package gdsc.smlm.fitting.nonlinear.gradient;
import gdsc.smlm.function.NonLinearFunction;
/*-----------------------------------------------------------------------------
* GDSC SMLM Software
*
* Copyright (C) 2016 Alex Herbert
* Genome Damage and Stability Centre
* University of Sussex, UK
*
* 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.
*---------------------------------------------------------------------------*/
/**
* Calculates the Hessian matrix (the square matrix of second-order partial derivatives of a function)
* and the 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).
* <p>
* This calculator 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 MLEGradientCalculator6 extends MLEGradientCalculator
{
/**
* Instantiates a new MLE gradient calculator.
*/
public MLEGradientCalculator6()
{
super(6);
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.fitting.nonlinear.gradient.MLEGradientCalculator#zero(double[][], double[])
*/
@Override
protected void zero(final double[][] alpha, final double[] beta)
{
alpha[0][0] = 0;
alpha[1][0] = 0;
alpha[1][1] = 0;
alpha[2][0] = 0;
alpha[2][1] = 0;
alpha[2][2] = 0;
alpha[3][0] = 0;
alpha[3][1] = 0;
alpha[3][2] = 0;
alpha[3][3] = 0;
alpha[4][0] = 0;
alpha[4][1] = 0;
alpha[4][2] = 0;
alpha[4][3] = 0;
alpha[4][4] = 0;
alpha[5][0] = 0;
alpha[5][1] = 0;
alpha[5][2] = 0;
alpha[5][3] = 0;
alpha[5][4] = 0;
alpha[5][5] = 0;
beta[0] = 0;
beta[1] = 0;
beta[2] = 0;
beta[3] = 0;
beta[4] = 0;
beta[5] = 0;
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.fitting.nonlinear.gradient.MLEGradientCalculator#compute(double[][], double[], double[], double,
* double)
*/
@Override
protected void compute(final double[][] alpha, final double[] beta, final double[] dfi_da, final double fi,
final double xi)
{
final double xi_fi = xi / fi;
final double xi_fi2 = xi_fi / fi;
final double e = 1 - (xi_fi);
alpha[0][0] += dfi_da[0] * xi_fi2 * dfi_da[0];
double w;
w = dfi_da[1] * xi_fi2;
alpha[1][0] += w * dfi_da[0];
alpha[1][1] += w * dfi_da[1];
w = dfi_da[2] * xi_fi2;
alpha[2][0] += w * dfi_da[0];
alpha[2][1] += w * dfi_da[1];
alpha[2][2] += w * dfi_da[2];
w = dfi_da[3] * xi_fi2;
alpha[3][0] += w * dfi_da[0];
alpha[3][1] += w * dfi_da[1];
alpha[3][2] += w * dfi_da[2];
alpha[3][3] += w * dfi_da[3];
w = dfi_da[4] * xi_fi2;
alpha[4][0] += w * dfi_da[0];
alpha[4][1] += w * dfi_da[1];
alpha[4][2] += w * dfi_da[2];
alpha[4][3] += w * dfi_da[3];
alpha[4][4] += w * dfi_da[4];
w = dfi_da[5] * xi_fi2;
alpha[5][0] += w * dfi_da[0];
alpha[5][1] += w * dfi_da[1];
alpha[5][2] += w * dfi_da[2];
alpha[5][3] += w * dfi_da[3];
alpha[5][4] += w * dfi_da[4];
alpha[5][5] += w * dfi_da[5];
beta[0] -= e * dfi_da[0];
beta[1] -= e * dfi_da[1];
beta[2] -= e * dfi_da[2];
beta[3] -= e * dfi_da[3];
beta[4] -= e * dfi_da[4];
beta[5] -= e * dfi_da[5];
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.fitting.nonlinear.gradient.MLEGradientCalculator#symmetric(double[][])
*/
@Override
protected void symmetric(final double[][] alpha)
{
alpha[0][1] = alpha[1][0];
alpha[0][2] = alpha[2][0];
alpha[0][3] = alpha[3][0];
alpha[0][4] = alpha[4][0];
alpha[0][5] = alpha[5][0];
alpha[1][2] = alpha[2][1];
alpha[1][3] = alpha[3][1];
alpha[1][4] = alpha[4][1];
alpha[1][5] = alpha[5][1];
alpha[2][3] = alpha[3][2];
alpha[2][4] = alpha[4][2];
alpha[2][5] = alpha[5][2];
alpha[3][4] = alpha[4][3];
alpha[3][5] = alpha[5][3];
alpha[4][5] = alpha[5][4];
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.fitting.nonlinear.gradient.GradientCalculator#fisherInformationDiagonal(int, double[],
* gdsc.smlm.function.NonLinearFunction)
*/
@Override
public double[] fisherInformationDiagonal(final int n, final double[] a, final NonLinearFunction func)
{
final double[] dy_da = new double[a.length];
final double[] alpha = new double[nparams];
func.initialise(a);
for (int i = 0; i < n; i++)
{
final double yi = 1.0 / func.eval(i, dy_da);
alpha[0] += dy_da[0] * dy_da[0] * yi;
alpha[1] += dy_da[1] * dy_da[1] * yi;
alpha[2] += dy_da[2] * dy_da[2] * yi;
alpha[3] += dy_da[3] * dy_da[3] * yi;
alpha[4] += dy_da[4] * dy_da[4] * yi;
alpha[5] += dy_da[5] * dy_da[5] * yi;
}
checkGradients(alpha, nparams);
return alpha;
}
}