Examples with Fraction org.apache.commons.math3.fraction.Fraction used on opensource projects

Example 6 with Fraction

use of org.apache.commons.math3.fraction.Fraction in project GDSC-SMLM by aherbert.

the class PCPALMMolecules method performDistanceAnalysis.

private void performDistanceAnalysis(double[][] intraHist, int p99) {
    // We want to know the fraction of distances between molecules at the 99th percentile
    // that are intra- rather than inter-molecule.
    // Do single linkage clustering of closest pair at this distance and count the number of 
    // links that are inter and intra.
    // Convert molecules for clustering
    ArrayList<ClusterPoint> points = new ArrayList<ClusterPoint>(molecules.size());
    for (Molecule m : molecules) // Precision was used to store the molecule ID
    points.add(ClusterPoint.newClusterPoint((int) m.precision, m.x, m.y, m.photons));
    ClusteringEngine engine = new ClusteringEngine(Prefs.getThreads(), ClusteringAlgorithm.PARTICLE_SINGLE_LINKAGE, new IJTrackProgress());
    IJ.showStatus("Clustering to check inter-molecule distances");
    engine.setTrackJoins(true);
    ArrayList<Cluster> clusters = engine.findClusters(points, intraHist[0][p99]);
    IJ.showStatus("");
    if (clusters != null) {
        double[] intraIdDistances = engine.getIntraIdDistances();
        double[] interIdDistances = engine.getInterIdDistances();
        int all = interIdDistances.length + intraIdDistances.length;
        log("  * Fraction of inter-molecule particle linkage @ %s nm = %s %%", Utils.rounded(intraHist[0][p99], 4), (all > 0) ? Utils.rounded(100.0 * interIdDistances.length / all, 4) : "0");
        // Show a double cumulative histogram plot
        double[][] intraIdHist = Maths.cumulativeHistogram(intraIdDistances, false);
        double[][] interIdHist = Maths.cumulativeHistogram(interIdDistances, false);
        // Plot
        String title = TITLE + " molecule linkage distance";
        Plot2 plot = new Plot2(title, "Distance", "Frequency", intraIdHist[0], intraIdHist[1]);
        double max = (intraIdHist[1].length > 0) ? intraIdHist[1][intraIdHist[1].length - 1] : 0;
        if (interIdHist[1].length > 0)
            max = FastMath.max(max, interIdHist[1][interIdHist[1].length - 1]);
        plot.setLimits(0, intraIdHist[0][intraIdHist[0].length - 1], 0, max);
        plot.setColor(Color.blue);
        plot.addPoints(interIdHist[0], interIdHist[1], Plot2.LINE);
        plot.setColor(Color.black);
        Utils.display(title, plot);
    } else {
        log("Aborted clustering to check inter-molecule distances");
    }
}

Example 7 with Fraction

use of org.apache.commons.math3.fraction.Fraction 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 (blinkingDistribution == 3) {
        log("  - Clusters = %d", nMolecules);
        log("  - Simulation size = %s um", Utils.rounded(simulationSize, 4));
        log("  - Molecules/cluster = %s", Utils.rounded(blinkingRate, 4));
        log("  - Blinking distribution = %s", BLINKING_DISTRIBUTION[blinkingDistribution]);
        log("  - p-Value = %s", Utils.rounded(p, 4));
    } else {
        log("  - Molecules = %d", nMolecules);
        log("  - Simulation size = %s um", Utils.rounded(simulationSize, 4));
        log("  - Blinking rate = %s", Utils.rounded(blinkingRate, 4));
        log("  - Blinking distribution = %s", BLINKING_DISTRIBUTION[blinkingDistribution]);
    }
    log("  - Average precision = %s nm", Utils.rounded(sigmaS, 4));
    log("  - Clusters simulation = " + CLUSTER_SIMULATION[clusterSimulation]);
    if (clusterSimulation > 0) {
        log("  - Cluster number = %s +/- %s", Utils.rounded(clusterNumber, 4), Utils.rounded(clusterNumberSD, 4));
        log("  - Cluster radius = %s nm", Utils.rounded(clusterRadius, 4));
    }
    final double nmPerPixel = 100;
    double width = simulationSize * 1000.0;
    // Allow a border of 3 x sigma for +/- precision
    //if (blinkingRate > 1)
    width -= 3 * sigmaS;
    RandomGenerator randomGenerator = new Well19937c(System.currentTimeMillis() + System.identityHashCode(this));
    RandomDataGenerator dataGenerator = new RandomDataGenerator(randomGenerator);
    UniformDistribution dist = new UniformDistribution(null, new double[] { width, width, 0 }, randomGenerator.nextInt());
    molecules = new ArrayList<Molecule>(nMolecules);
    // Create some dummy results since the calibration is required for later analysis
    results = new MemoryPeakResults();
    results.setCalibration(new gdsc.smlm.results.Calibration(nmPerPixel, 1, 100));
    results.setSource(new NullSource("Molecule Simulation"));
    results.begin();
    int count = 0;
    // Generate a sequence of coordinates
    ArrayList<double[]> xyz = new ArrayList<double[]>((int) (nMolecules * 1.1));
    Statistics statsRadius = new Statistics();
    Statistics statsSize = new Statistics();
    String maskTitle = TITLE + " Cluster Mask";
    ByteProcessor bp = null;
    double maskScale = 0;
    if (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 = lowResolutionImageSize;
        int[] mask = null;
        // scale is in nm/pixel
        maskScale = width / maskSize;
        ArrayList<double[]> clusterCentres = new ArrayList<double[]>();
        int totalSteps = 1 + (int) Math.ceil(nMolecules / clusterNumber);
        if (clusterSimulation == 2 || 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, randomGenerator);
            double[] centre;
            IJ.showStatus("Computing clusters mask");
            int roiRadius = (int) Math.round((clusterRadius * 2) / maskScale);
            if (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 * Math.pow(clusterRadius / maskScale, 2)));
            }
            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
                double cx = centre[0] / maskScale;
                double cy = centre[1] / maskScale;
                fillMask(mask, maskSize, (int) cx, (int) cy, roiRadius, 0);
                //Utils.display("Mask", new ColorProcessor(maskSize, maskSize, mask));
                try {
                    maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, randomGenerator);
                } catch (IllegalArgumentException e) {
                    // 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;
                }
            }
            IJ.showProgress(1);
            IJ.showStatus("");
        } else {
            // Pick centres randomly from the distribution 
            while (clusterCentres.size() < totalSteps) clusterCentres.add(dist.next());
        }
        if (showClusterMask || clusterSimulation == 3) {
            // Show the mask for the clusters
            if (mask == null)
                mask = new int[maskSize * maskSize];
            else
                Arrays.fill(mask, 0);
            int roiRadius = (int) Math.round((clusterRadius) / maskScale);
            for (double[] c : clusterCentres) {
                double cx = c[0] / maskScale;
                double cy = c[1] / maskScale;
                fillMask(mask, maskSize, (int) cx, (int) cy, roiRadius, 1);
            }
            if (clusterSimulation == 3) {
                // We have the mask. Now pick points at random from the mask.
                MaskDistribution maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, randomGenerator);
                // Allocate each molecule position to a parent circle so defining clusters.
                int[][] clusters = new int[clusterCentres.size()][];
                int[] clusterSize = new int[clusters.length];
                for (int i = 0; i < nMolecules; i++) {
                    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++) {
                        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
                    double[] com = new double[2];
                    for (int n = 0; n < size; n++) {
                        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++) {
                        double dx = xyz.get(clusters[j][n])[0] - com[0];
                        double dy = xyz.get(clusters[j][n])[1] - com[1];
                        statsRadius.add(Math.sqrt(dx * dx + dy * dy));
                    }
                }
            }
            if (showClusterMask) {
                bp = new ByteProcessor(maskSize, maskSize);
                for (int i = 0; i < mask.length; i++) if (mask[i] != 0)
                    bp.set(i, 128);
                Utils.display(maskTitle, bp);
            }
        }
        // Use the simulated cluster centres to create clusters of the desired size
        if (clusterSimulation == 1 || clusterSimulation == 2) {
            for (double[] clusterCentre : clusterCentres) {
                int clusterN = (int) Math.round((clusterNumberSD > 0) ? dataGenerator.nextGaussian(clusterNumber, clusterNumberSD) : clusterNumber);
                if (clusterN < 1)
                    continue;
                //double[] clusterCentre = dist.next();
                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.
                    double[] com = new double[3];
                    int j = 0;
                    while (j < clusterN) {
                        // Generate a random point within a circle uniformly
                        // http://stackoverflow.com/questions/5837572/generate-a-random-point-within-a-circle-uniformly
                        double t = 2.0 * Math.PI * randomGenerator.nextDouble();
                        double u = randomGenerator.nextDouble() + randomGenerator.nextDouble();
                        double r = clusterRadius * ((u > 1) ? 2 - u : u);
                        double x = r * Math.cos(t);
                        double y = r * Math.sin(t);
                        double[] xy = new double[] { clusterCentre[0] + x, clusterCentre[1] + y };
                        xyz.add(xy);
                        for (int k = 0; k < 2; k++) com[k] += xy[k];
                        j++;
                    }
                    // 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(j);
                    if (j == 1) {
                        statsRadius.add(0);
                    } else {
                        for (int k = 0; k < 2; k++) com[k] /= j;
                        while (j > 0) {
                            double dx = xyz.get(xyz.size() - j)[0] - com[0];
                            double dy = xyz.get(xyz.size() - j)[1] - com[1];
                            statsRadius.add(Math.sqrt(dx * dx + dy * dy));
                            j--;
                        }
                    }
                }
            }
        }
    } else {
        // Random distribution
        for (int i = 0; i < nMolecules; 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 = sigmaS / Math.sqrt(2);
    // Show optional histograms
    StoredDataStatistics intraDistances = null;
    StoredData blinks = null;
    if (showHistograms) {
        int capacity = (int) (xyz.size() * blinkingRate);
        intraDistances = new StoredDataStatistics(capacity);
        blinks = new StoredData(capacity);
    }
    Statistics statsSigma = new Statistics();
    for (int i = 0; i < xyz.size(); i++) {
        int nOccurrences = getBlinks(dataGenerator, blinkingRate);
        if (showHistograms)
            blinks.add(nOccurrences);
        final int size = molecules.size();
        // Get coordinates in nm
        final double[] moleculeXyz = xyz.get(i);
        if (bp != null && nOccurrences > 0) {
            bp.putPixel((int) Math.round(moleculeXyz[0] / maskScale), (int) Math.round(moleculeXyz[1] / maskScale), 255);
        }
        while (nOccurrences-- > 0) {
            final double[] localisationXy = Arrays.copyOf(moleculeXyz, 2);
            // Add random precision
            if (sigma1D > 0) {
                final double dx = dataGenerator.nextGaussian(0, sigma1D);
                final double dy = dataGenerator.nextGaussian(0, 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];
            molecules.add(new Molecule(x, y, i, 1));
            // Store in pixels
            float[] params = new float[7];
            params[Gaussian2DFunction.X_POSITION] = (float) (x / nmPerPixel);
            params[Gaussian2DFunction.Y_POSITION] = (float) (y / nmPerPixel);
            results.addf(i + 1, (int) x, (int) y, 0, 0, 0, params, null);
        }
        if (molecules.size() > size) {
            count++;
            if (showHistograms) {
                int newCount = molecules.size() - size;
                if (newCount == 1) {
                    //intraDistances.add(0);
                    continue;
                }
                // Get the distance matrix between these molecules
                double[][] matrix = new double[newCount][newCount];
                for (int ii = size, x = 0; ii < molecules.size(); ii++, x++) {
                    for (int jj = size + 1, y = 1; jj < molecules.size(); jj++, y++) {
                        final double d2 = molecules.get(ii).distance2(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));
            }
        }
    }
    results.end();
    if (bp != null)
        Utils.display(maskTitle, bp);
    // Used for debugging
    //System.out.printf("  * Molecules = %d (%d activated)\n", xyz.size(), count);
    //if (clusterSimulation > 0)
    //	System.out.printf("  * Cluster number = %s +/- %s. Radius = %s +/- %s\n",
    //			Utils.rounded(statsSize.getMean(), 4), Utils.rounded(statsSize.getStandardDeviation(), 4),
    //			Utils.rounded(statsRadius.getMean(), 4), Utils.rounded(statsRadius.getStandardDeviation(), 4));
    log("Simulation results");
    log("  * Molecules = %d (%d activated)", xyz.size(), count);
    log("  * Blinking rate = %s", Utils.rounded((double) molecules.size() / xyz.size(), 4));
    log("  * Precision (Mean-displacement) = %s nm", (statsSigma.getN() > 0) ? Utils.rounded(Math.sqrt(statsSigma.getMean()), 4) : "0");
    if (showHistograms) {
        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);
            double[][] intraHist = plot(intraDistances, "Intra-molecule particle linkage distance", false);
            // Determine 95th and 99th percentile
            int p99 = intraHist[0].length - 1;
            double limit1 = 0.99 * intraHist[1][p99];
            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)", Utils.rounded(intraDistances.getMean(), 4), Utils.rounded(intraHist[0][p95], 4), Utils.rounded(intraHist[0][p99], 4), Utils.rounded(intraHist[0][intraHist[0].length - 1], 4));
            if (distanceAnalysis) {
                performDistanceAnalysis(intraHist, p99);
            }
        }
    }
    if (clusterSimulation > 0) {
        log("  * Cluster number = %s +/- %s", Utils.rounded(statsSize.getMean(), 4), Utils.rounded(statsSize.getStandardDeviation(), 4));
        log("  * Cluster radius = %s +/- %s nm (mean distance to centre-of-mass)", Utils.rounded(statsRadius.getMean(), 4), Utils.rounded(statsRadius.getStandardDeviation(), 4));
    }
}

Example 8 with Fraction

use of org.apache.commons.math3.fraction.Fraction in project gatk by broadinstitute.

the class AlleleFractionInitializer method initialMinorFractions.

/**
     *  Initialize minor fractions assuming no allelic bias <p></p>
     *
     * We integrate over f to get posterior probabilities (responsibilities) of alt / ref minor
     * that is, responsibility of alt minor is int_{0 to 1/2} f^a (1-f)^r df
     *          responsibility of ref minor is int_{0 to 1/2} f^r (1-f)^a df
     * these are proportional to I(1/2, a + 1, r + 1) and I(1/2, r + 1, a + 1),
     * respectively, where I is the (incomplete) regularized Beta function.
     * By definition these likelihoods sum to 1, ie they are already normalized. <p></p>
     *
     * Finally, we set each minor fraction to the responsibility-weighted total count of
     * reads in minor allele divided by total reads, ignoring outliers.
     */
private AlleleFractionState.MinorFractions initialMinorFractions(final AlleleFractionData data) {
    final int numSegments = data.getNumSegments();
    final AlleleFractionState.MinorFractions result = new AlleleFractionState.MinorFractions(numSegments);
    for (int segment = 0; segment < numSegments; segment++) {
        double responsibilityWeightedMinorAlleleReadCount = 0.0;
        double responsibilityWeightedTotalReadCount = 0.0;
        for (final AllelicCount count : data.getCountsInSegment(segment)) {
            final int a = count.getAltReadCount();
            final int r = count.getRefReadCount();
            double altMinorResponsibility;
            try {
                altMinorResponsibility = Beta.regularizedBeta(0.5, a + 1, r + 1);
            } catch (final MaxCountExceededException e) {
                //if the special function can't be computed, give an all-or-nothing responsibility
                altMinorResponsibility = a < r ? 1.0 : 0.0;
            }
            responsibilityWeightedMinorAlleleReadCount += altMinorResponsibility * a + (1 - altMinorResponsibility) * r;
            responsibilityWeightedTotalReadCount += a + r;
        }
        // we achieve a flat prior via a single pseudocount for minor and non-minor reads, hence the  +1 and +2
        result.add((responsibilityWeightedMinorAlleleReadCount + 1) / (responsibilityWeightedTotalReadCount + 2));
    }
    return result;
}

Example 9 with Fraction

use of org.apache.commons.math3.fraction.Fraction in project gatk by broadinstitute.

the class StrandArtifact method annotate.

@Override
public void annotate(final ReferenceContext ref, final VariantContext vc, final Genotype g, final GenotypeBuilder gb, final ReadLikelihoods<Allele> likelihoods) {
    Utils.nonNull(gb);
    Utils.nonNull(vc);
    Utils.nonNull(likelihoods);
    // do not annotate the genotype fields for normal
    if (g.isHomRef()) {
        return;
    }
    pi.put(NO_ARTIFACT, 0.95);
    pi.put(ART_FWD, 0.025);
    pi.put(ART_REV, 0.025);
    // We use the allele with highest LOD score
    final double[] tumorLods = GATKProtectedVariantContextUtils.getAttributeAsDoubleArray(vc, GATKVCFConstants.TUMOR_LOD_KEY, () -> null, -1);
    final int indexOfMaxTumorLod = MathUtils.maxElementIndex(tumorLods);
    final Allele altAlelle = vc.getAlternateAllele(indexOfMaxTumorLod);
    final Collection<ReadLikelihoods<Allele>.BestAllele<Allele>> bestAlleles = likelihoods.bestAlleles(g.getSampleName());
    final int numFwdAltReads = (int) bestAlleles.stream().filter(ba -> !ba.read.isReverseStrand() && ba.isInformative() && ba.allele.equals(altAlelle)).count();
    final int numRevAltReads = (int) bestAlleles.stream().filter(ba -> ba.read.isReverseStrand() && ba.isInformative() && ba.allele.equals(altAlelle)).count();
    final int numFwdReads = (int) bestAlleles.stream().filter(ba -> !ba.read.isReverseStrand() && ba.isInformative()).count();
    final int numRevReads = (int) bestAlleles.stream().filter(ba -> ba.read.isReverseStrand() && ba.isInformative()).count();
    final int numAltReads = numFwdAltReads + numRevAltReads;
    final int numReads = numFwdReads + numRevReads;
    final EnumMap<StrandArtifactZ, Double> unnormalized_posterior_probabilities = new EnumMap<>(StrandArtifactZ.class);
    final EnumMap<StrandArtifactZ, Double> maximum_a_posteriori_allele_fraction_estimates = new EnumMap<>(StrandArtifactZ.class);
    /*** Compute the posterior probability of ARTIFACT_FWD and ARTIFACT_REV; it's a double integral over f and epsilon ***/
    // the integrand is a polynomial of degree n, where n is the number of reads at the locus
    // thus to integrate exactly with Gauss-Legendre we need (n/2)+1 points
    final int numIntegPointsForAlleleFraction = numReads / 2 + 1;
    final int numIntegPointsForEpsilon = (numReads + ALPHA + BETA - 2) / 2 + 1;
    final double likelihoodForArtifactFwd = IntegrationUtils.integrate2d((f, epsilon) -> getIntegrandGivenArtifact(f, epsilon, numFwdReads, numRevReads, numFwdAltReads, numRevAltReads), 0.0, 1.0, numIntegPointsForAlleleFraction, 0.0, 1.0, numIntegPointsForEpsilon);
    final double likelihoodForArtifactRev = IntegrationUtils.integrate2d((f, epsilon) -> getIntegrandGivenArtifact(f, epsilon, numRevReads, numFwdReads, numRevAltReads, numFwdAltReads), 0.0, 1.0, numIntegPointsForAlleleFraction, 0.0, 1.0, numIntegPointsForEpsilon);
    unnormalized_posterior_probabilities.put(ART_FWD, pi.get(ART_FWD) * likelihoodForArtifactFwd);
    unnormalized_posterior_probabilities.put(ART_REV, pi.get(ART_REV) * likelihoodForArtifactRev);
    /*** Compute the posterior probability of NO_ARTIFACT; evaluate a single integral over the allele fraction ***/
    final double likelihoodForNoArtifact = IntegrationUtils.integrate(f -> getIntegrandGivenNoArtifact(f, numFwdReads, numRevReads, numFwdAltReads, numRevAltReads), 0.0, 1.0, numIntegPointsForAlleleFraction);
    unnormalized_posterior_probabilities.put(NO_ARTIFACT, pi.get(NO_ARTIFACT) * likelihoodForNoArtifact);
    final double[] posterior_probabilities = MathUtils.normalizeFromRealSpace(unnormalized_posterior_probabilities.values().stream().mapToDouble(Double::doubleValue).toArray());
    /*** Compute the maximum a posteriori estimate for allele fraction given strand artifact ***/
    // For a fixed f, integrate the double integral over epsilons. This gives us the likelihood p(x^+, x^- | f, z) for a fixed f, which is proportional to
    // the posterior probability of p(f | x^+, x^-, z)
    final int numSamplePoints = 100;
    final double[] samplePoints = GATKProtectedMathUtils.createEvenlySpacedPoints(0.0, 1.0, numSamplePoints);
    double[] likelihoodsGivenForwardArtifact = new double[numSamplePoints];
    double[] likelihoodsGivenReverseArtifact = new double[numSamplePoints];
    for (int i = 0; i < samplePoints.length; i++) {
        final double f = samplePoints[i];
        likelihoodsGivenForwardArtifact[i] = IntegrationUtils.integrate(epsilon -> getIntegrandGivenArtifact(f, epsilon, numFwdReads, numRevReads, numFwdAltReads, numRevAltReads), 0.0, 1.0, numIntegPointsForEpsilon);
        likelihoodsGivenReverseArtifact[i] = IntegrationUtils.integrate(epsilon -> getIntegrandGivenArtifact(f, epsilon, numRevReads, numFwdReads, numRevAltReads, numFwdAltReads), 0.0, 1.0, numIntegPointsForEpsilon);
    }
    final int maxAlleleFractionIndexFwd = MathUtils.maxElementIndex(likelihoodsGivenForwardArtifact);
    final int maxAlleleFractionIndexRev = MathUtils.maxElementIndex(likelihoodsGivenReverseArtifact);
    maximum_a_posteriori_allele_fraction_estimates.put(ART_FWD, samplePoints[maxAlleleFractionIndexFwd]);
    maximum_a_posteriori_allele_fraction_estimates.put(ART_REV, samplePoints[maxAlleleFractionIndexRev]);
    // In the absence of strand artifact, MAP estimate for f reduces to the sample alt allele fraction
    maximum_a_posteriori_allele_fraction_estimates.put(NO_ARTIFACT, (double) numAltReads / numReads);
    gb.attribute(POSTERIOR_PROBABILITIES_KEY, posterior_probabilities);
    gb.attribute(MAP_ALLELE_FRACTIONS_KEY, maximum_a_posteriori_allele_fraction_estimates.values().stream().mapToDouble(Double::doubleValue).toArray());
}

Example 10 with Fraction

use of org.apache.commons.math3.fraction.Fraction in project gatk-protected by broadinstitute.

the class AlleleFractionInitializer method initialMinorFractions.

/**
     *  Initialize minor fractions assuming no allelic bias <p></p>
     *
     * We integrate over f to get posterior probabilities (responsibilities) of alt / ref minor
     * that is, responsibility of alt minor is int_{0 to 1/2} f^a (1-f)^r df
     *          responsibility of ref minor is int_{0 to 1/2} f^r (1-f)^a df
     * these are proportional to I(1/2, a + 1, r + 1) and I(1/2, r + 1, a + 1),
     * respectively, where I is the (incomplete) regularized Beta function.
     * By definition these likelihoods sum to 1, ie they are already normalized. <p></p>
     *
     * Finally, we set each minor fraction to the responsibility-weighted total count of
     * reads in minor allele divided by total reads, ignoring outliers.
     */
private AlleleFractionState.MinorFractions initialMinorFractions(final AlleleFractionData data) {
    final int numSegments = data.getNumSegments();
    final AlleleFractionState.MinorFractions result = new AlleleFractionState.MinorFractions(numSegments);
    for (int segment = 0; segment < numSegments; segment++) {
        double responsibilityWeightedMinorAlleleReadCount = 0.0;
        double responsibilityWeightedTotalReadCount = 0.0;
        for (final AllelicCount count : data.getCountsInSegment(segment)) {
            final int a = count.getAltReadCount();
            final int r = count.getRefReadCount();
            double altMinorResponsibility;
            try {
                altMinorResponsibility = Beta.regularizedBeta(0.5, a + 1, r + 1);
            } catch (final MaxCountExceededException e) {
                //if the special function can't be computed, give an all-or-nothing responsibility
                altMinorResponsibility = a < r ? 1.0 : 0.0;
            }
            responsibilityWeightedMinorAlleleReadCount += altMinorResponsibility * a + (1 - altMinorResponsibility) * r;
            responsibilityWeightedTotalReadCount += a + r;
        }
        // we achieve a flat prior via a single pseudocount for minor and non-minor reads, hence the  +1 and +2
        result.add((responsibilityWeightedMinorAlleleReadCount + 1) / (responsibilityWeightedTotalReadCount + 2));
    }
    return result;
}