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

Example 6 with MultivariateMatrixFunction

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

the class PCPALMFitting method fitRandomModel.

/**
	 * Fits the correlation curve with r>0 to the random model using the estimated density and precision. Parameters
	 * must be fit within a tolerance of the starting values.
	 * 
	 * @param gr
	 * @param sigmaS
	 *            The estimated precision
	 * @param proteinDensity
	 *            The estimate protein density
	 * @return The fitted parameters [precision, density]
	 */
private double[] fitRandomModel(double[][] gr, double sigmaS, double proteinDensity, String resultColour) {
    final RandomModelFunction function = new RandomModelFunction();
    randomModel = function;
    log("Fitting %s: Estimated precision = %f nm, estimated protein density = %g um^-2", randomModel.getName(), sigmaS, proteinDensity * 1e6);
    randomModel.setLogging(true);
    for (int i = offset; i < gr[0].length; i++) {
        // Only fit the curve above the estimated resolution (points below it will be subject to error)
        if (gr[0][i] > sigmaS * fitAboveEstimatedPrecision)
            randomModel.addPoint(gr[0][i], gr[1][i]);
    }
    LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
    Optimum optimum;
    try {
        //@formatter:off
        LeastSquaresProblem problem = new LeastSquaresBuilder().maxEvaluations(Integer.MAX_VALUE).maxIterations(3000).start(new double[] { sigmaS, proteinDensity }).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 = optimizer.optimize(problem);
    } catch (TooManyIterationsException e) {
        log("Failed to fit %s: Too many iterations (%s)", randomModel.getName(), e.getMessage());
        return null;
    } catch (ConvergenceException e) {
        log("Failed to fit %s: %s", randomModel.getName(), e.getMessage());
        return null;
    }
    randomModel.setLogging(false);
    double[] parameters = optimum.getPoint().toArray();
    // Ensure the width is positive
    parameters[0] = Math.abs(parameters[0]);
    double ss = optimum.getResiduals().dotProduct(optimum.getResiduals());
    ic1 = Maths.getAkaikeInformationCriterionFromResiduals(ss, randomModel.size(), parameters.length);
    final double fitSigmaS = parameters[0];
    final double fitProteinDensity = parameters[1];
    // Check the fitted parameters are within tolerance of the initial estimates
    double e1 = parameterDrift(sigmaS, fitSigmaS);
    double e2 = parameterDrift(proteinDensity, fitProteinDensity);
    log("  %s fit: SS = %f. cAIC = %f. %d evaluations", randomModel.getName(), ss, ic1, optimum.getEvaluations());
    log("  %s parameters:", randomModel.getName());
    log("    Average precision = %s nm (%s%%)", Utils.rounded(fitSigmaS, 4), Utils.rounded(e1, 4));
    log("    Average protein density = %s um^-2 (%s%%)", Utils.rounded(fitProteinDensity * 1e6, 4), Utils.rounded(e2, 4));
    valid1 = true;
    if (fittingTolerance > 0 && (Math.abs(e1) > fittingTolerance || Math.abs(e2) > fittingTolerance)) {
        log("  Failed to fit %s within tolerance (%s%%): Average precision = %f nm (%s%%), average protein density = %g um^-2 (%s%%)", randomModel.getName(), Utils.rounded(fittingTolerance, 4), fitSigmaS, Utils.rounded(e1, 4), fitProteinDensity * 1e6, Utils.rounded(e2, 4));
        valid1 = false;
    }
    if (valid1) {
        // ---------
        // TODO - My data does not comply with this criteria. 
        // This could be due to the PC-PALM Molecule code limiting the nmPerPixel to fit the images in memory 
        // thus removing correlations at small r.
        // It could also be due to the nature of the random simulations being 3D not 2D membranes 
        // as per the PC-PALM paper. 
        // ---------
        // Evaluate g(r)protein where:
        // g(r)peaks = g(r)protein + g(r)stoch
        // g(r)peaks ~ 1           + g(r)stoch
        // Verify g(r)protein should be <1.5 for all r>0
        double[] gr_stoch = randomModel.value(parameters);
        double[] gr_peaks = randomModel.getY();
        double[] gr_ = randomModel.getX();
        //SummaryStatistics stats = new SummaryStatistics();
        for (int i = 0; i < gr_peaks.length; i++) {
            // Only evaluate above the fitted average precision 
            if (gr_[i] < fitSigmaS)
                continue;
            // Note the RandomModelFunction evaluates g(r)stoch + 1;
            double gr_protein_i = gr_peaks[i] - (gr_stoch[i] - 1);
            if (gr_protein_i > gr_protein_threshold) {
                // Failed fit
                log("  Failed to fit %s: g(r)protein %s > %s @ r=%s", randomModel.getName(), Utils.rounded(gr_protein_i, 4), Utils.rounded(gr_protein_threshold, 4), Utils.rounded(gr_[i], 4));
                valid1 = false;
            }
        //stats.addValue(gr_i);
        //System.out.printf("g(r)protein @ %f = %f\n", gr[0][i], gr_protein_i);
        }
    }
    addResult(randomModel.getName(), resultColour, valid1, fitSigmaS, fitProteinDensity, 0, 0, 0, 0, ic1);
    return parameters;
}

Example 7 with MultivariateMatrixFunction

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

the class PCPALMFitting method fitClusteredModel.

/**
	 * Fits the correlation curve with r>0 to the clustered model using the estimated density and precision. Parameters
	 * must be fit within a tolerance of the starting values.
	 * 
	 * @param gr
	 * @param sigmaS
	 *            The estimated precision
	 * @param proteinDensity
	 *            The estimated protein density
	 * @return The fitted parameters [precision, density, clusterRadius, clusterDensity]
	 */
private double[] fitClusteredModel(double[][] gr, double sigmaS, double proteinDensity, String resultColour) {
    final ClusteredModelFunctionGradient function = new ClusteredModelFunctionGradient();
    clusteredModel = function;
    log("Fitting %s: Estimated precision = %f nm, estimated protein density = %g um^-2", clusteredModel.getName(), sigmaS, proteinDensity * 1e6);
    clusteredModel.setLogging(true);
    for (int i = offset; i < gr[0].length; i++) {
        // Only fit the curve above the estimated resolution (points below it will be subject to error)
        if (gr[0][i] > sigmaS * fitAboveEstimatedPrecision)
            clusteredModel.addPoint(gr[0][i], gr[1][i]);
    }
    double[] parameters;
    // The model is: sigma, density, range, amplitude
    double[] initialSolution = new double[] { sigmaS, proteinDensity, sigmaS * 5, 1 };
    int evaluations = 0;
    // Constrain the fitting to be close to the estimated precision (sigmaS) and protein density.
    // LVM fitting does not support constrained fitting so use a bounded optimiser.
    SumOfSquaresModelFunction clusteredModelMulti = new SumOfSquaresModelFunction(clusteredModel);
    double[] x = clusteredModelMulti.x;
    // Put some bounds around the initial guess. Use the fitting tolerance (in %) if provided.
    double limit = (fittingTolerance > 0) ? 1 + fittingTolerance / 100 : 2;
    double[] lB = new double[] { initialSolution[0] / limit, initialSolution[1] / limit, 0, 0 };
    // The amplitude and range should not extend beyond the limits of the g(r) curve.
    double[] uB = new double[] { initialSolution[0] * limit, initialSolution[1] * limit, Maths.max(x), Maths.max(gr[1]) };
    log("Fitting %s using a bounded search: %s < precision < %s & %s < density < %s", clusteredModel.getName(), Utils.rounded(lB[0], 4), Utils.rounded(uB[0], 4), Utils.rounded(lB[1] * 1e6, 4), Utils.rounded(uB[1] * 1e6, 4));
    PointValuePair constrainedSolution = runBoundedOptimiser(gr, initialSolution, lB, uB, clusteredModelMulti);
    if (constrainedSolution == null)
        return null;
    parameters = constrainedSolution.getPointRef();
    evaluations = boundedEvaluations;
    // Refit using a LVM  
    if (useLSE) {
        log("Re-fitting %s using a gradient optimisation", clusteredModel.getName());
        LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
        Optimum lvmSolution;
        try {
            //@formatter:off
            LeastSquaresProblem problem = new LeastSquaresBuilder().maxEvaluations(Integer.MAX_VALUE).maxIterations(3000).start(parameters).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
            lvmSolution = optimizer.optimize(problem);
            evaluations += lvmSolution.getEvaluations();
            double ss = lvmSolution.getResiduals().dotProduct(lvmSolution.getResiduals());
            if (ss < constrainedSolution.getValue()) {
                log("Re-fitting %s improved the SS from %s to %s (-%s%%)", clusteredModel.getName(), Utils.rounded(constrainedSolution.getValue(), 4), Utils.rounded(ss, 4), Utils.rounded(100 * (constrainedSolution.getValue() - ss) / constrainedSolution.getValue(), 4));
                parameters = lvmSolution.getPoint().toArray();
            }
        } catch (TooManyIterationsException e) {
            log("Failed to re-fit %s: Too many iterations (%s)", clusteredModel.getName(), e.getMessage());
        } catch (ConvergenceException e) {
            log("Failed to re-fit %s: %s", clusteredModel.getName(), e.getMessage());
        }
    }
    clusteredModel.setLogging(false);
    // Ensure the width is positive
    parameters[0] = Math.abs(parameters[0]);
    //parameters[2] = Math.abs(parameters[2]);
    double ss = 0;
    double[] obs = clusteredModel.getY();
    double[] exp = clusteredModel.value(parameters);
    for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]);
    ic2 = Maths.getAkaikeInformationCriterionFromResiduals(ss, clusteredModel.size(), parameters.length);
    final double fitSigmaS = parameters[0];
    final double fitProteinDensity = parameters[1];
    //The radius of the cluster domain
    final double domainRadius = parameters[2];
    //The density of the cluster domain
    final double domainDensity = parameters[3];
    // This is from the PC-PALM paper. However that paper fits the g(r)protein exponential convolved in 2D
    // with the g(r)PSF. In this method we have just fit the exponential
    final double nCluster = 2 * domainDensity * Math.PI * domainRadius * domainRadius * fitProteinDensity;
    double e1 = parameterDrift(sigmaS, fitSigmaS);
    double e2 = parameterDrift(proteinDensity, fitProteinDensity);
    log("  %s fit: SS = %f. cAIC = %f. %d evaluations", clusteredModel.getName(), ss, ic2, evaluations);
    log("  %s parameters:", clusteredModel.getName());
    log("    Average precision = %s nm (%s%%)", Utils.rounded(fitSigmaS, 4), Utils.rounded(e1, 4));
    log("    Average protein density = %s um^-2 (%s%%)", Utils.rounded(fitProteinDensity * 1e6, 4), Utils.rounded(e2, 4));
    log("    Domain radius = %s nm", Utils.rounded(domainRadius, 4));
    log("    Domain density = %s", Utils.rounded(domainDensity, 4));
    log("    nCluster = %s", Utils.rounded(nCluster, 4));
    // Check the fitted parameters are within tolerance of the initial estimates
    valid2 = true;
    if (fittingTolerance > 0 && (Math.abs(e1) > fittingTolerance || Math.abs(e2) > fittingTolerance)) {
        log("  Failed to fit %s within tolerance (%s%%): Average precision = %f nm (%s%%), average protein density = %g um^-2 (%s%%)", clusteredModel.getName(), Utils.rounded(fittingTolerance, 4), fitSigmaS, Utils.rounded(e1, 4), fitProteinDensity * 1e6, Utils.rounded(e2, 4));
        valid2 = false;
    }
    // Check extra parameters. Domain radius should be higher than the precision. Density should be positive
    if (domainRadius < fitSigmaS) {
        log("  Failed to fit %s: Domain radius is smaller than the average precision (%s < %s)", clusteredModel.getName(), Utils.rounded(domainRadius, 4), Utils.rounded(fitSigmaS, 4));
        valid2 = false;
    }
    if (domainDensity < 0) {
        log("  Failed to fit %s: Domain density is negative (%s)", clusteredModel.getName(), Utils.rounded(domainDensity, 4));
        valid2 = false;
    }
    if (ic2 > ic1) {
        log("  Failed to fit %s - Information Criterion has increased %s%%", clusteredModel.getName(), Utils.rounded((100 * (ic2 - ic1) / ic1), 4));
        valid2 = false;
    }
    addResult(clusteredModel.getName(), resultColour, valid2, fitSigmaS, fitProteinDensity, domainRadius, domainDensity, nCluster, 0, ic2);
    return parameters;
}

Example 8 with MultivariateMatrixFunction

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

the class PCPALMMolecules method optimiseLeastSquares.

private double[] optimiseLeastSquares(float[] x, float[] y, double[] initialSolution) {
    // Least-squares optimisation using numerical gradients
    final SkewNormalDifferentiableFunction function = new SkewNormalDifferentiableFunction(initialSolution);
    function.addData(x, y);
    LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer();
    //@formatter:off
    LeastSquaresProblem problem = new LeastSquaresBuilder().maxEvaluations(Integer.MAX_VALUE).maxIterations(3000).start(initialSolution).target(function.calculateTarget()).weight(new DiagonalMatrix(function.calculateWeights())).model(function, new MultivariateMatrixFunction() {

        public double[][] value(double[] point) throws IllegalArgumentException {
            return function.jacobian(point);
        }
    }).build();
    //@formatter:on
    Optimum optimum = optimizer.optimize(problem);
    double[] skewParameters = optimum.getPoint().toArray();
    return skewParameters;
}