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

Example 1 with MultivariateFunction

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

the class FIRE method findMin.

private UnivariatePointValuePair findMin(UnivariatePointValuePair current, SimplexOptimizer o, MultivariateFunction f, double qValue) {
    try {
        NelderMeadSimplex simplex = new NelderMeadSimplex(1);
        double[] initialSolution = { qValue };
        PointValuePair solution = o.optimize(new MaxEval(1000), new InitialGuess(initialSolution), simplex, new ObjectiveFunction(f), GoalType.MINIMIZE);
        UnivariatePointValuePair next = (solution == null) ? null : new UnivariatePointValuePair(solution.getPointRef()[0], solution.getValue());
        if (next == null)
            return current;
        //System.out.printf("Simplex [%f]  %f = %f\n", qValue, next.getPoint(), next.getValue());
        if (current != null)
            return (next.getValue() < current.getValue()) ? next : current;
        return next;
    } catch (Exception e) {
        return current;
    }
}

Example 2 with MultivariateFunction

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

the class FIRE method findMin.

private PointValuePair findMin(PointValuePair current, SimplexOptimizer o, MultivariateFunction f, double[] initialSolution) {
    try {
        NelderMeadSimplex simplex = new NelderMeadSimplex(initialSolution.length);
        PointValuePair next = o.optimize(new MaxEval(1000), new InitialGuess(initialSolution), simplex, new ObjectiveFunction(f), GoalType.MINIMIZE);
        if (next == null)
            return current;
        //		Arrays.toString(next.getPointRef()), next.getValue());
        if (current != null)
            return (next.getValue() < current.getValue()) ? next : current;
        return next;
    } catch (Exception e) {
        return current;
    }
}

Example 3 with MultivariateFunction

use of org.apache.commons.math3.analysis.MultivariateFunction 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 4 with MultivariateFunction

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

the class EMGainAnalysis method fit.

/**
	 * Fit the EM-gain distribution (Gaussian * Gamma)
	 * 
	 * @param h
	 *            The distribution
	 */
private void fit(int[] h) {
    final int[] limits = limits(h);
    final double[] x = getX(limits);
    final double[] y = getY(h, limits);
    Plot2 plot = new Plot2(TITLE, "ADU", "Frequency");
    double yMax = Maths.max(y);
    plot.setLimits(limits[0], limits[1], 0, yMax);
    plot.setColor(Color.black);
    plot.addPoints(x, y, Plot2.DOT);
    Utils.display(TITLE, plot);
    // Estimate remaining parameters. 
    // Assuming a gamma_distribution(shape,scale) then mean = shape * scale
    // scale = gain
    // shape = Photons = mean / gain
    double mean = getMean(h) - bias;
    // Note: if the bias is too high then the mean will be negative. Just move the bias.
    while (mean < 0) {
        bias -= 1;
        mean += 1;
    }
    double photons = mean / gain;
    if (simulate)
        Utils.log("Simulated bias=%d, gain=%s, noise=%s, photons=%s", (int) _bias, Utils.rounded(_gain), Utils.rounded(_noise), Utils.rounded(_photons));
    Utils.log("Estimate bias=%d, gain=%s, noise=%s, photons=%s", (int) bias, Utils.rounded(gain), Utils.rounded(noise), Utils.rounded(photons));
    final int max = (int) x[x.length - 1];
    double[] g = pdf(max, photons, gain, noise, (int) bias);
    plot.setColor(Color.blue);
    plot.addPoints(x, g, Plot2.LINE);
    Utils.display(TITLE, plot);
    // Perform a fit
    CustomPowellOptimizer o = new CustomPowellOptimizer(1e-6, 1e-16, 1e-6, 1e-16);
    double[] startPoint = new double[] { photons, gain, noise, bias };
    int maxEval = 3000;
    String[] paramNames = { "Photons", "Gain", "Noise", "Bias" };
    // Set bounds
    double[] lower = new double[] { 0, 0.5 * gain, 0, bias - noise };
    double[] upper = new double[] { 2 * photons, 2 * gain, gain, bias + noise };
    // Restart until converged.
    // TODO - Maybe fix this with a better optimiser. This needs to be tested on real data.
    PointValuePair solution = null;
    for (int iter = 0; iter < 3; iter++) {
        IJ.showStatus("Fitting histogram ... Iteration " + iter);
        try {
            // Basic Powell optimiser
            MultivariateFunction fun = getFunction(limits, y, max, maxEval);
            PointValuePair optimum = o.optimize(new MaxEval(maxEval), new ObjectiveFunction(fun), GoalType.MINIMIZE, new InitialGuess((solution == null) ? startPoint : solution.getPointRef()));
            if (solution == null || optimum.getValue() < solution.getValue()) {
                double[] point = optimum.getPointRef();
                // Check the bounds
                for (int i = 0; i < point.length; i++) {
                    if (point[i] < lower[i] || point[i] > upper[i]) {
                        throw new RuntimeException(String.format("Fit out of of estimated range: %s %f", paramNames[i], point[i]));
                    }
                }
                solution = optimum;
            }
        } catch (Exception e) {
            IJ.log("Powell error: " + e.getMessage());
            if (e instanceof TooManyEvaluationsException) {
                maxEval = (int) (maxEval * 1.5);
            }
        }
        try {
            // Bounded Powell optimiser
            MultivariateFunction fun = getFunction(limits, y, max, maxEval);
            MultivariateFunctionMappingAdapter adapter = new MultivariateFunctionMappingAdapter(fun, lower, upper);
            PointValuePair optimum = o.optimize(new MaxEval(maxEval), new ObjectiveFunction(adapter), GoalType.MINIMIZE, new InitialGuess(adapter.boundedToUnbounded((solution == null) ? startPoint : solution.getPointRef())));
            double[] point = adapter.unboundedToBounded(optimum.getPointRef());
            optimum = new PointValuePair(point, optimum.getValue());
            if (solution == null || optimum.getValue() < solution.getValue()) {
                solution = optimum;
            }
        } catch (Exception e) {
            IJ.log("Bounded Powell error: " + e.getMessage());
            if (e instanceof TooManyEvaluationsException) {
                maxEval = (int) (maxEval * 1.5);
            }
        }
    }
    IJ.showStatus("");
    IJ.showProgress(1);
    if (solution == null) {
        Utils.log("Failed to fit the distribution");
        return;
    }
    double[] point = solution.getPointRef();
    photons = point[0];
    gain = point[1];
    noise = point[2];
    bias = (int) Math.round(point[3]);
    String label = String.format("Fitted bias=%d, gain=%s, noise=%s, photons=%s", (int) bias, Utils.rounded(gain), Utils.rounded(noise), Utils.rounded(photons));
    Utils.log(label);
    if (simulate) {
        Utils.log("Relative Error bias=%s, gain=%s, noise=%s, photons=%s", Utils.rounded(relativeError(bias, _bias)), Utils.rounded(relativeError(gain, _gain)), Utils.rounded(relativeError(noise, _noise)), Utils.rounded(relativeError(photons, _photons)));
    }
    // Show the PoissonGammaGaussian approximation
    double[] f = null;
    if (showApproximation) {
        f = new double[x.length];
        PoissonGammaGaussianFunction fun = new PoissonGammaGaussianFunction(1.0 / gain, noise);
        final double expected = photons * gain;
        for (int i = 0; i < f.length; i++) {
            f[i] = fun.likelihood(x[i] - bias, expected);
        //System.out.printf("x=%d, g=%f, f=%f, error=%f\n", (int) x[i], g[i], f[i],
        //		gdsc.smlm.fitting.utils.DoubleEquality.relativeError(g[i], f[i]));
        }
        yMax = Maths.maxDefault(yMax, f);
    }
    // Replot
    g = pdf(max, photons, gain, noise, (int) bias);
    plot = new Plot2(TITLE, "ADU", "Frequency");
    plot.setLimits(limits[0], limits[1], 0, yMax * 1.05);
    plot.setColor(Color.black);
    plot.addPoints(x, y, Plot2.DOT);
    plot.setColor(Color.red);
    plot.addPoints(x, g, Plot2.LINE);
    plot.addLabel(0, 0, label);
    if (showApproximation) {
        plot.setColor(Color.blue);
        plot.addPoints(x, f, Plot2.LINE);
    }
    Utils.display(TITLE, plot);
}