/*
    * 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.
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  /*
   * 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.analysis.differentiation.DSFactory;
  import org.hipparchus.analysis.differentiation.DerivativeStructure;
  import org.hipparchus.analysis.differentiation.Gradient;
  import org.hipparchus.analysis.polynomials.PolynomialFunction;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.util.FastMath;
  import org.junit.jupiter.api.Test;
  
  import java.util.Random;
  
  import static org.junit.jupiter.api.Assertions.assertEquals;
  import static org.junit.jupiter.api.Assertions.assertThrows;
  import static org.junit.jupiter.api.Assertions.assertTrue;
  
  class HermiteInterpolatorTest {
  
      @Test
      void testZero() {
          HermiteInterpolator interpolator = new HermiteInterpolator();
          interpolator.addSamplePoint(0.0, new double[] { 0.0 });
          DSFactory factory = new DSFactory(1, 1);
          for (double x = -10; x < 10; x += 1.0) {
              DerivativeStructure y = interpolator.value(factory.variable(0, x))[0];
              assertEquals(0.0, y.getValue(), 1.0e-15);
              assertEquals(0.0, y.getPartialDerivative(1), 1.0e-15);
          }
          checkPolynomial(new PolynomialFunction(new double[] { 0.0 }),
                          interpolator.getPolynomials()[0]);
      }
  
      @Test
      void testQuadratic() {
          HermiteInterpolator interpolator = new HermiteInterpolator();
          interpolator.addSamplePoint(0.0, new double[] { 2.0 });
          interpolator.addSamplePoint(1.0, new double[] { 0.0 });
          interpolator.addSamplePoint(2.0, new double[] { 0.0 });
          DSFactory factory = new DSFactory(1, 1);
          for (double x = -10; x < 10; x += 1.0) {
              DerivativeStructure y = interpolator.value(factory.variable(0, x))[0];
              assertEquals((x - 1.0) * (x - 2.0), y.getValue(), 1.0e-15);
              assertEquals(2 * x - 3.0, y.getPartialDerivative(1), 1.0e-15);
          }
          checkPolynomial(new PolynomialFunction(new double[] { 2.0, -3.0, 1.0 }),
                          interpolator.getPolynomials()[0]);
      }
  
      @Test
      void testMixedDerivatives() {
          HermiteInterpolator interpolator = new HermiteInterpolator();
          interpolator.addSamplePoint(0.0, new double[] { 1.0 }, new double[] { 2.0 });
          interpolator.addSamplePoint(1.0, new double[] { 4.0 });
          interpolator.addSamplePoint(2.0, new double[] { 5.0 }, new double[] { 2.0 });
          DSFactory factory = new DSFactory(1, 1);
          assertEquals(4, interpolator.getPolynomials()[0].degree());
          DerivativeStructure y0 = interpolator.value(factory.variable(0, 0.0))[0];
          assertEquals(1.0, y0.getValue(), 1.0e-15);
          assertEquals(2.0, y0.getPartialDerivative(1), 1.0e-15);
          double[][] d0 = interpolator.derivatives(0.0, 1);
          assertEquals(1.0, d0[0][0], 1.0e-15);
          assertEquals(2.0, d0[1][0], 1.0e-15);
          assertEquals(4.0, interpolator.value(1.0)[0], 1.0e-15);
          DerivativeStructure y2 = interpolator.value(factory.variable(0, 2.0))[0];
          assertEquals(5.0, y2.getValue(), 1.0e-15);
          assertEquals(2.0, y2.getPartialDerivative(1), 1.0e-15);
          double[][] d2 = interpolator.derivatives(2.0, 1);
          assertEquals(5.0, d2[0][0], 1.0e-15);
          assertEquals(2.0, d2[1][0], 1.0e-15);
          checkPolynomial(new PolynomialFunction(new double[] { 1.0, 2.0, 4.0, -4.0, 1.0 }),
                          interpolator.getPolynomials()[0]);
      }
  
      @Test
      void testRandomPolynomialsValuesOnly() {
  
          Random random = new Random(0x42b1e7dbd361a932l);
  
         for (int i = 0; i < 100; ++i) {
 
             int maxDegree = 0;
             PolynomialFunction[] p = new PolynomialFunction[5];
             for (int k = 0; k < p.length; ++k) {
                 int degree = random.nextInt(7);
                 p[k] = randomPolynomial(degree, random);
                 maxDegree = FastMath.max(maxDegree, degree);
             }
 
             HermiteInterpolator interpolator = new HermiteInterpolator();
             for (int j = 0; j < 1 + maxDegree; ++j) {
                 double x = 0.1 * j;
                 double[] values = new double[p.length];
                 for (int k = 0; k < p.length; ++k) {
                     values[k] = p[k].value(x);
                 }
                 interpolator.addSamplePoint(x, values);
             }
 
             for (double x = 0; x < 2; x += 0.1) {
                 double[] values = interpolator.value(x);
                 assertEquals(p.length, values.length);
                 for (int k = 0; k < p.length; ++k) {
                     assertEquals(p[k].value(x), values[k], 1.0e-8 * FastMath.abs(p[k].value(x)));
                 }
             }
 
             PolynomialFunction[] result = interpolator.getPolynomials();
             for (int k = 0; k < p.length; ++k) {
                 checkPolynomial(p[k], result[k]);
             }
 
         }
     }
 
     @Test
     void testRandomPolynomialsFirstDerivative() {
 
         Random random = new Random(0x570803c982ca5d3bl);
 
         for (int i = 0; i < 100; ++i) {
 
             int maxDegree = 0;
             PolynomialFunction[] p      = new PolynomialFunction[5];
             PolynomialFunction[] pPrime = new PolynomialFunction[5];
             for (int k = 0; k < p.length; ++k) {
                 int degree = random.nextInt(7);
                 p[k]      = randomPolynomial(degree, random);
                 pPrime[k] = p[k].polynomialDerivative();
                 maxDegree = FastMath.max(maxDegree, degree);
             }
 
             HermiteInterpolator interpolator = new HermiteInterpolator();
             for (int j = 0; j < 1 + maxDegree / 2; ++j) {
                 double x = 0.1 * j;
                 double[] values      = new double[p.length];
                 double[] derivatives = new double[p.length];
                 for (int k = 0; k < p.length; ++k) {
                     values[k]      = p[k].value(x);
                     derivatives[k] = pPrime[k].value(x);
                 }
                 interpolator.addSamplePoint(x, values, derivatives);
             }
 
             DSFactory factory = new DSFactory(1, 1);
             for (double x = 0; x < 2; x += 0.1) {
                 DerivativeStructure[] y = interpolator.value(factory.variable(0, x));
                 assertEquals(p.length, y.length);
                 for (int k = 0; k < p.length; ++k) {
                     assertEquals(p[k].value(x), y[k].getValue(), 1.0e-8 * FastMath.abs(p[k].value(x)));
                     assertEquals(pPrime[k].value(x), y[k].getPartialDerivative(1), 4.0e-8 * FastMath.abs(p[k].value(x)));
                 }
             }
 
             PolynomialFunction[] result = interpolator.getPolynomials();
             for (int k = 0; k < p.length; ++k) {
                 checkPolynomial(p[k], result[k]);
             }
 
         }
     }
 
     @Test
     void testSine() {
         HermiteInterpolator interpolator = new HermiteInterpolator();
         for (double x = 0; x < FastMath.PI; x += 0.5) {
             interpolator.addSamplePoint(x, new double[] { FastMath.sin(x) });
         }
         DSFactory factory = new DSFactory(1, 2);
         for (double x = 0.1; x <= 2.9; x += 0.01) {
             DerivativeStructure y = interpolator.value(factory.variable(0, x))[0];
             assertEquals( FastMath.sin(x), y.getValue(), 3.5e-5);
             assertEquals( FastMath.cos(x), y.getPartialDerivative(1), 1.3e-4);
             assertEquals(-FastMath.sin(x), y.getPartialDerivative(2), 2.9e-3);
         }
     }
 
     @Test
     void testSquareRoot() {
         HermiteInterpolator interpolator = new HermiteInterpolator();
         for (double x = 1.0; x < 3.6; x += 0.5) {
             interpolator.addSamplePoint(x, new double[] { FastMath.sqrt(x) });
         }
         DSFactory factory = new DSFactory(1, 1);
         for (double x = 1.1; x < 3.5; x += 0.01) {
             DerivativeStructure y = interpolator.value(factory.variable(0, x))[0];
             assertEquals(FastMath.sqrt(x), y.getValue(), 1.5e-4);
             assertEquals(0.5 / FastMath.sqrt(x), y.getPartialDerivative(1), 8.5e-4);
         }
     }
 
     @Test
     void testWikipedia() {
         // this test corresponds to the example from Wikipedia page:
         // http://en.wikipedia.org/wiki/Hermite_interpolation
         HermiteInterpolator interpolator = new HermiteInterpolator();
         interpolator.addSamplePoint(-1, new double[] { 2 }, new double[] { -8 }, new double[] { 56 });
         interpolator.addSamplePoint( 0, new double[] { 1 }, new double[] {  0 }, new double[] {  0 });
         interpolator.addSamplePoint( 1, new double[] { 2 }, new double[] {  8 }, new double[] { 56 });
         DSFactory factory = new DSFactory(1, 1);
         for (double x = -1.0; x <= 1.0; x += 0.125) {
             DerivativeStructure y = interpolator.value(factory.variable(0, x))[0];
             double x2 = x * x;
             double x4 = x2 * x2;
             double x8 = x4 * x4;
             assertEquals(x8 + 1, y.getValue(), 1.0e-15);
             assertEquals(8 * x4 * x2 * x, y.getPartialDerivative(1), 1.0e-15);
         }
         checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 0, 0, 0, 0, 0, 0, 1 }),
                         interpolator.getPolynomials()[0]);
     }
 
     @Test
     void testWikipediaGradient() {
         // this test corresponds to the example from Wikipedia page:
         // http://en.wikipedia.org/wiki/Hermite_interpolation
         HermiteInterpolator interpolator = new HermiteInterpolator();
         interpolator.addSamplePoint(-1, new double[] { 2 }, new double[] { -8 }, new double[] { 56 });
         interpolator.addSamplePoint( 0, new double[] { 1 }, new double[] {  0 }, new double[] {  0 });
         interpolator.addSamplePoint( 1, new double[] { 2 }, new double[] {  8 }, new double[] { 56 });
         for (double x = -1.0; x <= 1.0; x += 0.125) {
             Gradient y = interpolator.value(Gradient.variable(1, 0, x))[0];
             double x2 = x * x;
             double x4 = x2 * x2;
             double x8 = x4 * x4;
             assertEquals(x8 + 1, y.getValue(), 1.0e-15);
             assertEquals(8 * x4 * x2 * x, y.getPartialDerivative(0), 1.0e-15);
         }
         checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 0, 0, 0, 0, 0, 0, 1 }),
                         interpolator.getPolynomials()[0]);
     }
 
     @Test
     void testOnePointParabola() {
         HermiteInterpolator interpolator = new HermiteInterpolator();
         interpolator.addSamplePoint(0, new double[] { 1 }, new double[] { 1 }, new double[] { 2 });
         DSFactory factory = new DSFactory(1, 1);
         for (double x = -1.0; x <= 1.0; x += 0.125) {
             DerivativeStructure y = interpolator.value(factory.variable(0, x))[0];
             assertEquals(1 + x * (1 + x), y.getValue(), 1.0e-15);
             assertEquals(1 + 2 * x, y.getPartialDerivative(1), 1.0e-15);
         }
         checkPolynomial(new PolynomialFunction(new double[] { 1, 1, 1 }),
                         interpolator.getPolynomials()[0]);
     }
 
     private PolynomialFunction randomPolynomial(int degree, Random random) {
         double[] coeff = new double[ 1 + degree];
         for (int j = 0; j < degree; ++j) {
             coeff[j] = random.nextDouble();
         }
         return new PolynomialFunction(coeff);
     }
 
     @Test
     void testEmptySample() {
         assertThrows(MathIllegalArgumentException.class, () -> {
             new HermiteInterpolator().value(0.0);
         });
     }
 
     @Test
     void testDuplicatedAbscissa() {
         assertThrows(MathIllegalArgumentException.class, () -> {
             HermiteInterpolator interpolator = new HermiteInterpolator();
             interpolator.addSamplePoint(1.0, new double[]{0.0});
             interpolator.addSamplePoint(1.0, new double[]{1.0});
         });
     }
 
     private void checkPolynomial(PolynomialFunction expected, PolynomialFunction result) {
         assertTrue(result.degree() >= expected.degree());
         double[] cE = expected.getCoefficients();
         double[] cR = result.getCoefficients();
         for (int i = 0; i < cE.length; ++i) {
             assertEquals(cE[i], cR[i], 1.0e-8 * FastMath.abs(cE[i]));
         }
         for (int i = cE.length; i < cR.length; ++i) {
             assertEquals(0.0, cR[i], 1.0e-9);
         }
     }
 
 }