NormedRdToNormedRd.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>NormedRdToNormedRd</i> is the Abstract Class underlying the f : Validated Normed R<sup>d</sup> To
  83.  * Validated Normed R<sup>d</sup> Function Spaces. 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 NormedRdToNormedRd extends org.drip.spaces.rxtord.NormedRxToNormedRd {
  106.     private org.drip.spaces.metric.RdNormed _rdInput = null;
  107.     private org.drip.spaces.metric.RdNormed _rdOutput = null;
  108.     private org.drip.function.definition.RdToRd _funcRdToRd = null;

  110.     protected NormedRdToNormedRd (
  111.         final org.drip.spaces.metric.RdNormed rdInput,
  112.         final org.drip.spaces.metric.RdNormed rdOutput,
  113.         final org.drip.function.definition.RdToRd funcRdToRd)
  114.         throws java.lang.Exception
  115.     {
  116.         if (null == (_rdInput = rdInput) || null == (_rdOutput = rdOutput))
  117.             throw new java.lang.Exception ("NormedRdToNormedRd ctr: Invalid Inputs");

  119.         _funcRdToRd = funcRdToRd;
  120.     }

  122.     /**
  123.      * Retrieve the Underlying RdToRd Function
  124.      * 
  125.      * @return The Underlying RdToRd Function
  126.      */

  128.     public org.drip.function.definition.RdToRd function()
  129.     {
  130.         return _funcRdToRd;
  131.     }

  133.     /**
  134.      * Retrieve the Population R^d ESS (Essential Spectrum) Array
  135.      * 
  136.      * @return The Population R^d ESS (Essential Spectrum) Array
  137.      */

  139.     public double[] populationRdESS()
  140.     {
  141.         return _funcRdToRd.evaluate (_rdInput.populationMode());
  142.     }

  144.     /**
  145.      * Retrieve the Population R^d Supremum Norm
  146.      * 
  147.      * @return The Population R^d Supremum Norm
  148.      */

  150.     public double[] populationRdSupremumNorm()
  151.     {
  152.         return populationRdESS();
  153.     }

  155.     @Override public org.drip.spaces.metric.RdNormed inputMetricVectorSpace()
  156.     {
  157.         return _rdInput;
  158.     }

  160.     @Override public org.drip.spaces.metric.RdNormed outputMetricVectorSpace()
  161.     {
  162.         return _rdOutput;
  163.     }

  165.     @Override public double[] sampleSupremumNorm (
  166.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  167.     {
  168.         if (null == _funcRdToRd || null == gvvi || !gvvi.tensorSpaceType().match (_rdInput) || ! (gvvi
  169.             instanceof org.drip.spaces.instance.ValidatedRd))
  170.             return null;

  172.         org.drip.spaces.instance.ValidatedRd vrdInstance = (org.drip.spaces.instance.ValidatedRd) gvvi;

  174.         double[][] aadblInstance = vrdInstance.instance();

  176.         int iNumSample = aadblInstance.length;

  178.         int iOutputDimension = _rdOutput.dimension();

  180.         double[] adblSupremumNorm = _funcRdToRd.evaluate (aadblInstance[0]);

  182.         if (null == adblSupremumNorm || iOutputDimension != adblSupremumNorm.length ||
  183.             !org.drip.numerical.common.NumberUtil.IsValid (adblSupremumNorm))
  184.             return null;

  186.         for (int i = 0; i < iOutputDimension; ++i)
  187.             adblSupremumNorm[i] = java.lang.Math.abs (adblSupremumNorm[i]);

  189.         for (int i = 1; i < iNumSample; ++i) {
  190.             double[] adblSampleNorm = _funcRdToRd.evaluate (aadblInstance[i]);

  192.             if (null == adblSampleNorm || iOutputDimension != adblSampleNorm.length) return null;

  194.             for (int j = 0; j < iOutputDimension; ++j) {
  195.                 if (!org.drip.numerical.common.NumberUtil.IsValid (adblSampleNorm[j])) return null;

  197.                 if (adblSampleNorm[j] > adblSupremumNorm[j]) adblSupremumNorm[j] = adblSampleNorm[j];
  198.             }
  199.         }

  201.         return adblSupremumNorm;
  202.     }

  204.     @Override public double[] sampleMetricNorm (
  205.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi)
  206.     {
  207.         int iPNorm = outputMetricVectorSpace().pNorm();

  209.         if (java.lang.Integer.MAX_VALUE == iPNorm) return sampleSupremumNorm (gvvi);

  211.         if (null == _funcRdToRd || null == gvvi || !gvvi.tensorSpaceType().match (_rdInput) || ! (gvvi
  212.             instanceof org.drip.spaces.instance.ValidatedRd))
  213.             return null;

  215.         int iOutputDimension = _rdOutput.dimension();

  217.         double[][] aadblInstance = ((org.drip.spaces.instance.ValidatedRd) gvvi).instance();

  219.         double[] adblMetricNorm = new double[iOutputDimension];
  220.         int iNumSample = aadblInstance.length;

  222.         for (int i = 0; i < iNumSample; ++i)
  223.             adblMetricNorm[i] = 0.;

  225.         for (int i = 0; i < iNumSample; ++i) {
  226.             double[] adblPointValue = _funcRdToRd.evaluate (aadblInstance[i]);

  228.             if (null == adblPointValue || iOutputDimension != adblPointValue.length) return null;

  230.             for (int j = 0; j < iOutputDimension; ++j) {
  231.                 if (!org.drip.numerical.common.NumberUtil.IsValid (adblPointValue[j])) return null;

  233.                 adblMetricNorm[j] += java.lang.Math.pow (java.lang.Math.abs (adblPointValue[j]), iPNorm);
  234.             }
  235.         }

  237.         for (int i = 0; i < iNumSample; ++i)
  238.             adblMetricNorm[i] = java.lang.Math.pow (adblMetricNorm[i], 1. / iPNorm);

  240.         return adblMetricNorm;
  241.     }

  243.     @Override public double[] populationESS()
  244.     {
  245.         return _funcRdToRd.evaluate (_rdInput.populationMode());
  246.     }

  248.     @Override public double[] populationSupremumNorm()
  249.     {
  250.         return populationESS();
  251.     }
  252. }
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