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1   /*
2    * Licensed to the Hipparchus project under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The Hipparchus project licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      https://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.hipparchus.special.elliptic.jacobi;
18  
19  import org.hipparchus.CalculusFieldElement;
20  import org.hipparchus.util.FastMath;
21  import org.hipparchus.util.FieldSinCos;
22  
23  /** Algorithm for computing the principal Jacobi functions for parameters slightly above zero.
24   * <p>
25   * The algorithm for evaluating the functions is based on approximation
26   * in terms of circular functions. It is given in Abramowitz and Stegun,
27   * sections 16.13.
28   * </p>
29   * @param <T> the type of the field elements
30   * @since 2.0
31   */
32  class FieldNearZeroParameter<T extends CalculusFieldElement<T>> extends FieldJacobiElliptic<T> {
33  
34      /** Simple constructor.
35       * @param m parameter of the Jacobi elliptic function (must be zero or slightly positive here)
36       */
37      FieldNearZeroParameter(final T m) {
38          super(m);
39      }
40  
41      /** {@inheritDoc} */
42      @Override
43      public FieldCopolarN<T> valuesN(final T u) {
44          final FieldSinCos<T> sc     = FastMath.sinCos(u);
45          final T              factor = getM().multiply(u.subtract(sc.sin().multiply(sc.cos()))).multiply(0.25);
46          return new FieldCopolarN<>(sc.sin().subtract(factor.multiply(sc.cos())),             // equation 16.13.1
47                          sc.cos().add(factor.multiply(sc.sin())),                             // equation 16.13.2
48                          getM().multiply(sc.sin()).multiply(sc.sin()).multiply(-0.5).add(1)); // equation 16.13.3
49      }
50  
51  }