HighamHall54FieldIntegrator.java

  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.  */

  18. package org.apache.commons.math4.legacy.ode.nonstiff;

  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. import org.apache.commons.math4.legacy.core.MathArrays;


  27. /**
  28.  * This class implements the 5(4) Higham and Hall integrator for
  29.  * Ordinary Differential Equations.
  30.  *
  31.  * <p>This integrator is an embedded Runge-Kutta integrator
  32.  * of order 5(4) used in local extrapolation mode (i.e. the solution
  33.  * is computed using the high order formula) with stepsize control
  34.  * (and automatic step initialization) and continuous output. This
  35.  * method uses 7 functions evaluations per step.</p>
  36.  *
  37.  * @param <T> the type of the field elements
  38.  * @since 3.6
  39.  */

  41. public class HighamHall54FieldIntegrator<T extends RealFieldElement<T>>
  42.     extends EmbeddedRungeKuttaFieldIntegrator<T> {

  44.     /** Integrator method name. */
  45.     private static final String METHOD_NAME = "Higham-Hall 5(4)";

  47.     /** Error weights Butcher array. */
  48.     private final T[] e ;

  50.     /** Simple constructor.
  51.      * Build a fifth order Higham and Hall integrator with the given step bounds
  52.      * @param field field to which the time and state vector elements belong
  53.      * @param minStep minimal step (sign is irrelevant, regardless of
  54.      * integration direction, forward or backward), the last step can
  55.      * be smaller than this
  56.      * @param maxStep maximal step (sign is irrelevant, regardless of
  57.      * integration direction, forward or backward), the last step can
  58.      * be smaller than this
  59.      * @param scalAbsoluteTolerance allowed absolute error
  60.      * @param scalRelativeTolerance allowed relative error
  61.      */
  62.     public HighamHall54FieldIntegrator(final Field<T> field,
  63.                                        final double minStep, final double maxStep,
  64.                                        final double scalAbsoluteTolerance,
  65.                                        final double scalRelativeTolerance) {
  66.         super(field, METHOD_NAME, -1,
  67.               minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
  68.         e = MathArrays.buildArray(field, 7);
  69.         e[0] = fraction(-1,  20);
  70.         e[1] = field.getZero();
  71.         e[2] = fraction(81, 160);
  72.         e[3] = fraction(-6,   5);
  73.         e[4] = fraction(25,  32);
  74.         e[5] = fraction( 1,  16);
  75.         e[6] = fraction(-1,  10);
  76.     }

  78.     /** Simple constructor.
  79.      * Build a fifth order Higham and Hall integrator with the given step bounds
  80.      * @param field field to which the time and state vector elements belong
  81.      * @param minStep minimal step (sign is irrelevant, regardless of
  82.      * integration direction, forward or backward), the last step can
  83.      * be smaller than this
  84.      * @param maxStep maximal step (sign is irrelevant, regardless of
  85.      * integration direction, forward or backward), the last step can
  86.      * be smaller than this
  87.      * @param vecAbsoluteTolerance allowed absolute error
  88.      * @param vecRelativeTolerance allowed relative error
  89.      */
  90.     public HighamHall54FieldIntegrator(final Field<T> field,
  91.                                        final double minStep, final double maxStep,
  92.                                        final double[] vecAbsoluteTolerance,
  93.                                        final double[] vecRelativeTolerance) {
  94.         super(field, METHOD_NAME, -1,
  95.               minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
  96.         e = MathArrays.buildArray(field, 7);
  97.         e[0] = fraction(-1,  20);
  98.         e[1] = field.getZero();
  99.         e[2] = fraction(81, 160);
  100.         e[3] = fraction(-6,   5);
  101.         e[4] = fraction(25,  32);
  102.         e[5] = fraction( 1,  16);
  103.         e[6] = fraction(-1,  10);
  104.     }

  106.     /** {@inheritDoc} */
  107.     @Override
  108.     public T[] getC() {
  109.         final T[] c = MathArrays.buildArray(getField(), 6);
  110.         c[0] = fraction(2, 9);
  111.         c[1] = fraction(1, 3);
  112.         c[2] = fraction(1, 2);
  113.         c[3] = fraction(3, 5);
  114.         c[4] = getField().getOne();
  115.         c[5] = getField().getOne();
  116.         return c;
  117.     }

  119.     /** {@inheritDoc} */
  120.     @Override
  121.     public T[][] getA() {
  122.         final T[][] a = MathArrays.buildArray(getField(), 6, -1);
  123.         for (int i = 0; i < a.length; ++i) {
  124.             a[i] = MathArrays.buildArray(getField(), i + 1);
  125.         }
  126.         a[0][0] = fraction(     2,     9);
  127.         a[1][0] = fraction(     1,    12);
  128.         a[1][1] = fraction(     1,     4);
  129.         a[2][0] = fraction(     1,     8);
  130.         a[2][1] = getField().getZero();
  131.         a[2][2] = fraction(     3,     8);
  132.         a[3][0] = fraction(    91,   500);
  133.         a[3][1] = fraction(   -27,   100);
  134.         a[3][2] = fraction(    78,   125);
  135.         a[3][3] = fraction(     8,   125);
  136.         a[4][0] = fraction(   -11,    20);
  137.         a[4][1] = fraction(    27,    20);
  138.         a[4][2] = fraction(    12,     5);
  139.         a[4][3] = fraction(   -36,     5);
  140.         a[4][4] = fraction(     5,     1);
  141.         a[5][0] = fraction(     1,    12);
  142.         a[5][1] = getField().getZero();
  143.         a[5][2] = fraction(    27,    32);
  144.         a[5][3] = fraction(    -4,     3);
  145.         a[5][4] = fraction(   125,    96);
  146.         a[5][5] = fraction(     5,    48);
  147.         return a;
  148.     }

  150.     /** {@inheritDoc} */
  151.     @Override
  152.     public T[] getB() {
  153.         final T[] b = MathArrays.buildArray(getField(), 7);
  154.         b[0] = fraction(  1, 12);
  155.         b[1] = getField().getZero();
  156.         b[2] = fraction( 27, 32);
  157.         b[3] = fraction( -4,  3);
  158.         b[4] = fraction(125, 96);
  159.         b[5] = fraction(  5, 48);
  160.         b[6] = getField().getZero();
  161.         return b;
  162.     }

  164.     /** {@inheritDoc} */
  165.     @Override
  166.     protected HighamHall54FieldStepInterpolator<T>
  167.         createInterpolator(final boolean forward, T[][] yDotK,
  168.                            final FieldODEStateAndDerivative<T> globalPreviousState,
  169.                            final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper) {
  170.         return new HighamHall54FieldStepInterpolator<>(getField(), forward, yDotK,
  171.                                                         globalPreviousState, globalCurrentState,
  172.                                                         globalPreviousState, globalCurrentState,
  173.                                                         mapper);
  174.     }

  176.     /** {@inheritDoc} */
  177.     @Override
  178.     public int getOrder() {
  179.         return 5;
  180.     }

  182.     /** {@inheritDoc} */
  183.     @Override
  184.     protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) {

  186.         T error = getField().getZero();

  188.         for (int j = 0; j < mainSetDimension; ++j) {
  189.             T errSum = yDotK[0][j].multiply(e[0]);
  190.             for (int l = 1; l < e.length; ++l) {
  191.                 errSum = errSum.add(yDotK[l][j].multiply(e[l]));
  192.             }

  194.             final T yScale = RealFieldElement.max(y0[j].abs(), y1[j].abs());
  195.             final T tol    = (vecAbsoluteTolerance == null) ?
  196.                              yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) :
  197.                              yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]);
  198.             final T ratio  = h.multiply(errSum).divide(tol);
  199.             error = error.add(ratio.multiply(ratio));
  200.         }

  202.         return error.divide(mainSetDimension).sqrt();
  203.     }
  204. }
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