NormedR1ContinuousToR1Continuous.java

package org.drip.spaces.rxtor1;

/*
 * -*- 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>NormedR1ContinuousToR1Continuous</i> implements the f : Validated Normed R<sup>1</sup> Continuous To
 * Validated Normed R<sup>1</sup> Continuous Function Spaces. The Reference we've used is:
 *
 * <br><br>
 *  <ul>
 *      <li>
 *          Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and the Approximation of Operators</i>
 *              <b>Cambridge University Press</b> Cambridge UK 
 *      </li>
 *  </ul>
 *
 * <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 Library</a></li>
 *      <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>
 *      <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>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class NormedR1ContinuousToR1Continuous extends org.drip.spaces.rxtor1.NormedR1ToNormedR1 {

    /**
     * NormedR1ContinuousToR1Continuous Function Space Constructor
     * 
     * @param r1ContinuousInput The R^1 Input Metric Vector Space
     * @param r1ContinuousOutput The R^1 Output Metric Vector Space
     * @param funcR1ToR1 The R^1 To R^1 Function
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public NormedR1ContinuousToR1Continuous (
        final org.drip.spaces.metric.R1Continuous r1ContinuousInput,
        final org.drip.spaces.metric.R1Continuous r1ContinuousOutput,
        final org.drip.function.definition.R1ToR1 funcR1ToR1)
        throws java.lang.Exception
    {
        super (r1ContinuousInput, r1ContinuousOutput, funcR1ToR1);
    }

    @Override public double populationMetricNorm()
        throws java.lang.Exception
    {
        final int iPNorm = outputMetricVectorSpace().pNorm();

        if (java.lang.Integer.MAX_VALUE == iPNorm) return populationSupremumMetricNorm();

        org.drip.spaces.tensor.R1GeneralizedVector gvR1Input = inputMetricVectorSpace();

        org.drip.spaces.metric.R1Continuous r1Continuous = (org.drip.spaces.metric.R1Continuous) gvR1Input;

        final org.drip.function.definition.R1ToR1 funcR1ToR1 = function();

        final org.drip.measure.continuous.R1Univariate distR1 = r1Continuous.borelSigmaMeasure();

        if (null == distR1 || null == funcR1ToR1)
            throw new java.lang.Exception
                ("NormedR1ContinuousToR1Continuous::populationMetricNorm => Invalid Inputs");

        org.drip.function.definition.R1ToR1 funcDensityR1ToR1 = new org.drip.function.definition.R1ToR1
            (null) {
            @Override public double evaluate (
                final double dblX)
                throws java.lang.Exception
            {
                return java.lang.Math.pow (java.lang.Math.abs (funcR1ToR1.evaluate (dblX)), iPNorm) *
                    distR1.density (dblX);
            }
        };

        double dblLeftEdge = r1Continuous.leftEdge();

        double dblRightEdge = r1Continuous.rightEdge();

        return java.lang.Math.pow (funcDensityR1ToR1.integrate (dblLeftEdge, dblRightEdge) /
            distR1.incremental (dblLeftEdge, dblRightEdge), 1. / iPNorm);
    }
}