/*
    * 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
    *
    *      http://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.
   */
  package org.apache.commons.math4.legacy.analysis.polynomials;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test case for Lagrange form of polynomial function.
   * <p>
   * We use n+1 points to interpolate a polynomial of degree n. This should
   * give us the exact same polynomial as result. Thus we can use a very
   * small tolerance to account only for round-off errors.
   *
   */
  public final class PolynomialFunctionLagrangeFormTest {
  
      /**
       * Test of polynomial for the linear function.
       */
      @Test
      public void testLinearFunction() {
          PolynomialFunctionLagrangeForm p;
          double[] c;
          double z;
          double expected;
          double result;
          double tolerance = 1E-12;
  
          // p(x) = 1.5x - 4
          double x[] = { 0.0, 3.0 };
          double y[] = { -4.0, 0.5 };
          p = new PolynomialFunctionLagrangeForm(x, y);
  
          z = 2.0; expected = -1.0; result = p.value(z);
          Assert.assertEquals(expected, result, tolerance);
  
          z = 4.5; expected = 2.75; result = p.value(z);
          Assert.assertEquals(expected, result, tolerance);
  
          z = 6.0; expected = 5.0; result = p.value(z);
          Assert.assertEquals(expected, result, tolerance);
  
          Assert.assertEquals(1, p.degree());
  
          c = p.getCoefficients();
          Assert.assertEquals(2, c.length);
          Assert.assertEquals(-4.0, c[0], tolerance);
          Assert.assertEquals(1.5, c[1], tolerance);
      }
  
      /**
       * Test of polynomial for the quadratic function.
       */
      @Test
      public void testQuadraticFunction() {
          PolynomialFunctionLagrangeForm p;
          double[] c;
          double z;
          double expected;
          double result;
          double tolerance = 1E-12;
  
          // p(x) = 2x^2 + 5x - 3 = (2x - 1)(x + 3)
          double x[] = { 0.0, -1.0, 0.5 };
          double y[] = { -3.0, -6.0, 0.0 };
          p = new PolynomialFunctionLagrangeForm(x, y);
  
          z = 1.0; expected = 4.0; result = p.value(z);
          Assert.assertEquals(expected, result, tolerance);
  
          z = 2.5; expected = 22.0; result = p.value(z);
          Assert.assertEquals(expected, result, tolerance);
  
          z = -2.0; expected = -5.0; result = p.value(z);
          Assert.assertEquals(expected, result, tolerance);
  
          Assert.assertEquals(2, p.degree());
  
          c = p.getCoefficients();
          Assert.assertEquals(3, c.length);
          Assert.assertEquals(-3.0, c[0], tolerance);
          Assert.assertEquals(5.0, c[1], tolerance);
          Assert.assertEquals(2.0, c[2], tolerance);
     }
 
     /**
      * Test of polynomial for the quintic function.
      */
     @Test
     public void testQuinticFunction() {
         PolynomialFunctionLagrangeForm p;
         double[] c;
         double z;
         double expected;
         double result;
         double tolerance = 1E-12;
 
         // p(x) = x^5 - x^4 - 7x^3 + x^2 + 6x = x(x^2 - 1)(x + 2)(x - 3)
         double x[] = { 1.0, -1.0, 2.0, 3.0, -3.0, 0.5 };
         double y[] = { 0.0, 0.0, -24.0, 0.0, -144.0, 2.34375 };
         p = new PolynomialFunctionLagrangeForm(x, y);
 
         z = 0.0; expected = 0.0; result = p.value(z);
         Assert.assertEquals(expected, result, tolerance);
 
         z = -2.0; expected = 0.0; result = p.value(z);
         Assert.assertEquals(expected, result, tolerance);
 
         z = 4.0; expected = 360.0; result = p.value(z);
         Assert.assertEquals(expected, result, tolerance);
 
         Assert.assertEquals(5, p.degree());
 
         c = p.getCoefficients();
         Assert.assertEquals(6, c.length);
         Assert.assertEquals(0.0, c[0], tolerance);
         Assert.assertEquals(6.0, c[1], tolerance);
         Assert.assertEquals(1.0, c[2], tolerance);
         Assert.assertEquals(-7.0, c[3], tolerance);
         Assert.assertEquals(-1.0, c[4], tolerance);
         Assert.assertEquals(1.0, c[5], tolerance);
     }
 
     /**
      * Test of parameters for the polynomial.
      */
     @Test
     public void testParameters() {
 
         try {
             // bad input array length
             double x[] = { 1.0 };
             double y[] = { 2.0 };
             new PolynomialFunctionLagrangeForm(x, y);
             Assert.fail("Expecting MathIllegalArgumentException - bad input array length");
         } catch (MathIllegalArgumentException ex) {
             // expected
         }
         try {
             // mismatch input arrays
             double x[] = { 1.0, 2.0, 3.0, 4.0 };
             double y[] = { 0.0, -4.0, -24.0 };
             new PolynomialFunctionLagrangeForm(x, y);
             Assert.fail("Expecting MathIllegalArgumentException - mismatch input arrays");
         } catch (MathIllegalArgumentException ex) {
             // expected
         }
     }
 }