Examples with PolynomialFunction org.apache.commons.math3.analysis.polynomials.PolynomialFunction used on opensource projects

Example 1 with PolynomialFunction

use of org.apache.commons.math3.analysis.polynomials.PolynomialFunction 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 PolynomialFunction

use of org.apache.commons.math3.analysis.polynomials.PolynomialFunction in project GDSC-SMLM by aherbert.

the class MeanVarianceTest method run.

/*
	 * (non-Javadoc)
	 * 
	 * @see ij.plugin.PlugIn#run(java.lang.String)
	 */
public void run(String arg) {
    SMLMUsageTracker.recordPlugin(this.getClass(), arg);
    if (Utils.isExtraOptions()) {
        ImagePlus imp = WindowManager.getCurrentImage();
        if (imp.getStackSize() > 1) {
            GenericDialog gd = new GenericDialog(TITLE);
            gd.addMessage("Perform single image analysis on the current image?");
            gd.addNumericField("Bias", _bias, 0);
            gd.showDialog();
            if (gd.wasCanceled())
                return;
            singleImage = true;
            _bias = Math.abs(gd.getNextNumber());
        } else {
            IJ.error(TITLE, "Single-image mode requires a stack");
            return;
        }
    }
    List<ImageSample> images;
    String inputDirectory = "";
    if (singleImage) {
        IJ.showStatus("Loading images...");
        images = getImages();
        if (images.size() == 0) {
            IJ.error(TITLE, "Not enough images for analysis");
            return;
        }
    } else {
        inputDirectory = IJ.getDirectory("Select image series ...");
        if (inputDirectory == null)
            return;
        SeriesOpener series = new SeriesOpener(inputDirectory, false, 0);
        series.setVariableSize(true);
        if (series.getNumberOfImages() < 3) {
            IJ.error(TITLE, "Not enough images in the selected directory");
            return;
        }
        if (!IJ.showMessageWithCancel(TITLE, String.format("Analyse %d images, first image:\n%s", series.getNumberOfImages(), series.getImageList()[0]))) {
            return;
        }
        IJ.showStatus("Loading images");
        images = getImages(series);
        if (images.size() < 3) {
            IJ.error(TITLE, "Not enough images for analysis");
            return;
        }
        if (images.get(0).exposure != 0) {
            IJ.error(TITLE, "First image in series must have exposure 0 (Bias image)");
            return;
        }
    }
    boolean emMode = (arg != null && arg.contains("em"));
    GenericDialog gd = new GenericDialog(TITLE);
    gd.addMessage("Set the output options:");
    gd.addCheckbox("Show_table", showTable);
    gd.addCheckbox("Show_charts", showCharts);
    if (emMode) {
        // Ask the user for the camera gain ...
        gd.addMessage("Estimating the EM-gain requires the camera gain without EM readout enabled");
        gd.addNumericField("Camera_gain (ADU/e-)", cameraGain, 4);
    }
    gd.showDialog();
    if (gd.wasCanceled())
        return;
    showTable = gd.getNextBoolean();
    showCharts = gd.getNextBoolean();
    if (emMode) {
        cameraGain = gd.getNextNumber();
    }
    IJ.showStatus("Computing mean & variance");
    final double nImages = images.size();
    for (int i = 0; i < images.size(); i++) {
        IJ.showStatus(String.format("Computing mean & variance %d/%d", i + 1, images.size()));
        images.get(i).compute(singleImage, i / nImages, (i + 1) / nImages);
    }
    IJ.showProgress(1);
    IJ.showStatus("Computing results");
    // Allow user to input multiple bias images
    int start = 0;
    Statistics biasStats = new Statistics();
    Statistics noiseStats = new Statistics();
    final double bias;
    if (singleImage) {
        bias = _bias;
    } else {
        while (start < images.size()) {
            ImageSample sample = images.get(start);
            if (sample.exposure == 0) {
                biasStats.add(sample.means);
                for (PairSample pair : sample.samples) {
                    noiseStats.add(pair.variance);
                }
                start++;
            } else
                break;
        }
        bias = biasStats.getMean();
    }
    // Get the mean-variance data
    int total = 0;
    for (int i = start; i < images.size(); i++) total += images.get(i).samples.size();
    if (showTable && total > 2000) {
        gd = new GenericDialog(TITLE);
        gd.addMessage("Table output requires " + total + " entries.\n \nYou may want to disable the table.");
        gd.addCheckbox("Show_table", showTable);
        gd.showDialog();
        if (gd.wasCanceled())
            return;
        showTable = gd.getNextBoolean();
    }
    TextWindow results = (showTable) ? createResultsWindow() : null;
    double[] mean = new double[total];
    double[] variance = new double[mean.length];
    Statistics gainStats = (singleImage) ? new StoredDataStatistics(total) : new Statistics();
    final WeightedObservedPoints obs = new WeightedObservedPoints();
    for (int i = (singleImage) ? 0 : start, j = 0; i < images.size(); i++) {
        StringBuilder sb = (showTable) ? new StringBuilder() : null;
        ImageSample sample = images.get(i);
        for (PairSample pair : sample.samples) {
            if (j % 16 == 0)
                IJ.showProgress(j, total);
            mean[j] = pair.getMean();
            variance[j] = pair.variance;
            // Gain is in ADU / e
            double gain = variance[j] / (mean[j] - bias);
            gainStats.add(gain);
            obs.add(mean[j], variance[j]);
            if (emMode) {
                gain /= (2 * cameraGain);
            }
            if (showTable) {
                sb.append(sample.title).append("\t");
                sb.append(sample.exposure).append("\t");
                sb.append(pair.slice1).append("\t");
                sb.append(pair.slice2).append("\t");
                sb.append(IJ.d2s(pair.mean1, 2)).append("\t");
                sb.append(IJ.d2s(pair.mean2, 2)).append("\t");
                sb.append(IJ.d2s(mean[j], 2)).append("\t");
                sb.append(IJ.d2s(variance[j], 2)).append("\t");
                sb.append(Utils.rounded(gain, 4)).append("\n");
            }
            j++;
        }
        if (showTable)
            results.append(sb.toString());
    }
    IJ.showProgress(1);
    if (singleImage) {
        StoredDataStatistics stats = (StoredDataStatistics) gainStats;
        Utils.log(TITLE);
        if (emMode) {
            double[] values = stats.getValues();
            MathArrays.scaleInPlace(0.5, values);
            stats = new StoredDataStatistics(values);
        }
        if (showCharts) {
            // Plot the gain over time
            String title = TITLE + " Gain vs Frame";
            Plot2 plot = new Plot2(title, "Slice", "Gain", Utils.newArray(gainStats.getN(), 1, 1.0), stats.getValues());
            PlotWindow pw = Utils.display(title, plot);
            // Show a histogram
            String label = String.format("Mean = %s, Median = %s", Utils.rounded(stats.getMean()), Utils.rounded(stats.getMedian()));
            int id = Utils.showHistogram(TITLE, stats, "Gain", 0, 1, 100, true, label);
            if (Utils.isNewWindow()) {
                Point point = pw.getLocation();
                point.x = pw.getLocation().x;
                point.y += pw.getHeight();
                WindowManager.getImage(id).getWindow().setLocation(point);
            }
        }
        Utils.log("Single-image mode: %s camera", (emMode) ? "EM-CCD" : "Standard");
        final double gain = stats.getMedian();
        if (emMode) {
            final double totalGain = gain;
            final double emGain = totalGain / cameraGain;
            Utils.log("  Gain = 1 / %s (ADU/e-)", Utils.rounded(cameraGain, 4));
            Utils.log("  EM-Gain = %s", Utils.rounded(emGain, 4));
            Utils.log("  Total Gain = %s (ADU/e-)", Utils.rounded(totalGain, 4));
        } else {
            cameraGain = gain;
            Utils.log("  Gain = 1 / %s (ADU/e-)", Utils.rounded(cameraGain, 4));
        }
    } else {
        IJ.showStatus("Computing fit");
        // Sort
        int[] indices = rank(mean);
        mean = reorder(mean, indices);
        variance = reorder(variance, indices);
        // Compute optimal coefficients.
        // a - b x
        final double[] init = { 0, 1 / gainStats.getMean() };
        final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(2).withStartPoint(init);
        final double[] best = fitter.fit(obs.toList());
        // Construct the polynomial that best fits the data.
        final PolynomialFunction fitted = new PolynomialFunction(best);
        if (showCharts) {
            // Plot mean verses variance. Gradient is gain in ADU/e.
            String title = TITLE + " results";
            Plot2 plot = new Plot2(title, "Mean", "Variance");
            double[] xlimits = Maths.limits(mean);
            double[] ylimits = Maths.limits(variance);
            double xrange = (xlimits[1] - xlimits[0]) * 0.05;
            if (xrange == 0)
                xrange = 0.05;
            double yrange = (ylimits[1] - ylimits[0]) * 0.05;
            if (yrange == 0)
                yrange = 0.05;
            plot.setLimits(xlimits[0] - xrange, xlimits[1] + xrange, ylimits[0] - yrange, ylimits[1] + yrange);
            plot.setColor(Color.blue);
            plot.addPoints(mean, variance, Plot2.CROSS);
            plot.setColor(Color.red);
            plot.addPoints(new double[] { mean[0], mean[mean.length - 1] }, new double[] { fitted.value(mean[0]), fitted.value(mean[mean.length - 1]) }, Plot2.LINE);
            Utils.display(title, plot);
        }
        final double avBiasNoise = Math.sqrt(noiseStats.getMean());
        Utils.log(TITLE);
        Utils.log("  Directory = %s", inputDirectory);
        Utils.log("  Bias = %s +/- %s (ADU)", Utils.rounded(bias, 4), Utils.rounded(avBiasNoise, 4));
        Utils.log("  Variance = %s + %s * mean", Utils.rounded(best[0], 4), Utils.rounded(best[1], 4));
        if (emMode) {
            final double emGain = best[1] / (2 * cameraGain);
            // Noise is standard deviation of the bias image divided by the total gain (in ADU/e-)
            final double totalGain = emGain * cameraGain;
            Utils.log("  Read Noise = %s (e-) [%s (ADU)]", Utils.rounded(avBiasNoise / totalGain, 4), Utils.rounded(avBiasNoise, 4));
            Utils.log("  Gain = 1 / %s (ADU/e-)", Utils.rounded(1 / cameraGain, 4));
            Utils.log("  EM-Gain = %s", Utils.rounded(emGain, 4));
            Utils.log("  Total Gain = %s (ADU/e-)", Utils.rounded(totalGain, 4));
        } else {
            // Noise is standard deviation of the bias image divided by the gain (in ADU/e-)
            cameraGain = best[1];
            final double readNoise = avBiasNoise / cameraGain;
            Utils.log("  Read Noise = %s (e-) [%s (ADU)]", Utils.rounded(readNoise, 4), Utils.rounded(readNoise * cameraGain, 4));
            Utils.log("  Gain = 1 / %s (ADU/e-)", Utils.rounded(1 / cameraGain, 4));
        }
    }
    IJ.showStatus("");
}