Examples of org.apache.commons.math3.ode.ContinuousOutputModel

org.apache.commons.math3.ode.ContinuousOutputModel
This class stores all information provided by an ODE integrator during the integration process and build a continuous model of the solution from this.
This class act as a step handler from the integrator point of view. It is called iteratively during the integration process and stores a copy of all steps information in a sorted collection for later use. Once the integration process is over, the user can use the {@link #setInterpolatedTime setInterpolatedTime} and {@link #getInterpolatedState getInterpolatedState} to retrieve thisinformation at any time. It is important to wait for the integration to be over before attempting to call {@link #setInterpolatedTime setInterpolatedTime} because some internalvariables are set only once the last step has been handled.

This is useful for example if the main loop of the user application should remain independent from the integration process or if one needs to mimic the behaviour of an analytical model despite a numerical model is used (i.e. one needs the ability to get the model value at any time or to navigate through the data).

If problem modeling is done with several separate integration phases for contiguous intervals, the same ContinuousOutputModel can be used as step handler for all integration phases as long as they are performed in order and in the same direction. As an example, one can extrapolate the trajectory of a satellite with one model (i.e. one set of differential equations) up to the beginning of a maneuver, use another more complex model including thrusters modeling and accurate attitude control during the maneuver, and revert to the first model after the end of the maneuver. If the same continuous output model handles the steps of all integration phases, the user do not need to bother when the maneuver begins or ends, he has all the data available in a transparent manner.

An important feature of this class is that it implements the Serializable interface. This means that the result of an integration can be serialized and reused later (if stored into a persistent medium like a filesystem or a database) or elsewhere (if sent to another application). Only the result of the integration is stored, there is no reference to the integrated problem by itself.

One should be aware that the amount of data stored in a ContinuousOutputModel instance can be important if the state vector is large, if the integration interval is long or if the steps are small (which can result from small tolerance settings in {@link org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator adaptivestep size integrators}).
@see StepHandler @see StepInterpolator @since 1.2

      
      List<SiteWithPolynomial> nearestSites =
          nearestSiteMap.get(site);
      
      RealVector vector = new ArrayRealVector(SITES_FOR_APPROX);
      RealMatrix matrix = new Array2DRowRealMatrix(
          SITES_FOR_APPROX, DefaultPolynomial.NUM_COEFFS);
      
      for (int row = 0; row < SITES_FOR_APPROX; row++) {
        SiteWithPolynomial nearSite = nearestSites.get(row);
        DefaultPolynomial.populateMatrix(matrix, row, nearSite.pos.x, nearSite.pos.z);

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     * @param matrix matrix with columns representing variables to correlate
     * @return correlation matrix
     */
    public RealMatrix computeCorrelationMatrix(final RealMatrix matrix) {
        int nVars = matrix.getColumnDimension();
        RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
        for (int i = 0; i < nVars; i++) {
            for (int j = 0; j < i; j++) {
                double corr = correlation(matrix.getColumn(i), matrix.getColumn(j));
                outMatrix.setEntry(i, j, corr);
                outMatrix.setEntry(j, i, corr);
            }
            outMatrix.setEntry(i, i, 1d);
        }
        return outMatrix;
    }

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        // solve the rectangular system in the least square sense
        // to get the best estimate of the Nordsieck vector [s2 ... sk]
        QRDecomposition decomposition;
        decomposition = new QRDecomposition(new Array2DRowRealMatrix(a, false));
        RealMatrix x = decomposition.getSolver().solve(new Array2DRowRealMatrix(b, false));
        return new Array2DRowRealMatrix(x.getData(), false);
    }

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    for (SiteWithPolynomial site : sites) {
      
      List<SiteWithPolynomial> nearestSites =
          nearestSiteMap.get(site);
      
      RealVector vector = new ArrayRealVector(SITES_FOR_APPROX);
      RealMatrix matrix = new Array2DRowRealMatrix(
          SITES_FOR_APPROX, DefaultPolynomial.NUM_COEFFS);
      
      for (int row = 0; row < SITES_FOR_APPROX; row++) {
        SiteWithPolynomial nearSite = nearestSites.get(row);
        DefaultPolynomial.populateMatrix(matrix, row, nearSite.pos.x, nearSite.pos.z);
        vector.setEntry(row, nearSite.pos.y);
      }
      
      QRDecomposition qr = new QRDecomposition(matrix);
      RealVector solution = qr.getSolver().solve(vector);
        
      double[] coeffs = solution.toArray();
      
      for (double coeff : coeffs) {
        if (coeff > 10e3) {
          continue calculatePolynomials;
        }

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                return Double.compare(weightedResidual(o1),
                                      weightedResidual(o2));
            }


            private double weightedResidual(final PointVectorValuePair pv) {
                final RealVector v = new ArrayRealVector(pv.getValueRef(), false);
                final RealVector r = target.subtract(v);
                return r.dotProduct(weight.operate(r));
            }
        };
    }

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            MaxCountExceededException, NoBracketingException  {


        TestProblem3 pb = new TestProblem3(0.9);
        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
        LutherIntegrator integ = new LutherIntegrator(step);
        integ.addStepHandler(new ContinuousOutputModel());
        integ.integrate(pb,
                        pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);


        ByteArrayOutputStream bos = new ByteArrayOutputStream();
        ObjectOutputStream    oos = new ObjectOutputStream(bos);
        for (StepHandler handler : integ.getStepHandlers()) {
            oos.writeObject(handler);
        }


        Assert.assertTrue(bos.size() > 1200000);
        Assert.assertTrue(bos.size() < 1250000);


        ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
        ObjectInputStream     ois = new ObjectInputStream(bis);
        ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();


        Random random = new Random(347588535632l);
        double maxError = 0.0;
        for (int i = 0; i < 1000; ++i) {
            double r = random.nextDouble();
            double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
            cm.setInterpolatedTime(time);
            double[] interpolatedY = cm.getInterpolatedState ();
            double[] theoreticalY  = pb.computeTheoreticalState(time);
            double dx = interpolatedY[0] - theoreticalY[0];
            double dy = interpolatedY[1] - theoreticalY[1];
            double error = dx * dx + dy * dy;
            if (error > maxError) {

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           NumberIsTooSmallException, DimensionMismatchException,
           MaxCountExceededException, NoBracketingException {


        TestProblem1 pb = new TestProblem1();
        AdamsBashforthIntegrator integ = new AdamsBashforthIntegrator(4, 0.0, 1.0, 1.0e-10, 1.0e-10);
        integ.addStepHandler(new ContinuousOutputModel());
        integ.integrate(pb,
                        pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);


        ByteArrayOutputStream bos = new ByteArrayOutputStream();
        ObjectOutputStream    oos = new ObjectOutputStream(bos);
        for (StepHandler handler : integ.getStepHandlers()) {
            oos.writeObject(handler);
        }


        Assert.assertTrue(bos.size () >  25500);
        Assert.assertTrue(bos.size () <  26500);


        ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
        ObjectInputStream     ois = new ObjectInputStream(bis);
        ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();


        Random random = new Random(347588535632l);
        double maxError = 0.0;
        for (int i = 0; i < 1000; ++i) {
            double r = random.nextDouble();
            double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
            cm.setInterpolatedTime(time);
            double[] interpolatedY = cm.getInterpolatedState ();
            double[] theoreticalY  = pb.computeTheoreticalState(time);
            double dx = interpolatedY[0] - theoreticalY[0];
            double dy = interpolatedY[1] - theoreticalY[1];
            double error = dx * dx + dy * dy;
            if (error > maxError) {

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           MaxCountExceededException, NoBracketingException {


    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    EulerIntegrator integ = new EulerIntegrator(step);
    integ.addStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    for (StepHandler handler : integ.getStepHandlers()) {
        oos.writeObject(handler);
    }


    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
    ObjectInputStream     ois = new ObjectInputStream(bis);
    ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();


    Random random = new Random(347588535632l);
    double maxError = 0.0;
    for (int i = 0; i < 1000; ++i) {
      double r = random.nextDouble();
      double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
      cm.setInterpolatedTime(time);
      double[] interpolatedY = cm.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(time);
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {

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    double scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = scalAbsoluteTolerance;
    DormandPrince54Integrator integ = new DormandPrince54Integrator(minStep, maxStep,
                                                                    scalAbsoluteTolerance,
                                                                    scalRelativeTolerance);
    integ.addStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    for (StepHandler handler : integ.getStepHandlers()) {
        oos.writeObject(handler);
    }


    Assert.assertTrue(bos.size () > 135000);
    Assert.assertTrue(bos.size () < 145000);


    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
    ObjectInputStream     ois = new ObjectInputStream(bis);
    ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();


    Random random = new Random(347588535632l);
    double maxError = 0.0;
    for (int i = 0; i < 1000; ++i) {
      double r = random.nextDouble();
      double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
      cm.setInterpolatedTime(time);
      double[] interpolatedY = cm.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(time);
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {

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    double relTolerance = 1.0e-8;


    GraggBulirschStoerIntegrator integ =
      new GraggBulirschStoerIntegrator(minStep, maxStep,
                                       absTolerance, relTolerance);
    integ.addStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    for (StepHandler handler : integ.getStepHandlers()) {
        oos.writeObject(handler);
    }


    Assert.assertTrue(bos.size () > 35000);
    Assert.assertTrue(bos.size () < 36000);


    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
    ObjectInputStream     ois = new ObjectInputStream(bis);
    ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();


    Random random = new Random(347588535632l);
    double maxError = 0.0;
    for (int i = 0; i < 1000; ++i) {
      double r = random.nextDouble();
      double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
      cm.setInterpolatedTime(time);
      double[] interpolatedY = cm.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(time);
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {

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org.apache.commons.math3.analysis.function.Sin

org.apache.commons.math3.analysis.function.Sinc

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