (
  223.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
  224.         final org.drip.function.definition.R1ToR1 funcR1ToR1FatShatter)
  225.     {
  226.         if (null == gvvi || null == funcR1ToR1FatShatter) return null;

  228.         int iSampleSize = -1;

  230.         if (gvvi instanceof org.drip.spaces.instance.ValidatedR1) {
  231.             double[] adblInstance = ((org.drip.spaces.instance.ValidatedR1) gvvi).instance();

  233.             if (null == adblInstance) return null;

  235.             iSampleSize = adblInstance.length;
  236.         } else if (gvvi instanceof org.drip.spaces.instance.ValidatedRd) {
  237.             double[][] aadblInstance = ((org.drip.spaces.instance.ValidatedRd) gvvi).instance();

  239.             if (null == aadblInstance) return null;

  241.             iSampleSize = aadblInstance.length;
  242.         }

  244.         try {
  245.             return new org.drip.spaces.cover.ScaleSensitiveCoveringBounds (funcR1ToR1FatShatter,
  246.                 iSampleSize);
  247.         } catch (java.lang.Exception e) {
  248.             e.printStackTrace();
  249.         }

  251.         return null;
  252.     }

  254.     /**
  255.      * Compute the Output Dimension
  256.      * 
  257.      * @return The Output Dimension
  258.      * 
  259.      * @throws java.lang.Exception Thrown if the Output Dimension is Invalid
  260.      */

  262.     public int outputDimension()
  263.         throws java.lang.Exception
  264.     {
  265.         org.drip.spaces.metric.GeneralizedMetricVectorSpace gmvsOutput = outputMetricVectorSpace();

  267.         if (!(gmvsOutput instanceof org.drip.spaces.metric.R1Continuous) && !(gmvsOutput instanceof
  268.             org.drip.spaces.metric.RdContinuousBanach))
  269.             throw new java.lang.Exception ("NormedRxToNormedRxFinite::dimension => Invalid Inputs");

  271.         return gmvsOutput instanceof org.drip.spaces.metric.R1Continuous ? 1 :
  272.             ((org.drip.spaces.metric.RdContinuousBanach) gmvsOutput).dimension();
  273.     }

  275.     /**
  276.      * Compute the Maurey Covering Number Upper Bounds for Operator Population Metric Norm
  277.      * 
  278.      * @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator
  279.      *  Population Metric Norm
  280.      */

  282.     public org.drip.spaces.cover.MaureyOperatorCoveringBounds populationMetricCoveringBounds()
  283.     {
  284.         try {
  285.             return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
  286.                 outputDimension(), operatorPopulationMetricNorm());
  287.         } catch (java.lang.Exception e) {
  288.             e.printStackTrace();
  289.         }

  291.         return null;
  292.     }

  294.     /**
  295.      * Compute the Maurey Covering Number Upper Bounds for Operator Population Supremum Norm
  296.      * 
  297.      * @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator
  298.      *  Population Supremum Norm
  299.      */

  301.     public org.drip.spaces.cover.MaureyOperatorCoveringBounds populationSupremumCoveringBounds()
  302.     {
  303.         try {
  304.             return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
  305.                 outputDimension(), operatorPopulationSupremumNorm());
  306.         } catch (java.lang.Exception e) {
  307.             e.printStackTrace();
  308.         }

  310.         return null;
  311.     }

  313.     /**
  314.      * Compute the Maurey Covering Number Upper Bounds for Operator Sample Metric Norm
  315.      * 
  316.      * @param gvvi The Validated Vector Space Instance
  317.      * 
  318.      * @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator Sample
  319.      *  Metric Norm
  320.      */

  322.     public org.drip.spaces.cover.MaureyOperatorCoveringBounds sampleMetricCoveringBounds (
  323.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  324.     {
  325.         try {
  326.             return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
  327.                 outputDimension(), operatorSampleMetricNorm (gvvi));
  328.         } catch (java.lang.Exception e) {
  329.             e.printStackTrace();
  330.         }

  332.         return null;
  333.     }

  335.     /**
  336.      * Compute the Maurey Covering Number Upper Bounds for Operator Sample Supremum Norm
  337.      * 
  338.      * @param gvvi The Validated Vector Space Instance
  339.      * 
  340.      * @return The Maurey Operator Covering Number Upper Bounds Instance Corresponding to the Operator Sample
  341.      *  Supremum Norm
  342.      */

  344.     public org.drip.spaces.cover.MaureyOperatorCoveringBounds sampleSupremumCoveringBounds (
  345.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  346.     {
  347.         try {
  348.             return new org.drip.spaces.cover.MaureyOperatorCoveringBounds (_dblMaureyConstant,
  349.                 outputDimension(), operatorSampleSupremumNorm (gvvi));
  350.         } catch (java.lang.Exception e) {
  351.             e.printStackTrace();
  352.         }

  354.         return null;
  355.     }
  356. }
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