/*
    * 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.differentiation;
  
  import org.apache.commons.math4.legacy.TestUtils;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  
  /**
   * Test for class {@link JacobianFunction}.
   */
  public class JacobianFunctionTest {
  
      @Test
      public void testSphere() {
          SphereMapping    f = new SphereMapping(10.0);
          JacobianFunction j = new JacobianFunction(f);
          for (double latitude = -1.5; latitude < 1.5; latitude += 0.1) {
              for (double longitude = -3.1; longitude < 3.1; longitude += 0.1) {
                  double[] point = new double[] { latitude, longitude };
                  double[][] referenceJacobian  = f.jacobian(point);
                  double[][] testJacobian       = j.value(point);
                  Assert.assertEquals(referenceJacobian.length, testJacobian.length);
                  for (int i = 0; i < 3; ++i) {
                      TestUtils.assertEquals(referenceJacobian[i], testJacobian[i], 2.0e-15);
                  }
              }
          }
      }
  
      /* Maps (latitude, longitude) to (x, y, z) */
      private static final class SphereMapping implements MultivariateDifferentiableVectorFunction {
  
          private final double radius;
  
          SphereMapping(final double radius) {
              this.radius = radius;
          }
  
          @Override
          public double[] value(double[] point) {
              final double cLat = JdkMath.cos(point[0]);
              final double sLat = JdkMath.sin(point[0]);
              final double cLon = JdkMath.cos(point[1]);
              final double sLon = JdkMath.sin(point[1]);
              return new double[] {
                  radius * cLon * cLat,
                  radius * sLon * cLat,
                  radius * sLat
              };
          }
  
          @Override
          public DerivativeStructure[] value(DerivativeStructure[] point) {
              final DerivativeStructure cLat = point[0].cos();
              final DerivativeStructure sLat = point[0].sin();
              final DerivativeStructure cLon = point[1].cos();
              final DerivativeStructure sLon = point[1].sin();
              return new DerivativeStructure[] {
                  cLon.multiply(cLat).multiply(radius),
                  sLon.multiply(cLat).multiply(radius),
                  sLat.multiply(radius)
              };
          }
  
          public double[][] jacobian(double[] point) {
              final double cLat = JdkMath.cos(point[0]);
              final double sLat = JdkMath.sin(point[0]);
              final double cLon = JdkMath.cos(point[1]);
              final double sLon = JdkMath.sin(point[1]);
              return new double[][] {
                  { -radius * cLon * sLat, -radius * sLon * cLat },
                  { -radius * sLon * sLat,  radius * cLon * cLat },
                  {  radius * cLat,         0  }
              };
          }
      }
  }