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.util.FastMath;
20 import org.hipparchus.util.SinCos;
21
22 /** Algorithm for computing the principal Jacobi functions for parameters slightly above zero.
23 * <p>
24 * The algorithm for evaluating the functions is based on approximation
25 * in terms of circular functions. It is given in Abramowitz and Stegun,
26 * sections 16.13.
27 * </p>
28 * @since 2.0
29 */
30 class NearZeroParameter extends JacobiElliptic {
31
32 /** Simple constructor.
33 * @param m parameter of the Jacobi elliptic function (must be zero or slightly positive here)
34 */
35 NearZeroParameter(final double m) {
36 super(m);
37 }
38
39 /** {@inheritDoc} */
40 @Override
41 public CopolarN valuesN(final double u) {
42 final SinCos sc = FastMath.sinCos(u);
43 final double factor = 0.25 * getM() * (u - sc.sin() * sc.cos());
44 return new CopolarN(sc.sin() - factor * sc.cos(), // equation 16.13.1
45 sc.cos() + factor * sc.sin(), // equation 16.13.2
46 1 - 0.5 * getM() * sc.sin() * sc.sin()); // equation 16.13.3
47 }
48
49 }