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 Gill 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> + θ h) = y (t<sub>n</sub>)
35 * + θ (h/6) [ (6 - 9 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
36 * + ( 6 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
37 * + ( - 3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
38 * ]
39 * </li>
40 * <li>Using reference point at step start:<br>
41 * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
42 * - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
43 * + (2 + 2 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
44 * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
45 * ]
46 * </li>
47 * </ul>
48 * where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
49 * are the four evaluations of the derivatives already computed during
50 * the step.</p>
51 *
52 * @see GillFieldIntegrator
53 * @param <T> the type of the field elements
54 * @since 3.6
55 */
56
57 class GillFieldStepInterpolator<T extends RealFieldElement<T>>
58 extends RungeKuttaFieldStepInterpolator<T> {
59
60 /** First Gill coefficient. */
61 private final T one_minus_inv_sqrt_2;
62
63 /** Second Gill coefficient. */
64 private final T one_plus_inv_sqrt_2;
65
66 /** Simple constructor.
67 * @param field field to which the time and state vector elements belong
68 * @param forward integration direction indicator
69 * @param yDotK slopes at the intermediate points
70 * @param globalPreviousState start of the global step
71 * @param globalCurrentState end of the global step
72 * @param softPreviousState start of the restricted step
73 * @param softCurrentState end of the restricted step
74 * @param mapper equations mapper for the all equations
75 */
76 GillFieldStepInterpolator(final Field<T> field, final boolean forward,
77 final T[][] yDotK,
78 final FieldODEStateAndDerivative<T> globalPreviousState,
79 final FieldODEStateAndDerivative<T> globalCurrentState,
80 final FieldODEStateAndDerivative<T> softPreviousState,
81 final FieldODEStateAndDerivative<T> softCurrentState,
82 final FieldEquationsMapper<T> mapper) {
83 super(field, forward, yDotK,
84 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
85 mapper);
86 final T sqrt = field.getZero().add(0.5).sqrt();
87 one_minus_inv_sqrt_2 = field.getOne().subtract(sqrt);
88 one_plus_inv_sqrt_2 = field.getOne().add(sqrt);
89 }
90
91 /** {@inheritDoc} */
92 @Override
93 protected GillFieldStepInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
94 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
95 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
96 final FieldODEStateAndDerivative<T> newSoftPreviousState,
97 final FieldODEStateAndDerivative<T> newSoftCurrentState,
98 final FieldEquationsMapper<T> newMapper) {
99 return new GillFieldStepInterpolator<>(newField, newForward, newYDotK,
100 newGlobalPreviousState, newGlobalCurrentState,
101 newSoftPreviousState, newSoftCurrentState,
102 newMapper);
103 }
104
105 /** {@inheritDoc} */
106 @SuppressWarnings("unchecked")
107 @Override
108 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
109 final T time, final T theta,
110 final T thetaH, final T oneMinusThetaH) {
111
112 final T one = time.getField().getOne();
113 final T twoTheta = theta.multiply(2);
114 final T fourTheta2 = twoTheta.multiply(twoTheta);
115 final T coeffDot1 = theta.multiply(twoTheta.subtract(3)).add(1);
116 final T cDot23 = twoTheta.multiply(one.subtract(theta));
117 final T coeffDot2 = cDot23.multiply(one_minus_inv_sqrt_2);
118 final T coeffDot3 = cDot23.multiply(one_plus_inv_sqrt_2);
119 final T coeffDot4 = theta.multiply(twoTheta.subtract(1));
120 final T[] interpolatedState;
121 final T[] interpolatedDerivatives;
122
123 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
124 final T s = thetaH.divide(6.0);
125 final T c23 = s.multiply(theta.multiply(6).subtract(fourTheta2));
126 final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(9)).add(6));
127 final T coeff2 = c23.multiply(one_minus_inv_sqrt_2);
128 final T coeff3 = c23.multiply(one_plus_inv_sqrt_2);
129 final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3)));
130 interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
131 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
132 } else {
133 final T s = oneMinusThetaH.divide(-6.0);
134 final T c23 = s.multiply(twoTheta.add(2).subtract(fourTheta2));
135 final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(5)).add(1));
136 final T coeff2 = c23.multiply(one_minus_inv_sqrt_2);
137 final T coeff3 = c23.multiply(one_plus_inv_sqrt_2);
138 final T coeff4 = s.multiply(fourTheta2.add(theta).add(1));
139 interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
140 interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
141 }
142
143 return new FieldODEStateAndDerivative<>(time, interpolatedState, interpolatedDerivatives);
144 }
145 }