Examples with Sum org.apache.commons.math3.stat.descriptive.summary.Sum used on opensource projects

Example 1 with Sum

use of org.apache.commons.math3.stat.descriptive.summary.Sum in project GDSC-SMLM by aherbert.

the class EMGainAnalysis method getFunction.

private MultivariateFunction getFunction(final int[] limits, final double[] y, final int max, final int maxEval) {
    MultivariateFunction fun = new MultivariateFunction() {

        int eval = 0;

        public double value(double[] point) {
            IJ.showProgress(++eval, maxEval);
            if (Utils.isInterrupted())
                throw new TooManyEvaluationsException(maxEval);
            // Compute the sum of squares between the two functions
            double photons = point[0];
            double gain = point[1];
            double noise = point[2];
            int bias = (int) Math.round(point[3]);
            //System.out.printf("[%d] = %s\n", eval, Arrays.toString(point));
            final double[] g = pdf(max, photons, gain, noise, bias);
            double ss = 0;
            for (int c = limits[0]; c <= limits[1]; c++) {
                final double d = g[c] - y[c];
                ss += d * d;
            }
            return ss;
        }
    };
    return fun;
}

Example 2 with Sum

use of org.apache.commons.math3.stat.descriptive.summary.Sum in project GDSC-SMLM by aherbert.

the class DiffusionRateTest method msdAnalysis.

/**
	 * Tabulate the observed MSD for different jump distances
	 * 
	 * @param points
	 */
private void msdAnalysis(ArrayList<Point> points) {
    if (myMsdAnalysisSteps == 0)
        return;
    IJ.showStatus("MSD analysis ...");
    IJ.showProgress(1, myMsdAnalysisSteps);
    // This will only be fast if the list is an array
    Point[] list = points.toArray(new Point[points.size()]);
    // Compute the base MSD
    Point origin = new Point(0, 0, 0);
    double sum = origin.distance2(list[0]);
    int count = 1;
    for (int i = 1; i < list.length; i++) {
        Point last = list[i - 1];
        Point current = list[i];
        if (last.id == current.id) {
            sum += last.distance2(current);
        } else {
            sum += origin.distance2(current);
        }
        count++;
    }
    createMsdTable((sum / count) * settings.stepsPerSecond / conversionFactor);
    // Create a new set of points that have coordinates that 
    // are the rolling average over the number of aggregate steps
    RollingArray x = new RollingArray(aggregateSteps);
    RollingArray y = new RollingArray(aggregateSteps);
    int id = 0;
    int length = 0;
    for (Point p : points) {
        if (p.id != id) {
            x.reset();
            y.reset();
        }
        id = p.id;
        x.add(p.x);
        y.add(p.y);
        // Only create a point if the full aggregation size is reached
        if (x.isFull()) {
            list[length++] = new Point(id, x.getAverage(), y.getAverage());
        }
    }
    // Q - is this useful?
    final double p = myPrecision / settings.pixelPitch;
    final long seed = System.currentTimeMillis() + System.identityHashCode(this);
    RandomGenerator rand = new Well19937c(seed);
    final int totalSteps = (int) Math.ceil(settings.seconds * settings.stepsPerSecond - aggregateSteps);
    final int limit = Math.min(totalSteps, myMsdAnalysisSteps);
    final int interval = Utils.getProgressInterval(limit);
    final ArrayList<String> results = new ArrayList<String>(totalSteps);
    for (int step = 1; step <= myMsdAnalysisSteps; step++) {
        if (step % interval == 0)
            IJ.showProgress(step, limit);
        sum = 0;
        count = 0;
        for (int i = step; i < length; i++) {
            Point last = list[i - step];
            Point current = list[i];
            if (last.id == current.id) {
                if (p == 0) {
                    sum += last.distance2(current);
                    count++;
                } else {
                    // is the same if enough samples are present
                    for (int ii = 1; ii-- > 0; ) {
                        sum += last.distance2(current, p, rand);
                        count++;
                    }
                }
            }
        }
        if (count == 0)
            break;
        results.add(addResult(step, sum, count));
        // Flush to auto-space the columns
        if (step == 9) {
            msdTable.getTextPanel().append(results);
            results.clear();
        }
    }
    msdTable.getTextPanel().append(results);
    IJ.showProgress(1);
}

Example 3 with Sum

use of org.apache.commons.math3.stat.descriptive.summary.Sum in project GDSC-SMLM by aherbert.

the class JumpDistanceAnalysis method doFitJumpDistanceHistogram.

/**
	 * Fit the jump distance histogram using a cumulative sum with the given number of species.
	 * <p>
	 * Results are sorted by the diffusion coefficient ascending.
	 * 
	 * @param jdHistogram
	 *            The cumulative jump distance histogram. X-axis is um^2, Y-axis is cumulative probability. Must be
	 *            monototic ascending.
	 * @param estimatedD
	 *            The estimated diffusion coefficient
	 * @param n
	 *            The number of species in the mixed population
	 * @return Array containing: { D (um^2), Fractions }. Can be null if no fit was made.
	 */
private double[][] doFitJumpDistanceHistogram(double[][] jdHistogram, double estimatedD, int n) {
    calibrated = isCalibrated();
    if (n == 1) {
        // Fit using a single population model
        LevenbergMarquardtOptimizer lvmOptimizer = new LevenbergMarquardtOptimizer();
        try {
            final JumpDistanceCumulFunction function = new JumpDistanceCumulFunction(jdHistogram[0], jdHistogram[1], estimatedD);
            //@formatter:off
            LeastSquaresProblem problem = new LeastSquaresBuilder().maxEvaluations(Integer.MAX_VALUE).maxIterations(3000).start(function.guess()).target(function.getY()).weight(new DiagonalMatrix(function.getWeights())).model(function, new MultivariateMatrixFunction() {

                public double[][] value(double[] point) throws IllegalArgumentException {
                    return function.jacobian(point);
                }
            }).build();
            //@formatter:on
            Optimum lvmSolution = lvmOptimizer.optimize(problem);
            double[] fitParams = lvmSolution.getPoint().toArray();
            // True for an unweighted fit
            ss = lvmSolution.getResiduals().dotProduct(lvmSolution.getResiduals());
            //ss = calculateSumOfSquares(function.getY(), function.value(fitParams));
            lastIC = ic = Maths.getAkaikeInformationCriterionFromResiduals(ss, function.x.length, 1);
            double[] coefficients = fitParams;
            double[] fractions = new double[] { 1 };
            logger.info("Fit Jump distance (N=1) : %s, SS = %s, IC = %s (%d evaluations)", formatD(fitParams[0]), Maths.rounded(ss, 4), Maths.rounded(ic, 4), lvmSolution.getEvaluations());
            return new double[][] { coefficients, fractions };
        } catch (TooManyIterationsException e) {
            logger.info("LVM optimiser failed to fit (N=1) : Too many iterations : %s", e.getMessage());
        } catch (ConvergenceException e) {
            logger.info("LVM optimiser failed to fit (N=1) : %s", e.getMessage());
        }
    }
    // Uses a weighted sum of n exponential functions, each function models a fraction of the particles.
    // An LVM fit cannot restrict the parameters so the fractions do not go below zero.
    // Use the CustomPowell/CMEASOptimizer which supports bounded fitting.
    MixedJumpDistanceCumulFunctionMultivariate function = new MixedJumpDistanceCumulFunctionMultivariate(jdHistogram[0], jdHistogram[1], estimatedD, n);
    double[] lB = function.getLowerBounds();
    int evaluations = 0;
    PointValuePair constrainedSolution = null;
    MaxEval maxEval = new MaxEval(20000);
    CustomPowellOptimizer powellOptimizer = createCustomPowellOptimizer();
    try {
        // The Powell algorithm can use more general bounds: 0 - Infinity
        constrainedSolution = powellOptimizer.optimize(maxEval, new ObjectiveFunction(function), new InitialGuess(function.guess()), new SimpleBounds(lB, function.getUpperBounds(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)), new CustomPowellOptimizer.BasisStep(function.step()), GoalType.MINIMIZE);
        evaluations = powellOptimizer.getEvaluations();
        logger.debug("Powell optimiser fit (N=%d) : SS = %f (%d evaluations)", n, constrainedSolution.getValue(), evaluations);
    } catch (TooManyEvaluationsException e) {
        logger.info("Powell optimiser failed to fit (N=%d) : Too many evaluations (%d)", n, powellOptimizer.getEvaluations());
    } catch (TooManyIterationsException e) {
        logger.info("Powell optimiser failed to fit (N=%d) : Too many iterations (%d)", n, powellOptimizer.getIterations());
    } catch (ConvergenceException e) {
        logger.info("Powell optimiser failed to fit (N=%d) : %s", n, e.getMessage());
    }
    if (constrainedSolution == null) {
        logger.info("Trying CMAES optimiser with restarts ...");
        double[] uB = function.getUpperBounds();
        SimpleBounds bounds = new SimpleBounds(lB, uB);
        // The sigma determines the search range for the variables. It should be 1/3 of the initial search region.
        double[] s = new double[lB.length];
        for (int i = 0; i < s.length; i++) s[i] = (uB[i] - lB[i]) / 3;
        OptimizationData sigma = new CMAESOptimizer.Sigma(s);
        OptimizationData popSize = new CMAESOptimizer.PopulationSize((int) (4 + Math.floor(3 * Math.log(function.x.length))));
        // Iterate this for stability in the initial guess
        CMAESOptimizer cmaesOptimizer = createCMAESOptimizer();
        for (int i = 0; i <= fitRestarts; i++) {
            // Try from the initial guess
            try {
                PointValuePair solution = cmaesOptimizer.optimize(new InitialGuess(function.guess()), new ObjectiveFunction(function), GoalType.MINIMIZE, bounds, sigma, popSize, maxEval);
                if (constrainedSolution == null || solution.getValue() < constrainedSolution.getValue()) {
                    evaluations = cmaesOptimizer.getEvaluations();
                    constrainedSolution = solution;
                    logger.debug("CMAES optimiser [%da] fit (N=%d) : SS = %f (%d evaluations)", i, n, solution.getValue(), evaluations);
                }
            } catch (TooManyEvaluationsException e) {
            }
            if (constrainedSolution == null)
                continue;
            // Try from the current optimum
            try {
                PointValuePair solution = cmaesOptimizer.optimize(new InitialGuess(constrainedSolution.getPointRef()), new ObjectiveFunction(function), GoalType.MINIMIZE, bounds, sigma, popSize, maxEval);
                if (solution.getValue() < constrainedSolution.getValue()) {
                    evaluations = cmaesOptimizer.getEvaluations();
                    constrainedSolution = solution;
                    logger.debug("CMAES optimiser [%db] fit (N=%d) : SS = %f (%d evaluations)", i, n, solution.getValue(), evaluations);
                }
            } catch (TooManyEvaluationsException e) {
            }
        }
        if (constrainedSolution != null) {
            // Re-optimise with Powell?
            try {
                PointValuePair solution = powellOptimizer.optimize(maxEval, new ObjectiveFunction(function), new InitialGuess(constrainedSolution.getPointRef()), new SimpleBounds(lB, function.getUpperBounds(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)), new CustomPowellOptimizer.BasisStep(function.step()), GoalType.MINIMIZE);
                if (solution.getValue() < constrainedSolution.getValue()) {
                    evaluations = cmaesOptimizer.getEvaluations();
                    constrainedSolution = solution;
                    logger.info("Powell optimiser re-fit (N=%d) : SS = %f (%d evaluations)", n, constrainedSolution.getValue(), evaluations);
                }
            } catch (TooManyEvaluationsException e) {
            } catch (TooManyIterationsException e) {
            } catch (ConvergenceException e) {
            }
        }
    }
    if (constrainedSolution == null) {
        logger.info("Failed to fit N=%d", n);
        return null;
    }
    double[] fitParams = constrainedSolution.getPointRef();
    ss = constrainedSolution.getValue();
    // TODO - Try a bounded BFGS optimiser
    // Try and improve using a LVM fit
    final MixedJumpDistanceCumulFunctionGradient functionGradient = new MixedJumpDistanceCumulFunctionGradient(jdHistogram[0], jdHistogram[1], estimatedD, n);
    Optimum lvmSolution;
    LevenbergMarquardtOptimizer lvmOptimizer = new LevenbergMarquardtOptimizer();
    try {
        //@formatter:off
        LeastSquaresProblem problem = new LeastSquaresBuilder().maxEvaluations(Integer.MAX_VALUE).maxIterations(3000).start(fitParams).target(functionGradient.getY()).weight(new DiagonalMatrix(functionGradient.getWeights())).model(functionGradient, new MultivariateMatrixFunction() {

            public double[][] value(double[] point) throws IllegalArgumentException {
                return functionGradient.jacobian(point);
            }
        }).build();
        //@formatter:on
        lvmSolution = lvmOptimizer.optimize(problem);
        // True for an unweighted fit
        double ss = lvmSolution.getResiduals().dotProduct(lvmSolution.getResiduals());
        // All fitted parameters must be above zero
        if (ss < this.ss && Maths.min(lvmSolution.getPoint().toArray()) > 0) {
            logger.info("  Re-fitting improved the SS from %s to %s (-%s%%)", Maths.rounded(this.ss, 4), Maths.rounded(ss, 4), Maths.rounded(100 * (this.ss - ss) / this.ss, 4));
            fitParams = lvmSolution.getPoint().toArray();
            this.ss = ss;
            evaluations += lvmSolution.getEvaluations();
        }
    } catch (TooManyIterationsException e) {
        logger.error("Failed to re-fit : Too many iterations : %s", e.getMessage());
    } catch (ConvergenceException e) {
        logger.error("Failed to re-fit : %s", e.getMessage());
    }
    // Since the fractions must sum to one we subtract 1 degree of freedom from the number of parameters
    ic = Maths.getAkaikeInformationCriterionFromResiduals(ss, function.x.length, fitParams.length - 1);
    double[] d = new double[n];
    double[] f = new double[n];
    double sum = 0;
    for (int i = 0; i < d.length; i++) {
        f[i] = fitParams[i * 2];
        sum += f[i];
        d[i] = fitParams[i * 2 + 1];
    }
    for (int i = 0; i < f.length; i++) f[i] /= sum;
    // Sort by coefficient size
    sort(d, f);
    double[] coefficients = d;
    double[] fractions = f;
    logger.info("Fit Jump distance (N=%d) : %s (%s), SS = %s, IC = %s (%d evaluations)", n, formatD(d), format(f), Maths.rounded(ss, 4), Maths.rounded(ic, 4), evaluations);
    if (isValid(d, f)) {
        lastIC = ic;
        return new double[][] { coefficients, fractions };
    }
    return null;
}

Example 4 with Sum

use of org.apache.commons.math3.stat.descriptive.summary.Sum in project GDSC-SMLM by aherbert.

the class JumpDistanceAnalysis method doFitJumpDistancesMLE.

/**
	 * Fit the jump distances using a maximum likelihood estimation with the given number of species.
	 * | *
	 * <p>
	 * Results are sorted by the diffusion coefficient ascending.
	 * 
	 * @param jumpDistances
	 *            The jump distances (in um^2)
	 * @param estimatedD
	 *            The estimated diffusion coefficient
	 * @param n
	 *            The number of species in the mixed population
	 * @return Array containing: { D (um^2), Fractions }. Can be null if no fit was made.
	 */
private double[][] doFitJumpDistancesMLE(double[] jumpDistances, double estimatedD, int n) {
    MaxEval maxEval = new MaxEval(20000);
    CustomPowellOptimizer powellOptimizer = createCustomPowellOptimizer();
    calibrated = isCalibrated();
    if (n == 1) {
        try {
            final JumpDistanceFunction function = new JumpDistanceFunction(jumpDistances, estimatedD);
            // The Powell algorithm can use more general bounds: 0 - Infinity
            SimpleBounds bounds = new SimpleBounds(function.getLowerBounds(), function.getUpperBounds(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY));
            PointValuePair solution = powellOptimizer.optimize(maxEval, new ObjectiveFunction(function), new InitialGuess(function.guess()), bounds, new CustomPowellOptimizer.BasisStep(function.step()), GoalType.MAXIMIZE);
            double[] fitParams = solution.getPointRef();
            ll = solution.getValue();
            lastIC = ic = Maths.getAkaikeInformationCriterion(ll, jumpDistances.length, 1);
            double[] coefficients = fitParams;
            double[] fractions = new double[] { 1 };
            logger.info("Fit Jump distance (N=1) : %s, MLE = %s, IC = %s (%d evaluations)", formatD(fitParams[0]), Maths.rounded(ll, 4), Maths.rounded(ic, 4), powellOptimizer.getEvaluations());
            return new double[][] { coefficients, fractions };
        } catch (TooManyEvaluationsException e) {
            logger.info("Powell optimiser failed to fit (N=1) : Too many evaluation (%d)", powellOptimizer.getEvaluations());
        } catch (TooManyIterationsException e) {
            logger.info("Powell optimiser failed to fit (N=1) : Too many iterations (%d)", powellOptimizer.getIterations());
        } catch (ConvergenceException e) {
            logger.info("Powell optimiser failed to fit (N=1) : %s", e.getMessage());
        }
        return null;
    }
    MixedJumpDistanceFunction function = new MixedJumpDistanceFunction(jumpDistances, estimatedD, n);
    double[] lB = function.getLowerBounds();
    int evaluations = 0;
    PointValuePair constrainedSolution = null;
    try {
        // The Powell algorithm can use more general bounds: 0 - Infinity
        constrainedSolution = powellOptimizer.optimize(maxEval, new ObjectiveFunction(function), new InitialGuess(function.guess()), new SimpleBounds(lB, function.getUpperBounds(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)), new CustomPowellOptimizer.BasisStep(function.step()), GoalType.MAXIMIZE);
        evaluations = powellOptimizer.getEvaluations();
        logger.debug("Powell optimiser fit (N=%d) : MLE = %f (%d evaluations)", n, constrainedSolution.getValue(), powellOptimizer.getEvaluations());
    } catch (TooManyEvaluationsException e) {
        logger.info("Powell optimiser failed to fit (N=%d) : Too many evaluation (%d)", n, powellOptimizer.getEvaluations());
    } catch (TooManyIterationsException e) {
        logger.info("Powell optimiser failed to fit (N=%d) : Too many iterations (%d)", n, powellOptimizer.getIterations());
    } catch (ConvergenceException e) {
        logger.info("Powell optimiser failed to fit (N=%d) : %s", n, e.getMessage());
    }
    if (constrainedSolution == null) {
        logger.info("Trying CMAES optimiser with restarts ...");
        double[] uB = function.getUpperBounds();
        SimpleBounds bounds = new SimpleBounds(lB, uB);
        // Try a bounded CMAES optimiser since the Powell optimiser appears to be 
        // sensitive to the order of the parameters. It is not good when the fast particle
        // is the minority fraction. Could this be due to too low an upper bound?
        // The sigma determines the search range for the variables. It should be 1/3 of the initial search region.
        double[] s = new double[lB.length];
        for (int i = 0; i < s.length; i++) s[i] = (uB[i] - lB[i]) / 3;
        OptimizationData sigma = new CMAESOptimizer.Sigma(s);
        OptimizationData popSize = new CMAESOptimizer.PopulationSize((int) (4 + Math.floor(3 * Math.log(function.x.length))));
        // Iterate this for stability in the initial guess
        CMAESOptimizer cmaesOptimizer = createCMAESOptimizer();
        for (int i = 0; i <= fitRestarts; i++) {
            // Try from the initial guess
            try {
                PointValuePair solution = cmaesOptimizer.optimize(new InitialGuess(function.guess()), new ObjectiveFunction(function), GoalType.MAXIMIZE, bounds, sigma, popSize, maxEval);
                if (constrainedSolution == null || solution.getValue() > constrainedSolution.getValue()) {
                    evaluations = cmaesOptimizer.getEvaluations();
                    constrainedSolution = solution;
                    logger.debug("CMAES optimiser [%da] fit (N=%d) : MLE = %f (%d evaluations)", i, n, solution.getValue(), evaluations);
                }
            } catch (TooManyEvaluationsException e) {
            }
            if (constrainedSolution == null)
                continue;
            // Try from the current optimum
            try {
                PointValuePair solution = cmaesOptimizer.optimize(new InitialGuess(constrainedSolution.getPointRef()), new ObjectiveFunction(function), GoalType.MAXIMIZE, bounds, sigma, popSize, maxEval);
                if (solution.getValue() > constrainedSolution.getValue()) {
                    evaluations = cmaesOptimizer.getEvaluations();
                    constrainedSolution = solution;
                    logger.debug("CMAES optimiser [%db] fit (N=%d) : MLE = %f (%d evaluations)", i, n, solution.getValue(), evaluations);
                }
            } catch (TooManyEvaluationsException e) {
            }
        }
        if (constrainedSolution != null) {
            try {
                // Re-optimise with Powell?
                PointValuePair solution = powellOptimizer.optimize(maxEval, new ObjectiveFunction(function), new InitialGuess(constrainedSolution.getPointRef()), new SimpleBounds(lB, function.getUpperBounds(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)), new CustomPowellOptimizer.BasisStep(function.step()), GoalType.MAXIMIZE);
                if (solution.getValue() > constrainedSolution.getValue()) {
                    evaluations = cmaesOptimizer.getEvaluations();
                    constrainedSolution = solution;
                    logger.info("Powell optimiser re-fit (N=%d) : MLE = %f (%d evaluations)", n, constrainedSolution.getValue(), powellOptimizer.getEvaluations());
                }
            } catch (TooManyEvaluationsException e) {
            } catch (TooManyIterationsException e) {
            } catch (ConvergenceException e) {
            }
        }
    }
    if (constrainedSolution == null) {
        logger.info("Failed to fit N=%d", n);
        return null;
    }
    double[] fitParams = constrainedSolution.getPointRef();
    ll = constrainedSolution.getValue();
    // Since the fractions must sum to one we subtract 1 degree of freedom from the number of parameters
    ic = Maths.getAkaikeInformationCriterion(ll, jumpDistances.length, fitParams.length - 1);
    double[] d = new double[n];
    double[] f = new double[n];
    double sum = 0;
    for (int i = 0; i < d.length; i++) {
        f[i] = fitParams[i * 2];
        sum += f[i];
        d[i] = fitParams[i * 2 + 1];
    }
    for (int i = 0; i < f.length; i++) f[i] /= sum;
    // Sort by coefficient size
    sort(d, f);
    double[] coefficients = d;
    double[] fractions = f;
    logger.info("Fit Jump distance (N=%d) : %s (%s), MLE = %s, IC = %s (%d evaluations)", n, formatD(d), format(f), Maths.rounded(ll, 4), Maths.rounded(ic, 4), evaluations);
    if (isValid(d, f)) {
        lastIC = ic;
        return new double[][] { coefficients, fractions };
    }
    return null;
}

Example 5 with Sum

use of org.apache.commons.math3.stat.descriptive.summary.Sum in project GDSC-SMLM by aherbert.

the class BinomialFitter method fitBinomial.

/**
	 * Fit the binomial distribution (n,p) to the cumulative histogram. Performs fitting assuming a fixed n value and
	 * attempts to optimise p.
	 * 
	 * @param histogram
	 *            The input histogram
	 * @param mean
	 *            The histogram mean (used to estimate p). Calculated if NaN.
	 * @param n
	 *            The n to evaluate
	 * @param zeroTruncated
	 *            True if the model should ignore n=0 (zero-truncated binomial)
	 * @return The best fit (n, p)
	 * @throws IllegalArgumentException
	 *             If any of the input data values are negative
	 * @throws IllegalArgumentException
	 *             If any fitting a zero truncated binomial and there are no values above zero
	 */
public PointValuePair fitBinomial(double[] histogram, double mean, int n, boolean zeroTruncated) {
    if (Double.isNaN(mean))
        mean = getMean(histogram);
    if (zeroTruncated && histogram[0] > 0) {
        log("Fitting zero-truncated histogram but there are zero values - Renormalising to ignore zero");
        double cumul = 0;
        for (int i = 1; i < histogram.length; i++) cumul += histogram[i];
        if (cumul == 0)
            throw new IllegalArgumentException("Fitting zero-truncated histogram but there are no non-zero values");
        histogram[0] = 0;
        for (int i = 1; i < histogram.length; i++) histogram[i] /= cumul;
    }
    int nFittedPoints = Math.min(histogram.length, n + 1) - ((zeroTruncated) ? 1 : 0);
    if (nFittedPoints < 1) {
        log("No points to fit (%d): Histogram.length = %d, n = %d, zero-truncated = %b", nFittedPoints, histogram.length, n, zeroTruncated);
        return null;
    }
    // The model is only fitting the probability p
    // For a binomial n*p = mean => p = mean/n
    double[] initialSolution = new double[] { FastMath.min(mean / n, 1) };
    // Create the function
    BinomialModelFunction function = new BinomialModelFunction(histogram, n, zeroTruncated);
    double[] lB = new double[1];
    double[] uB = new double[] { 1 };
    SimpleBounds bounds = new SimpleBounds(lB, uB);
    // Fit
    // CMAESOptimizer or BOBYQAOptimizer support bounds
    // CMAESOptimiser based on Matlab code:
    // https://www.lri.fr/~hansen/cmaes.m
    // Take the defaults from the Matlab documentation
    int maxIterations = 2000;
    //Double.NEGATIVE_INFINITY;
    double stopFitness = 0;
    boolean isActiveCMA = true;
    int diagonalOnly = 0;
    int checkFeasableCount = 1;
    RandomGenerator random = new Well19937c();
    boolean generateStatistics = false;
    ConvergenceChecker<PointValuePair> checker = new SimpleValueChecker(1e-6, 1e-10);
    // The sigma determines the search range for the variables. It should be 1/3 of the initial search region.
    OptimizationData sigma = new CMAESOptimizer.Sigma(new double[] { (uB[0] - lB[0]) / 3 });
    OptimizationData popSize = new CMAESOptimizer.PopulationSize((int) (4 + Math.floor(3 * Math.log(2))));
    try {
        PointValuePair solution = null;
        boolean noRefit = maximumLikelihood;
        if (n == 1 && zeroTruncated) {
            // No need to fit
            solution = new PointValuePair(new double[] { 1 }, 0);
            noRefit = true;
        } else {
            GoalType goalType = (maximumLikelihood) ? GoalType.MAXIMIZE : GoalType.MINIMIZE;
            // Iteratively fit
            CMAESOptimizer opt = new CMAESOptimizer(maxIterations, stopFitness, isActiveCMA, diagonalOnly, checkFeasableCount, random, generateStatistics, checker);
            for (int iteration = 0; iteration <= fitRestarts; iteration++) {
                try {
                    // Start from the initial solution
                    PointValuePair result = opt.optimize(new InitialGuess(initialSolution), new ObjectiveFunction(function), goalType, bounds, sigma, popSize, new MaxIter(maxIterations), new MaxEval(maxIterations * 2));
                    //		opt.getEvaluations());
                    if (solution == null || result.getValue() < solution.getValue()) {
                        solution = result;
                    }
                } catch (TooManyEvaluationsException e) {
                } catch (TooManyIterationsException e) {
                }
                if (solution == null)
                    continue;
                try {
                    // Also restart from the current optimum
                    PointValuePair result = opt.optimize(new InitialGuess(solution.getPointRef()), new ObjectiveFunction(function), goalType, bounds, sigma, popSize, new MaxIter(maxIterations), new MaxEval(maxIterations * 2));
                    //		opt.getEvaluations());
                    if (result.getValue() < solution.getValue()) {
                        solution = result;
                    }
                } catch (TooManyEvaluationsException e) {
                } catch (TooManyIterationsException e) {
                }
            }
            if (solution == null)
                return null;
        }
        if (noRefit) {
            // Although we fit the log-likelihood, return the sum-of-squares to allow 
            // comparison across different n
            double p = solution.getPointRef()[0];
            double ss = 0;
            double[] obs = function.p;
            double[] exp = function.getP(p);
            for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]);
            return new PointValuePair(solution.getPointRef(), ss);
        } else // We can do a LVM refit if the number of fitted points is more than 1
        if (nFittedPoints > 1) {
            // Improve SS fit with a gradient based LVM optimizer
            LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
            try {
                final BinomialModelFunctionGradient gradientFunction = new BinomialModelFunctionGradient(histogram, n, zeroTruncated);
                //@formatter:off
                LeastSquaresProblem problem = new LeastSquaresBuilder().maxEvaluations(Integer.MAX_VALUE).maxIterations(3000).start(solution.getPointRef()).target(gradientFunction.p).weight(new DiagonalMatrix(gradientFunction.getWeights())).model(gradientFunction, new MultivariateMatrixFunction() {

                    public double[][] value(double[] point) throws IllegalArgumentException {
                        return gradientFunction.jacobian(point);
                    }
                }).build();
                //@formatter:on
                Optimum lvmSolution = optimizer.optimize(problem);
                // Check the pValue is valid since the LVM is not bounded.
                double p = lvmSolution.getPoint().getEntry(0);
                if (p <= 1 && p >= 0) {
                    // True if the weights are 1
                    double ss = lvmSolution.getResiduals().dotProduct(lvmSolution.getResiduals());
                    //	ss += (obs[i] - exp[i]) * (obs[i] - exp[i]);
                    if (ss < solution.getValue()) {
                        //		Utils.rounded(100 * (solution.getValue() - ss) / solution.getValue(), 4));
                        return new PointValuePair(lvmSolution.getPoint().toArray(), ss);
                    }
                }
            } catch (TooManyIterationsException e) {
                log("Failed to re-fit: Too many iterations: %s", e.getMessage());
            } catch (ConvergenceException e) {
                log("Failed to re-fit: %s", e.getMessage());
            } catch (Exception e) {
            // Ignore this ...
            }
        }
        return solution;
    } catch (Exception e) {
        log("Failed to fit Binomial distribution with N=%d : %s", n, e.getMessage());
    }
    return null;
}