Examples with UniformDistribution uk.ac.sussex.gdsc.smlm.model.UniformDistribution used on opensource projects

Example 1 with UniformDistribution

use of uk.ac.sussex.gdsc.smlm.model.UniformDistribution in project GDSC-SMLM by aherbert.

the class CreateData method createUniformDistribution.

/**
 * Create distribution within an XY border.
 *
 * @param border the border
 * @return the uniform distribution
 */
private UniformDistribution createUniformDistribution(double border) {
    final double depth = (settings.getFixedDepth()) ? settings.getDepth() / settings.getPixelPitch() : settings.getDepth() / (2 * settings.getPixelPitch());
    // Ensure the focal plane is in the middle of the zDepth
    final double[] max = new double[] { settings.getSize() / 2.0 - border, settings.getSize() / 2.0 - border, depth };
    final double[] min = new double[3];
    for (int i = 0; i < 3; i++) {
        min[i] = -max[i];
    }
    if (settings.getFixedDepth()) {
        min[2] = max[2];
    }
    // Try using different distributions:
    if (settings.getDistribution().equals(DISTRIBUTION[UNIFORM_HALTON])) {
        return new UniformDistribution(min, max, createRandomGenerator().nextInt());
    }
    if (settings.getDistribution().equals(DISTRIBUTION[UNIFORM_SOBOL])) {
        final SobolSequenceGenerator rvg = new SobolSequenceGenerator(3);
        rvg.skipTo(createRandomGenerator().nextInt());
        return new UniformDistribution(min, max, rvg);
    }
    // Create a distribution using random generators for each dimension
    return new UniformDistribution(min, max, this::createRandomGenerator);
}

Example 2 with UniformDistribution

use of uk.ac.sussex.gdsc.smlm.model.UniformDistribution in project GDSC-SMLM by aherbert.

the class BlinkEstimatorTest method estimateBlinking.

private TIntHashSet estimateBlinking(UniformRandomProvider rg, double blinkingRate, double ton, double toff, int particles, double fixedFraction, boolean timeAtLowerBound, boolean doAssert) {
    Assumptions.assumeTrue(TestSettings.allow(TestComplexity.MAXIMUM));
    final SpatialIllumination activationIllumination = new UniformIllumination(100);
    int totalSteps = 100;
    final double eAct = totalSteps * 0.3 * activationIllumination.getAveragePhotons();
    final ImageModel imageModel = new ActivationEnergyImageModel(eAct, activationIllumination, ton, 0, toff, 0, blinkingRate, rg);
    final double[] max = new double[] { 256, 256, 32 };
    final double[] min = new double[3];
    final SpatialDistribution distribution = new UniformDistribution(min, max, rg.nextInt());
    final List<CompoundMoleculeModel> compounds = new ArrayList<>(1);
    final 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);
    final List<CompoundMoleculeModel> molecules = imageModel.createMolecules(compounds, particles, distribution, false);
    // Activate fluorophores
    final List<? extends FluorophoreSequenceModel> fluorophores = imageModel.createFluorophores(molecules, totalSteps);
    totalSteps = checkTotalSteps(totalSteps, fluorophores);
    final 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;
    // logger.info("Photons = %f", photonStats.getMean());
    // 
    // List<FluorophoreSequenceModel> newFluorophores = new
    // ArrayList<FluorophoreSequenceModel>(fluorophores.size());
    // for (FluorophoreSequenceModel f : fluorophores)
    // {
    // if (id[f.getId()])
    // newFluorophores.add(f);
    // }
    // fluorophores = newFluorophores;
    final MemoryPeakResults results = new MemoryPeakResults();
    final CalibrationWriter calibration = new CalibrationWriter();
    calibration.setNmPerPixel(pixelPitch);
    calibration.setExposureTime(msPerFrame);
    calibration.setCountPerPhoton(1);
    results.setCalibration(calibration.getCalibration());
    results.setPsf(PsfHelper.create(PSFType.ONE_AXIS_GAUSSIAN_2D));
    final float b = 0;
    float intensity;
    final float z = 0;
    for (final LocalisationModel l : localisations) {
        // Remove by intensity threshold and optionally at random.
        if (l.getIntensity() < minPhotons || rg.nextDouble() < probabilityDelete) {
            continue;
        }
        final int frame = l.getTime();
        intensity = (float) l.getIntensity();
        final float x = (float) l.getX();
        final float y = (float) l.getY();
        final float[] params = Gaussian2DPeakResultHelper.createParams(b, intensity, x, y, z, psfWidth);
        results.add(frame, 0, 0, 0, 0, 0, 0, params, null);
    }
    // Add random localisations
    // Intensity doesn't matter at the moment for tracing
    intensity = (float) photons;
    for (int i = (int) (localisations.size() * probabilityAdd); i-- > 0; ) {
        final int frame = 1 + rg.nextInt(totalSteps);
        final float x = (float) (rg.nextDouble() * max[0]);
        final float y = (float) (rg.nextDouble() * max[1]);
        final float[] params = Gaussian2DPeakResultHelper.createParams(b, intensity, x, y, z, psfWidth);
        results.add(frame, 0, 0, 0, 0, 0, 0, params, null);
    }
    // Get actual simulated stats ...
    final Statistics statsNBlinks = new Statistics();
    final Statistics statsTOn = new Statistics();
    final Statistics statsTOff = new Statistics();
    final Statistics statsSampledNBlinks = new Statistics();
    final Statistics statsSampledTOn = new Statistics();
    final StoredDataStatistics statsSampledTOff = new StoredDataStatistics();
    for (final FluorophoreSequenceModel f : fluorophores) {
        statsNBlinks.add(f.getNumberOfBlinks());
        statsTOn.add(f.getOnTimes());
        statsTOff.add(f.getOffTimes());
        final int[] on = f.getSampledOnTimes();
        statsSampledNBlinks.add(on.length);
        statsSampledTOn.add(on);
        statsSampledTOff.add(f.getSampledOffTimes());
    }
    logger.info(FunctionUtils.getSupplier("N = %d (%d), N-blinks = %f, tOn = %f, tOff = %f, Fixed = %f", fluorophores.size(), localisations.size(), blinkingRate, ton, toff, fixedFraction));
    logger.info(FunctionUtils.getSupplier("Actual N-blinks = %f (%f), tOn = %f (%f), tOff = %f (%f), 95%% = %f, max = %f", statsNBlinks.getMean(), statsSampledNBlinks.getMean(), statsTOn.getMean(), statsSampledTOn.getMean(), statsTOff.getMean(), statsSampledTOff.getMean(), statsSampledTOff.getStatistics().getPercentile(95), statsSampledTOff.getStatistics().getMax()));
    logger.info("-=-=--=-");
    final BlinkEstimator be = new BlinkEstimator();
    be.setMaxDarkTime((int) (toff * 10));
    be.setMsPerFrame(msPerFrame);
    be.setRelativeDistance(false);
    final double d = ImageModel.getRandomMoveDistance(diffusionRate);
    be.setSearchDistance((fixedFraction < 1) ? Math.sqrt(2 * d * d) * 3 : 0);
    be.setTimeAtLowerBound(timeAtLowerBound);
    // Assertions.assertTrue("Max dark time must exceed the dark time of the data (otherwise no
    // plateau)",
    // be.maxDarkTime > statsSampledTOff.getStatistics().getMax());
    final int nMolecules = fluorophores.size();
    if (usePopulationStatistics) {
        blinkingRate = statsNBlinks.getMean();
        toff = statsTOff.getMean();
    } else {
        blinkingRate = statsSampledNBlinks.getMean();
        toff = statsSampledTOff.getMean();
    }
    // See if any fitting regime gets a correct answer
    final TIntHashSet ok = new TIntHashSet();
    for (int numberOfFittedPoints = MIN_FITTED_POINTS; numberOfFittedPoints <= MAX_FITTED_POINTS; numberOfFittedPoints++) {
        be.setNumberOfFittedPoints(numberOfFittedPoints);
        be.computeBlinkingRate(results, true);
        final double moleculesError = DoubleEquality.relativeError(nMolecules, be.getNMolecules());
        final double blinksError = DoubleEquality.relativeError(blinkingRate, be.getNBlinks());
        final double offError = DoubleEquality.relativeError(toff * msPerFrame, be.getTOff());
        logger.info(FunctionUtils.getSupplier("Error %d: N = %f, blinks = %f, tOff = %f : %f", numberOfFittedPoints, moleculesError, blinksError, offError, (moleculesError + blinksError + offError) / 3));
        if (moleculesError < relativeError && blinksError < relativeError && offError < relativeError) {
            ok.add(numberOfFittedPoints);
            logger.info("-=-=--=-");
            logger.info(FunctionUtils.getSupplier("*** Correct at %d fitted points ***", numberOfFittedPoints));
            if (doAssert) {
                break;
            }
        }
    // if (!be.isIncreaseNFittedPoints())
    // break;
    }
    logger.info("-=-=--=-");
    if (doAssert) {
        Assertions.assertFalse(ok.isEmpty());
    }
    // relativeError);
    return ok;
}

Example 3 with UniformDistribution

use of uk.ac.sussex.gdsc.smlm.model.UniformDistribution in project GDSC-SMLM by aherbert.

the class PcPalmMolecules method runSimulation.

private void runSimulation(boolean resultsAvailable) {
    if (resultsAvailable && !showSimulationDialog()) {
        return;
    }
    startLog();
    log("Simulation parameters");
    if (settings.blinkingDistribution == 3) {
        log("  - Clusters = %d", settings.numberOfMolecules);
        log("  - Simulation size = %s um", MathUtils.rounded(settings.simulationSize, 4));
        log("  - Molecules/cluster = %s", MathUtils.rounded(settings.blinkingRate, 4));
        log("  - Blinking distribution = %s", Settings.BLINKING_DISTRIBUTION[settings.blinkingDistribution]);
        log("  - p-Value = %s", MathUtils.rounded(settings.pvalue, 4));
    } else {
        log("  - Molecules = %d", settings.numberOfMolecules);
        log("  - Simulation size = %s um", MathUtils.rounded(settings.simulationSize, 4));
        log("  - Blinking rate = %s", MathUtils.rounded(settings.blinkingRate, 4));
        log("  - Blinking distribution = %s", Settings.BLINKING_DISTRIBUTION[settings.blinkingDistribution]);
    }
    log("  - Average precision = %s nm", MathUtils.rounded(settings.sigmaS, 4));
    log("  - Clusters simulation = " + Settings.CLUSTER_SIMULATION[settings.clusterSimulation]);
    if (settings.clusterSimulation > 0) {
        log("  - Cluster number = %s +/- %s", MathUtils.rounded(settings.clusterNumber, 4), MathUtils.rounded(settings.clusterNumberStdDev, 4));
        log("  - Cluster radius = %s nm", MathUtils.rounded(settings.clusterRadius, 4));
    }
    final double nmPerPixel = 100;
    final double width = settings.simulationSize * 1000.0;
    final UniformRandomProvider rng = UniformRandomProviders.create();
    final UniformDistribution dist = new UniformDistribution(null, new double[] { width, width, 0 }, rng.nextInt());
    final NormalizedGaussianSampler gauss = SamplerUtils.createNormalizedGaussianSampler(rng);
    settings.molecules = new ArrayList<>(settings.numberOfMolecules);
    // Create some dummy results since the calibration is required for later analysis
    settings.results = new MemoryPeakResults(PsfHelper.create(PSFType.CUSTOM));
    settings.results.setCalibration(CalibrationHelper.create(nmPerPixel, 1, 100));
    settings.results.setSource(new NullSource("Molecule Simulation"));
    settings.results.begin();
    int count = 0;
    // Generate a sequence of coordinates
    final ArrayList<double[]> xyz = new ArrayList<>((int) (settings.numberOfMolecules * 1.1));
    final Statistics statsRadius = new Statistics();
    final Statistics statsSize = new Statistics();
    final String maskTitle = TITLE + " Cluster Mask";
    ByteProcessor bp = null;
    double maskScale = 0;
    if (settings.clusterSimulation > 0) {
        // Simulate clusters.
        // Note: In the Veatch et al. paper (Plos 1, e31457) correlation functions are built using
        // circles with small radii of 4-8 Arbitrary Units (AU) or large radii of 10-30 AU. A
        // fluctuations model is created at T = 1.075 Tc. It is not clear exactly how the particles
        // are distributed.
        // It may be that a mask is created first using the model. The particles are placed on the
        // mask using a specified density. This simulation produces a figure to show either a damped
        // cosine function (circles) or an exponential (fluctuations). The number of particles in
        // each circle may be randomly determined just by density. The figure does not discuss the
        // derivation of the cluster size statistic.
        // 
        // If this plugin simulation is run with a uniform distribution and blinking rate of 1 then
        // the damped cosine function is reproduced. The curve crosses g(r)=1 at a value equivalent
        // to the average distance to the centre-of-mass of each drawn cluster, not the input cluster
        // radius parameter (which is a hard upper limit on the distance to centre).
        final int maskSize = settings.lowResolutionImageSize;
        int[] mask = null;
        // scale is in nm/pixel
        maskScale = width / maskSize;
        final ArrayList<double[]> clusterCentres = new ArrayList<>();
        int totalSteps = 1 + (int) Math.ceil(settings.numberOfMolecules / settings.clusterNumber);
        if (settings.clusterSimulation == 2 || settings.clusterSimulation == 3) {
            // Clusters are non-overlapping circles
            // Ensure the circles do not overlap by using an exclusion mask that accumulates
            // out-of-bounds pixels by drawing the last cluster (plus some border) on an image. When no
            // more pixels are available then stop generating molecules.
            // This is done by cumulatively filling a mask and using the MaskDistribution to select
            // a new point. This may be slow but it works.
            // TODO - Allow clusters of different sizes...
            mask = new int[maskSize * maskSize];
            Arrays.fill(mask, 255);
            MaskDistribution maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, rng);
            double[] centre;
            IJ.showStatus("Computing clusters mask");
            final int roiRadius = (int) Math.round((settings.clusterRadius * 2) / maskScale);
            if (settings.clusterSimulation == 3) {
                // Generate a mask of circles then sample from that.
                // If we want to fill the mask completely then adjust the total steps to be the number of
                // circles that can fit inside the mask.
                totalSteps = (int) (maskSize * maskSize / (Math.PI * MathUtils.pow2(settings.clusterRadius / maskScale)));
            }
            while ((centre = maskDistribution.next()) != null && clusterCentres.size() < totalSteps) {
                IJ.showProgress(clusterCentres.size(), totalSteps);
                // The mask returns the coordinates with the centre of the image at 0,0
                centre[0] += width / 2;
                centre[1] += width / 2;
                clusterCentres.add(centre);
                // Fill in the mask around the centre to exclude any more circles that could overlap
                final double cx = centre[0] / maskScale;
                final double cy = centre[1] / maskScale;
                fillMask(mask, maskSize, (int) cx, (int) cy, roiRadius, 0);
                try {
                    maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, rng);
                } catch (final IllegalArgumentException ex) {
                    // This can happen when there are no more non-zero pixels
                    log("WARNING: No more room for clusters on the mask area (created %d of estimated %d)", clusterCentres.size(), totalSteps);
                    break;
                }
            }
            ImageJUtils.finished();
        } else {
            // Pick centres randomly from the distribution
            while (clusterCentres.size() < totalSteps) {
                clusterCentres.add(dist.next());
            }
        }
        final double scaledRadius = settings.clusterRadius / maskScale;
        if (settings.showClusterMask || settings.clusterSimulation == 3) {
            // Show the mask for the clusters
            if (mask == null) {
                mask = new int[maskSize * maskSize];
            } else {
                Arrays.fill(mask, 0);
            }
            final int roiRadius = (int) Math.round(scaledRadius);
            for (final double[] c : clusterCentres) {
                final double cx = c[0] / maskScale;
                final double cy = c[1] / maskScale;
                fillMask(mask, maskSize, (int) cx, (int) cy, roiRadius, 1);
            }
            if (settings.clusterSimulation == 3) {
                // We have the mask. Now pick points at random from the mask.
                final MaskDistribution maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, rng);
                // Allocate each molecule position to a parent circle so defining clusters.
                final int[][] clusters = new int[clusterCentres.size()][];
                final int[] clusterSize = new int[clusters.length];
                for (int i = 0; i < settings.numberOfMolecules; i++) {
                    final double[] centre = maskDistribution.next();
                    // The mask returns the coordinates with the centre of the image at 0,0
                    centre[0] += width / 2;
                    centre[1] += width / 2;
                    xyz.add(centre);
                    // Output statistics on cluster size and number.
                    // TODO - Finding the closest cluster could be done better than an all-vs-all comparison
                    double max = distance2(centre, clusterCentres.get(0));
                    int cluster = 0;
                    for (int j = 1; j < clusterCentres.size(); j++) {
                        final double d2 = distance2(centre, clusterCentres.get(j));
                        if (d2 < max) {
                            max = d2;
                            cluster = j;
                        }
                    }
                    // Assign point i to cluster
                    centre[2] = cluster;
                    if (clusterSize[cluster] == 0) {
                        clusters[cluster] = new int[10];
                    }
                    if (clusters[cluster].length <= clusterSize[cluster]) {
                        clusters[cluster] = Arrays.copyOf(clusters[cluster], (int) (clusters[cluster].length * 1.5));
                    }
                    clusters[cluster][clusterSize[cluster]++] = i;
                }
                // Generate real cluster size statistics
                for (int j = 0; j < clusterSize.length; j++) {
                    final int size = clusterSize[j];
                    if (size == 0) {
                        continue;
                    }
                    statsSize.add(size);
                    if (size == 1) {
                        statsRadius.add(0);
                        continue;
                    }
                    // Find centre of cluster and add the distance to each point
                    final double[] com = new double[2];
                    for (int n = 0; n < size; n++) {
                        final double[] xy = xyz.get(clusters[j][n]);
                        for (int k = 0; k < 2; k++) {
                            com[k] += xy[k];
                        }
                    }
                    for (int k = 0; k < 2; k++) {
                        com[k] /= size;
                    }
                    for (int n = 0; n < size; n++) {
                        final double dx = xyz.get(clusters[j][n])[0] - com[0];
                        final double dy = xyz.get(clusters[j][n])[1] - com[1];
                        statsRadius.add(Math.sqrt(dx * dx + dy * dy));
                    }
                }
            }
            if (settings.showClusterMask) {
                bp = new ByteProcessor(maskSize, maskSize);
                for (int i = 0; i < mask.length; i++) {
                    if (mask[i] != 0) {
                        bp.set(i, 128);
                    }
                }
                ImageJUtils.display(maskTitle, bp);
            }
        }
        // Use the simulated cluster centres to create clusters of the desired size
        if (settings.clusterSimulation == 1 || settings.clusterSimulation == 2) {
            for (final double[] clusterCentre : clusterCentres) {
                final int clusterN = (int) Math.round((settings.clusterNumberStdDev > 0) ? settings.clusterNumber + gauss.sample() * settings.clusterNumberStdDev : settings.clusterNumber);
                if (clusterN < 1) {
                    continue;
                }
                if (clusterN == 1) {
                    // No need for a cluster around a point
                    xyz.add(clusterCentre);
                    statsRadius.add(0);
                    statsSize.add(1);
                } else {
                    // Generate N random points within a circle of the chosen cluster radius.
                    // Locate the centre-of-mass and the average distance to the centre.
                    final double[] com = new double[3];
                    int size = 0;
                    while (size < clusterN) {
                        // Generate a random point within a circle uniformly
                        // http://stackoverflow.com/questions/5837572/generate-a-random-point-within-a-circle-uniformly
                        final double t = 2.0 * Math.PI * rng.nextDouble();
                        final double u = rng.nextDouble() + rng.nextDouble();
                        final double r = settings.clusterRadius * ((u > 1) ? 2 - u : u);
                        final double x = r * Math.cos(t);
                        final double y = r * Math.sin(t);
                        final double[] xy = new double[] { clusterCentre[0] + x, clusterCentre[1] + y };
                        xyz.add(xy);
                        for (int k = 0; k < 2; k++) {
                            com[k] += xy[k];
                        }
                        size++;
                    }
                    // Add the distance of the points from the centre of the cluster.
                    // Note this does not account for the movement due to precision.
                    statsSize.add(size);
                    if (size == 1) {
                        statsRadius.add(0);
                    } else {
                        for (int k = 0; k < 2; k++) {
                            com[k] /= size;
                        }
                        while (size > 0) {
                            final double dx = xyz.get(xyz.size() - size)[0] - com[0];
                            final double dy = xyz.get(xyz.size() - size)[1] - com[1];
                            statsRadius.add(Math.sqrt(dx * dx + dy * dy));
                            size--;
                        }
                    }
                }
            }
        }
    } else {
        // Random distribution
        for (int i = 0; i < settings.numberOfMolecules; i++) {
            xyz.add(dist.next());
        }
    }
    // The Gaussian sigma should be applied so the overall distance from the centre
    // ( sqrt(x^2+y^2) ) has a standard deviation of sigmaS?
    final double sigma1D = settings.sigmaS / Math.sqrt(2);
    // Show optional histograms
    StoredDataStatistics intraDistances = null;
    StoredData blinks = null;
    if (settings.showHistograms) {
        final int capacity = (int) (xyz.size() * settings.blinkingRate);
        intraDistances = new StoredDataStatistics(capacity);
        blinks = new StoredData(capacity);
    }
    final Statistics statsSigma = new Statistics();
    for (int i = 0; i < xyz.size(); i++) {
        int occurrences = getBlinks(rng, settings.blinkingRate);
        if (blinks != null) {
            blinks.add(occurrences);
        }
        final int size = settings.molecules.size();
        // Get coordinates in nm
        final double[] moleculeXyz = xyz.get(i);
        if (bp != null && occurrences > 0) {
            bp.putPixel((int) Math.round(moleculeXyz[0] / maskScale), (int) Math.round(moleculeXyz[1] / maskScale), 255);
        }
        while (occurrences-- > 0) {
            final double[] localisationXy = Arrays.copyOf(moleculeXyz, 2);
            // Add random precision
            if (sigma1D > 0) {
                final double dx = gauss.sample() * sigma1D;
                final double dy = gauss.sample() * sigma1D;
                localisationXy[0] += dx;
                localisationXy[1] += dy;
                if (!dist.isWithinXy(localisationXy)) {
                    continue;
                }
                // Calculate mean-squared displacement
                statsSigma.add(dx * dx + dy * dy);
            }
            final double x = localisationXy[0];
            final double y = localisationXy[1];
            settings.molecules.add(new Molecule(x, y, i, 1));
            // Store in pixels
            final float xx = (float) (x / nmPerPixel);
            final float yy = (float) (y / nmPerPixel);
            final float[] params = PeakResult.createParams(0, 0, xx, yy, 0);
            settings.results.add(i + 1, (int) xx, (int) yy, 0, 0, 0, 0, params, null);
        }
        if (settings.molecules.size() > size) {
            count++;
            if (intraDistances != null) {
                final int newCount = settings.molecules.size() - size;
                if (newCount == 1) {
                    // No intra-molecule distances
                    continue;
                }
                // Get the distance matrix between these molecules
                final double[][] matrix = new double[newCount][newCount];
                for (int ii = size, x = 0; ii < settings.molecules.size(); ii++, x++) {
                    for (int jj = size + 1, y = 1; jj < settings.molecules.size(); jj++, y++) {
                        final double d2 = settings.molecules.get(ii).distance2(settings.molecules.get(jj));
                        matrix[x][y] = matrix[y][x] = d2;
                    }
                }
                // Get the maximum distance for particle linkage clustering of this molecule
                double max = 0;
                for (int x = 0; x < newCount; x++) {
                    // Compare to all-other molecules and get the minimum distance
                    // needed to join at least one
                    double linkDistance = Double.POSITIVE_INFINITY;
                    for (int y = 0; y < newCount; y++) {
                        if (x == y) {
                            continue;
                        }
                        if (matrix[x][y] < linkDistance) {
                            linkDistance = matrix[x][y];
                        }
                    }
                    // Check if this is larger
                    if (max < linkDistance) {
                        max = linkDistance;
                    }
                }
                intraDistances.add(Math.sqrt(max));
            }
        }
    }
    settings.results.end();
    if (bp != null) {
        final ImagePlus imp = ImageJUtils.display(maskTitle, bp);
        final Calibration cal = imp.getCalibration();
        cal.setUnit("nm");
        cal.pixelWidth = cal.pixelHeight = maskScale;
    }
    log("Simulation results");
    log("  * Molecules = %d (%d activated)", xyz.size(), count);
    log("  * Blinking rate = %s", MathUtils.rounded((double) settings.molecules.size() / xyz.size(), 4));
    log("  * Precision (Mean-displacement) = %s nm", (statsSigma.getN() > 0) ? MathUtils.rounded(Math.sqrt(statsSigma.getMean()), 4) : "0");
    if (intraDistances != null) {
        if (intraDistances.getN() == 0) {
            log("  * Mean Intra-Molecule particle linkage distance = 0 nm");
            log("  * Fraction of inter-molecule particle linkage @ 0 nm = 0 %%");
        } else {
            plot(blinks, "Blinks/Molecule", true);
            final double[][] intraHist = plot(intraDistances, "Intra-molecule particle linkage distance", false);
            // Determine 95th and 99th percentile
            // Will not be null as we requested a non-integer histogram.
            int p99 = intraHist[0].length - 1;
            final double limit1 = 0.99 * intraHist[1][p99];
            final double limit2 = 0.95 * intraHist[1][p99];
            while (intraHist[1][p99] > limit1 && p99 > 0) {
                p99--;
            }
            int p95 = p99;
            while (intraHist[1][p95] > limit2 && p95 > 0) {
                p95--;
            }
            log("  * Mean Intra-Molecule particle linkage distance = %s nm" + " (95%% = %s, 99%% = %s, 100%% = %s)", MathUtils.rounded(intraDistances.getMean(), 4), MathUtils.rounded(intraHist[0][p95], 4), MathUtils.rounded(intraHist[0][p99], 4), MathUtils.rounded(intraHist[0][intraHist[0].length - 1], 4));
            if (settings.distanceAnalysis) {
                performDistanceAnalysis(intraHist, p99);
            }
        }
    }
    if (settings.clusterSimulation > 0) {
        log("  * Cluster number = %s +/- %s", MathUtils.rounded(statsSize.getMean(), 4), MathUtils.rounded(statsSize.getStandardDeviation(), 4));
        log("  * Cluster radius = %s +/- %s nm (mean distance to centre-of-mass)", MathUtils.rounded(statsRadius.getMean(), 4), MathUtils.rounded(statsRadius.getStandardDeviation(), 4));
    }
}