Examples with TooManyEvaluationsException org.apache.commons.math3.exception.TooManyEvaluationsException used on opensource projects

Example 6 with TooManyEvaluationsException

use of org.apache.commons.math3.exception.TooManyEvaluationsException in project GDSC-SMLM by aherbert.

the class PoissonGammaGaussianFunction method likelihood.

/**
	 * Compute the likelihood
	 * 
	 * @param o
	 *            The observed count
	 * @param e
	 *            The expected count
	 * @return The likelihood
	 */
public double likelihood(final double o, final double e) {
    // Use the same variables as the Python code
    final double cij = o;
    // convert to photons
    final double eta = alpha * e;
    if (sigma == 0) {
        // No convolution with a Gaussian. Simply evaluate for a Poisson-Gamma distribution.
        final double p;
        // Any observed count above zero
        if (cij > 0.0) {
            // The observed count converted to photons
            final double nij = alpha * cij;
            // The limit on eta * nij is therefore (709/2)^2 = 125670.25
            if (eta * nij > 10000) {
                // Approximate Bessel function i1(x) when using large x:
                // i1(x) ~ exp(x)/sqrt(2*pi*x)
                // However the entire equation is logged (creating transform),
                // evaluated then raised to e to prevent overflow error on 
                // large exp(x)
                final double transform = 0.5 * Math.log(alpha * eta / cij) - nij - eta + 2 * Math.sqrt(eta * nij) - Math.log(twoSqrtPi * Math.pow(eta * nij, 0.25));
                p = FastMath.exp(transform);
            } else {
                // Second part of equation 135
                p = Math.sqrt(alpha * eta / cij) * FastMath.exp(-nij - eta) * Bessel.I1(2 * Math.sqrt(eta * nij));
            }
        } else if (cij == 0.0) {
            p = FastMath.exp(-eta);
        } else {
            p = 0;
        }
        return (p > minimumProbability) ? p : minimumProbability;
    } else if (useApproximation) {
        return mortensenApproximation(cij, eta);
    } else {
        // This code is the full evaluation of equation 7 from the supplementary information  
        // of the paper Chao, et al (2013) Nature Methods 10, 335-338.
        // It is the full evaluation of a Poisson-Gamma-Gaussian convolution PMF. 
        // Read noise
        final double sk = sigma;
        // Gain
        final double g = 1.0 / alpha;
        // Observed pixel value
        final double z = o;
        // Expected number of photons
        final double vk = eta;
        // Compute the integral to infinity of:
        // exp( -((z-u)/(sqrt(2)*s)).^2 - u/g ) * sqrt(vk*u/g) .* besseli(1, 2 * sqrt(vk*u/g)) ./ u;
        // vk / g
        final double vk_g = vk * alpha;
        final double sqrt2sigma = Math.sqrt(2) * sk;
        // Specify the function to integrate
        UnivariateFunction f = new UnivariateFunction() {

            public double value(double u) {
                return eval(sqrt2sigma, z, vk_g, g, u);
            }
        };
        // Integrate to infinity is not necessary. The convolution of the function with the 
        // Gaussian should be adequately sampled using a nxSD around the maximum.
        // Find a bracket containing the maximum
        double lower, upper;
        double maxU = Math.max(1, o);
        double rLower = maxU;
        double rUpper = maxU + 1;
        double f1 = f.value(rLower);
        double f2 = f.value(rUpper);
        // Calculate the simple integral and the range
        double sum = f1 + f2;
        boolean searchUp = f2 > f1;
        if (searchUp) {
            while (f2 > f1) {
                f1 = f2;
                rUpper += 1;
                f2 = f.value(rUpper);
                sum += f2;
            }
            maxU = rUpper - 1;
        } else {
            // Ensure that u stays above zero
            while (f1 > f2 && rLower > 1) {
                f2 = f1;
                rLower -= 1;
                f1 = f.value(rLower);
                sum += f1;
            }
            maxU = (rLower > 1) ? rLower + 1 : rLower;
        }
        lower = Math.max(0, maxU - 5 * sk);
        upper = maxU + 5 * sk;
        if (useSimpleIntegration && lower > 0) {
            // remaining points in the range
            for (double u = rLower - 1; u >= lower; u -= 1) {
                sum += f.value(u);
            }
            for (double u = rUpper + 1; u <= upper; u += 1) {
                sum += f.value(u);
            }
        } else {
            // Use Legendre-Gauss integrator
            try {
                final double relativeAccuracy = 1e-4;
                final double absoluteAccuracy = 1e-8;
                final int minimalIterationCount = 3;
                final int maximalIterationCount = 32;
                final int integrationPoints = 16;
                // Use an integrator that does not use the boundary since u=0 is undefined (divide by zero)
                UnivariateIntegrator i = new IterativeLegendreGaussIntegrator(integrationPoints, relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
                sum = i.integrate(2000, f, lower, upper);
            } catch (TooManyEvaluationsException ex) {
                return mortensenApproximation(cij, eta);
            }
        }
        // Compute the final probability
        //final double 
        f1 = z / sqrt2sigma;
        final double p = (FastMath.exp(-vk) / (sqrt2pi * sk)) * (FastMath.exp(-(f1 * f1)) + sum);
        return (p > minimumProbability) ? p : minimumProbability;
    }
}

Example 7 with TooManyEvaluationsException

use of org.apache.commons.math3.exception.TooManyEvaluationsException 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 8 with TooManyEvaluationsException

use of org.apache.commons.math3.exception.TooManyEvaluationsException 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);
}

Example 9 with TooManyEvaluationsException

use of org.apache.commons.math3.exception.TooManyEvaluationsException in project gatk by broadinstitute.

the class RobustBrentSolver method doSolve.

@Override
protected double doSolve() throws TooManyEvaluationsException, NoBracketingException {
    final double min = getMin();
    final double max = getMax();
    final double[] xSearchGrid = createHybridSearchGrid(min, max, numBisections, depth);
    final double[] fSearchGrid = Arrays.stream(xSearchGrid).map(this::computeObjectiveValue).toArray();
    /* find bracketing intervals on the search grid */
    final List<Bracket> bracketsList = detectBrackets(xSearchGrid, fSearchGrid);
    if (bracketsList.isEmpty()) {
        throw new NoBracketingException(min, max, fSearchGrid[0], fSearchGrid[fSearchGrid.length - 1]);
    }
    final BrentSolver solver = new BrentSolver(getRelativeAccuracy(), getAbsoluteAccuracy(), getFunctionValueAccuracy());
    final List<Double> roots = bracketsList.stream().map(b -> solver.solve(getMaxEvaluations(), this::computeObjectiveValue, b.min, b.max, 0.5 * (b.min + b.max))).collect(Collectors.toList());
    if (roots.size() == 1 || meritFunc == null) {
        return roots.get(0);
    }
    final double[] merits = roots.stream().mapToDouble(meritFunc::value).toArray();
    final int bestRootIndex = IntStream.range(0, roots.size()).boxed().max((i, j) -> (int) (merits[i] - merits[j])).get();
    return roots.get(bestRootIndex);
}

Example 10 with TooManyEvaluationsException

use of org.apache.commons.math3.exception.TooManyEvaluationsException in project gatk by broadinstitute.

the class CoverageModelEMComputeBlock method cloneWithUpdatedTargetUnexplainedVarianceTargetResolved.

/**
     * Performs the M-step for target-specific unexplained variance and clones the compute block
     * with the updated value.
     *
     * @param maxIters maximum number of iterations
     * @param psiUpperLimit upper limit for the unexplained variance
     * @param absTol absolute error tolerance (used in root finding)
     * @param relTol relative error tolerance (used in root finding)
     * @param numBisections number of bisections (used in root finding)
     * @param refinementDepth depth of search (used in root finding)
     *
     * @return a new instance of {@link CoverageModelEMComputeBlock}
     */
@QueriesICG
public CoverageModelEMComputeBlock cloneWithUpdatedTargetUnexplainedVarianceTargetResolved(final int maxIters, final double psiUpperLimit, final double absTol, final double relTol, final int numBisections, final int refinementDepth, final int numThreads) {
    Utils.validateArg(maxIters > 0, "At least one iteration is required");
    Utils.validateArg(psiUpperLimit >= 0, "The upper limit must be non-negative");
    Utils.validateArg(absTol >= 0, "The absolute error tolerance must be non-negative");
    Utils.validateArg(relTol >= 0, "The relative error tolerance must be non-negative");
    Utils.validateArg(numBisections >= 0, "The number of bisections must be non-negative");
    Utils.validateArg(refinementDepth >= 0, "The refinement depth must be non-negative");
    Utils.validateArg(numThreads > 0, "Number of execution threads must be positive");
    /* fetch the required caches */
    final INDArray Psi_t = getINDArrayFromCache(CoverageModelICGCacheNode.Psi_t);
    final INDArray M_st = getINDArrayFromCache(CoverageModelICGCacheNode.M_st);
    final INDArray Sigma_st = getINDArrayFromCache(CoverageModelICGCacheNode.Sigma_st);
    final INDArray gamma_s = getINDArrayFromCache(CoverageModelICGCacheNode.gamma_s);
    final INDArray B_st = getINDArrayFromCache(CoverageModelICGCacheNode.B_st);
    final ForkJoinPool forkJoinPool = new ForkJoinPool(numThreads);
    final List<ImmutablePair<Double, Integer>> res;
    try {
        res = forkJoinPool.submit(() -> {
            return IntStream.range(0, numTargets).parallel().mapToObj(ti -> {
                final UnivariateFunction objFunc = psi -> calculateTargetSpecificVarianceSolverObjectiveFunction(ti, psi, M_st, Sigma_st, gamma_s, B_st);
                final UnivariateFunction meritFunc = psi -> calculateTargetSpecificVarianceSolverMeritFunction(ti, psi, M_st, Sigma_st, gamma_s, B_st);
                final RobustBrentSolver solver = new RobustBrentSolver(relTol, absTol, CoverageModelGlobalConstants.DEFAULT_FUNCTION_EVALUATION_ACCURACY, meritFunc, numBisections, refinementDepth);
                double newPsi;
                try {
                    newPsi = solver.solve(maxIters, objFunc, 0, psiUpperLimit);
                } catch (NoBracketingException | TooManyEvaluationsException e) {
                    newPsi = Psi_t.getDouble(ti);
                }
                return new ImmutablePair<>(newPsi, solver.getEvaluations());
            }).collect(Collectors.toList());
        }).get();
    } catch (InterruptedException | ExecutionException ex) {
        throw new RuntimeException("Failure in concurrent update of target-specific unexplained variance");
    }
    final INDArray newPsi_t = Nd4j.create(res.stream().mapToDouble(p -> p.left).toArray(), Psi_t.shape());
    final int maxIterations = Collections.max(res.stream().mapToInt(p -> p.right).boxed().collect(Collectors.toList()));
    final double errNormInfinity = CoverageModelEMWorkspaceMathUtils.getINDArrayNormInfinity(newPsi_t.sub(Psi_t));
    return cloneWithUpdatedPrimitiveAndSignal(CoverageModelICGCacheNode.Psi_t, newPsi_t, SubroutineSignal.builder().put(StandardSubroutineSignals.RESIDUAL_ERROR_NORM, errNormInfinity).put(StandardSubroutineSignals.ITERATIONS, maxIterations).build());
}