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 }