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1   /*
2    * Licensed to the Apache Software Foundation (ASF) 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 ASF 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    *      http://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  
18  package org.apache.commons.math4.legacy.ode.nonstiff;
19  
20  import org.apache.commons.math4.legacy.core.Field;
21  import org.apache.commons.math4.legacy.core.RealFieldElement;
22  import org.apache.commons.math4.legacy.ode.FieldEquationsMapper;
23  import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative;
24  
25  /**
26   * This class implements a step interpolator for the classical fourth
27   * order Runge-Kutta integrator.
28   *
29   * <p>This interpolator allows to compute dense output inside the last
30   * step computed. The interpolation equation is consistent with the
31   * integration scheme :
32   * <ul>
33   *   <li>Using reference point at step start:<br>
34   *   y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub>)
35   *                    + &theta; (h/6) [  (6 - 9 &theta; + 4 &theta;<sup>2</sup>) y'<sub>1</sub>
36   *                                     + (    6 &theta; - 4 &theta;<sup>2</sup>) (y'<sub>2</sub> + y'<sub>3</sub>)
37   *                                     + (   -3 &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
38   *                                    ]
39   *   </li>
40   *   <li>Using reference point at step end:<br>
41   *   y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub> + h)
42   *                    + (1 - &theta;) (h/6) [ (-4 &theta;^2 + 5 &theta; - 1) y'<sub>1</sub>
43   *                                          +(4 &theta;^2 - 2 &theta; - 2) (y'<sub>2</sub> + y'<sub>3</sub>)
44   *                                          -(4 &theta;^2 +   &theta; + 1) y'<sub>4</sub>
45   *                                        ]
46   *   </li>
47   * </ul>
48   *
49   * where &theta; belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub> are the four
50   * evaluations of the derivatives already computed during the
51   * step.</p>
52   *
53   * @see ClassicalRungeKuttaFieldIntegrator
54   * @param <T> the type of the field elements
55   * @since 3.6
56   */
57  
58  class ClassicalRungeKuttaFieldStepInterpolator<T extends RealFieldElement<T>>
59      extends RungeKuttaFieldStepInterpolator<T> {
60  
61      /** Simple constructor.
62       * @param field field to which the time and state vector elements belong
63       * @param forward integration direction indicator
64       * @param yDotK slopes at the intermediate points
65       * @param globalPreviousState start of the global step
66       * @param globalCurrentState end of the global step
67       * @param softPreviousState start of the restricted step
68       * @param softCurrentState end of the restricted step
69       * @param mapper equations mapper for the all equations
70       */
71      ClassicalRungeKuttaFieldStepInterpolator(final Field<T> field, final boolean forward,
72                                               final T[][] yDotK,
73                                               final FieldODEStateAndDerivative<T> globalPreviousState,
74                                               final FieldODEStateAndDerivative<T> globalCurrentState,
75                                               final FieldODEStateAndDerivative<T> softPreviousState,
76                                               final FieldODEStateAndDerivative<T> softCurrentState,
77                                               final FieldEquationsMapper<T> mapper) {
78          super(field, forward, yDotK,
79                globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
80                mapper);
81      }
82  
83      /** {@inheritDoc} */
84      @Override
85      protected ClassicalRungeKuttaFieldStepInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
86                                                                   final FieldODEStateAndDerivative<T> newGlobalPreviousState,
87                                                                   final FieldODEStateAndDerivative<T> newGlobalCurrentState,
88                                                                   final FieldODEStateAndDerivative<T> newSoftPreviousState,
89                                                                   final FieldODEStateAndDerivative<T> newSoftCurrentState,
90                                                                   final FieldEquationsMapper<T> newMapper) {
91          return new ClassicalRungeKuttaFieldStepInterpolator<>(newField, newForward, newYDotK,
92                                                                 newGlobalPreviousState, newGlobalCurrentState,
93                                                                 newSoftPreviousState, newSoftCurrentState,
94                                                                 newMapper);
95      }
96  
97      /** {@inheritDoc} */
98      @SuppressWarnings("unchecked")
99      @Override
100     protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
101                                                                                    final T time, final T theta,
102                                                                                    final T thetaH, final T oneMinusThetaH) {
103 
104         final T one                       = time.getField().getOne();
105         final T oneMinusTheta             = one.subtract(theta);
106         final T oneMinus2Theta            = one.subtract(theta.multiply(2));
107         final T coeffDot1                 = oneMinusTheta.multiply(oneMinus2Theta);
108         final T coeffDot23                = theta.multiply(oneMinusTheta).multiply(2);
109         final T coeffDot4                 = theta.multiply(oneMinus2Theta).negate();
110         final T[] interpolatedState;
111         final T[] interpolatedDerivatives;
112 
113         if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
114             final T fourTheta2      = theta.multiply(theta).multiply(4);
115             final T s               = thetaH.divide(6.0);
116             final T coeff1          = s.multiply(fourTheta2.subtract(theta.multiply(9)).add(6));
117             final T coeff23         = s.multiply(theta.multiply(6).subtract(fourTheta2));
118             final T coeff4          = s.multiply(fourTheta2.subtract(theta.multiply(3)));
119             interpolatedState       = previousStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
120             interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
121         } else {
122             final T fourTheta       = theta.multiply(4);
123             final T s               = oneMinusThetaH.divide(6);
124             final T coeff1          = s.multiply(theta.multiply(fourTheta.negate().add(5)).subtract(1));
125             final T coeff23         = s.multiply(theta.multiply(fourTheta.subtract(2)).subtract(2));
126             final T coeff4          = s.multiply(theta.multiply(fourTheta.negate().subtract(1)).subtract(1));
127             interpolatedState       = currentStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
128             interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
129         }
130 
131         return new FieldODEStateAndDerivative<>(time, interpolatedState, interpolatedDerivatives);
132     }
133 }