-
Notifications
You must be signed in to change notification settings - Fork 143
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Merge pull request #22 from Reneh107/Runge_Kutta_56
Add Runge Kutta 56 integrator to coefficient list + Unit test
- Loading branch information
Showing
6 changed files
with
393 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
275 changes: 275 additions & 0 deletions
275
Tudat/Mathematics/NumericalIntegrators/UnitTests/unitTestRungeKuttaFehlberg56Integrator.cpp
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,275 @@ | ||
| /* Copyright (c) 2010-2016, Delft University of Technology | ||
| * All rights reserved. | ||
| * | ||
| * Redistribution and use in source and binary forms, with or without modification, are | ||
| * permitted provided that the following conditions are met: | ||
| * - Redistributions of source code must retain the above copyright notice, this list of | ||
| * conditions and the following disclaimer. | ||
| * - Redistributions in binary form must reproduce the above copyright notice, this list of | ||
| * conditions and the following disclaimer in the documentation and/or other materials | ||
| * provided with the distribution. | ||
| * - Neither the name of the Delft University of Technology nor the names of its contributors | ||
| * may be used to endorse or promote products derived from this software without specific | ||
| * prior written permission. | ||
| * | ||
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS | ||
| * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF | ||
| * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE | ||
| * COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, | ||
| * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE | ||
| * GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED | ||
| * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING | ||
| * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | ||
| * OF THE POSSIBILITY OF SUCH DAMAGE. | ||
| * | ||
| * Changelog | ||
| * YYMMDD Author Comment | ||
| * 120203 B. Tong Minh Copied RungeKutta4Stepsize unit test. | ||
| * 120207 K. Kumar Adapted to use modified benchmark functions in Tudat Core. | ||
| * 120213 K. Kumar Modified getCurrentInterval( ) to getIndependentVariable( ); | ||
| * transferred to Boost unit test framework. | ||
| * 120321 K. Kumar Updated (Burden and Faires, 2011) benchmark function call. | ||
| * 120323 K. Kumar Rewrote unit tests to use benchmark data from | ||
| * (Burden and Faires, 2011); removed test against benchmark | ||
| * functions; renamed file to RFK45 unit test. Other unit tests | ||
| * for other Runge-Kutta methods will appear in other dedicated | ||
| * unit test files. | ||
| * 120327 K. Kumar Added missing comments; added unit test based on output data | ||
| * generated by (The Mathworks, 2012). | ||
| * 120328 K. Kumar Moved (Burden and Faires, 2011) test class to its own file; | ||
| * modified MATLAB unit tests to test forward and backwards in | ||
| * time and "forced" and "free" adaptive step size adjustment and | ||
| * moved to separate file (added call to function to run Matlab | ||
| * tests); added rollback tests for all cases. | ||
| * 120404 K. Kumar Updated Matlab unit test by adding discrete-event data file. | ||
| * 130118 K. Kumar Rewrote unit test to make use of testing code for numerical | ||
| * integrators migrated to Tudat Core. | ||
| * 130906 K. Kumar Updated error tolerances for MuPAD-based tests. | ||
| * | ||
| * 160321 R. Hoogendoorn Created Runge Kutta 56 test | ||
| * | ||
| * References | ||
| * Burden, R.L., Faires, J.D. Numerical Analysis, 7th Edition, Books/Cole, 2001. | ||
| * Montenbruck, O., Gill, E. Satellite Orbits: Models, Methods, Applications, Springer, 2005. | ||
| * The MathWorks, Inc. RKF54b, Symbolic Math Toolbox, 2012. | ||
| * | ||
| * Notes | ||
| * For the tests using data from the Symbolic Math Toolbox (MathWorks, 2012), the single step | ||
| * and full integration error tolerances were picked to be as small as possible, without | ||
| * causing the tests to fail. These values are not deemed to indicate any bugs in the code; | ||
| * however, it is important to take these discrepancies into account when using this numerical | ||
| * integrator. | ||
| * | ||
| */ | ||
|
|
||
| #define BOOST_TEST_MAIN | ||
|
|
||
| #include <limits> | ||
| #include <string> | ||
|
|
||
| #include <cmath> | ||
|
|
||
| #include <Eigen/Core> | ||
|
|
||
| #include <boost/test/unit_test.hpp> | ||
|
|
||
| #include "Tudat/Mathematics/NumericalIntegrators/rungeKuttaVariableStepSizeIntegrator.h" | ||
| #include "Tudat/Mathematics/NumericalIntegrators/rungeKuttaCoefficients.h" | ||
| #include "Tudat/Mathematics/NumericalIntegrators/UnitTests/numericalIntegratorTestFunctions.h" | ||
|
|
||
| namespace tudat | ||
| { | ||
| namespace unit_tests | ||
| { | ||
|
|
||
| BOOST_AUTO_TEST_SUITE( test_runge_kutta_fehlberg_56_integrator ) | ||
|
|
||
| using numerical_integrator_test_functions::computeNonAutonomousModelStateDerivative; | ||
| using numerical_integrator_test_functions::computeVanDerPolStateDerivative; | ||
| using numerical_integrator_test_functions::computeFehlbergLogirithmicTestODEStateDerivative; | ||
| using numerical_integrator_test_functions::computeAnalyticalStateFehlbergODE; | ||
|
|
||
| using namespace numerical_integrators; | ||
|
|
||
| //! Compare with analytical solution of Fehlberg | ||
| BOOST_AUTO_TEST_CASE( test_RungeKuttaFehlberg56_Integrator_Fehlberg_Benchmark ) | ||
| { | ||
| RungeKuttaCoefficients coeff56 = | ||
| RungeKuttaCoefficients::get( RungeKuttaCoefficients::rungeKuttaFehlberg56); | ||
|
|
||
| // Integrator settings | ||
| double minimumStepSize = std::numeric_limits< double >::epsilon( ); | ||
| double maximumStepSize = std::numeric_limits< double >::infinity( ); | ||
| double initialStepSize = 1E-6; // Don't make this too small | ||
| double relativeTolerance = 1E-16; | ||
| double absoluteTolerance = 1E-16; | ||
|
|
||
| // Initial conditions | ||
| double initialTime = 0.0; | ||
| double finalTime = 5.0; | ||
| Eigen::Vector2d initialState( exp( 1.0 ), 1.0); | ||
|
|
||
| // Setup integrator | ||
| RungeKuttaVariableStepSizeIntegratorXd integrator56( | ||
| coeff56, computeFehlbergLogirithmicTestODEStateDerivative, | ||
| initialTime, initialState, minimumStepSize, | ||
| maximumStepSize, relativeTolerance, absoluteTolerance ); | ||
|
|
||
|
|
||
| // Obtain numerical solution | ||
| Eigen::Vector2d numericalSolution = integrator56.integrateTo( finalTime, initialStepSize ); | ||
|
|
||
| // Analytical solution | ||
| // (page 30, Fehlberg, E. (1968). Classical Fifth-, Sixth-, Seventh- and Eigth-Order Runge-Kutta | ||
| // Formulas with Stepsize Control) | ||
| Eigen::Vector2d analyticalSolution = | ||
| computeAnalyticalStateFehlbergODE( finalTime, initialState ); | ||
|
|
||
| Eigen::Vector2d computedError = numericalSolution - analyticalSolution; | ||
| BOOST_CHECK_SMALL( std::fabs( computedError( 0 ) ), 1E-12 ); | ||
| BOOST_CHECK_SMALL( std::fabs( computedError( 1 ) ), 1E-12 ); | ||
|
|
||
| // Error calculated by -> Fehlberg, E. (1968) page 30 | ||
| // Initial stepsize unknown.. | ||
| Eigen::VectorXd fehlbergError( 2 ); | ||
| fehlbergError << 0.1072E-12, -0.2190E-12; | ||
|
|
||
| // Sign check | ||
| // Not always same sign -> initial step size = 1 or 1E-2, failure: computedError( 1 ), | ||
| // fehlbergError( 1 ) not same sign | ||
| BOOST_CHECK_GE( computedError( 0 ) / fehlbergError( 0 ), 0.0 ); | ||
| BOOST_CHECK_GE( computedError( 1 ) / fehlbergError( 1 ), 0.0 ); | ||
|
|
||
| // Check error is similar in magnitude | ||
| BOOST_CHECK_SMALL( std::fabs( computedError( 0 ) / fehlbergError( 0 ) ), 3.0); | ||
| BOOST_CHECK_SMALL( std::fabs( computedError( 1 ) / fehlbergError( 1 ) ), 1.0); | ||
| } | ||
|
|
||
|
|
||
| //! Test Compare with Runge Kutta 78 | ||
| BOOST_AUTO_TEST_CASE( test_RungeKuttaFehlberg56_Integrator_Compare78 ) | ||
| { | ||
| // Setup integrator | ||
| RungeKuttaCoefficients coeff56 = | ||
| RungeKuttaCoefficients::get( RungeKuttaCoefficients::rungeKuttaFehlberg56); | ||
|
|
||
| RungeKuttaCoefficients coeff78 = | ||
| RungeKuttaCoefficients::get( RungeKuttaCoefficients::rungeKuttaFehlberg78); | ||
|
|
||
| // Integrator settings | ||
| double minimumStepSize = std::numeric_limits< double >::epsilon( ); | ||
| double maximumStepSize = std::numeric_limits< double >::infinity( ); | ||
| double initialStepSize = 1E-4; // Don't make this too small | ||
| double relativeTolerance = 1E-15; | ||
| double absoluteTolerance = 1E-15; | ||
|
|
||
| // Initial conditions | ||
| double initialTime = 0.5; | ||
| Eigen::VectorXd InitialState( 1 ); | ||
| InitialState << 0.5; // 1 large error | ||
|
|
||
| // Setup integrator | ||
| RungeKuttaVariableStepSizeIntegratorXd integrator56( | ||
| coeff56, computeNonAutonomousModelStateDerivative, initialTime, InitialState, | ||
| minimumStepSize, maximumStepSize, relativeTolerance, absoluteTolerance ); | ||
|
|
||
| RungeKuttaVariableStepSizeIntegratorXd integrator78( | ||
| coeff78, computeNonAutonomousModelStateDerivative, initialTime, InitialState, | ||
| minimumStepSize, maximumStepSize, relativeTolerance, absoluteTolerance ); | ||
|
|
||
| double endTime = 1.5; | ||
| Eigen::VectorXd solution56 = integrator56.integrateTo( endTime, initialStepSize ); | ||
| Eigen::VectorXd solution78 = integrator78.integrateTo( endTime, initialStepSize ); | ||
|
|
||
| Eigen::VectorXd difference = solution78 - solution56; | ||
|
|
||
| BOOST_CHECK_SMALL( std::fabs( difference( 0 ) ), 1E-13 ); | ||
| } | ||
|
|
||
| //! Test Compare with Runge Kutta 78 | ||
| BOOST_AUTO_TEST_CASE( test_RungeKuttaFehlberg56_Integrator_Compare78_v2 ) | ||
| { | ||
| // Setup integrator | ||
| RungeKuttaCoefficients coeff56 = | ||
| RungeKuttaCoefficients::get( | ||
| RungeKuttaCoefficients::rungeKuttaFehlberg56 ); | ||
|
|
||
| RungeKuttaCoefficients coeff78 = | ||
| RungeKuttaCoefficients::get( | ||
| RungeKuttaCoefficients::rungeKuttaFehlberg78 ); | ||
|
|
||
| // Integrator settings | ||
| double minimumStepSize = std::numeric_limits< double >::epsilon( ); | ||
| double maximumStepSize = std::numeric_limits< double >::infinity( ); | ||
| double initialStepSize = 1.0; // Don't make this too small | ||
| double relativeTolerance = 1E-10; | ||
| double absoluteTolerance = 1E-10; | ||
|
|
||
| // Initial conditions | ||
| double initialTime = 0.2; | ||
| Eigen::VectorXd InitialState( 1 ); | ||
| InitialState << -1.0; | ||
|
|
||
| // Setup integrator | ||
| RungeKuttaVariableStepSizeIntegratorXd integrator56( | ||
| coeff56, computeNonAutonomousModelStateDerivative, initialTime, InitialState, | ||
| minimumStepSize, maximumStepSize, relativeTolerance, absoluteTolerance ); | ||
|
|
||
| RungeKuttaVariableStepSizeIntegratorXd integrator78( | ||
| coeff78, computeNonAutonomousModelStateDerivative, initialTime, InitialState, | ||
| minimumStepSize, maximumStepSize, relativeTolerance, absoluteTolerance ); | ||
|
|
||
| double endTime = 2.0; | ||
| Eigen::VectorXd solution56 = integrator56.integrateTo( endTime, initialStepSize ); | ||
| Eigen::VectorXd solution78 = integrator78.integrateTo( endTime, initialStepSize ); | ||
|
|
||
| Eigen::VectorXd difference = solution78 - solution56; | ||
|
|
||
| BOOST_CHECK_SMALL( std::fabs( difference( 0 ) ), 1E-8 ); | ||
| } | ||
|
|
||
| //! Test Compare with Runge Kutta 78 | ||
| BOOST_AUTO_TEST_CASE( test_RungeKuttaFehlberg56_Integrator_Compare78_VanDerPol ) | ||
| { | ||
| // Setup integrator | ||
| RungeKuttaCoefficients coeff56 = | ||
| RungeKuttaCoefficients::get( RungeKuttaCoefficients::rungeKuttaFehlberg56 ); | ||
|
|
||
| RungeKuttaCoefficients coeff78 = | ||
| RungeKuttaCoefficients::get( RungeKuttaCoefficients::rungeKuttaFehlberg78 ); | ||
|
|
||
| // Integrator settings | ||
| double minimumStepSize = std::numeric_limits< double >::epsilon( ); | ||
| double maximumStepSize = std::numeric_limits< double >::infinity( ); | ||
| double initialStepSize = 1; // Don't make this too small | ||
| double relativeTolerance = 1E-15; | ||
| double absoluteTolerance = 1E-15; | ||
|
|
||
| // Initial conditions | ||
| double initialTime = 0.2; | ||
| Eigen::VectorXd InitialState( 2 ); | ||
| InitialState << -1.0, 1.0; | ||
|
|
||
| // Setup integrator | ||
| RungeKuttaVariableStepSizeIntegratorXd integrator56( | ||
| coeff56, computeVanDerPolStateDerivative, initialTime, InitialState, minimumStepSize, | ||
| maximumStepSize, relativeTolerance, absoluteTolerance ); | ||
|
|
||
| RungeKuttaVariableStepSizeIntegratorXd integrator78( | ||
| coeff78, computeVanDerPolStateDerivative, initialTime, InitialState, minimumStepSize, | ||
| maximumStepSize, relativeTolerance, absoluteTolerance ); | ||
|
|
||
| double endTime = 1.4; | ||
| Eigen::VectorXd solution56 = integrator56.integrateTo(endTime,initialStepSize); | ||
| Eigen::VectorXd solution78 = integrator78.integrateTo(endTime,initialStepSize); | ||
|
|
||
| Eigen::VectorXd difference = solution78 - solution56; | ||
|
|
||
| BOOST_CHECK_SMALL( std::fabs( difference( 0 ) ), 1E-13 ); | ||
| BOOST_CHECK_SMALL( std::fabs( difference( 1 ) ), 1E-13 ); | ||
| } | ||
|
|
||
| BOOST_AUTO_TEST_SUITE_END( ) | ||
|
|
||
| } // namespace unit_tests | ||
| } // namespace tudat |
Oops, something went wrong.