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Diffstat (limited to 'src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java')
-rw-r--r-- | src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java | 132 |
1 files changed, 132 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java new file mode 100644 index 0000000..6ea8564 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java @@ -0,0 +1,132 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to You under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package org.apache.commons.math.ode.nonstiff; + +import org.apache.commons.math.util.FastMath; + + +/** + * This class implements the 5(4) Higham and Hall integrator for + * Ordinary Differential Equations. + * + * <p>This integrator is an embedded Runge-Kutta integrator + * of order 5(4) used in local extrapolation mode (i.e. the solution + * is computed using the high order formula) with stepsize control + * (and automatic step initialization) and continuous output. This + * method uses 7 functions evaluations per step.</p> + * + * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ + * @since 1.2 + */ + +public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator { + + /** Integrator method name. */ + private static final String METHOD_NAME = "Higham-Hall 5(4)"; + + /** Time steps Butcher array. */ + private static final double[] STATIC_C = { + 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0 + }; + + /** Internal weights Butcher array. */ + private static final double[][] STATIC_A = { + {2.0/9.0}, + {1.0/12.0, 1.0/4.0}, + {1.0/8.0, 0.0, 3.0/8.0}, + {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0}, + {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0}, + {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0} + }; + + /** Propagation weights Butcher array. */ + private static final double[] STATIC_B = { + 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0 + }; + + /** Error weights Butcher array. */ + private static final double[] STATIC_E = { + -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 + }; + + /** Simple constructor. + * Build a fifth order Higham and Hall integrator with the given step bounds + * @param minStep minimal step (must be positive even for backward + * integration), the last step can be smaller than this + * @param maxStep maximal step (must be positive even for backward + * integration) + * @param scalAbsoluteTolerance allowed absolute error + * @param scalRelativeTolerance allowed relative error + */ + public HighamHall54Integrator(final double minStep, final double maxStep, + final double scalAbsoluteTolerance, + final double scalRelativeTolerance) { + super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), + minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); + } + + /** Simple constructor. + * Build a fifth order Higham and Hall integrator with the given step bounds + * @param minStep minimal step (must be positive even for backward + * integration), the last step can be smaller than this + * @param maxStep maximal step (must be positive even for backward + * integration) + * @param vecAbsoluteTolerance allowed absolute error + * @param vecRelativeTolerance allowed relative error + */ + public HighamHall54Integrator(final double minStep, final double maxStep, + final double[] vecAbsoluteTolerance, + final double[] vecRelativeTolerance) { + super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), + minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); + } + + /** {@inheritDoc} */ + @Override + public int getOrder() { + return 5; + } + + /** {@inheritDoc} */ + @Override + protected double estimateError(final double[][] yDotK, + final double[] y0, final double[] y1, + final double h) { + + double error = 0; + + for (int j = 0; j < mainSetDimension; ++j) { + double errSum = STATIC_E[0] * yDotK[0][j]; + for (int l = 1; l < STATIC_E.length; ++l) { + errSum += STATIC_E[l] * yDotK[l][j]; + } + + final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])); + final double tol = (vecAbsoluteTolerance == null) ? + (scalAbsoluteTolerance + scalRelativeTolerance * yScale) : + (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale); + final double ratio = h * errSum / tol; + error += ratio * ratio; + + } + + return FastMath.sqrt(error / mainSetDimension); + + } + +} |