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


import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
import org.apache.commons.math4.legacy.exception.MaxCountExceededException;
import org.apache.commons.math4.legacy.exception.NoBracketingException;
import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
import org.apache.commons.math4.legacy.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math4.legacy.ode.FirstOrderIntegrator;
import org.apache.commons.math4.legacy.ode.TestProblem1;
import org.apache.commons.math4.legacy.ode.TestProblem2;
import org.apache.commons.math4.legacy.ode.TestProblem3;
import org.apache.commons.math4.legacy.ode.TestProblem4;
import org.apache.commons.math4.legacy.ode.TestProblem5;
import org.apache.commons.math4.legacy.ode.TestProblem6;
import org.apache.commons.math4.legacy.ode.TestProblemAbstract;
import org.apache.commons.math4.legacy.ode.TestProblemHandler;
import org.apache.commons.math4.legacy.ode.events.EventHandler;
import org.apache.commons.math4.legacy.ode.sampling.StepHandler;
import org.apache.commons.math4.legacy.ode.sampling.StepInterpolator;
import org.apache.commons.math4.core.jdkmath.JdkMath;
import org.junit.Assert;
import org.junit.Test;

public class ClassicalRungeKuttaIntegratorTest {

  @Test
  public void testMissedEndEvent()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      final double   t0     = 1878250320.0000029;
      final double   tEvent = 1878250379.9999986;
      final double[] k      = { 1.0e-4, 1.0e-5, 1.0e-6 };
      FirstOrderDifferentialEquations ode = new FirstOrderDifferentialEquations() {

          @Override
        public int getDimension() {
              return k.length;
          }

          @Override
        public void computeDerivatives(double t, double[] y, double[] yDot) {
              for (int i = 0; i < y.length; ++i) {
                  yDot[i] = k[i] * y[i];
              }
          }
      };

      ClassicalRungeKuttaIntegrator integrator = new ClassicalRungeKuttaIntegrator(60.0);

      double[] y0   = new double[k.length];
      for (int i = 0; i < y0.length; ++i) {
          y0[i] = i + 1;
      }
      double[] y    = new double[k.length];

      double finalT = integrator.integrate(ode, t0, y0, tEvent, y);
      Assert.assertEquals(tEvent, finalT, 5.0e-6);
      for (int i = 0; i < y.length; ++i) {
          Assert.assertEquals(y0[i] * JdkMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
      }

      integrator.addEventHandler(new EventHandler() {

          @Override
        public void init(double t0, double[] y0, double t) {
          }

          @Override
        public void resetState(double t, double[] y) {
          }

          @Override
        public double g(double t, double[] y) {
              return t - tEvent;
          }

          @Override
        public Action eventOccurred(double t, double[] y, boolean increasing) {
              Assert.assertEquals(tEvent, t, 5.0e-6);
              return Action.CONTINUE;
          }
      }, Double.POSITIVE_INFINITY, 1.0e-20, 100);
      finalT = integrator.integrate(ode, t0, y0, tEvent + 120, y);
      Assert.assertEquals(tEvent + 120, finalT, 5.0e-6);
      for (int i = 0; i < y.length; ++i) {
          Assert.assertEquals(y0[i] * JdkMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
      }

  }

  @Test
  public void testSanityChecks()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                        0.0, new double[pb.getDimension()+10],
                                                        1.0, new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
    } catch(DimensionMismatchException ie) {
    }
    try  {
        TestProblem1 pb = new TestProblem1();
        new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                          0.0, new double[pb.getDimension()],
                                                          1.0, new double[pb.getDimension()+10]);
          Assert.fail("an exception should have been thrown");
      } catch(DimensionMismatchException ie) {
      }
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                        0.0, new double[pb.getDimension()],
                                                        0.0, new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
    } catch(NumberIsTooSmallException ie) {
    }
  }

  @Test
  public void testDecreasingSteps()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    for (TestProblemAbstract pb : new TestProblemAbstract[] {
        new TestProblem1(), new TestProblem2(), new TestProblem3(),
        new TestProblem4(), new TestProblem5(), new TestProblem6()
    }) {

      double previousValueError = Double.NaN;
      double previousTimeError = Double.NaN;
      for (int i = 4; i < 10; ++i) {

        double step = (pb.getFinalTime() - pb.getInitialTime()) * JdkMath.pow(2.0, -i);

        FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        EventHandler[] functions = pb.getEventsHandlers();
        for (int l = 0; l < functions.length; ++l) {
          integ.addEventHandler(functions[l],
                                     Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
        }
        Assert.assertEquals(functions.length, integ.getEventHandlers().size());
        double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                                          pb.getFinalTime(), new double[pb.getDimension()]);
        if (functions.length == 0) {
            Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
        }

        double error = handler.getMaximalValueError();
        if (i > 4) {
          Assert.assertTrue(error < 1.01 * JdkMath.abs(previousValueError));
        }
        previousValueError = error;

        double timeError = handler.getMaximalTimeError();
        if (i > 4) {
          Assert.assertTrue(timeError <= JdkMath.abs(previousTimeError));
        }
        previousTimeError = timeError;

        integ.clearEventHandlers();
        Assert.assertEquals(0, integ.getEventHandlers().size());
      }

    }

  }

  @Test
  public void testSmallStep()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    Assert.assertTrue(handler.getLastError() < 2.0e-13);
    Assert.assertTrue(handler.getMaximalValueError() < 4.0e-12);
    Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    Assert.assertEquals("classical Runge-Kutta", integ.getName());
  }

  @Test
  public void testBigStep()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    Assert.assertTrue(handler.getLastError() > 0.0004);
    Assert.assertTrue(handler.getMaximalValueError() > 0.005);
    Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

  }

  @Test
  public void testBackward()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    TestProblem5 pb = new TestProblem5();
    double step = JdkMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    Assert.assertTrue(handler.getLastError() < 5.0e-10);
    Assert.assertTrue(handler.getMaximalValueError() < 7.0e-10);
    Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    Assert.assertEquals("classical Runge-Kutta", integ.getName());
  }

  @Test
  public void testKepler()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    final TestProblem3 pb  = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    integ.addStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);
  }

  private static class KeplerHandler implements StepHandler {
    KeplerHandler(TestProblem3 pb) {
      this.pb = pb;
      maxError = 0;
    }
    @Override
    public void init(double t0, double[] y0, double t) {
      maxError = 0;
    }
    @Override
    public void handleStep(StepInterpolator interpolator, boolean isLast)
        throws MaxCountExceededException {

      double[] interpolatedY = interpolator.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(interpolator.getCurrentTime());
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {
        maxError = error;
      }
      if (isLast) {
        // even with more than 1000 evaluations per period,
        // RK4 is not able to integrate such an eccentric
        // orbit with a good accuracy
        Assert.assertTrue(maxError > 0.005);
      }
    }
    private double maxError = 0;
    private TestProblem3 pb;
  }

  @Test
  public void testStepSize()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      final double step = 1.23456;
      FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
      integ.addStepHandler(new StepHandler() {
          @Override
        public void handleStep(StepInterpolator interpolator, boolean isLast) {
              if (! isLast) {
                  Assert.assertEquals(step,
                               interpolator.getCurrentTime() - interpolator.getPreviousTime(),
                               1.0e-12);
              }
          }
          @Override
        public void init(double t0, double[] y0, double t) {
          }
      });
      integ.integrate(new FirstOrderDifferentialEquations() {
          @Override
        public void computeDerivatives(double t, double[] y, double[] dot) {
              dot[0] = 1.0;
          }
          @Override
        public int getDimension() {
              return 1;
          }
      }, 0.0, new double[] { 0.0 }, 5.0, new double[1]);
  }

  @Test
  public void testTooLargeFirstStep() {

      RungeKuttaIntegrator integ = new ClassicalRungeKuttaIntegrator(0.5);
      final double start = 0.0;
      final double end   = 0.001;
      FirstOrderDifferentialEquations equations = new FirstOrderDifferentialEquations() {

          @Override
        public int getDimension() {
              return 1;
          }

          @Override
        public void computeDerivatives(double t, double[] y, double[] yDot) {
              Assert.assertTrue(t >= JdkMath.nextAfter(start, Double.NEGATIVE_INFINITY));
              Assert.assertTrue(t <= JdkMath.nextAfter(end,   Double.POSITIVE_INFINITY));
              yDot[0] = -100.0 * y[0];
          }

      };

      integ.integrate(equations, start, new double[] { 1.0 }, end, new double[1]);

  }

}