List of usage examples for org.apache.commons.math3.optim PointVectorValuePair getValue
@Override public double[] getValue()
From source file:gdsc.smlm.ij.plugins.BlinkEstimator.java
/** * Fit the dark time to counts of molecules curve. Only use the first n fitted points. * <p>//w ww . j ava 2 s.c om * Calculates:<br/> * N = The number of photoblinking molecules in the sample<br/> * nBlink = The average number of blinks per flourophore<br/> * tOff = The off-time * * @param td * The dark time * @param ntd * The counts of molecules * @param nFittedPoints * @param log * Write the fitting results to the ImageJ log window * @return The fitted parameters [N, nBlink, tOff], or null if no fit was possible */ public double[] fit(double[] td, double[] ntd, int nFittedPoints, boolean log) { blinkingModel = new BlinkingFunction(); blinkingModel.setLogging(true); for (int i = 0; i < nFittedPoints; i++) blinkingModel.addPoint(td[i], ntd[i]); // Different convergence thresholds seem to have no effect on the resulting fit, only the number of // iterations for convergence double initialStepBoundFactor = 100; double costRelativeTolerance = 1e-6; double parRelativeTolerance = 1e-6; double orthoTolerance = 1e-6; double threshold = Precision.SAFE_MIN; LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(initialStepBoundFactor, costRelativeTolerance, parRelativeTolerance, orthoTolerance, threshold); try { double[] obs = blinkingModel.getY(); PointVectorValuePair optimum = optimizer.optimize(new MaxIter(1000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return blinkingModel.jacobian(point); } }), new ModelFunction(blinkingModel), new Target(obs), new Weight(blinkingModel.getWeights()), new InitialGuess(new double[] { ntd[0], 0.1, td[1] })); blinkingModel.setLogging(false); double[] parameters = optimum.getPoint(); double[] exp = optimum.getValue(); double mean = 0; for (double d : obs) mean += d; mean /= obs.length; double ssResiduals = 0, ssTotal = 0; for (int i = 0; i < obs.length; i++) { ssResiduals += (obs[i] - exp[i]) * (obs[i] - exp[i]); ssTotal += (obs[i] - mean) * (obs[i] - mean); } r2 = 1 - ssResiduals / ssTotal; adjustedR2 = getAdjustedCoefficientOfDetermination(ssResiduals, ssTotal, obs.length, parameters.length); if (log) { Utils.log(" Fit %d points. R^2 = %s. Adjusted R^2 = %s", obs.length, Utils.rounded(r2, 4), Utils.rounded(adjustedR2, 4)); Utils.log(" N=%s, nBlink=%s, tOff=%s (%s frames)", Utils.rounded(parameters[0], 4), Utils.rounded(parameters[1], 4), Utils.rounded(parameters[2], 4), Utils.rounded(parameters[2] / msPerFrame, 4)); } return parameters; } catch (TooManyIterationsException e) { if (log) Utils.log(" Failed to fit %d points: Too many iterations (%d)", blinkingModel.size(), optimizer.getIterations()); return null; } catch (ConvergenceException e) { if (log) Utils.log(" Failed to fit %d points", blinkingModel.size()); return null; } }
From source file:gdsc.smlm.fitting.BinomialFitter.java
/** * Fit the binomial distribution (n,p) to the cumulative histogram. Performs fitting assuming a fixed n value and * attempts to optimise p.//from w w w. j a v a 2s. c om * * @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 stopFitness = 0; //Double.NEGATIVE_INFINITY; 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)); //System.out.printf("CMAES Iter %d initial = %g (%d)\n", iteration, result.getValue(), // 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)); //System.out.printf("CMAES Iter %d restart = %g (%d)\n", iteration, result.getValue(), // 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); } // We can do a LVM refit if the number of fitted points is more than 1 else 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); PointVectorValuePair lvmSolution = optimizer.optimize(new MaxIter(3000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return gradientFunction.jacobian(point); } }), new ModelFunction(gradientFunction), new Target(gradientFunction.p), new Weight(gradientFunction.getWeights()), new InitialGuess(solution.getPointRef())); double ss = 0; double[] obs = gradientFunction.p; double[] exp = lvmSolution.getValue(); for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]); // Check the pValue is valid since the LVM is not bounded. double p = lvmSolution.getPointRef()[0]; if (ss < solution.getValue() && p <= 1 && p >= 0) { //log("Re-fitting improved the SS from %s to %s (-%s%%)", // Utils.rounded(solution.getValue(), 4), Utils.rounded(ss, 4), // Utils.rounded(100 * (solution.getValue() - ss) / solution.getValue(), 4)); return new PointValuePair(lvmSolution.getPoint(), ss); } } catch (TooManyIterationsException e) { log("Failed to re-fit: Too many iterations (%d)", optimizer.getIterations()); } 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; }
From source file:gdsc.smlm.ij.plugins.TraceDiffusion.java
/** * Fit the MSD using a linear fit that must pass through 0,0. * <p>//from w ww.j a v a 2 s .co m * Update the plot by adding the fit line. * * @param x * @param y * @param title * @param plot * @return */ private double fitMSD(double[] x, double[] y, String title, Plot2 plot) { double D = 0; LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); PointVectorValuePair lvmSolution; try { final LinearFunction function = new LinearFunction(x, y, settings.fitLength); double[] parameters = new double[] { function.guess() }; lvmSolution = optimizer.optimize(new MaxIter(3000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return function.jacobian(point); } }), new ModelFunction(function), new Target(function.getY()), new Weight(function.getWeights()), new InitialGuess(parameters)); double ss = 0; double[] obs = function.getY(); double[] exp = lvmSolution.getValue(); for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]); D = lvmSolution.getPoint()[0] / 4; Utils.log("Linear fit (%d points) : Gradient = %s, D = %s um^2/s, SS = %f (%d evaluations)", obs.length, Utils.rounded(lvmSolution.getPoint()[0], 4), Utils.rounded(D, 4), ss, optimizer.getEvaluations()); // Add the fit to the plot plot.setColor(Color.magenta); plot.drawLine(0, 0, x[x.length - 1], x[x.length - 1] * 4 * D); display(title, plot); } catch (TooManyIterationsException e) { Utils.log("Failed to fit : Too many iterations (%d)", optimizer.getIterations()); } catch (ConvergenceException e) { Utils.log("Failed to fit : %s", e.getMessage()); } return D; }
From source file:gdsc.smlm.ij.plugins.pcpalm.PCPALMFitting.java
/** * 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. * /*from w w w .java2 s . c o m*/ * @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 myFunction = new ClusteredModelFunctionGradient(); clusteredModel = myFunction; 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(); PointVectorValuePair lvmSolution; try { lvmSolution = optimizer.optimize(new MaxIter(3000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return myFunction.jacobian(point); } }), new ModelFunction(myFunction), new Target(myFunction.getY()), new Weight(myFunction.getWeights()), new InitialGuess(parameters)); evaluations += optimizer.getEvaluations(); double ss = 0; double[] obs = clusteredModel.getY(); double[] exp = lvmSolution.getValue(); for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]); 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(); } } catch (TooManyIterationsException e) { log("Failed to re-fit %s: Too many iterations (%d)", clusteredModel.getName(), optimizer.getIterations()); } 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.getInformationCriterion(ss, clusteredModel.size(), parameters.length); final double fitSigmaS = parameters[0]; final double fitProteinDensity = parameters[1]; final double domainRadius = parameters[2]; //The radius of the cluster domain final double domainDensity = parameters[3]; //The density of the cluster domain // 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; }
From source file:gdsc.smlm.ij.plugins.pcpalm.PCPALMFitting.java
/** * 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. * /*w w w .j av a 2 s . co m*/ * @param gr * @param sigmaS * The estimated precision * @param proteinDensity * The estimated protein density * @return The fitted parameters [precision, density, clusterRadius, clusterDensity] */ private double[] fitEmulsionModel(double[][] gr, double sigmaS, double proteinDensity, String resultColour) { final EmulsionModelFunctionGradient myFunction = new EmulsionModelFunctionGradient(); emulsionModel = myFunction; log("Fitting %s: Estimated precision = %f nm, estimated protein density = %g um^-2", emulsionModel.getName(), sigmaS, proteinDensity * 1e6); emulsionModel.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) emulsionModel.addPoint(gr[0][i], gr[1][i]); } double[] parameters; // The model is: sigma, density, range, amplitude, alpha double[] initialSolution = new double[] { sigmaS, proteinDensity, sigmaS * 5, 1, sigmaS * 5 }; 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 emulsionModelMulti = new SumOfSquaresModelFunction(emulsionModel); double[] x = emulsionModelMulti.x; double[] y = emulsionModelMulti.y; // Range should be equal to the first time the g(r) curve crosses 1 for (int i = 0; i < x.length; i++) if (y[i] < 1) { initialSolution[4] = initialSolution[2] = (i > 0) ? (x[i - 1] + x[i]) * 0.5 : x[i]; break; } // 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, 0 }; // The amplitude and range should not extend beyond the limits of the g(r) curve. // TODO - Find out the expected range for the alpha parameter. double[] uB = new double[] { initialSolution[0] * limit, initialSolution[1] * limit, Maths.max(x), Maths.max(gr[1]), Maths.max(x) * 2 }; log("Fitting %s using a bounded search: %s < precision < %s & %s < density < %s", emulsionModel.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, emulsionModelMulti); if (constrainedSolution == null) return null; parameters = constrainedSolution.getPointRef(); evaluations = boundedEvaluations; // Refit using a LVM if (useLSE) { log("Re-fitting %s using a gradient optimisation", emulsionModel.getName()); LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); PointVectorValuePair lvmSolution; try { lvmSolution = optimizer.optimize(new MaxIter(3000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return myFunction.jacobian(point); } }), new ModelFunction(myFunction), new Target(myFunction.getY()), new Weight(myFunction.getWeights()), new InitialGuess(parameters)); evaluations += optimizer.getEvaluations(); double ss = 0; double[] obs = emulsionModel.getY(); double[] exp = lvmSolution.getValue(); for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]); if (ss < constrainedSolution.getValue()) { log("Re-fitting %s improved the SS from %s to %s (-%s%%)", emulsionModel.getName(), Utils.rounded(constrainedSolution.getValue(), 4), Utils.rounded(ss, 4), Utils.rounded( 100 * (constrainedSolution.getValue() - ss) / constrainedSolution.getValue(), 4)); parameters = lvmSolution.getPoint(); } } catch (TooManyIterationsException e) { log("Failed to re-fit %s: Too many iterations (%d)", emulsionModel.getName(), optimizer.getIterations()); } catch (ConvergenceException e) { log("Failed to re-fit %s: %s", emulsionModel.getName(), e.getMessage()); } } emulsionModel.setLogging(false); // Ensure the width is positive parameters[0] = Math.abs(parameters[0]); //parameters[2] = Math.abs(parameters[2]); double ss = 0; double[] obs = emulsionModel.getY(); double[] exp = emulsionModel.value(parameters); for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]); ic3 = Maths.getInformationCriterion(ss, emulsionModel.size(), parameters.length); final double fitSigmaS = parameters[0]; final double fitProteinDensity = parameters[1]; final double domainRadius = parameters[2]; //The radius of the cluster domain final double domainDensity = parameters[3]; //The density of the cluster domain final double coherence = parameters[4]; //The coherence length between circles // This is from the PC-PALM paper. It may not be correct for the emulsion model. 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", emulsionModel.getName(), ss, ic3, evaluations); log(" %s parameters:", emulsionModel.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(" Domain coherence = %s", Utils.rounded(coherence, 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%%)", emulsionModel.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)", emulsionModel.getName(), Utils.rounded(domainRadius, 4), Utils.rounded(fitSigmaS, 4)); valid2 = false; } if (domainDensity < 0) { log(" Failed to fit %s: Domain density is negative (%s)", emulsionModel.getName(), Utils.rounded(domainDensity, 4)); valid2 = false; } if (ic3 > ic1) { log(" Failed to fit %s - Information Criterion has increased %s%%", emulsionModel.getName(), Utils.rounded((100 * (ic3 - ic1) / ic1), 4)); valid2 = false; } addResult(emulsionModel.getName(), resultColour, valid2, fitSigmaS, fitProteinDensity, domainRadius, domainDensity, nCluster, coherence, ic3); return parameters; }
From source file:gdsc.smlm.ij.plugins.pcpalm.PCPALMFitting.java
/** * 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. * //w w w .ja va 2 s .c o m * @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 myFunction = new RandomModelFunction(); randomModel = myFunction; 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(); PointVectorValuePair optimum; try { optimum = optimizer.optimize(new MaxIter(3000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return myFunction.jacobian(point); } }), new ModelFunction(myFunction), new Target(myFunction.getY()), new Weight(myFunction.getWeights()), new InitialGuess(new double[] { sigmaS, proteinDensity })); } catch (TooManyIterationsException e) { log("Failed to fit %s: Too many iterations (%d)", randomModel.getName(), optimizer.getIterations()); return null; } catch (ConvergenceException e) { log("Failed to fit %s: %s", randomModel.getName(), e.getMessage()); return null; } randomModel.setLogging(false); double[] parameters = optimum.getPoint(); // Ensure the width is positive parameters[0] = Math.abs(parameters[0]); double ss = 0; double[] obs = randomModel.getY(); double[] exp = optimum.getValue(); for (int i = 0; i < obs.length; i++) ss += (obs[i] - exp[i]) * (obs[i] - exp[i]); ic1 = Maths.getInformationCriterion(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, optimizer.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; }
From source file:gdsc.smlm.ij.plugins.TraceDiffusion.java
/** * Fit the jump distance histogram using a cumulative sum as detailed in * <p>//from w w w . j a v a2 s. c o m * Update the plot by adding the fit line. * * @param jumpDistances * @param jdHistogram * @param title * @param plot * @return */ private double[][] fitJumpDistance(StoredDataStatistics jumpDistances, double[][] jdHistogram, String title, Plot2 plot) { final double meanDistance = Math.sqrt(jumpDistances.getMean()) * 1e3; final double beta = meanDistance / precision; Utils.log( "Jump Distance analysis : N = %d, Time = %d frames (%s seconds). Mean Distance = %s nm, Precision = %s nm, Beta = %s", jumpDistances.getN(), settings.jumpDistance, Utils.rounded(settings.jumpDistance * exposureTime, 4), Utils.rounded(meanDistance, 4), Utils.rounded(precision, 4), Utils.rounded(beta, 4)); int n = 0; int N = 10; double[] SS = new double[N]; Arrays.fill(SS, -1); double[] ic = new double[N]; Arrays.fill(ic, Double.POSITIVE_INFINITY); double[][] coefficients = new double[N][]; double[][] fractions = new double[N][]; double[][] fitParams = new double[N][]; double bestIC = Double.POSITIVE_INFINITY; int best = -1; // Guess the D final double estimatedD = jumpDistances.getMean() / 4; Utils.log("Estimated D = %s um^2/s", Utils.rounded(estimatedD, 4)); // Fit using a single population model LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer(); try { final JumpDistanceFunction function = new JumpDistanceFunction(jdHistogram[0], jdHistogram[1], estimatedD); PointVectorValuePair lvmSolution = optimizer.optimize(new MaxIter(3000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return function.jacobian(point); } }), new ModelFunction(function), new Target(function.getY()), new Weight(function.getWeights()), new InitialGuess(function.guess())); fitParams[n] = lvmSolution.getPointRef(); SS[n] = calculateSumOfSquares(function.getY(), lvmSolution.getValueRef()); ic[n] = Maths.getInformationCriterion(SS[n], function.x.length, 1); coefficients[n] = fitParams[n]; fractions[n] = new double[] { 1 }; Utils.log("Fit Jump distance (N=%d) : D = %s um^2/s, SS = %f, IC = %s (%d evaluations)", n + 1, Utils.rounded(fitParams[n][0], 4), SS[n], Utils.rounded(ic[n], 4), optimizer.getEvaluations()); bestIC = ic[n]; best = 0; addToPlot(function, fitParams[n], jdHistogram, title, plot, Color.magenta); } catch (TooManyIterationsException e) { Utils.log("Failed to fit : Too many iterations (%d)", optimizer.getIterations()); } catch (ConvergenceException e) { Utils.log("Failed to fit : %s", e.getMessage()); } n++; // Fit using a mixed population model. // Vary n from 2 to N. Stop when the fit fails or the fit is worse. int bestMulti = -1; double bestMultiIC = Double.POSITIVE_INFINITY; while (n < N) { // 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 CMEASOptimizer which supports bounded fitting. MixedJumpDistanceFunctionMultivariate mixedFunction = new MixedJumpDistanceFunctionMultivariate( jdHistogram[0], jdHistogram[1], estimatedD, n + 1); double[] lB = mixedFunction.getLowerBounds(); double[] uB = mixedFunction.getUpperBounds(); SimpleBounds bounds = new SimpleBounds(lB, uB); int maxIterations = 2000; double stopFitness = 0; //Double.NEGATIVE_INFINITY; boolean isActiveCMA = true; int diagonalOnly = 20; 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. 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(mixedFunction.x.length)))); // Iterate this for stability in the initial guess CMAESOptimizer opt = new CMAESOptimizer(maxIterations, stopFitness, isActiveCMA, diagonalOnly, checkFeasableCount, random, generateStatistics, checker); int evaluations = 0; PointValuePair constrainedSolution = null; for (int i = 0; i <= settings.fitRestarts; i++) { // Try from the initial guess try { PointValuePair solution = opt.optimize(new InitialGuess(mixedFunction.guess()), new ObjectiveFunction(mixedFunction), GoalType.MINIMIZE, bounds, sigma, popSize, new MaxIter(maxIterations), new MaxEval(maxIterations * 2)); if (constrainedSolution == null || solution.getValue() < constrainedSolution.getValue()) { evaluations = opt.getEvaluations(); constrainedSolution = solution; //Utils.log("[%da] Fit Jump distance (N=%d) : SS = %f (%d evaluations)", i, n + 1, // solution.getValue(), evaluations); } } catch (TooManyEvaluationsException e) { } if (constrainedSolution == null) continue; // Try from the current optimum try { PointValuePair solution = opt.optimize(new InitialGuess(constrainedSolution.getPointRef()), new ObjectiveFunction(mixedFunction), GoalType.MINIMIZE, bounds, sigma, popSize, new MaxIter(maxIterations), new MaxEval(maxIterations * 2)); if (constrainedSolution == null || solution.getValue() < constrainedSolution.getValue()) { evaluations = opt.getEvaluations(); constrainedSolution = solution; //Utils.log("[%db] Fit Jump distance (N=%d) : SS = %f (%d evaluations)", i, n + 1, // solution.getValue(), evaluations); } } catch (TooManyEvaluationsException e) { } } if (constrainedSolution == null) { Utils.log("Failed to fit N=%d", n + 1); break; } fitParams[n] = constrainedSolution.getPointRef(); SS[n] = constrainedSolution.getValue(); // TODO - Try a bounded BFGS optimiser // Try and improve using a LVM fit final MixedJumpDistanceFunctionGradient mixedFunctionGradient = new MixedJumpDistanceFunctionGradient( jdHistogram[0], jdHistogram[1], estimatedD, n + 1); PointVectorValuePair lvmSolution; try { lvmSolution = optimizer.optimize(new MaxIter(3000), new MaxEval(Integer.MAX_VALUE), new ModelFunctionJacobian(new MultivariateMatrixFunction() { public double[][] value(double[] point) throws IllegalArgumentException { return mixedFunctionGradient.jacobian(point); } }), new ModelFunction(mixedFunctionGradient), new Target(mixedFunctionGradient.getY()), new Weight(mixedFunctionGradient.getWeights()), new InitialGuess(fitParams[n])); double ss = calculateSumOfSquares(mixedFunctionGradient.getY(), lvmSolution.getValue()); // All fitted parameters must be above zero if (ss < SS[n] && Maths.min(lvmSolution.getPoint()) > 0) { //Utils.log(" Re-fitting improved the SS from %s to %s (-%s%%)", Utils.rounded(SS[n], 4), // Utils.rounded(ss, 4), Utils.rounded(100 * (SS[n] - ss) / SS[n], 4)); fitParams[n] = lvmSolution.getPoint(); SS[n] = ss; evaluations += optimizer.getEvaluations(); } } catch (TooManyIterationsException e) { //Utils.log("Failed to re-fit : Too many evaluations (%d)", optimizer.getEvaluations()); } catch (ConvergenceException e) { //Utils.log("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[n] = Maths.getInformationCriterion(SS[n], mixedFunction.x.length, fitParams[n].length - 1); double[] d = new double[n + 1]; double[] f = new double[n + 1]; double sum = 0; for (int i = 0; i < d.length; i++) { f[i] = fitParams[n][i * 2]; sum += f[i]; d[i] = fitParams[n][i * 2 + 1]; } for (int i = 0; i < f.length; i++) f[i] /= sum; // Sort by coefficient size sort(d, f); coefficients[n] = d; fractions[n] = f; Utils.log("Fit Jump distance (N=%d) : D = %s um^2/s (%s), SS = %f, IC = %s (%d evaluations)", n + 1, format(d), format(f), SS[n], Utils.rounded(ic[n], 4), evaluations); boolean valid = true; for (int i = 0; i < f.length; i++) { // Check the fit has fractions above the minimum fraction if (f[i] < minFraction) { Utils.log("Fraction is less than the minimum fraction: %s < %s", Utils.rounded(f[i]), Utils.rounded(minFraction)); valid = false; break; } // Check the coefficients are different if (i + 1 < f.length && d[i] / d[i + 1] < minDifference) { Utils.log("Coefficients are not different: %s / %s = %s < %s", Utils.rounded(d[i]), Utils.rounded(d[i + 1]), Utils.rounded(d[i] / d[i + 1]), Utils.rounded(minDifference)); valid = false; break; } } if (!valid) break; // Store the best model if (bestIC > ic[n]) { bestIC = ic[n]; best = n; } // Store the best multi model if (bestMultiIC < ic[n]) { break; } bestMultiIC = ic[n]; bestMulti = n; n++; } // Add the best fit to the plot and return the parameters. if (bestMulti > -1) { Function function = new MixedJumpDistanceFunctionMultivariate(jdHistogram[0], jdHistogram[1], 0, bestMulti + 1); addToPlot(function, fitParams[bestMulti], jdHistogram, title, plot, Color.yellow); } if (best > -1) { Utils.log("Best fit achieved using %d population%s: D = %s um^2/s, Fractions = %s", best + 1, (best == 0) ? "" : "s", format(coefficients[best]), format(fractions[best])); } return (best > -1) ? new double[][] { coefficients[best], fractions[best] } : null; }