001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    
018    package org.apache.commons.math3.ode.nonstiff;
019    
020    import org.apache.commons.math3.util.FastMath;
021    
022    
023    /**
024     * This class implements the 5(4) Higham and Hall integrator for
025     * Ordinary Differential Equations.
026     *
027     * <p>This integrator is an embedded Runge-Kutta integrator
028     * of order 5(4) used in local extrapolation mode (i.e. the solution
029     * is computed using the high order formula) with stepsize control
030     * (and automatic step initialization) and continuous output. This
031     * method uses 7 functions evaluations per step.</p>
032     *
033     * @version $Id: HighamHall54Integrator.java 1416643 2012-12-03 19:37:14Z tn $
034     * @since 1.2
035     */
036    
037    public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
038    
039      /** Integrator method name. */
040      private static final String METHOD_NAME = "Higham-Hall 5(4)";
041    
042      /** Time steps Butcher array. */
043      private static final double[] STATIC_C = {
044        2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
045      };
046    
047      /** Internal weights Butcher array. */
048      private static final double[][] STATIC_A = {
049        {2.0/9.0},
050        {1.0/12.0, 1.0/4.0},
051        {1.0/8.0, 0.0, 3.0/8.0},
052        {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
053        {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
054        {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
055      };
056    
057      /** Propagation weights Butcher array. */
058      private static final double[] STATIC_B = {
059        1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
060      };
061    
062      /** Error weights Butcher array. */
063      private static final double[] STATIC_E = {
064        -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0
065      };
066    
067      /** Simple constructor.
068       * Build a fifth order Higham and Hall integrator with the given step bounds
069       * @param minStep minimal step (sign is irrelevant, regardless of
070       * integration direction, forward or backward), the last step can
071       * be smaller than this
072       * @param maxStep maximal step (sign is irrelevant, regardless of
073       * integration direction, forward or backward), the last step can
074       * be smaller than this
075       * @param scalAbsoluteTolerance allowed absolute error
076       * @param scalRelativeTolerance allowed relative error
077       */
078      public HighamHall54Integrator(final double minStep, final double maxStep,
079                                    final double scalAbsoluteTolerance,
080                                    final double scalRelativeTolerance) {
081        super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
082              minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
083      }
084    
085      /** Simple constructor.
086       * Build a fifth order Higham and Hall integrator with the given step bounds
087       * @param minStep minimal step (sign is irrelevant, regardless of
088       * integration direction, forward or backward), the last step can
089       * be smaller than this
090       * @param maxStep maximal step (sign is irrelevant, regardless of
091       * integration direction, forward or backward), the last step can
092       * be smaller than this
093       * @param vecAbsoluteTolerance allowed absolute error
094       * @param vecRelativeTolerance allowed relative error
095       */
096      public HighamHall54Integrator(final double minStep, final double maxStep,
097                                    final double[] vecAbsoluteTolerance,
098                                    final double[] vecRelativeTolerance) {
099        super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
100              minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
101      }
102    
103      /** {@inheritDoc} */
104      @Override
105      public int getOrder() {
106        return 5;
107      }
108    
109      /** {@inheritDoc} */
110      @Override
111      protected double estimateError(final double[][] yDotK,
112                                     final double[] y0, final double[] y1,
113                                     final double h) {
114    
115        double error = 0;
116    
117        for (int j = 0; j < mainSetDimension; ++j) {
118          double errSum = STATIC_E[0] * yDotK[0][j];
119          for (int l = 1; l < STATIC_E.length; ++l) {
120            errSum += STATIC_E[l] * yDotK[l][j];
121          }
122    
123          final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j]));
124          final double tol = (vecAbsoluteTolerance == null) ?
125                             (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
126                             (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
127          final double ratio  = h * errSum / tol;
128          error += ratio * ratio;
129    
130        }
131    
132        return FastMath.sqrt(error / mainSetDimension);
133    
134      }
135    
136    }