/*
    * 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.polynomials;
  
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.analysis.differentiation.*;
  import org.hipparchus.complex.Complex;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.random.RandomDataGenerator;
  import org.hipparchus.util.Binary64;
  import org.hipparchus.util.FastMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Tests the FieldPolynomialFunction implementation of a UnivariateFunction.
   *
   */
  public final class FieldPolynomialFunctionTest {
      /** Error tolerance for tests */
      protected double tolerance = 1e-12;
  
      /**
       * tests the value of a constant polynomial.
       *
       * <p>value of this is 2.5 everywhere.</p>
       */
      @Test
      public void testConstants() {
          double c0 = 2.5;
          FieldPolynomialFunction<Binary64> f = buildD64(c0);
  
          // verify that we are equal to c[0] at several (nonsymmetric) places
          Assert.assertEquals(c0, f.value(0).getReal(), tolerance);
          Assert.assertEquals(c0, f.value(-1).getReal(), tolerance);
          Assert.assertEquals(c0, f.value(-123.5).getReal(), tolerance);
          Assert.assertEquals(c0, f.value(3).getReal(), tolerance);
          Assert.assertEquals(c0, f.value(new Binary64(456.89)).getReal(), tolerance);
  
          Assert.assertEquals(0, f.degree());
          Assert.assertEquals(0, f.polynomialDerivative().value(0).getReal(), tolerance);
  
          Assert.assertEquals(0, f.polynomialDerivative().polynomialDerivative().value(0).getReal(), tolerance);
      }
  
      /**
       * tests the value of a linear polynomial.
       *
       * <p>This will test the function f(x) = 3*x - 1.5</p>
       * <p>This will have the values
       *  <tt>f(0) = -1.5, f(-1) = -4.5, f(-2.5) = -9,
       *      f(0.5) = 0, f(1.5) = 3</tt> and {@code f(3) = 7.5}
       * </p>
       */
      @Test
      public void testLinear() {
         FieldPolynomialFunction<Binary64> f = buildD64(-1.5, 3);
  
          // verify that we are equal to c[0] when x=0
          Assert.assertEquals(-1.5, f.value(new Binary64(0)).getReal(), tolerance);
  
          // now check a few other places
          Assert.assertEquals(-4.5, f.value(new Binary64(-1)).getReal(), tolerance);
          Assert.assertEquals(-9, f.value(new Binary64(-2.5)).getReal(), tolerance);
          Assert.assertEquals(0, f.value(new Binary64(0.5)).getReal(), tolerance);
          Assert.assertEquals(3, f.value(new Binary64(1.5)).getReal(), tolerance);
          Assert.assertEquals(7.5, f.value(new Binary64(3)).getReal(), tolerance);
  
          Assert.assertEquals(1, f.degree());
  
          Assert.assertEquals(0, f.polynomialDerivative().polynomialDerivative().value(0).getReal(), tolerance);
      }
  
      /**
       * Tests a second order polynomial.
       * <p> This will test the function f(x) = 2x^2 - 3x -2 = (2x+1)(x-2)</p>
       */
      @Test
      public void testQuadratic() {
          FieldPolynomialFunction<Binary64> f = buildD64(-2, -3, 2);
 
         // verify that we are equal to c[0] when x=0
         Assert.assertEquals(-2, f.value(0).getReal(), tolerance);
 
         // now check a few other places
         Assert.assertEquals(0, f.value(-0.5).getReal(), tolerance);
         Assert.assertEquals(0, f.value(2).getReal(), tolerance);
         Assert.assertEquals(-2, f.value(1.5).getReal(), tolerance);
         Assert.assertEquals(7, f.value(-1.5).getReal(), tolerance);
         Assert.assertEquals(265.5312, f.value(12.34).getReal(), tolerance);
     }
 
     /**
      * This will test the quintic function
      *   f(x) = x^2(x-5)(x+3)(x-1) = x^5 - 3x^4 -13x^3 + 15x^2</p>
      */
     @Test
     public void testQuintic() {
         FieldPolynomialFunction<Binary64> f = buildD64(0, 0, 15, -13, -3, 1);
 
         // verify that we are equal to c[0] when x=0
         Assert.assertEquals(0, f.value(0).getReal(), tolerance);
 
         // now check a few other places
         Assert.assertEquals(0, f.value(5).getReal(), tolerance);
         Assert.assertEquals(0, f.value(1).getReal(), tolerance);
         Assert.assertEquals(0, f.value(-3).getReal(), tolerance);
         Assert.assertEquals(54.84375, f.value(-1.5).getReal(), tolerance);
         Assert.assertEquals(-8.06637, f.value(1.3).getReal(), tolerance);
 
         Assert.assertEquals(5, f.degree());
     }
 
     /**
      * tests the firstDerivative function by comparison
      *
      * <p>This will test the functions
      * {@code f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6}
      * and {@code h(x) = 6x - 4}
      */
     @Test
     public void testfirstDerivativeComparison() {
         double[] f_coeff = { 3, 6, -2, 1 };
         double[] g_coeff = { 6, -4, 3 };
         double[] h_coeff = { -4, 6 };
 
         FieldPolynomialFunction<Binary64> f = buildD64(f_coeff);
         FieldPolynomialFunction<Binary64> g = buildD64(g_coeff);
         FieldPolynomialFunction<Binary64> h = buildD64(h_coeff);
 
         // compare f' = g
         Assert.assertEquals(f.polynomialDerivative().value(0).getReal(), g.value(0).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(1).getReal(), g.value(1).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(100).getReal(), g.value(100).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(4.1).getReal(), g.value(4.1).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(-3.25).getReal(), g.value(-3.25).getReal(), tolerance);
 
         // compare g' = h
         Assert.assertEquals(g.polynomialDerivative().value(FastMath.PI).getReal(), h.value(FastMath.PI).getReal(), tolerance);
         Assert.assertEquals(g.polynomialDerivative().value(FastMath.E).getReal(),  h.value(FastMath.E).getReal(),  tolerance);
     }
 
     @Test
     public void testAddition() {
         FieldPolynomialFunction<Binary64> p1 = buildD64( -2, 1 );
         FieldPolynomialFunction<Binary64> p2 = buildD64( 2, -1, 0 );
         checkNullPolynomial(p1.add(p2));
 
         p2 = p1.add(p1);
         checkCoeffs(Double.MIN_VALUE, p2, -4, 2);
 
         p1 = buildD64( 1, -4, 2 );
         p2 = buildD64( -1, 3, -2 );
         p1 = p1.add(p2);
         Assert.assertEquals(1, p1.degree());
         checkCoeffs(Double.MIN_VALUE, p1, 0, -1);
     }
 
     @Test
     public void testSubtraction() {
         FieldPolynomialFunction<Binary64> p1 = buildD64( -2, 1 );
         checkNullPolynomial(p1.subtract(p1));
 
         FieldPolynomialFunction<Binary64> p2 = buildD64( -2, 6 );
         p2 = p2.subtract(p1);
         checkCoeffs(Double.MIN_VALUE, p2, 0, 5);
 
         p1 = buildD64( 1, -4, 2 );
         p2 = buildD64( -1, 3, 2 );
         p1 = p1.subtract(p2);
         Assert.assertEquals(1, p1.degree());
         checkCoeffs(Double.MIN_VALUE, p1, 2, -7);
     }
 
     @Test
     public void testMultiplication() {
         FieldPolynomialFunction<Binary64> p1 = buildD64( -3, 2 );
         FieldPolynomialFunction<Binary64> p2 = buildD64( 3, 2, 1 );
         checkCoeffs(Double.MIN_VALUE, p1.multiply(p2), -9, 0, 1, 2);
 
         p1 = buildD64( 0, 1 );
         p2 = p1;
         for (int i = 2; i < 10; ++i) {
             p2 = p2.multiply(p1);
             double[] c = new double[i + 1];
             c[i] = 1;
             checkCoeffs(Double.MIN_VALUE, p2, c);
         }
     }
 
     /**
      * tests the firstDerivative function by comparison
      *
      * <p>This will test the functions
      * {@code f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6}
      * and {@code h(x) = 6x - 4}
      */
     @Test
     public void testMath341() {
         double[] f_coeff = { 3, 6, -2, 1 };
         double[] g_coeff = { 6, -4, 3 };
         double[] h_coeff = { -4, 6 };
 
         FieldPolynomialFunction<Binary64> f = buildD64(f_coeff);
         FieldPolynomialFunction<Binary64> g = buildD64(g_coeff);
         FieldPolynomialFunction<Binary64> h = buildD64(h_coeff);
 
         // compare f' = g
         Assert.assertEquals(f.polynomialDerivative().value(0).getReal(), g.value(0).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(1).getReal(), g.value(1).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(100).getReal(), g.value(100).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(4.1).getReal(), g.value(4.1).getReal(), tolerance);
         Assert.assertEquals(f.polynomialDerivative().value(-3.25).getReal(), g.value(-3.25).getReal(), tolerance);
 
         // compare g' = h
         Assert.assertEquals(g.polynomialDerivative().value(FastMath.PI).getReal(), h.value(FastMath.PI).getReal(), tolerance);
         Assert.assertEquals(g.polynomialDerivative().value(FastMath.E).getReal(),  h.value(FastMath.E).getReal(),  tolerance);
     }
 
     @Test
     public void testAntiDerivative() {
         // 1 + 2x + 3x^2
         final double[] coeff = {1, 2, 3};
         final FieldPolynomialFunction<Binary64> p = buildD64(coeff);
         // x + x^2 + x^3
         checkCoeffs(Double.MIN_VALUE, p.antiDerivative(), 0, 1, 1, 1);
     }
 
     @Test
     public void testAntiDerivativeConstant() {
         final double[] coeff = {2};
         final FieldPolynomialFunction<Binary64> p = buildD64(coeff);
         checkCoeffs(Double.MIN_VALUE, p.antiDerivative(), 0, 2);
     }
 
     @Test
     public void testAntiDerivativeZero() {
         final double[] coeff = {0};
         final FieldPolynomialFunction<Binary64> p = buildD64(coeff);
         checkCoeffs(Double.MIN_VALUE, p.antiDerivative(), 0);
     }
 
     @Test
     public void testAntiDerivativeRandom() {
         final RandomDataGenerator ran = new RandomDataGenerator(1000);
         double[] coeff = null;
         FieldPolynomialFunction<Binary64> p = null;
         int d = 0;
         for (int i = 0; i < 20; i++) {
             d = ran.nextInt(1, 50);
             coeff = new double[d];
             for (int j = 0; j < d; j++) {
                 coeff[j] = ran.nextUniform(-100, 1000);
             }
             p = buildD64(coeff);
             checkInverseDifferentiation(p);
         }
     }
 
     @Test
     public void testIntegrate() {
         // -x^2
         final double[] coeff = {0, 0, -1};
         final FieldPolynomialFunction<Binary64> p = buildD64(coeff);
         Assert.assertEquals(-2d/3d, p.integrate(-1, 1).getReal(),Double.MIN_VALUE);
 
         // x(x-1)(x+1) - should integrate to 0 over [-1,1]
         final FieldPolynomialFunction<Binary64> p2 = buildD64(0, 1).
                                                       multiply(buildD64(-1, 1)).
                                                       multiply(buildD64(1, 1));
         Assert.assertEquals(0, p2.integrate(-1, 1).getReal(), Double.MIN_VALUE);
     }
 
     @Test(expected = MathIllegalArgumentException.class)
     public void testIntegrateInfiniteBounds() {
         final FieldPolynomialFunction<Binary64> p = buildD64(1);
         p.integrate(0, Double.POSITIVE_INFINITY);
     }
 
     @Test(expected = MathIllegalArgumentException.class)
     public void testIntegrateBadInterval() {
         final FieldPolynomialFunction<Binary64> p = buildD64(1);
         p.integrate(0, -1);
     }
 
     @Test
     public void testIssue259WithComplex() {
         final double nonZeroParameterForQuadraticCoeff = -1.;
         final Complex[] coefficients = buildImaginaryCoefficients(1., 2., nonZeroParameterForQuadraticCoeff);
         templateIssue259DisappearingCoefficients(coefficients);
     }
 
     @Test
     public void testIssue259WithGradient() {
         final double nonZeroParameterForQuadraticCoeff = -1.;
         final Gradient[] coefficients = buildUnivariateGradientCoefficients(1.,2., nonZeroParameterForQuadraticCoeff);
         templateIssue259DisappearingCoefficients(coefficients);
     }
 
     @Test
     public void testIssue259WithDerivativeStructure() {
         final double nonZeroParameterForQuadraticCoeff = -1.;
         final DerivativeStructure[] coefficients = buildUnivariateDSCoefficients(1.,2., nonZeroParameterForQuadraticCoeff);
         templateIssue259DisappearingCoefficients(coefficients);
     }
 
     @Test
     public void testIssue259WithUnivariateDerivative1() {
         final double nonZeroParameterForQuadraticCoeff = -1.;
         final UnivariateDerivative1[] coefficients = buildUnivariateDerivative1Coefficients(1.,2., nonZeroParameterForQuadraticCoeff);
         templateIssue259DisappearingCoefficients(coefficients);
     }
 
     @Test
     public void testIssue259WithUnivariateDerivative2() {
         final double nonZeroParameterForQuadraticCoeff = -1.;
         final UnivariateDerivative2[] coefficients = buildUnivariateDerivative2Coefficients(1.,2., nonZeroParameterForQuadraticCoeff);
         templateIssue259DisappearingCoefficients(coefficients);
     }
 
     private <T extends CalculusFieldElement<T>> void templateIssue259DisappearingCoefficients(T[] coefficients) {
         final FieldPolynomialFunction<T> polynomialFunction = new FieldPolynomialFunction<>(coefficients);
         Assert.assertEquals(coefficients.length, polynomialFunction.getCoefficients().length);
         for (int i = 0; i < coefficients.length; i++) {
             Assert.assertEquals(coefficients[i], polynomialFunction.getCoefficients()[i]);
         }
     }
 
     private <T extends CalculusFieldElement<T>> void checkInverseDifferentiation(FieldPolynomialFunction<T> p) {
         final T[] c0 = p.getCoefficients();
         final T[] c1 = p.antiDerivative().polynomialDerivative().getCoefficients();
         Assert.assertEquals(c0.length, c1.length);
         for (int i = 0; i < c0.length; ++i) {
             Assert.assertEquals(c0[i].getReal(), c1[i].getReal(), 1e-12);
         }
     }
 
     private <T extends CalculusFieldElement<T>> void checkCoeffs(final double tolerance, final FieldPolynomialFunction<T> p,
                                                                  final double... ref) {
         final T[] c = p.getCoefficients();
         Assert.assertEquals(ref.length, c.length);
         for (int i = 0; i < ref.length; ++i) {
             Assert.assertEquals(ref[i], c[i].getReal(), tolerance);
         }
     }
 
     private <T extends CalculusFieldElement<T>> void checkNullPolynomial(FieldPolynomialFunction<T> p) {
         for (T coefficient : p.getCoefficients()) {
             Assert.assertEquals(0, coefficient.getReal(), 1e-15);
         }
     }
 
     private FieldPolynomialFunction<Binary64> buildD64(double...c) {
         Binary64[] array = new Binary64[c.length];
         for (int i = 0; i < c.length; ++i) {
             array[i] = new Binary64(c[i]);
         }
         return new FieldPolynomialFunction<>(array);
     }
 
     private Complex[] buildImaginaryCoefficients(double...c) {
         Complex[] array = new Complex[c.length];
         for (int i = 0; i < c.length; ++i) {
             array[i] = new Complex(0., c[i]);
         }
         return array;
     }
 
     private DerivativeStructure[] buildUnivariateDSCoefficients(double...c) {
         DerivativeStructure[] array = new DerivativeStructure[c.length];
         final DSFactory factory = new DSFactory(1, 1);
         for (int i = 0; i < c.length; ++i) {
             array[i] = factory.variable(0, 0.).multiply(c[i]);
         }
         return array;
     }
 
     private Gradient[] buildUnivariateGradientCoefficients(double...c) {
         Gradient[] array = new Gradient[c.length];
         for (int i = 0; i < c.length; ++i) {
             array[i] = Gradient.variable(1, 0, 0.).multiply(c[i]);
         }
         return array;
     }
 
     private UnivariateDerivative1[] buildUnivariateDerivative1Coefficients(double...c) {
         UnivariateDerivative1[] array = new UnivariateDerivative1[c.length];
         for (int i = 0; i < c.length; ++i) {
             array[i] = new UnivariateDerivative1(0., c[i]);
         }
         return array;
     }
 
     private UnivariateDerivative2[] buildUnivariateDerivative2Coefficients(double...c) {
         UnivariateDerivative2[] array = new UnivariateDerivative2[c.length];
         for (int i = 0; i < c.length; ++i) {
             array[i] = new UnivariateDerivative2(0., c[i], 0.);
         }
         return array;
     }
 
 }