/*
    * 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.analysis.UnivariateFunction;
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.exception.MathIllegalStateException;
  import org.apache.commons.math4.legacy.exception.OutOfRangeException;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Tests the PolynomialSplineFunction implementation.
   *
   */
  public class PolynomialSplineFunctionTest {
  
      /** Error tolerance for tests */
      protected double tolerance = 1.0e-12;
  
      /**
       * Quadratic polynomials used in tests:
       *
       * x^2 + x            [-1, 0)
       * x^2 + x + 2        [0, 1)
       * x^2 + x + 4        [1, 2)
       *
       * Defined so that evaluation using PolynomialSplineFunction evaluation
       * algorithm agrees at knot point boundaries.
       */
      protected PolynomialFunction[] polynomials = {
          new PolynomialFunction(new double[] {0d, 1d, 1d}),
          new PolynomialFunction(new double[] {2d, 1d, 1d}),
          new PolynomialFunction(new double[] {4d, 1d, 1d})
      };
  
      /** Knot points  */
      protected double[] knots = {-1, 0, 1, 2};
  
      /** Derivative of test polynomials -- 2x + 1  */
      protected PolynomialFunction dp =
          new PolynomialFunction(new double[] {1d, 2d});
  
  
      @Test
      public void testConstructor() {
          PolynomialSplineFunction spline =
              new PolynomialSplineFunction(knots, polynomials);
          Assert.assertArrayEquals(knots, spline.getKnots(), 0.0);
          Assert.assertEquals(1d, spline.getPolynomials()[0].getCoefficients()[2], 0);
          Assert.assertEquals(3, spline.getN());
  
          try { // too few knots
              new PolynomialSplineFunction(new double[] {0}, polynomials);
              Assert.fail("Expecting MathIllegalArgumentException");
          } catch (MathIllegalArgumentException ex) {
              // expected
          }
  
          try { // too many knots
              new PolynomialSplineFunction(new double[] {0,1,2,3,4}, polynomials);
              Assert.fail("Expecting MathIllegalArgumentException");
          } catch (MathIllegalArgumentException ex) {
              // expected
          }
  
          try { // knots not increasing
              new PolynomialSplineFunction(new double[] {0,1, 3, 2}, polynomials);
              Assert.fail("Expecting MathIllegalArgumentException");
          } catch (MathIllegalArgumentException ex) {
              // expected
          }
      }
  
      @Test
      public void testValues() {
          PolynomialSplineFunction spline =
              new PolynomialSplineFunction(knots, polynomials);
          UnivariateFunction dSpline = spline.polynomialSplineDerivative();
  
          /**
           * interior points -- spline value at x should equal p(x - knot)
           * where knot is the largest knot point less than or equal to x and p
           * is the polynomial defined over the knot segment to which x belongs.
          */
         double x = -1;
         int index = 0;
         for (int i = 0; i < 10; i++) {
            x+=0.25;
            index = findKnot(knots, x);
            Assert.assertEquals("spline function evaluation failed for x=" + x,
                    polynomials[index].value(x - knots[index]), spline.value(x), tolerance);
            Assert.assertEquals("spline derivative evaluation failed for x=" + x,
                    dp.value(x - knots[index]), dSpline.value(x), tolerance);
         }
 
         // knot points -- centering should zero arguments
         for (int i = 0; i < 3; i++) {
             Assert.assertEquals("spline function evaluation failed for knot=" + knots[i],
                     polynomials[i].value(0), spline.value(knots[i]), tolerance);
             Assert.assertEquals("spline function evaluation failed for knot=" + knots[i],
                     dp.value(0), dSpline.value(knots[i]), tolerance);
         }
 
         try { //outside of domain -- under min
             x = spline.value(-1.5);
             Assert.fail("Expecting OutOfRangeException");
         } catch (OutOfRangeException ex) {
             // expected
         }
 
         try { //outside of domain -- over max
             x = spline.value(2.5);
             Assert.fail("Expecting OutOfRangeException");
         } catch (OutOfRangeException ex) {
             // expected
         }
     }
 
     @Test
     public void testIsValidPoint() {
         final PolynomialSplineFunction spline =
             new PolynomialSplineFunction(knots, polynomials);
         final double xMin = knots[0];
         final double xMax = knots[knots.length - 1];
 
         double x;
 
         x = xMin;
         Assert.assertTrue(spline.isValidPoint(x));
         // Ensure that no exception is thrown.
         spline.value(x);
 
         x = xMax;
         Assert.assertTrue(spline.isValidPoint(x));
         // Ensure that no exception is thrown.
         spline.value(x);
 
         final double xRange = xMax - xMin;
         x = xMin + xRange / 3.4;
         Assert.assertTrue(spline.isValidPoint(x));
         // Ensure that no exception is thrown.
         spline.value(x);
 
         final double small = 1e-8;
         x = xMin - small;
         Assert.assertFalse(spline.isValidPoint(x));
         // Ensure that an exception would have been thrown.
         try {
             spline.value(x);
             Assert.fail("OutOfRangeException expected");
         } catch (OutOfRangeException expected) {}
     }
 
     /**
      *  Do linear search to find largest knot point less than or equal to x.
      *  Implementation does binary search.
      */
      protected int findKnot(double[] knots, double x) {
          if (x < knots[0] || x >= knots[knots.length -1]) {
              throw new OutOfRangeException(x, knots[0], knots[knots.length -1]);
          }
          for (int i = 0; i < knots.length; i++) {
              if (knots[i] > x) {
                  return i - 1;
              }
          }
          throw new MathIllegalStateException();
      }
 }