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.special.elliptic.legendre.LegendreEllipticIntegral;
21
22 /** Algorithm for computing the principal Jacobi functions for parameter m in [0; 1].
23 * @param <T> the type of the field elements
24 * @since 2.0
25 */
26 class FieldBoundedParameter<T extends CalculusFieldElement<T>> extends FieldJacobiElliptic<T> {
27
28 /** Jacobi θ functions. */
29 private final FieldJacobiTheta<T> jacobiTheta;
30
31 /** Value of Jacobi θ functions at origin. */
32 private final FieldTheta<T> t0;
33
34 /** Scaling factor. */
35 private final T scaling;
36
37 /** Simple constructor.
38 * @param m parameter of the Jacobi elliptic function
39 */
40 FieldBoundedParameter(final T m) {
41
42 super(m);
43
44 // compute nome
45 final T q = LegendreEllipticIntegral.nome(m);
46
47 // prepare underlying Jacobi θ functions
48 this.jacobiTheta = new FieldJacobiTheta<>(q);
49 this.t0 = jacobiTheta.values(m.getField().getZero());
50 this.scaling = LegendreEllipticIntegral.bigK(m).reciprocal().multiply(m.getPi().multiply(0.5));
51
52 }
53
54 /** {@inheritDoc}
55 * <p>
56 * The algorithm for evaluating the functions is based on {@link FieldJacobiTheta
57 * Jacobi theta functions}.
58 * </p>
59 */
60 @Override
61 public FieldCopolarN<T> valuesN(T u) {
62
63 // evaluate Jacobi θ functions at argument
64 final FieldTheta<T> tZ = jacobiTheta.values(u.multiply(scaling));
65
66 // convert to Jacobi elliptic functions
67 final T sn = t0.theta3().multiply(tZ.theta1()).divide(t0.theta2().multiply(tZ.theta4()));
68 final T cn = t0.theta4().multiply(tZ.theta2()).divide(t0.theta2().multiply(tZ.theta4()));
69 final T dn = t0.theta4().multiply(tZ.theta3()).divide(t0.theta3().multiply(tZ.theta4()));
70
71 return new FieldCopolarN<>(sn, cn, dn);
72
73 }
74
75 }