SegmentBasisFunctionGenerator.java

package org.drip.spline.bspline;

/*
 * -*- 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
 * Copyright (C) 2014 Lakshmi Krishnamurthy
 * Copyright (C) 2013 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>SegmentBasisFunctionGenerator</i> generates B Spline Functions of different order. It provides the
 * following functionality:
 *  <ul>
 *      <li>
 *          Create a Tension Monic B Spline Basis Function.
 *      </li>
 *      <li>
 *          Construct a Sequence of Monic Basis Functions.
 *      </li>
 *      <li>
 *          Create a sequence of B Splines of the specified order from the given inputs.
 *      </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/SplineBuilderLibrary.md">Spline Builder Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/README.md">Basis Splines and Linear Compounders across a Broad Family of Spline Basis Functions</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/bspline/README.md">de Boor Rational/Exponential/Tension B-Splines</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class SegmentBasisFunctionGenerator {

    /**
     * Create a Tension Monic B Spline Basis Function
     * 
     * @param strHatType The Primitive Hat Type
     * @param strShapeControlType Type of the Shape Controller to be used - NONE, LINEAR/QUADRATIC Rational
     * @param adblPredictorOrdinate Array of Predictor Ordinates
     * @param iDerivOrder The Derivative Order
     * @param dblTension Tension
     * 
     * @return The Tension Monic B Spline Basis Function Instance
     */

    public static final org.drip.spline.bspline.SegmentBasisFunction Monic (
        final java.lang.String strHatType,
        final java.lang.String strShapeControlType,
        final double[] adblPredictorOrdinate,
        final int iDerivOrder,
        final double dblTension)
    {
        org.drip.spline.bspline.TensionBasisHat[] aTBH =
            org.drip.spline.bspline.BasisHatPairGenerator.GenerateHatPair (strHatType, strShapeControlType,
                adblPredictorOrdinate[0], adblPredictorOrdinate[1], adblPredictorOrdinate[2], iDerivOrder,
                    dblTension);

        if (null == aTBH || 2 != aTBH.length) return null;

        try {
            return new org.drip.spline.bspline.SegmentMonicBasisFunction (aTBH[0], aTBH[1]);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct a Sequence of Monic Basis Functions
     * 
     * @param strHatType The Primitive Hat Type
     * @param strShapeControlType Type of the Shape Controller to be used - NONE, LINEAR/QUADRATIC Rational
     * @param adblPredictorOrdinate Array of Predictor Ordinates
     * @param iDerivOrder The Derivative Order
     * @param dblTension Tension
     * 
     * @return Sequence of Tension Monic B Spline Basis Functions
     */

    public static final org.drip.spline.bspline.SegmentBasisFunction[] MonicSequence (
        final java.lang.String strHatType,
        final java.lang.String strShapeControlType,
        final double[] adblPredictorOrdinate,
        final int iDerivOrder,
        final double dblTension)
    {
        if (null == adblPredictorOrdinate) return null;

        int iNumMonic = adblPredictorOrdinate.length - 2;
        org.drip.spline.bspline.SegmentBasisFunction[] aSBFMonic = new
            org.drip.spline.bspline.SegmentBasisFunction[iNumMonic];

        if (0 >= iNumMonic) return null;

        for (int i = 0; i < iNumMonic; ++i) {
            TensionBasisHat[] aTBH = BasisHatPairGenerator.GenerateHatPair (strHatType, strShapeControlType,
                adblPredictorOrdinate[i], adblPredictorOrdinate[i + 1], adblPredictorOrdinate[i + 2],
                    iDerivOrder, dblTension);

            if (null == aTBH || 2 != aTBH.length) return null;

            try {
                aSBFMonic[i] = new org.drip.spline.bspline.SegmentMonicBasisFunction (aTBH[0], aTBH[1]);
            } catch (java.lang.Exception e) {
                e.printStackTrace();

                return null;
            }
        }

        return aSBFMonic;
    }

    /**
     * Create a sequence of B Splines of the specified order from the given inputs.
     * 
     * @param iTargetBSplineOrder Desired B Spline Order
     * @param aSBFPrev Array of Segment Basis Functions
     * 
     * @return The sequence of B Splines of the specified order.
     */

    public static final org.drip.spline.bspline.SegmentBasisFunction[] MulticSequence (
        final int iTargetBSplineOrder,
        final org.drip.spline.bspline.SegmentBasisFunction[] aSBFPrev)
    {
        if (2 >= iTargetBSplineOrder || null == aSBFPrev) return null;

        int iNumSBF = aSBFPrev.length - 1;
        org.drip.spline.bspline.SegmentBasisFunction[] aSBF = new
            org.drip.spline.bspline.SegmentBasisFunction[iNumSBF];

        if (1 > iNumSBF) return null;

        for (int i = 0; i < iNumSBF; ++i) {
            try {
                aSBF[i] = new org.drip.spline.bspline.SegmentMulticBasisFunction (aSBFPrev[i],
                    aSBFPrev[i + 1]);
            } catch (java.lang.Exception e) {
                e.printStackTrace();

                return null;
            }
        }

        return iTargetBSplineOrder == aSBF[0].bSplineOrder() ? aSBF : MulticSequence (iTargetBSplineOrder,
            aSBF);
    }
}