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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.math3.ode.nonstiff;
19  
20  import org.apache.commons.math3.ode.sampling.StepInterpolator;
21  import org.apache.commons.math3.util.FastMath;
22  
23  /**
24   * This class implements a step interpolator for the Gill fourth
25   * order Runge-Kutta integrator.
26   *
27   * <p>This interpolator allows to compute dense output inside the last
28   * step computed. The interpolation equation is consistent with the
29   * integration scheme :
30   * <ul>
31   *   <li>Using reference point at step start:<br>
32   *   y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub>)
33   *                    + &theta; (h/6) [ (6 - 9 &theta; + 4 &theta;<sup>2</sup>) y'<sub>1</sub>
34   *                                    + (    6 &theta; - 4 &theta;<sup>2</sup>) ((1-1/&radic;2) y'<sub>2</sub> + (1+1/&radic;2)) y'<sub>3</sub>)
35   *                                    + (  - 3 &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
36   *                                    ]
37   *   </li>
38   *   <li>Using reference point at step start:<br>
39   *   y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub> + h)
40   *                    - (1 - &theta;) (h/6) [ (1 - 5 &theta; + 4 &theta;<sup>2</sup>) y'<sub>1</sub>
41   *                                          + (2 + 2 &theta; - 4 &theta;<sup>2</sup>) ((1-1/&radic;2) y'<sub>2</sub> + (1+1/&radic;2)) y'<sub>3</sub>)
42   *                                          + (1 +   &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
43   *                                          ]
44   *   </li>
45   * </ul>
46   * </p>
47   * where &theta; belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
48   * are the four evaluations of the derivatives already computed during
49   * the step.</p>
50   *
51   * @see GillIntegrator
52   * @version $Id: GillStepInterpolator.java 1416643 2012-12-03 19:37:14Z tn $
53   * @since 1.2
54   */
55  
56  class GillStepInterpolator
57    extends RungeKuttaStepInterpolator {
58  
59      /** First Gill coefficient. */
60      private static final double ONE_MINUS_INV_SQRT_2 = 1 - FastMath.sqrt(0.5);
61  
62      /** Second Gill coefficient. */
63      private static final double ONE_PLUS_INV_SQRT_2 = 1 + FastMath.sqrt(0.5);
64  
65      /** Serializable version identifier. */
66      private static final long serialVersionUID = 20111120L;
67  
68    /** Simple constructor.
69     * This constructor builds an instance that is not usable yet, the
70     * {@link
71     * org.apache.commons.math3.ode.sampling.AbstractStepInterpolator#reinitialize}
72     * method should be called before using the instance in order to
73     * initialize the internal arrays. This constructor is used only
74     * in order to delay the initialization in some cases. The {@link
75     * RungeKuttaIntegrator} class uses the prototyping design pattern
76     * to create the step interpolators by cloning an uninitialized model
77     * and later initializing the copy.
78     */
79    public GillStepInterpolator() {
80    }
81  
82    /** Copy constructor.
83     * @param interpolator interpolator to copy from. The copy is a deep
84     * copy: its arrays are separated from the original arrays of the
85     * instance
86     */
87    public GillStepInterpolator(final GillStepInterpolator interpolator) {
88      super(interpolator);
89    }
90  
91    /** {@inheritDoc} */
92    @Override
93    protected StepInterpolator doCopy() {
94      return new GillStepInterpolator(this);
95    }
96  
97  
98    /** {@inheritDoc} */
99    @Override
100   protected void computeInterpolatedStateAndDerivatives(final double theta,
101                                           final double oneMinusThetaH) {
102 
103     final double twoTheta   = 2 * theta;
104     final double fourTheta2 = twoTheta * twoTheta;
105     final double coeffDot1  = theta * (twoTheta - 3) + 1;
106     final double cDot23     = twoTheta * (1 - theta);
107     final double coeffDot2  = cDot23  * ONE_MINUS_INV_SQRT_2;
108     final double coeffDot3  = cDot23  * ONE_PLUS_INV_SQRT_2;
109     final double coeffDot4  = theta * (twoTheta - 1);
110 
111     if ((previousState != null) && (theta <= 0.5)) {
112         final double s         = theta * h / 6.0;
113         final double c23       = s * (6 * theta - fourTheta2);
114         final double coeff1    = s * (6 - 9 * theta + fourTheta2);
115         final double coeff2    = c23  * ONE_MINUS_INV_SQRT_2;
116         final double coeff3    = c23  * ONE_PLUS_INV_SQRT_2;
117         final double coeff4    = s * (-3 * theta + fourTheta2);
118         for (int i = 0; i < interpolatedState.length; ++i) {
119             final double yDot1 = yDotK[0][i];
120             final double yDot2 = yDotK[1][i];
121             final double yDot3 = yDotK[2][i];
122             final double yDot4 = yDotK[3][i];
123             interpolatedState[i] =
124                     previousState[i] + coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 + coeff4 * yDot4;
125             interpolatedDerivatives[i] =
126                     coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
127         }
128     } else {
129         final double s      = oneMinusThetaH / 6.0;
130         final double c23    = s * (2 + twoTheta - fourTheta2);
131         final double coeff1 = s * (1 - 5 * theta + fourTheta2);
132         final double coeff2 = c23  * ONE_MINUS_INV_SQRT_2;
133         final double coeff3 = c23  * ONE_PLUS_INV_SQRT_2;
134         final double coeff4 = s * (1 + theta + fourTheta2);
135         for (int i = 0; i < interpolatedState.length; ++i) {
136             final double yDot1 = yDotK[0][i];
137             final double yDot2 = yDotK[1][i];
138             final double yDot3 = yDotK[2][i];
139             final double yDot4 = yDotK[3][i];
140             interpolatedState[i] =
141                     currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4;
142             interpolatedDerivatives[i] =
143                     coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
144         }
145     }
146 
147   }
148 
149 }