uk.ac.sussex.gdsc.smlm.fitting.nonlinear.gradient.MleLvmGradientProcedure Maven / Gradle / Ivy

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Genome Damage and Stability Centre SMLM Package Software for single molecule localisation microscopy (SMLM)
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/*-
 * #%L
 * Genome Damage and Stability Centre SMLM Package
 *
 * Software for single molecule localisation microscopy (SMLM)
 * %%
 * Copyright (C) 2011 - 2023 Alex Herbert
 * %%
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as
 * published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public
 * License along with this program.  If not, see
 * .
 * #L%
 */

package uk.ac.sussex.gdsc.smlm.fitting.nonlinear.gradient;

import uk.ac.sussex.gdsc.smlm.function.Gradient1Function;

/**
 * Calculates the scaled Hessian matrix (the square matrix of second-order partial derivatives of a
 * function) and the scaled gradient vector of the function's partial first derivatives with respect
 * to the parameters. This is used within the Levenberg-Marquardt method to fit a nonlinear model
 * with coefficients (a) for a set of data points (x, y).
 *
 * This procedure computes a modified Chi-squared expression to perform Maximum Likelihood
 * Estimation assuming Poisson model. See Laurence & Chromy (2010) Efficient maximum likelihood
 * estimator. Nature Methods 7, 338-339. The input data must be Poisson distributed for this to be
 * relevant.
 */
public class MleLvmGradientProcedure extends LsqLvmGradientProcedure {

  /**
   * Instantiates a new procedure.
   *
   * @param y Data to fit (must be positive)
   * @param func Gradient function
   */
  public MleLvmGradientProcedure(final double[] y, final Gradient1Function func) {
    super(y, func);
    // We could check that y is positive ...
  }

  @Override
  public void execute(double fi, double[] dfiDa) {
    ++yi;
    // Function must produce a strictly positive output.
    // ---
    // The code provided in Laurence & Chromy (2010) Nature Methods 7, 338-339, SI
    // effectively ignores any function value below zero. This could lead to a
    // situation where the best chisq value can be achieved by setting the output
    // function to produce 0 for all evaluations.
    // Optimally the function should be bounded to always produce a positive number.
    // ---
    if (fi > 0) {
      final double xi = y[yi];

      // We assume y[i] is positive but must handle zero
      if (xi > 0) {
        value += (fi - xi - xi * Math.log(fi / xi));
        final double xi_fi2 = xi / fi / fi;
        final double e = 1 - (xi / fi);
        for (int k = 0, i = 0; k < numberOfGradients; k++) {
          beta[k] -= e * dfiDa[k];
          final double wgt = dfiDa[k] * xi_fi2;
          for (int l = 0; l <= k; l++) {
            alpha[i++] += wgt * dfiDa[l];
          }
        }
      } else {
        value += fi;
        for (int k = 0; k < numberOfGradients; k++) {
          beta[k] -= dfiDa[k];
        }
      }
    }
  }

  @Override
  public void execute(double fi) {
    ++yi;
    // Function must produce a strictly positive output.
    if (fi > 0) {
      final double xi = y[yi];

      // We assume y[i] is positive but must handle zero
      if (xi > 0) {
        value += (fi - xi - xi * Math.log(fi / xi));
      } else {
        value += fi;
      }
    }
  }

  @Override
  protected void finishGradient() {
    // Move the factor of 2 to the end
    value *= 2;
  }

  @Override
  protected void finishValue() {
    // Move the factor of 2 to the end
    value *= 2;
  }
}