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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  
22  /** Algorithm for computing the principal Jacobi functions for negative parameter m.
23   * <p>
24   * The rules for negative parameter change are given in Abramowitz and Stegun, section 16.10.
25   * </p>
26   * @param <T> the type of the field elements
27   * @since 2.0
28   */
29  class FieldNegativeParameter<T extends CalculusFieldElement<T>> extends FieldJacobiElliptic<T> {
30  
31      /** Algorithm to use for the positive parameter. */
32      private final FieldJacobiElliptic<T> algorithm;
33  
34      /** Input scaling factor. */
35      private final T inputScale;
36  
37      /** output scaling factor. */
38      private final T outputScale;
39  
40      /** Simple constructor.
41       * @param m parameter of the Jacobi elliptic function (must be negative here)
42       */
43      FieldNegativeParameter(final T m) {
44          super(m);
45          final T omM = m.getField().getOne().subtract(m);
46          algorithm   = JacobiEllipticBuilder.build(m.negate().divide(omM));
47          inputScale  = FastMath.sqrt(omM);
48          outputScale = inputScale.reciprocal();
49      }
50  
51      /** {@inheritDoc} */
52      @Override
53      public FieldCopolarN<T> valuesN(final T u) {
54          final FieldCopolarD<T> trioD = new FieldCopolarD<>(algorithm.valuesN(u.multiply(inputScale)));
55          return new FieldCopolarN<>(outputScale.multiply(trioD.sd()), trioD.cd(), trioD.nd());
56      }
57  
58  }