FunctionSetBuilder.java

package org.drip.spline.basis;

/*
 * -*- 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>FunctionSetBuilder</i> implements the basis set and spline builder for the following types of splines:
 *
 * <br><br>
 *  <ul>
 *      <li>
 *          Exponential basis tension splines
 *      </li>
 *      <li>
 *          Hyperbolic basis tension splines
 *      </li>
 *      <li>
 *          Polynomial basis splines
 *      </li>
 *      <li>
 *          Bernstein Polynomial basis splines
 *      </li>
 *      <li>
 *          Kaklis Pandelis basis tension splines
 *      </li>
 *  </ul>
 * 
 * This elastic coefficients for the segment using Ck basis splines inside [0,...,1) - Globally
 *  [x_0,...,x_1) are extracted for:
 * 
 *          y = Estimator (Ck, x) * ShapeControl (x)
 * 
 *      where x is the normalized ordinate mapped as
 * 
 *          x becomes (x - x_i-1) / (x_i - x_i-1)
 * 
 * The inverse quadratic/rational spline is a typical shape controller spline used.
 *
 * <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/basis/README.md">Basis Spline Construction/Customization Parameters</a></li>
 *  </ul>
 * <br><br>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class FunctionSetBuilder {

    /**
     * This function implements the elastic coefficients for the segment using tension exponential basis
     *  splines inside - [0,...,1) - Globally [x_0,...,x_1). The segment equation is
     * 
     *      y = A + B * x + C * exp (Tension * x / (x_i - x_i-1)) + D * exp (-Tension * x / (x_i - x_i-1))
     * 
     *  where x is the normalized ordinate mapped as
     * 
     *      x .gte. (x - x_i-1) / (x_i - x_i-1)
     * 
     * @param etsp Exponential Tension Basis set Builder Parameters
     * 
     * @return Exponential Tension Basis Functions
     */

    public static final org.drip.spline.basis.FunctionSet ExponentialTensionBasisSet (
        final org.drip.spline.basis.ExponentialTensionSetParams etsp)
    {
        if (null == etsp) return null;

        double dblTension = etsp.tension();

        try {
            return new org.drip.spline.basis.FunctionSet (new org.drip.function.definition.R1ToR1[]
                {new org.drip.function.r1tor1.Polynomial (0), new org.drip.function.r1tor1.Polynomial (1),
                    new org.drip.function.r1tor1.ExponentialTension (java.lang.Math.E, dblTension), new
                        org.drip.function.r1tor1.ExponentialTension (java.lang.Math.E, -dblTension)});
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * This function implements the elastic coefficients for the segment using tension hyperbolic basis
     *  splines inside - [0,...,1) - Globally [x_0,...,x_1). The segment equation is
     * 
     *      y = A + B * x + C * sinh (Tension * x / (x_i - x_i-1)) + D * cosh (Tension * x / (x_i - x_i-1))
     * 
     *  where x is the normalized ordinate mapped as
     * 
     *      x .ge. (x - x_i-1) / (x_i - x_i-1)
     * 
     * @param etsp Exponential Tension Basis set Builder Parameters
     * 
     * @return Hyperbolic Tension Basis Set
     */

    public static final org.drip.spline.basis.FunctionSet HyperbolicTensionBasisSet (
        final org.drip.spline.basis.ExponentialTensionSetParams etsp)
    {
        if (null == etsp) return null;

        double dblTension = etsp.tension();

        try {
            return new org.drip.spline.basis.FunctionSet (new org.drip.function.definition.R1ToR1[]
                {new org.drip.function.r1tor1.Polynomial (0), new org.drip.function.r1tor1.Polynomial (1),
                    new org.drip.function.r1tor1.HyperbolicTension
                        (org.drip.function.r1tor1.HyperbolicTension.COSH, dblTension), new
                            org.drip.function.r1tor1.HyperbolicTension
                                (org.drip.function.r1tor1.HyperbolicTension.SINH, dblTension)});
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * This function implements the elastic coefficients for the segment using polynomial basis splines
     *      inside [0,...,1) - Globally [x_0,...,x_1):
     * 
     *          y = Sum (A_i*x^i) i = 0,...,n (0 and n inclusive)
     * 
     *      where x is the normalized ordinate mapped as
     * 
     *          x .gte. (x - x_i-1) / (x_i - x_i-1)
     * 
     * @param pfsp Polynomial Basis set Builder Parameters
     * 
     * @return The Polynomial Basis Spline Set
     */

    public static final org.drip.spline.basis.FunctionSet PolynomialBasisSet (
        final org.drip.spline.basis.PolynomialFunctionSetParams pfsp)
    {
        if (null == pfsp) return null;

        int iNumBasis = pfsp.numBasis();

        org.drip.function.definition.R1ToR1[] aAU = new
            org.drip.function.definition.R1ToR1[iNumBasis];

        try {
            for (int i = 0; i < iNumBasis; ++i)
                aAU[i] = new org.drip.function.r1tor1.Polynomial (i);

            return new org.drip.spline.basis.FunctionSet (aAU);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * This function implements the elastic coefficients for the segment using Bernstein polynomial basis
     *  splines inside - [0,...,1) - Globally [x_0,...,x_1):
     * 
     *          y = Sum (A_i*B^i(x)) i = 0,...,n (0 and n inclusive)
     * 
     *      where x is the normalized ordinate mapped as
     * 
     *          x .gte. (x - x_i-1) / (x_i - x_i-1)
     * 
     *      and B^i(x) is the Bernstein basis polynomial of order i.
     * 
     * @param pfsp Polynomial Basis set Builder Parameters
     * 
     * @return The Bernstein polynomial basis
     */

    public static final org.drip.spline.basis.FunctionSet BernsteinPolynomialBasisSet (
        final org.drip.spline.basis.PolynomialFunctionSetParams pfsp)
    {
        if (null == pfsp) return null;

        int iNumBasis = pfsp.numBasis();

        org.drip.function.definition.R1ToR1[] aAU = new
            org.drip.function.definition.R1ToR1[iNumBasis];

        try {
            for (int i = 0; i < iNumBasis; ++i)
                aAU[i] = new org.drip.function.r1tor1.BernsteinPolynomial (i, iNumBasis - 1 - i);

            return new org.drip.spline.basis.FunctionSet (aAU);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct KaklisPandelis from the polynomial tension basis function set
     * 
     *      y = A * (1-x) + B * x + C * x * (1-x)^m + D * x^m * (1-x)
     * 
     * @param kpsp Kaklis Pandelis Basis set Builder Parameters
     * 
     * @return The KaklisPandelis Basis Set
     */

    public static final org.drip.spline.basis.FunctionSet KaklisPandelisBasisSet (
        final org.drip.spline.basis.KaklisPandelisSetParams kpsp)
    {
        if (null == kpsp) return null;

        try {
            org.drip.function.definition.R1ToR1 auLinearPoly = new org.drip.function.r1tor1.Polynomial
                (1);

            org.drip.function.definition.R1ToR1 auReflectedLinearPoly = new
                org.drip.function.r1tor1.UnivariateReflection (auLinearPoly);

            org.drip.function.definition.R1ToR1 auKaklisPandelisPolynomial = new
                org.drip.function.r1tor1.Polynomial (kpsp.polynomialTensionDegree());

            return new org.drip.spline.basis.FunctionSet (new org.drip.function.definition.R1ToR1[]
                {auReflectedLinearPoly, auLinearPoly, new org.drip.function.r1tor1.UnivariateConvolution
                    (auLinearPoly, new org.drip.function.r1tor1.UnivariateReflection
                        (auKaklisPandelisPolynomial)), new org.drip.function.r1tor1.UnivariateConvolution
                            (auKaklisPandelisPolynomial, auReflectedLinearPoly)});
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct the Exponential Rational Basis Set
     * 
     *      y = A + B / (1+x) + C * exp(-x) + D * exp(-x) / (1+x)
     * 
     * @param ersp Exponential Rational Basis set Parameters
     * 
     * @return The Exponential Rational Basis Set
     */

    public static final org.drip.spline.basis.FunctionSet ExponentialRationalBasisSet (
        final org.drip.spline.basis.ExponentialRationalSetParams ersp)
    {
        if (null == ersp) return null;

        try {
            org.drip.function.definition.R1ToR1 auLinearPoly = new org.drip.function.r1tor1.Polynomial
                (0);

            org.drip.function.definition.R1ToR1 auLRSC = new
                org.drip.function.r1tor1.LinearRationalShapeControl (ersp.rationalTension());

            org.drip.function.definition.R1ToR1 auET = new
                org.drip.function.r1tor1.ExponentialTension (java.lang.Math.E, -ersp.exponentialTension());

            org.drip.function.definition.R1ToR1 auLRET = new
                org.drip.function.r1tor1.LinearRationalTensionExponential (-ersp.exponentialTension(),
                    ersp.rationalTension());

            return new org.drip.spline.basis.FunctionSet (new org.drip.function.definition.R1ToR1[]
                {auLinearPoly, auLRSC, auET, auLRET});
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct the Exponential Mixture Basis Set
     * 
     *      y = A + B * exp(-l_1 * x) + C * exp(-l_2 * x) + D * exp(-l_3 * x)
     * 
     * @param emsp Exponential Mixture Basis set Parameters
     * 
     * @return The Exponential Mixture Basis Set
     */

    public static final org.drip.spline.basis.FunctionSet ExponentialMixtureBasisSet (
        final org.drip.spline.basis.ExponentialMixtureSetParams emsp)
    {
        if (null == emsp) return null;

        try {
            org.drip.function.definition.R1ToR1 auLinearPoly = new
                org.drip.function.r1tor1.Polynomial (0);

            org.drip.function.definition.R1ToR1 auExp1 = new
                org.drip.function.r1tor1.ExponentialTension (java.lang.Math.E, -emsp.tension (0));

            org.drip.function.definition.R1ToR1 auExp2 = new
                org.drip.function.r1tor1.ExponentialTension (java.lang.Math.E, -emsp.tension (1));

            org.drip.function.definition.R1ToR1 auExp3 = new
                org.drip.function.r1tor1.ExponentialTension (java.lang.Math.E, -emsp.tension (2));

            return new org.drip.spline.basis.FunctionSet (new org.drip.function.definition.R1ToR1[]
                {auLinearPoly, auExp1, auExp2, auExp3});
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct the BSpline Basis Function Set
     * 
     * @param bssp BSpline Basis Set Parameters
     * 
     * @return The BSpline Basis Function Set
     */

    public static final org.drip.spline.basis.FunctionSet BSplineBasisSet (
        final org.drip.spline.basis.BSplineSequenceParams bssp)
    {
        if (null == bssp) return null;

        org.drip.spline.bspline.SegmentBasisFunction[] aSBF =
            org.drip.spline.bspline.SegmentBasisFunctionGenerator.MonicSequence (bssp.hat(),
                bssp.shapeControl(), bssp.predictorOrdinates(), bssp.procBasisDerivOrder(), bssp.tension());

        if (null == aSBF || bssp.numBasis() >= aSBF.length) return null;

        int iBSplineOrder = bssp.bSplineOrder();

        try {
            return new org.drip.spline.bspline.SegmentBasisFunctionSet (bssp.numBasis(), bssp.tension(), 2 ==
                iBSplineOrder ? aSBF : org.drip.spline.bspline.SegmentBasisFunctionGenerator.MulticSequence
                    (iBSplineOrder, aSBF));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    public static final void main (
        final java.lang.String[] astrArgs)
        throws java.lang.Exception
    {
        org.drip.spline.basis.BSplineSequenceParams bssp = new org.drip.spline.basis.BSplineSequenceParams
            (org.drip.spline.bspline.BasisHatPairGenerator.RAW_TENSION_HYPERBOLIC,
                org.drip.spline.bspline.BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR, 2, 4, 1., -1);

        org.drip.numerical.common.NumberUtil.Print1DArray ("BSSP", bssp.predictorOrdinates(), false);

        org.drip.spline.basis.FunctionSet fsBSS = BSplineBasisSet (bssp);

        System.out.println ("fsBSS Size = " + fsBSS.numBasis());
    }
}