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.FieldSinhCosh;
22
23 /** Algorithm for computing the principal Jacobi functions for parameters slightly below one.
24 * <p>
25 * The algorithm for evaluating the functions is based on approximation
26 * in terms of hyperbolic functions. It is given in Abramowitz and Stegun,
27 * sections 16.15.
28 * </p>
29 * @param <T> the type of the field elements
30 * @since 2.0
31 */
32 class FieldNearOneParameter<T extends CalculusFieldElement<T>> extends FieldJacobiElliptic<T> {
33
34 /** Complementary parameter of the Jacobi elliptic function. */
35 private final T m1Fourth;
36
37 /** Simple constructor.
38 * @param m parameter of the Jacobi elliptic function (must be one or slightly below one here)
39 */
40 FieldNearOneParameter(final T m) {
41 super(m);
42 this.m1Fourth = m.getField().getOne().subtract(m).multiply(0.25);
43 }
44
45 /** {@inheritDoc} */
46 @Override
47 public FieldCopolarN<T> valuesN(final T u) {
48 final FieldSinhCosh<T> sch = FastMath.sinhCosh(u);
49 final T sech = sch.cosh().reciprocal();
50 final T t = sch.sinh().multiply(sech);
51 final T factor = sch.sinh().multiply(sch.cosh()).subtract(u).multiply(sech).multiply(m1Fourth);
52 return new FieldCopolarN<>(t.add(factor.multiply(sech)), // equation 16.15.1
53 sech.subtract(factor.multiply(t)), // equation 16.15.2
54 sech.add(factor.multiply(t))); // equation 16.15.3
55 }
56
57 }