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.SinhCosh;
21
22 /** Algorithm for computing the principal Jacobi functions for parameters slightly below one.
23 * <p>
24 * The algorithm for evaluating the functions is based on approximation
25 * in terms of hyperbolic functions. It is given in Abramowitz and Stegun,
26 * sections 16.15.
27 * </p>
28 * @since 2.0
29 */
30 class NearOneParameter extends JacobiElliptic {
31
32 /** Complementary parameter of the Jacobi elliptic function. */
33 private final double m1;
34
35 /** Simple constructor.
36 * @param m parameter of the Jacobi elliptic function (must be one or slightly below one here)
37 */
38 NearOneParameter(final double m) {
39 super(m);
40 this.m1 = 1.0 - m;
41 }
42
43 /** {@inheritDoc} */
44 @Override
45 public CopolarN valuesN(final double u) {
46 final SinhCosh sch = FastMath.sinhCosh(u);
47 final double sech = 1.0 / sch.cosh();
48 final double t = sch.sinh() * sech;
49 final double factor = 0.25 * m1 * (sch.sinh() * sch.cosh() - u) * sech;
50 return new CopolarN(t + factor * sech, // equation 16.15.1
51 sech - factor * t, // equation 16.15.2
52 sech + factor * t); // equation 16.15.3
53 }
54
55 }