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  package org.apache.commons.math4.legacy.analysis.interpolation;
  
  import java.util.Random;
  
  import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure;
  import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunction;
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.exception.NoDataException;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  public class HermiteInterpolatorTest {
  
      @Test
      public void testZero() {
          HermiteInterpolator interpolator = new HermiteInterpolator();
          interpolator.addSamplePoint(0.0, new double[] { 0.0 });
          for (double x = -10; x < 10; x += 1.0) {
              DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
              Assert.assertEquals(0.0, y.getValue(), 1.0e-15);
              Assert.assertEquals(0.0, y.getPartialDerivative(1), 1.0e-15);
          }
          checkPolynomial(new PolynomialFunction(new double[] { 0.0 }),
                          interpolator.getPolynomials()[0]);
      }
  
      @Test
      public 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 });
          for (double x = -10; x < 10; x += 1.0) {
              DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
              Assert.assertEquals((x - 1.0) * (x - 2.0), y.getValue(), 1.0e-15);
              Assert.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
      public 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 });
          Assert.assertEquals(4, interpolator.getPolynomials()[0].degree());
          DerivativeStructure y0 = interpolator.value(new DerivativeStructure(1, 1, 0, 0.0))[0];
          Assert.assertEquals(1.0, y0.getValue(), 1.0e-15);
          Assert.assertEquals(2.0, y0.getPartialDerivative(1), 1.0e-15);
          Assert.assertEquals(4.0, interpolator.value(1.0)[0], 1.0e-15);
          DerivativeStructure y2 = interpolator.value(new DerivativeStructure(1, 1, 0, 2.0))[0];
          Assert.assertEquals(5.0, y2.getValue(), 1.0e-15);
          Assert.assertEquals(2.0, y2.getPartialDerivative(1), 1.0e-15);
          checkPolynomial(new PolynomialFunction(new double[] { 1.0, 2.0, 4.0, -4.0, 1.0 }),
                          interpolator.getPolynomials()[0]);
      }
  
      @Test
      public 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 = JdkMath.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);
                 Assert.assertEquals(p.length, values.length);
                 for (int k = 0; k < p.length; ++k) {
                     Assert.assertEquals(p[k].value(x), values[k], 1.0e-8 * JdkMath.abs(p[k].value(x)));
                 }
             }
 
             PolynomialFunction[] result = interpolator.getPolynomials();
             for (int k = 0; k < p.length; ++k) {
                 checkPolynomial(p[k], result[k]);
             }
         }
     }
 
     @Test
     public 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 = JdkMath.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);
             }
 
             for (double x = 0; x < 2; x += 0.1) {
                 DerivativeStructure[] y = interpolator.value(new DerivativeStructure(1, 1, 0, x));
                 Assert.assertEquals(p.length, y.length);
                 for (int k = 0; k < p.length; ++k) {
                     Assert.assertEquals(p[k].value(x), y[k].getValue(), 1.0e-8 * JdkMath.abs(p[k].value(x)));
                     Assert.assertEquals(pPrime[k].value(x), y[k].getPartialDerivative(1), 4.0e-8 * JdkMath.abs(p[k].value(x)));
                 }
             }
 
             PolynomialFunction[] result = interpolator.getPolynomials();
             for (int k = 0; k < p.length; ++k) {
                 checkPolynomial(p[k], result[k]);
             }
         }
     }
 
     @Test
     public void testSine() {
         HermiteInterpolator interpolator = new HermiteInterpolator();
         for (double x = 0; x < JdkMath.PI; x += 0.5) {
             interpolator.addSamplePoint(x, new double[] { JdkMath.sin(x) });
         }
         for (double x = 0.1; x <= 2.9; x += 0.01) {
             DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 2, 0, x))[0];
             Assert.assertEquals( JdkMath.sin(x), y.getValue(), 3.5e-5);
             Assert.assertEquals( JdkMath.cos(x), y.getPartialDerivative(1), 1.3e-4);
             Assert.assertEquals(-JdkMath.sin(x), y.getPartialDerivative(2), 2.9e-3);
         }
     }
 
     @Test
     public void testSquareRoot() {
         HermiteInterpolator interpolator = new HermiteInterpolator();
         for (double x = 1.0; x < 3.6; x += 0.5) {
             interpolator.addSamplePoint(x, new double[] { JdkMath.sqrt(x) });
         }
         for (double x = 1.1; x < 3.5; x += 0.01) {
             DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
             Assert.assertEquals(JdkMath.sqrt(x), y.getValue(), 1.5e-4);
             Assert.assertEquals(0.5 / JdkMath.sqrt(x), y.getPartialDerivative(1), 8.5e-4);
         }
     }
 
     @Test
     public 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 });
         for (double x = -1.0; x <= 1.0; x += 0.125) {
             DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
             double x2 = x * x;
             double x4 = x2 * x2;
             double x8 = x4 * x4;
             Assert.assertEquals(x8 + 1, y.getValue(), 1.0e-15);
             Assert.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
     public void testOnePointParabola() {
         HermiteInterpolator interpolator = new HermiteInterpolator();
         interpolator.addSamplePoint(0, new double[] { 1 }, new double[] { 1 }, new double[] { 2 });
         for (double x = -1.0; x <= 1.0; x += 0.125) {
             DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
             Assert.assertEquals(1 + x * (1 + x), y.getValue(), 1.0e-15);
             Assert.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(expected=NoDataException.class)
     public void testEmptySample() {
         new HermiteInterpolator().value(0.0);
     }
 
     @Test(expected=MathIllegalArgumentException.class)
     public void testDuplicatedAbscissa() {
         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) {
         Assert.assertTrue(result.degree() >= expected.degree());
         double[] cE = expected.getCoefficients();
         double[] cR = result.getCoefficients();
         for (int i = 0; i < cE.length; ++i) {
             Assert.assertEquals(cE[i], cR[i], 1.0e-8 * JdkMath.abs(cE[i]));
         }
         for (int i = cE.length; i < cR.length; ++i) {
             Assert.assertEquals(0.0, cR[i], 1.0e-9);
         }
     }
 }