/*
    * 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 org.hipparchus.UnitTestUtils;
  import org.hipparchus.analysis.UnivariateFunction;
  import org.hipparchus.analysis.polynomials.PolynomialFunction;
  import org.hipparchus.analysis.polynomials.PolynomialSplineFunction;
  import org.hipparchus.util.FastMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test the SplineInterpolator.
   *
   */
  public class SplineInterpolatorTest extends UnivariateInterpolatorAbstractTest {
  
      protected UnivariateInterpolator buildDoubleInterpolator() {
          return new SplineInterpolator();
      }
  
      protected FieldUnivariateInterpolator buildFieldInterpolator() {
          return new SplineInterpolator();
      }
  
      @Test
      public void testInterpolateSin() {
          double sineCoefficientTolerance = 1e-6;
          double sineInterpolationTolerance = 0.0043;
          double[] x =
              {
                  0.0,
                  FastMath.PI / 6d,
                  FastMath.PI / 2d,
                  5d * FastMath.PI / 6d,
                  FastMath.PI,
                  7d * FastMath.PI / 6d,
                  3d * FastMath.PI / 2d,
                  11d * FastMath.PI / 6d,
                  2.d * FastMath.PI };
          double[] y = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
          UnivariateInterpolator i = buildDoubleInterpolator();
          UnivariateFunction f = i.interpolate(x, y);
          verifyInterpolation(f, x, y);
          verifyConsistency((PolynomialSplineFunction) f, x);
  
          /* Check coefficients against values computed using R (version 1.8.1, Red Hat Linux 9)
           *
           * To replicate in R:
           *     x[1] <- 0
           *     x[2] <- pi / 6, etc, same for y[] (could use y <- scan() for y values)
           *     g <- splinefun(x, y, "natural")
           *     splinecoef <- eval(expression(z), envir = environment(g))
           *     print(splinecoef)
           */
          PolynomialFunction[] polynomials = ((PolynomialSplineFunction) f).getPolynomials();
          double[] target = {y[0], 1.002676d, 0d, -0.17415829d};
          UnitTestUtils.assertEquals(polynomials[0].getCoefficients(), target, sineCoefficientTolerance);
          target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
          UnitTestUtils.assertEquals(polynomials[1].getCoefficients(), target, sineCoefficientTolerance);
          target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
          UnitTestUtils.assertEquals(polynomials[2].getCoefficients(), target, sineCoefficientTolerance);
          target = new double[]{y[3], -8.594367e-01, -2.735672e-01, 0.17415829};
          UnitTestUtils.assertEquals(polynomials[3].getCoefficients(), target, sineCoefficientTolerance);
          target = new double[]{y[4], -1.002676, 6.548562e-17, 0.17415829};
          UnitTestUtils.assertEquals(polynomials[4].getCoefficients(), target, sineCoefficientTolerance);
          target = new double[]{y[5], -8.594367e-01, 2.735672e-01, 0.08707914};
          UnitTestUtils.assertEquals(polynomials[5].getCoefficients(), target, sineCoefficientTolerance);
          target = new double[]{y[6], 3.466465e-16, 5.471344e-01, -0.08707914};
          UnitTestUtils.assertEquals(polynomials[6].getCoefficients(), target, sineCoefficientTolerance);
          target = new double[]{y[7], 8.594367e-01, 2.735672e-01, -0.17415829};
          UnitTestUtils.assertEquals(polynomials[7].getCoefficients(), target, sineCoefficientTolerance);
  
          //Check interpolation
          Assert.assertEquals(FastMath.sqrt(2d) / 2d,f.value(FastMath.PI/4d),sineInterpolationTolerance);
          Assert.assertEquals(FastMath.sqrt(2d) / 2d,f.value(3d*FastMath.PI/4d),sineInterpolationTolerance);
      }
  
      /**
      * Verifies that interpolating polynomials satisfy consistency requirement:
      *    adjacent polynomials must agree through two derivatives at knot points
      */
     protected void verifyConsistency(PolynomialSplineFunction f, double[] x)
         {
         PolynomialFunction[] polynomials = f.getPolynomials();
         for (int i = 1; i < x.length - 2; i++) {
             // evaluate polynomials and derivatives at x[i + 1]
             Assert.assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
             Assert.assertEquals(polynomials[i].polynomialDerivative().value(x[i +1] - x[i]),
                                 polynomials[i + 1].polynomialDerivative().value(0), 0.5);
             Assert.assertEquals(polynomials[i].polynomialDerivative().polynomialDerivative().value(x[i +1] - x[i]),
                                 polynomials[i + 1].polynomialDerivative().polynomialDerivative().value(0), 0.5);
         }
     }
 
 }