Examples with MoleculeModel gdsc.smlm.model.MoleculeModel used on opensource projects

Example 1 with MoleculeModel

use of gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class DiffusionRateTest method run.

/*
	 * (non-Javadoc)
	 * 
	 * @see ij.plugin.PlugIn#run(java.lang.String)
	 */
public void run(String arg) {
    SMLMUsageTracker.recordPlugin(this.getClass(), arg);
    if (IJ.controlKeyDown()) {
        simpleTest();
        return;
    }
    extraOptions = Utils.isExtraOptions();
    if (!showDialog())
        return;
    lastSimulatedDataset[0] = lastSimulatedDataset[1] = "";
    lastSimulatedPrecision = 0;
    final int totalSteps = (int) Math.ceil(settings.seconds * settings.stepsPerSecond);
    conversionFactor = 1000000.0 / (settings.pixelPitch * settings.pixelPitch);
    // Diffusion rate is um^2/sec. Convert to pixels per simulation frame.
    final double diffusionRateInPixelsPerSecond = settings.diffusionRate * conversionFactor;
    final double diffusionRateInPixelsPerStep = diffusionRateInPixelsPerSecond / settings.stepsPerSecond;
    final double precisionInPixels = myPrecision / settings.pixelPitch;
    final boolean addError = myPrecision != 0;
    Utils.log(TITLE + " : D = %s um^2/sec, Precision = %s nm", Utils.rounded(settings.diffusionRate, 4), Utils.rounded(myPrecision, 4));
    Utils.log("Mean-displacement per dimension = %s nm/sec", Utils.rounded(1e3 * ImageModel.getRandomMoveDistance(settings.diffusionRate), 4));
    if (extraOptions)
        Utils.log("Step size = %s, precision = %s", Utils.rounded(ImageModel.getRandomMoveDistance(diffusionRateInPixelsPerStep)), Utils.rounded(precisionInPixels));
    // Convert diffusion co-efficient into the standard deviation for the random walk
    final double diffusionSigma = (settings.getDiffusionType() == DiffusionType.LINEAR_WALK) ? // Q. What should this be? At the moment just do 1D diffusion on a random vector
    ImageModel.getRandomMoveDistance(diffusionRateInPixelsPerStep) : ImageModel.getRandomMoveDistance(diffusionRateInPixelsPerStep);
    Utils.log("Simulation step-size = %s nm", Utils.rounded(settings.pixelPitch * diffusionSigma, 4));
    // Move the molecules and get the diffusion rate
    IJ.showStatus("Simulating ...");
    final long start = System.nanoTime();
    final long seed = System.currentTimeMillis() + System.identityHashCode(this);
    RandomGenerator[] random = new RandomGenerator[3];
    RandomGenerator[] random2 = new RandomGenerator[3];
    for (int i = 0; i < 3; i++) {
        random[i] = new Well19937c(seed + i * 12436);
        random2[i] = new Well19937c(seed + i * 678678 + 3);
    }
    Statistics[] stats2D = new Statistics[totalSteps];
    Statistics[] stats3D = new Statistics[totalSteps];
    StoredDataStatistics jumpDistances2D = new StoredDataStatistics(totalSteps);
    StoredDataStatistics jumpDistances3D = new StoredDataStatistics(totalSteps);
    for (int j = 0; j < totalSteps; j++) {
        stats2D[j] = new Statistics();
        stats3D[j] = new Statistics();
    }
    SphericalDistribution dist = new SphericalDistribution(settings.confinementRadius / settings.pixelPitch);
    Statistics asymptote = new Statistics();
    // Save results to memory
    MemoryPeakResults results = new MemoryPeakResults(totalSteps);
    Calibration cal = new Calibration(settings.pixelPitch, 1, 1000.0 / settings.stepsPerSecond);
    results.setCalibration(cal);
    results.setName(TITLE);
    int peak = 0;
    // Store raw coordinates
    ArrayList<Point> points = new ArrayList<Point>(totalSteps);
    StoredData totalJumpDistances1D = new StoredData(settings.particles);
    StoredData totalJumpDistances2D = new StoredData(settings.particles);
    StoredData totalJumpDistances3D = new StoredData(settings.particles);
    for (int i = 0; i < settings.particles; i++) {
        if (i % 16 == 0) {
            IJ.showProgress(i, settings.particles);
            if (Utils.isInterrupted())
                return;
        }
        // Increment the frame so that tracing analysis can distinguish traces
        peak++;
        double[] origin = new double[3];
        final int id = i + 1;
        MoleculeModel m = new MoleculeModel(id, origin.clone());
        if (addError)
            origin = addError(origin, precisionInPixels, random);
        if (useConfinement) {
            // Note: When using confinement the average displacement should asymptote
            // at the average distance of a point from the centre of a ball. This is 3r/4.
            // See: http://answers.yahoo.com/question/index?qid=20090131162630AAMTUfM
            // The equivalent in 2D is 2r/3. However although we are plotting 2D distance
            // this is a projection of the 3D position onto the plane and so the particles
            // will not be evenly spread (there will be clustering at centre caused by the
            // poles)
            final double[] axis = (settings.getDiffusionType() == DiffusionType.LINEAR_WALK) ? nextVector() : null;
            for (int j = 0; j < totalSteps; j++) {
                double[] xyz = m.getCoordinates();
                double[] originalXyz = xyz.clone();
                for (int n = confinementAttempts; n-- > 0; ) {
                    if (settings.getDiffusionType() == DiffusionType.GRID_WALK)
                        m.walk(diffusionSigma, random);
                    else if (settings.getDiffusionType() == DiffusionType.LINEAR_WALK)
                        m.slide(diffusionSigma, axis, random[0]);
                    else
                        m.move(diffusionSigma, random);
                    if (!dist.isWithin(m.getCoordinates())) {
                        // Reset position
                        for (int k = 0; k < 3; k++) xyz[k] = originalXyz[k];
                    } else {
                        // The move was allowed
                        break;
                    }
                }
                points.add(new Point(id, xyz));
                if (addError)
                    xyz = addError(xyz, precisionInPixels, random2);
                peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
            }
            asymptote.add(distance(m.getCoordinates()));
        } else {
            if (settings.getDiffusionType() == DiffusionType.GRID_WALK) {
                for (int j = 0; j < totalSteps; j++) {
                    m.walk(diffusionSigma, random);
                    double[] xyz = m.getCoordinates();
                    points.add(new Point(id, xyz));
                    if (addError)
                        xyz = addError(xyz, precisionInPixels, random2);
                    peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
                }
            } else if (settings.getDiffusionType() == DiffusionType.LINEAR_WALK) {
                final double[] axis = nextVector();
                for (int j = 0; j < totalSteps; j++) {
                    m.slide(diffusionSigma, axis, random[0]);
                    double[] xyz = m.getCoordinates();
                    points.add(new Point(id, xyz));
                    if (addError)
                        xyz = addError(xyz, precisionInPixels, random2);
                    peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
                }
            } else {
                for (int j = 0; j < totalSteps; j++) {
                    m.move(diffusionSigma, random);
                    double[] xyz = m.getCoordinates();
                    points.add(new Point(id, xyz));
                    if (addError)
                        xyz = addError(xyz, precisionInPixels, random2);
                    peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
                }
            }
        }
        // Debug: record all the particles so they can be analysed
        // System.out.printf("%f %f %f\n", m.getX(), m.getY(), m.getZ());
        final double[] xyz = m.getCoordinates();
        double d2 = 0;
        totalJumpDistances1D.add(d2 = xyz[0] * xyz[0]);
        totalJumpDistances2D.add(d2 += xyz[1] * xyz[1]);
        totalJumpDistances3D.add(d2 += xyz[2] * xyz[2]);
    }
    final double time = (System.nanoTime() - start) / 1000000.0;
    IJ.showProgress(1);
    MemoryPeakResults.addResults(results);
    lastSimulatedDataset[0] = results.getName();
    lastSimulatedPrecision = myPrecision;
    // Convert pixels^2/step to um^2/sec
    final double msd2D = (jumpDistances2D.getMean() / conversionFactor) / (results.getCalibration().getExposureTime() / 1000);
    final double msd3D = (jumpDistances3D.getMean() / conversionFactor) / (results.getCalibration().getExposureTime() / 1000);
    Utils.log("Raw data D=%s um^2/s, Precision = %s nm, N=%d, step=%s s, mean2D=%s um^2, MSD 2D = %s um^2/s, mean3D=%s um^2, MSD 3D = %s um^2/s", Utils.rounded(settings.diffusionRate), Utils.rounded(myPrecision), jumpDistances2D.getN(), Utils.rounded(results.getCalibration().getExposureTime() / 1000), Utils.rounded(jumpDistances2D.getMean() / conversionFactor), Utils.rounded(msd2D), Utils.rounded(jumpDistances3D.getMean() / conversionFactor), Utils.rounded(msd3D));
    aggregateIntoFrames(points, addError, precisionInPixels, random2);
    IJ.showStatus("Analysing results ...");
    if (showDiffusionExample) {
        showExample(totalSteps, diffusionSigma, random);
    }
    // Plot a graph of mean squared distance
    double[] xValues = new double[stats2D.length];
    double[] yValues2D = new double[stats2D.length];
    double[] yValues3D = new double[stats3D.length];
    double[] upper2D = new double[stats2D.length];
    double[] lower2D = new double[stats2D.length];
    double[] upper3D = new double[stats3D.length];
    double[] lower3D = new double[stats3D.length];
    SimpleRegression r2D = new SimpleRegression(false);
    SimpleRegression r3D = new SimpleRegression(false);
    final int firstN = (useConfinement) ? fitN : totalSteps;
    for (int j = 0; j < totalSteps; j++) {
        // Convert steps to seconds
        xValues[j] = (double) (j + 1) / settings.stepsPerSecond;
        // Convert values in pixels^2 to um^2
        final double mean2D = stats2D[j].getMean() / conversionFactor;
        final double mean3D = stats3D[j].getMean() / conversionFactor;
        final double sd2D = stats2D[j].getStandardDeviation() / conversionFactor;
        final double sd3D = stats3D[j].getStandardDeviation() / conversionFactor;
        yValues2D[j] = mean2D;
        yValues3D[j] = mean3D;
        upper2D[j] = mean2D + sd2D;
        lower2D[j] = mean2D - sd2D;
        upper3D[j] = mean3D + sd3D;
        lower3D[j] = mean3D - sd3D;
        if (j < firstN) {
            r2D.addData(xValues[j], yValues2D[j]);
            r3D.addData(xValues[j], yValues3D[j]);
        }
    }
    // TODO - Fit using the equation for 2D confined diffusion:
    // MSD = 4s^2 + R^2 (1 - 0.99e^(-1.84^2 Dt / R^2)
    // s = localisation precision
    // R = confinement radius
    // D = 2D diffusion coefficient
    // t = time
    final PolynomialFunction fitted2D, fitted3D;
    if (r2D.getN() > 0) {
        // Do linear regression to get diffusion rate
        final double[] best2D = new double[] { r2D.getIntercept(), r2D.getSlope() };
        fitted2D = new PolynomialFunction(best2D);
        final double[] best3D = new double[] { r3D.getIntercept(), r3D.getSlope() };
        fitted3D = new PolynomialFunction(best3D);
        // For 2D diffusion: d^2 = 4D
        // where: d^2 = mean-square displacement
        double D = best2D[1] / 4.0;
        String msg = "2D Diffusion rate = " + Utils.rounded(D, 4) + " um^2 / sec (" + Utils.timeToString(time) + ")";
        IJ.showStatus(msg);
        Utils.log(msg);
        D = best3D[1] / 6.0;
        Utils.log("3D Diffusion rate = " + Utils.rounded(D, 4) + " um^2 / sec (" + Utils.timeToString(time) + ")");
    } else {
        fitted2D = fitted3D = null;
    }
    // Create plots
    plotMSD(totalSteps, xValues, yValues2D, lower2D, upper2D, fitted2D, 2);
    plotMSD(totalSteps, xValues, yValues3D, lower3D, upper3D, fitted3D, 3);
    plotJumpDistances(TITLE, jumpDistances2D, 2, 1);
    plotJumpDistances(TITLE, jumpDistances3D, 3, 1);
    if (idCount > 0)
        new WindowOrganiser().tileWindows(idList);
    if (useConfinement)
        Utils.log("3D asymptote distance = %s nm (expected %.2f)", Utils.rounded(asymptote.getMean() * settings.pixelPitch, 4), 3 * settings.confinementRadius / 4);
}

Example 2 with MoleculeModel

use of gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class CreateData method convertRelativeToAbsolute.

/**
	 * Update the fluorophores relative coordinates to absolute
	 * 
	 * @param molecules
	 */
@SuppressWarnings("unused")
private void convertRelativeToAbsolute(List<CompoundMoleculeModel> molecules) {
    for (CompoundMoleculeModel c : molecules) {
        final double[] xyz = c.getCoordinates();
        for (int n = c.getSize(); n-- > 0; ) {
            MoleculeModel m = c.getMolecule(n);
            double[] xyz2 = m.getCoordinates();
            for (int i = 0; i < 3; i++) xyz2[i] += xyz[i];
        }
    }
}

Example 3 with MoleculeModel

use of gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class CreateData method createCompoundMolecules.

@SuppressWarnings("unchecked")
private List<CompoundMoleculeModel> createCompoundMolecules() {
    // Diffusion rate is um^2/sec. Convert to pixels per simulation frame.
    final double diffusionFactor = (1000000.0 / (settings.pixelPitch * settings.pixelPitch)) / settings.stepsPerSecond;
    List<CompoundMoleculeModel> compounds;
    if (settings.compoundMolecules) {
        // Try and load the compounds from the XML specification
        try {
            Object fromXML = createXStream().fromXML(settings.compoundText);
            List<Compound> rawCompounds = (List<Compound>) fromXML;
            // Convert from the XML serialised objects to the compound model
            compounds = new ArrayList<CompoundMoleculeModel>(rawCompounds.size());
            int id = 1;
            for (Compound c : rawCompounds) {
                MoleculeModel[] molecules = new MoleculeModel[c.atoms.length];
                for (int i = 0; i < c.atoms.length; i++) {
                    Atom a = c.atoms[i];
                    molecules[i] = new MoleculeModel(a.mass, a.x, a.y, a.z);
                }
                CompoundMoleculeModel m = new CompoundMoleculeModel(id++, 0, 0, 0, Arrays.asList(molecules));
                m.setFraction(c.fraction);
                m.setDiffusionRate(c.D * diffusionFactor);
                m.setDiffusionType(DiffusionType.fromString(c.diffusionType));
                compounds.add(m);
            }
            // Convert coordinates from nm to pixels
            final double scaleFactor = 1.0 / settings.pixelPitch;
            for (CompoundMoleculeModel c : compounds) {
                c.scale(scaleFactor);
            }
        } catch (Exception e) {
            IJ.error(TITLE, "Unable to create compound molecules");
            return null;
        }
    } else {
        // Create a simple compound with one molecule at the origin
        compounds = new ArrayList<CompoundMoleculeModel>(1);
        CompoundMoleculeModel m = new CompoundMoleculeModel(1, 0, 0, 0, Arrays.asList(new MoleculeModel(0, 0, 0, 0)));
        m.setDiffusionRate(settings.diffusionRate * diffusionFactor);
        m.setDiffusionType(settings.getDiffusionType());
        compounds.add(m);
    }
    return compounds;
}

Example 4 with MoleculeModel

use of gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class BlinkEstimatorTest method estimateBlinking.

private TIntHashSet estimateBlinking(double nBlinks, double tOn, double tOff, int particles, double fixedFraction, boolean timeAtLowerBound, boolean doAssert) {
    SpatialIllumination activationIllumination = new UniformIllumination(100);
    int totalSteps = 100;
    double eAct = totalSteps * 0.3 * activationIllumination.getAveragePhotons();
    ImageModel imageModel = new ActivationEnergyImageModel(eAct, activationIllumination, tOn, 0, tOff, 0, nBlinks);
    imageModel.setRandomGenerator(rand);
    double[] max = new double[] { 256, 256, 32 };
    double[] min = new double[3];
    SpatialDistribution distribution = new UniformDistribution(min, max, rand.nextInt());
    List<CompoundMoleculeModel> compounds = new ArrayList<CompoundMoleculeModel>(1);
    CompoundMoleculeModel c = new CompoundMoleculeModel(1, 0, 0, 0, Arrays.asList(new MoleculeModel(0, 0, 0, 0)));
    c.setDiffusionRate(diffusionRate);
    c.setDiffusionType(DiffusionType.RANDOM_WALK);
    compounds.add(c);
    List<CompoundMoleculeModel> molecules = imageModel.createMolecules(compounds, particles, distribution, false);
    // Activate fluorophores
    List<? extends FluorophoreSequenceModel> fluorophores = imageModel.createFluorophores(molecules, totalSteps);
    totalSteps = checkTotalSteps(totalSteps, fluorophores);
    List<LocalisationModel> localisations = imageModel.createImage(molecules, fixedFraction, totalSteps, photons, 0.5, false);
    //		// Remove localisations to simulate missed counts. 
    //		List<LocalisationModel> newLocalisations = new ArrayList<LocalisationModel>(localisations.size());
    //		boolean[] id = new boolean[fluorophores.size() + 1];
    //		Statistics photonStats = new Statistics();
    //		for (LocalisationModel l : localisations)
    //		{
    //			photonStats.add(l.getIntensity());
    //			// Remove by intensity threshold and optionally at random.
    //			if (l.getIntensity() < minPhotons || rand.nextDouble() < pDelete)
    //				continue;
    //			newLocalisations.add(l);
    //			id[l.getId()] = true;
    //		}
    //		localisations = newLocalisations;
    //		System.out.printf("Photons = %f\n", photonStats.getMean());
    //
    //		List<FluorophoreSequenceModel> newFluorophores = new ArrayList<FluorophoreSequenceModel>(fluorophores.size());
    //		for (FluorophoreSequenceModel f : fluorophores)
    //		{
    //			if (id[f.getId()])
    //				newFluorophores.add(f);
    //		}
    //		fluorophores = newFluorophores;
    MemoryPeakResults results = new MemoryPeakResults();
    results.setCalibration(new Calibration(pixelPitch, 1, msPerFrame));
    for (LocalisationModel l : localisations) {
        // Remove by intensity threshold and optionally at random.
        if (l.getIntensity() < minPhotons || rand.nextDouble() < pDelete)
            continue;
        float[] params = new float[7];
        params[Gaussian2DFunction.X_POSITION] = (float) l.getX();
        params[Gaussian2DFunction.Y_POSITION] = (float) l.getY();
        params[Gaussian2DFunction.X_SD] = params[Gaussian2DFunction.Y_SD] = psfWidth;
        params[Gaussian2DFunction.SIGNAL] = (float) (l.getIntensity());
        results.addf(l.getTime(), 0, 0, 0, 0, 0, params, null);
    }
    // Add random localisations
    for (int i = (int) (localisations.size() * pAdd); i-- > 0; ) {
        float[] params = new float[7];
        params[Gaussian2DFunction.X_POSITION] = (float) (rand.nextDouble() * max[0]);
        params[Gaussian2DFunction.Y_POSITION] = (float) (rand.nextDouble() * max[1]);
        params[Gaussian2DFunction.X_SD] = params[Gaussian2DFunction.Y_SD] = psfWidth;
        // Intensity doesn't matter at the moment for tracing
        params[Gaussian2DFunction.SIGNAL] = (float) (photons);
        results.addf(1 + rand.nextInt(totalSteps), 0, 0, 0, 0, 0, params, null);
    }
    // Get actual simulated stats ...
    Statistics statsNBlinks = new Statistics();
    Statistics statsTOn = new Statistics();
    Statistics statsTOff = new Statistics();
    Statistics statsSampledNBlinks = new Statistics();
    Statistics statsSampledTOn = new Statistics();
    StoredDataStatistics statsSampledTOff = new StoredDataStatistics();
    for (FluorophoreSequenceModel f : fluorophores) {
        statsNBlinks.add(f.getNumberOfBlinks());
        statsTOn.add(f.getOnTimes());
        statsTOff.add(f.getOffTimes());
        int[] on = f.getSampledOnTimes();
        statsSampledNBlinks.add(on.length);
        statsSampledTOn.add(on);
        statsSampledTOff.add(f.getSampledOffTimes());
    }
    System.out.printf("N = %d (%d), N-blinks = %f, tOn = %f, tOff = %f, Fixed = %f\n", fluorophores.size(), localisations.size(), nBlinks, tOn, tOff, fixedFraction);
    System.out.printf("Actual N-blinks = %f (%f), tOn = %f (%f), tOff = %f (%f), 95%% = %f, max = %f\n", statsNBlinks.getMean(), statsSampledNBlinks.getMean(), statsTOn.getMean(), statsSampledTOn.getMean(), statsTOff.getMean(), statsSampledTOff.getMean(), statsSampledTOff.getStatistics().getPercentile(95), statsSampledTOff.getStatistics().getMax());
    System.out.printf("-=-=--=-\n");
    BlinkEstimator be = new BlinkEstimator();
    be.maxDarkTime = (int) (tOff * 10);
    be.msPerFrame = msPerFrame;
    be.relativeDistance = false;
    double d = ImageModel.getRandomMoveDistance(diffusionRate);
    be.searchDistance = (fixedFraction < 1) ? Math.sqrt(2 * d * d) * 3 : 0;
    be.timeAtLowerBound = timeAtLowerBound;
    be.showPlots = false;
    //Assert.assertTrue("Max dark time must exceed the dark time of the data (otherwise no plateau)",
    //		be.maxDarkTime > statsSampledTOff.getStatistics().getMax());
    int nMolecules = fluorophores.size();
    if (usePopulationStatistics) {
        nBlinks = statsNBlinks.getMean();
        tOff = statsTOff.getMean();
    } else {
        nBlinks = statsSampledNBlinks.getMean();
        tOff = statsSampledTOff.getMean();
    }
    // See if any fitting regime gets a correct answer
    TIntHashSet ok = new TIntHashSet();
    for (int nFittedPoints = MIN_FITTED_POINTS; nFittedPoints <= MAX_FITTED_POINTS; nFittedPoints++) {
        be.nFittedPoints = nFittedPoints;
        be.computeBlinkingRate(results, true);
        double moleculesError = DoubleEquality.relativeError(nMolecules, be.getNMolecules());
        double blinksError = DoubleEquality.relativeError(nBlinks, be.getNBlinks());
        double offError = DoubleEquality.relativeError(tOff * msPerFrame, be.getTOff());
        System.out.printf("Error %d: N = %f, blinks = %f, tOff = %f : %f\n", nFittedPoints, moleculesError, blinksError, offError, (moleculesError + blinksError + offError) / 3);
        if (moleculesError < relativeError && blinksError < relativeError && offError < relativeError) {
            ok.add(nFittedPoints);
            System.out.printf("-=-=--=-\n");
            System.out.printf("*** Correct at %d fitted points ***\n", nFittedPoints);
            if (doAssert)
                break;
        }
    //if (!be.isIncreaseNFittedPoints())
    //	break;
    }
    System.out.printf("-=-=--=-\n");
    if (doAssert)
        Assert.assertFalse(ok.isEmpty());
    //Assert.assertEquals("Invalid t-off", tOff * msPerFrame, be.getTOff(), tOff * msPerFrame * relativeError);
    return ok;
}

Example 5 with MoleculeModel

use of gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class DiffusionRateTest method showExample.

private void showExample(int totalSteps, double diffusionSigma, RandomGenerator[] random) {
    MoleculeModel m = new MoleculeModel(0, new double[3]);
    float[] xValues = new float[totalSteps];
    float[] x = new float[totalSteps];
    float[] y = new float[totalSteps];
    final double[] axis = (settings.getDiffusionType() == DiffusionType.LINEAR_WALK) ? nextVector() : null;
    for (int j = 0; j < totalSteps; j++) {
        if (settings.getDiffusionType() == DiffusionType.GRID_WALK)
            m.walk(diffusionSigma, random);
        else if (settings.getDiffusionType() == DiffusionType.LINEAR_WALK)
            m.slide(diffusionSigma, axis, random[0]);
        else
            m.move(diffusionSigma, random);
        x[j] = (float) (m.getX());
        y[j] = (float) (m.getY());
        xValues[j] = (float) ((j + 1) / settings.stepsPerSecond);
    }
    // Plot x and y coords on a timeline
    String title = TITLE + " example coordinates";
    Plot2 plot = new Plot2(title, "Time (seconds)", "Distance (um)");
    float[] xUm = convertToUm(x);
    float[] yUm = convertToUm(y);
    float[] limits = Maths.limits(xUm);
    limits = Maths.limits(limits, yUm);
    plot.setLimits(0, totalSteps / settings.stepsPerSecond, limits[0], limits[1]);
    plot.setColor(Color.red);
    plot.addPoints(xValues, xUm, Plot2.LINE);
    plot.setColor(Color.blue);
    plot.addPoints(xValues, yUm, Plot2.LINE);
    Utils.display(title, plot);
    // Scale up and draw 2D position
    for (int j = 0; j < totalSteps; j++) {
        x[j] *= magnification;
        y[j] *= magnification;
    }
    float[] limitsx = getLimits(x);
    float[] limitsy = getLimits(y);
    int width = (int) (limitsx[1] - limitsx[0]);
    int height = (int) (limitsy[1] - limitsy[0]);
    // Ensure we draw something, even it is a simple dot at the centre for no diffusion
    if (width == 0) {
        width = (int) (32 * magnification);
        limitsx[0] = -width / 2;
    }
    if (height == 0) {
        height = (int) (32 * magnification);
        limitsy[0] = -height / 2;
    }
    ImageProcessor ip = new ByteProcessor(width, height);
    // Adjust x and y using the minimum to centre
    x[0] -= limitsx[0];
    y[0] -= limitsy[0];
    for (int j = 1; j < totalSteps; j++) {
        // Adjust x and y using the minimum to centre
        x[j] -= limitsx[0];
        y[j] -= limitsy[0];
        // Draw a line
        ip.setColor(32 + (223 * j) / (totalSteps - 1));
        ip.drawLine(round(x[j - 1]), round(y[j - 1]), round(x[j]), round(y[j]));
    }
    // Draw the final position
    ip.putPixel((int) round(x[totalSteps - 1]), (int) round(y[totalSteps - 1]), 255);
    ImagePlus imp = Utils.display(TITLE + " example", ip);
    // Apply the fire lookup table
    WindowManager.setTempCurrentImage(imp);
    LutLoader lut = new LutLoader();
    lut.run("fire");
    WindowManager.setTempCurrentImage(null);
}