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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.math.ode.nonstiff;
19  
20  import org.apache.commons.math.linear.Array2DRowRealMatrix;
21  import org.apache.commons.math.ode.DerivativeException;
22  import org.apache.commons.math.ode.FirstOrderDifferentialEquations;
23  import org.apache.commons.math.ode.IntegratorException;
24  import org.apache.commons.math.ode.MultistepIntegrator;
25  
26  
27  /** Base class for {@link AdamsBashforthIntegrator Adams-Bashforth} and
28   * {@link AdamsMoultonIntegrator Adams-Moulton} integrators.
29   * @version $Revision: 790368 $ $Date: 2009-07-01 16:31:50 -0400 (Wed, 01 Jul 2009) $
30   * @since 2.0
31   */
32  public abstract class AdamsIntegrator extends MultistepIntegrator {
33  
34      /** Transformer. */
35      private final AdamsNordsieckTransformer transformer;
36  
37      /**
38       * Build an Adams integrator with the given order and step control prameters.
39       * @param name name of the method
40       * @param nSteps number of steps of the method excluding the one being computed
41       * @param order order of the method
42       * @param minStep minimal step (must be positive even for backward
43       * integration), the last step can be smaller than this
44       * @param maxStep maximal step (must be positive even for backward
45       * integration)
46       * @param scalAbsoluteTolerance allowed absolute error
47       * @param scalRelativeTolerance allowed relative error
48       * @exception IllegalArgumentException if order is 1 or less
49       */
50      public AdamsIntegrator(final String name, final int nSteps, final int order,
51                             final double minStep, final double maxStep,
52                             final double scalAbsoluteTolerance,
53                             final double scalRelativeTolerance)
54          throws IllegalArgumentException {
55          super(name, nSteps, order, minStep, maxStep,
56                scalAbsoluteTolerance, scalRelativeTolerance);
57          transformer = AdamsNordsieckTransformer.getInstance(nSteps);
58      }
59  
60      /**
61       * Build an Adams integrator with the given order and step control parameters.
62       * @param name name of the method
63       * @param nSteps number of steps of the method excluding the one being computed
64       * @param order order of the method
65       * @param minStep minimal step (must be positive even for backward
66       * integration), the last step can be smaller than this
67       * @param maxStep maximal step (must be positive even for backward
68       * integration)
69       * @param vecAbsoluteTolerance allowed absolute error
70       * @param vecRelativeTolerance allowed relative error
71       * @exception IllegalArgumentException if order is 1 or less
72       */
73      public AdamsIntegrator(final String name, final int nSteps, final int order,
74                             final double minStep, final double maxStep,
75                             final double[] vecAbsoluteTolerance,
76                             final double[] vecRelativeTolerance)
77          throws IllegalArgumentException {
78          super(name, nSteps, order, minStep, maxStep,
79                vecAbsoluteTolerance, vecRelativeTolerance);
80          transformer = AdamsNordsieckTransformer.getInstance(nSteps);
81      }
82  
83      /** {@inheritDoc} */
84      @Override
85      public abstract double integrate(final FirstOrderDifferentialEquations equations,
86                                       final double t0, final double[] y0,
87                                       final double t, final double[] y)
88          throws DerivativeException, IntegratorException;
89  
90      /** {@inheritDoc} */
91      @Override
92      protected Array2DRowRealMatrix initializeHighOrderDerivatives(final double[] first,
93                                                          final double[][] multistep) {
94          return transformer.initializeHighOrderDerivatives(first, multistep);
95      }
96  
97      /** Update the high order scaled derivatives for Adams integrators (phase 1).
98       * <p>The complete update of high order derivatives has a form similar to:
99       * <pre>
100      * r<sub>n+1</sub> = (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub>
101      * </pre>
102      * this method computes the P<sup>-1</sup> A P r<sub>n</sub> part.</p>
103      * @param highOrder high order scaled derivatives
104      * (h<sup>2</sup>/2 y'', ... h<sup>k</sup>/k! y(k))
105      * @return updated high order derivatives
106      * @see #updateHighOrderDerivativesPhase2(double[], double[], Array2DRowRealMatrix)
107      */
108     public Array2DRowRealMatrix updateHighOrderDerivativesPhase1(final Array2DRowRealMatrix highOrder) {
109         return transformer.updateHighOrderDerivativesPhase1(highOrder);
110     }
111 
112     /** Update the high order scaled derivatives Adams integrators (phase 2).
113      * <p>The complete update of high order derivatives has a form similar to:
114      * <pre>
115      * r<sub>n+1</sub> = (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub>
116      * </pre>
117      * this method computes the (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u part.</p>
118      * <p>Phase 1 of the update must already have been performed.</p>
119      * @param start first order scaled derivatives at step start
120      * @param end first order scaled derivatives at step end
121      * @param highOrder high order scaled derivatives, will be modified
122      * (h<sup>2</sup>/2 y'', ... h<sup>k</sup>/k! y(k))
123      * @see #updateHighOrderDerivativesPhase1(Array2DRowRealMatrix)
124      */
125     public void updateHighOrderDerivativesPhase2(final double[] start,
126                                                  final double[] end,
127                                                  final Array2DRowRealMatrix highOrder) {
128         transformer.updateHighOrderDerivativesPhase2(start, end, highOrder);
129     }
130 
131 }