/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.analysis.interpolation;
  
  import java.lang.reflect.Array;
  
  import org.hipparchus.Field;
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.analysis.polynomials.FieldPolynomialFunction;
  import org.hipparchus.analysis.polynomials.FieldPolynomialSplineFunction;
  import org.hipparchus.analysis.polynomials.PolynomialFunction;
  import org.hipparchus.analysis.polynomials.PolynomialSplineFunction;
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.exception.NullArgumentException;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.Precision;
  
  /**
   * Computes a cubic spline interpolation for the data set using the Akima
   * algorithm, as originally formulated by Hiroshi Akima in his 1970 paper
   * <a href="http://doi.acm.org/10.1145/321607.321609">A New Method of
   * Interpolation and Smooth Curve Fitting Based on Local Procedures.</a>
   * J. ACM 17, 4 (October 1970), 589-602. DOI=10.1145/321607.321609
   * <p>
   * This implementation is based on the Akima implementation in the CubicSpline
   * class in the Math.NET Numerics library. The method referenced is
   * CubicSpline.InterpolateAkimaSorted
   * </p>
   * <p>
   * The {@link #interpolate(double[], double[]) interpolate} method returns a
   * {@link PolynomialSplineFunction} consisting of n cubic polynomials, defined
   * over the subintervals determined by the x values, {@code x[0] < x[i] ... < x[n]}.
   * The Akima algorithm requires that {@code n >= 5}.
   * </p>
   */
  public class AkimaSplineInterpolator
      implements UnivariateInterpolator, FieldUnivariateInterpolator {
  
      /** The minimum number of points that are needed to compute the function. */
      private static final int MINIMUM_NUMBER_POINTS = 5;
  
      /** Weight modifier to avoid overshoots. */
      private final boolean useModifiedWeights;
  
      /** Simple constructor.
       * <p>
       * This constructor is equivalent to call {@link #AkimaSplineInterpolator(boolean)
       * AkimaSplineInterpolator(false)}, i.e. to use original Akima weights
       * </p>
       * @since 2.1
       */
      public AkimaSplineInterpolator() {
          this(false);
      }
  
      /** Simple constructor.
       * <p>
       * The weight modification is described in <a
       * href="https://blogs.mathworks.com/cleve/2019/04/29/makima-piecewise-cubic-interpolation/">
       * Makima Piecewise Cubic Interpolation</a>. It attempts to avoid overshoots
       * near near constant slopes sub-samples.
       * </p>
       * @param useModifiedWeights if true, use modified weights to avoid overshoots
       * @since 2.1
       */
      public AkimaSplineInterpolator(final boolean useModifiedWeights) {
          this.useModifiedWeights = useModifiedWeights;
      }
  
      /**
       * Computes an interpolating function for the data set.
       *
       * @param xvals the arguments for the interpolation points
       * @param yvals the values for the interpolation points
       * @return a function which interpolates the data set
       * @throws MathIllegalArgumentException if {@code xvals} and {@code yvals} have
       *         different sizes.
       * @throws MathIllegalArgumentException if {@code xvals} is not sorted in
      *         strict increasing order.
      * @throws MathIllegalArgumentException if the size of {@code xvals} is smaller
      *         than 5.
      */
     @Override
     public PolynomialSplineFunction interpolate(double[] xvals,
                                                 double[] yvals)
         throws MathIllegalArgumentException {
         if (xvals == null ||
             yvals == null) {
             throw new NullArgumentException();
         }
 
         MathArrays.checkEqualLength(xvals, yvals);
 
         if (xvals.length < MINIMUM_NUMBER_POINTS) {
             throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_OF_POINTS,
                                                 xvals.length,
                                                 MINIMUM_NUMBER_POINTS, true);
         }
 
         MathArrays.checkOrder(xvals);
 
         final int numberOfDiffAndWeightElements = xvals.length - 1;
 
         final double[] differences = new double[numberOfDiffAndWeightElements];
         final double[] weights = new double[numberOfDiffAndWeightElements];
 
         for (int i = 0; i < differences.length; i++) {
             differences[i] = (yvals[i + 1] - yvals[i]) / (xvals[i + 1] - xvals[i]);
         }
 
         for (int i = 1; i < weights.length; i++) {
             weights[i] = FastMath.abs(differences[i] - differences[i - 1]);
             if (useModifiedWeights) {
                 // modify weights to avoid overshoots near constant slopes sub-samples
                 weights[i] += FastMath.abs(differences[i] + differences[i - 1]);
             }
         }
 
         // Prepare Hermite interpolation scheme.
         final double[] firstDerivatives = new double[xvals.length];
 
         for (int i = 2; i < firstDerivatives.length - 2; i++) {
             final double wP = weights[i + 1];
             final double wM = weights[i - 1];
             if (Precision.equals(wP, 0.0) &&
                 Precision.equals(wM, 0.0)) {
                 final double xv = xvals[i];
                 final double xvP = xvals[i + 1];
                 final double xvM = xvals[i - 1];
                 firstDerivatives[i] = (((xvP - xv) * differences[i - 1]) + ((xv - xvM) * differences[i])) / (xvP - xvM);
             } else {
                 firstDerivatives[i] = ((wP * differences[i - 1]) + (wM * differences[i])) / (wP + wM);
             }
         }
 
         firstDerivatives[0] = differentiateThreePoint(xvals, yvals, 0, 0, 1, 2);
         firstDerivatives[1] = differentiateThreePoint(xvals, yvals, 1, 0, 1, 2);
         firstDerivatives[xvals.length - 2] = differentiateThreePoint(xvals, yvals, xvals.length - 2,
                                                                      xvals.length - 3, xvals.length - 2,
                                                                      xvals.length - 1);
         firstDerivatives[xvals.length - 1] = differentiateThreePoint(xvals, yvals, xvals.length - 1,
                                                                      xvals.length - 3, xvals.length - 2,
                                                                      xvals.length - 1);
 
         return interpolateHermiteSorted(xvals, yvals, firstDerivatives);
 
     }
 
     /**
      * Computes an interpolating function for the data set.
      *
      * @param xvals the arguments for the interpolation points
      * @param yvals the values for the interpolation points
      * @param <T> the type of the field elements
      * @return a function which interpolates the data set
      * @throws MathIllegalArgumentException if {@code xvals} and {@code yvals} have
      *         different sizes.
      * @throws MathIllegalArgumentException if {@code xvals} is not sorted in
      *         strict increasing order.
      * @throws MathIllegalArgumentException if the size of {@code xvals} is smaller
      *         than 5.
      * @since 1.5
      */
     @Override
     public <T extends CalculusFieldElement<T>> FieldPolynomialSplineFunction<T> interpolate(final T[] xvals,
                                                                                         final T[] yvals)
         throws MathIllegalArgumentException {
         if (xvals == null ||
             yvals == null) {
             throw new NullArgumentException();
         }
 
         MathArrays.checkEqualLength(xvals, yvals);
 
         if (xvals.length < MINIMUM_NUMBER_POINTS) {
             throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_OF_POINTS,
                                                 xvals.length,
                                                 MINIMUM_NUMBER_POINTS, true);
         }
 
         MathArrays.checkOrder(xvals);
 
         final Field<T> field = xvals[0].getField();
         final int numberOfDiffAndWeightElements = xvals.length - 1;
 
         final T[] differences = MathArrays.buildArray(field, numberOfDiffAndWeightElements);
         final T[] weights     = MathArrays.buildArray(field, numberOfDiffAndWeightElements);
 
         for (int i = 0; i < differences.length; i++) {
             differences[i] = yvals[i + 1].subtract(yvals[i]).divide(xvals[i + 1].subtract(xvals[i]));
         }
 
         for (int i = 1; i < weights.length; i++) {
             weights[i] = FastMath.abs(differences[i].subtract(differences[i - 1]));
         }
 
         // Prepare Hermite interpolation scheme.
         final T[] firstDerivatives = MathArrays.buildArray(field, xvals.length);
 
         for (int i = 2; i < firstDerivatives.length - 2; i++) {
             final T wP = weights[i + 1];
             final T wM = weights[i - 1];
             if (Precision.equals(wP.getReal(), 0.0) &&
                 Precision.equals(wM.getReal(), 0.0)) {
                 final T xv = xvals[i];
                 final T xvP = xvals[i + 1];
                 final T xvM = xvals[i - 1];
                 firstDerivatives[i] =     xvP.subtract(xv).multiply(differences[i - 1]).
                                       add(xv.subtract(xvM).multiply(differences[i])).
                                       divide(xvP.subtract(xvM));
             } else {
                 firstDerivatives[i] =     wP.multiply(differences[i - 1]).
                                       add(wM.multiply(differences[i])).
                                       divide(wP.add(wM));
             }
         }
 
         firstDerivatives[0] = differentiateThreePoint(xvals, yvals, 0, 0, 1, 2);
         firstDerivatives[1] = differentiateThreePoint(xvals, yvals, 1, 0, 1, 2);
         firstDerivatives[xvals.length - 2] = differentiateThreePoint(xvals, yvals, xvals.length - 2,
                                                                      xvals.length - 3, xvals.length - 2,
                                                                      xvals.length - 1);
         firstDerivatives[xvals.length - 1] = differentiateThreePoint(xvals, yvals, xvals.length - 1,
                                                                      xvals.length - 3, xvals.length - 2,
                                                                      xvals.length - 1);
 
         return interpolateHermiteSorted(xvals, yvals, firstDerivatives);
 
     }
 
     /**
      * Three point differentiation helper, modeled off of the same method in the
      * Math.NET CubicSpline class. This is used by both the Apache Math and the
      * Math.NET Akima Cubic Spline algorithms
      *
      * @param xvals x values to calculate the numerical derivative with
      * @param yvals y values to calculate the numerical derivative with
      * @param indexOfDifferentiation index of the elemnt we are calculating the derivative around
      * @param indexOfFirstSample index of the first element to sample for the three point method
      * @param indexOfSecondsample index of the second element to sample for the three point method
      * @param indexOfThirdSample index of the third element to sample for the three point method
      * @return the derivative
      */
     private double differentiateThreePoint(double[] xvals, double[] yvals,
                                            int indexOfDifferentiation,
                                            int indexOfFirstSample,
                                            int indexOfSecondsample,
                                            int indexOfThirdSample) {
         final double x0 = yvals[indexOfFirstSample];
         final double x1 = yvals[indexOfSecondsample];
         final double x2 = yvals[indexOfThirdSample];
 
         final double t = xvals[indexOfDifferentiation] - xvals[indexOfFirstSample];
         final double t1 = xvals[indexOfSecondsample] - xvals[indexOfFirstSample];
         final double t2 = xvals[indexOfThirdSample] - xvals[indexOfFirstSample];
 
         final double a = (x2 - x0 - (t2 / t1 * (x1 - x0))) / (t2 * t2 - t1 * t2);
         final double b = (x1 - x0 - a * t1 * t1) / t1;
 
         return (2 * a * t) + b;
     }
 
     /**
      * Three point differentiation helper, modeled off of the same method in the
      * Math.NET CubicSpline class. This is used by both the Apache Math and the
      * Math.NET Akima Cubic Spline algorithms
      *
      * @param xvals x values to calculate the numerical derivative with
      * @param yvals y values to calculate the numerical derivative with
      * @param <T> the type of the field elements
      * @param indexOfDifferentiation index of the elemnt we are calculating the derivative around
      * @param indexOfFirstSample index of the first element to sample for the three point method
      * @param indexOfSecondsample index of the second element to sample for the three point method
      * @param indexOfThirdSample index of the third element to sample for the three point method
      * @return the derivative
      * @since 1.5
      */
     private <T extends CalculusFieldElement<T>> T differentiateThreePoint(T[] xvals, T[] yvals,
                                                                       int indexOfDifferentiation,
                                                                       int indexOfFirstSample,
                                                                       int indexOfSecondsample,
                                                                       int indexOfThirdSample) {
         final T x0 = yvals[indexOfFirstSample];
         final T x1 = yvals[indexOfSecondsample];
         final T x2 = yvals[indexOfThirdSample];
 
         final T t = xvals[indexOfDifferentiation].subtract(xvals[indexOfFirstSample]);
         final T t1 = xvals[indexOfSecondsample].subtract(xvals[indexOfFirstSample]);
         final T t2 = xvals[indexOfThirdSample].subtract(xvals[indexOfFirstSample]);
 
         final T a = x2.subtract(x0).subtract(t2.divide(t1).multiply(x1.subtract(x0))).
                     divide(t2.multiply(t2).subtract(t1.multiply(t2)));
         final T b = x1.subtract(x0).subtract(a.multiply(t1).multiply(t1)).divide(t1);
 
         return a.multiply(t).multiply(2).add(b);
     }
 
     /**
      * Creates a Hermite cubic spline interpolation from the set of (x,y) value
      * pairs and their derivatives. This is modeled off of the
      * InterpolateHermiteSorted method in the Math.NET CubicSpline class.
      *
      * @param xvals x values for interpolation
      * @param yvals y values for interpolation
      * @param firstDerivatives first derivative values of the function
      * @return polynomial that fits the function
      */
     private PolynomialSplineFunction interpolateHermiteSorted(double[] xvals,
                                                               double[] yvals,
                                                               double[] firstDerivatives) {
         MathArrays.checkEqualLength(xvals, yvals);
         MathArrays.checkEqualLength(xvals, firstDerivatives);
 
         final int minimumLength = 2;
         if (xvals.length < minimumLength) {
             throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_OF_POINTS,
                                                 xvals.length, minimumLength,
                                                 true);
         }
 
         final int size = xvals.length - 1;
         final PolynomialFunction[] polynomials = new PolynomialFunction[size];
         final double[] coefficients = new double[4];
 
         for (int i = 0; i < polynomials.length; i++) {
             final double w = xvals[i + 1] - xvals[i];
             final double w2 = w * w;
 
             final double yv = yvals[i];
             final double yvP = yvals[i + 1];
 
             final double fd = firstDerivatives[i];
             final double fdP = firstDerivatives[i + 1];
 
             coefficients[0] = yv;
             coefficients[1] = firstDerivatives[i];
             coefficients[2] = (3 * (yvP - yv) / w - 2 * fd - fdP) / w;
             coefficients[3] = (2 * (yv - yvP) / w + fd + fdP) / w2;
             polynomials[i] = new PolynomialFunction(coefficients);
         }
 
         return new PolynomialSplineFunction(xvals, polynomials);
 
     }
     /**
      * Creates a Hermite cubic spline interpolation from the set of (x,y) value
      * pairs and their derivatives. This is modeled off of the
      * InterpolateHermiteSorted method in the Math.NET CubicSpline class.
      *
      * @param xvals x values for interpolation
      * @param yvals y values for interpolation
      * @param firstDerivatives first derivative values of the function
      * @param <T> the type of the field elements
      * @return polynomial that fits the function
      * @since 1.5
      */
     private <T extends CalculusFieldElement<T>> FieldPolynomialSplineFunction<T> interpolateHermiteSorted(T[] xvals,
                                                                                                           T[] yvals,
                                                                                                           T[] firstDerivatives) {
         MathArrays.checkEqualLength(xvals, yvals);
         MathArrays.checkEqualLength(xvals, firstDerivatives);
 
         final int minimumLength = 2;
         if (xvals.length < minimumLength) {
             throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_OF_POINTS,
                                                 xvals.length, minimumLength,
                                                 true);
         }
 
         final Field<T> field = xvals[0].getField();
         final int size = xvals.length - 1;
         @SuppressWarnings("unchecked")
         final FieldPolynomialFunction<T>[] polynomials =
                         (FieldPolynomialFunction<T>[]) Array.newInstance(FieldPolynomialFunction.class, size);
         final T[] coefficients = MathArrays.buildArray(field, 4);
 
         for (int i = 0; i < polynomials.length; i++) {
             final T w = xvals[i + 1].subtract(xvals[i]);
             final T w2 = w.multiply(w);
 
             final T yv = yvals[i];
             final T yvP = yvals[i + 1];
 
             final T fd = firstDerivatives[i];
             final T fdP = firstDerivatives[i + 1];
 
             coefficients[0] = yv;
             coefficients[1] = firstDerivatives[i];
             final T ratio = yvP.subtract(yv).divide(w);
             coefficients[2] = ratio.multiply(+3).subtract(fd.add(fd)).subtract(fdP).divide(w);
             coefficients[3] = ratio.multiply(-2).add(fd).add(fdP).divide(w2);
             polynomials[i] = new FieldPolynomialFunction<>(coefficients);
         }
 
         return new FieldPolynomialSplineFunction<>(xvals, polynomials);
 
     }
 }