package gdsc.smlm.fitting.nonlinear.gradient;
import gdsc.smlm.function.NonLinearFunction;
/*-----------------------------------------------------------------------------
* GDSC SMLM Software
*
* Copyright (C) 2013 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).
*/
public class GradientCalculator3 extends GradientCalculator
{
public GradientCalculator3()
{
super(3);
}
/*
* (non-Javadoc)
*
* @see gdsc.fitting.model.GradientCalculator#findLinearised(int[], double[] double[], double[][], double[],
* gdsc.fitting.function.NonLinearFunction)
*/
public double findLinearised(int[] x, double[] y, double[] a, double[][] alpha, double[] beta,
NonLinearFunction func)
{
double ssx = 0;
final double[] dy_da = new double[3];
alpha[0][0] = 0;
alpha[1][0] = 0;
alpha[1][1] = 0;
alpha[2][0] = 0;
alpha[2][1] = 0;
alpha[2][2] = 0;
beta[0] = 0;
beta[1] = 0;
beta[2] = 0;
func.initialise(a);
if (func.canComputeWeights())
{
double[] w = new double[1];
for (int i = 0; i < x.length; i++)
{
final double dy = y[i] - func.eval(x[i], dy_da, w);
final double weight = getWeight(w[0]);
alpha[0][0] += dy_da[0] * weight * dy_da[0];
alpha[1][0] += dy_da[1] * weight * dy_da[0];
alpha[1][1] += dy_da[1] * weight * dy_da[1];
alpha[2][0] += dy_da[2] * weight * dy_da[0];
alpha[2][1] += dy_da[2] * weight * dy_da[1];
alpha[2][2] += dy_da[2] * weight * dy_da[2];
beta[0] += dy_da[0] * weight * dy;
beta[1] += dy_da[1] * weight * dy;
beta[2] += dy_da[2] * weight * dy;
ssx += dy * dy * weight;
}
}
else
{
for (int i = 0; i < x.length; i++)
{
double dy = y[i] - func.eval(x[i], dy_da);
alpha[0][0] += dy_da[0] * dy_da[0];
alpha[1][0] += dy_da[1] * dy_da[0];
alpha[1][1] += dy_da[1] * dy_da[1];
alpha[2][0] += dy_da[2] * dy_da[0];
alpha[2][1] += dy_da[2] * dy_da[1];
alpha[2][2] += dy_da[2] * dy_da[2];
beta[0] += dy_da[0] * dy;
beta[1] += dy_da[1] * dy;
beta[2] += dy_da[2] * dy;
ssx += dy * dy;
}
}
// Generate symmetric matrix
alpha[0][1] = alpha[1][0];
alpha[0][2] = alpha[2][0];
alpha[1][2] = alpha[2][1];
return checkGradients(alpha, beta, nparams, ssx);
}
/*
* (non-Javadoc)
*
* @see gdsc.fitting.nonlinear.gradient.GradientCalculator#findLinearised(int, double[] double[], double[][],
* double[], gdsc.fitting.function.NonLinearFunction)
*/
public double findLinearised(int n, double[] y, double[] a, double[][] alpha, double[] beta, NonLinearFunction func)
{
double ssx = 0;
final double[] dy_da = new double[3];
alpha[0][0] = 0;
alpha[1][0] = 0;
alpha[1][1] = 0;
alpha[2][0] = 0;
alpha[2][1] = 0;
alpha[2][2] = 0;
beta[0] = 0;
beta[1] = 0;
beta[2] = 0;
func.initialise(a);
if (func.canComputeWeights())
{
double[] w = new double[1];
for (int i = 0; i < n; i++)
{
final double dy = y[i] - func.eval(i, dy_da, w);
final double weight = getWeight(w[0]);
alpha[0][0] += dy_da[0] * weight * dy_da[0];
alpha[1][0] += dy_da[1] * weight * dy_da[0];
alpha[1][1] += dy_da[1] * weight * dy_da[1];
alpha[2][0] += dy_da[2] * weight * dy_da[0];
alpha[2][1] += dy_da[2] * weight * dy_da[1];
alpha[2][2] += dy_da[2] * weight * dy_da[2];
beta[0] += dy_da[0] * weight * dy;
beta[1] += dy_da[1] * weight * dy;
beta[2] += dy_da[2] * weight * dy;
ssx += dy * dy * weight;
}
}
else
{
for (int i = 0; i < n; i++)
{
double dy = y[i] - func.eval(i, dy_da);
alpha[0][0] += dy_da[0] * dy_da[0];
alpha[1][0] += dy_da[1] * dy_da[0];
alpha[1][1] += dy_da[1] * dy_da[1];
alpha[2][0] += dy_da[2] * dy_da[0];
alpha[2][1] += dy_da[2] * dy_da[1];
alpha[2][2] += dy_da[2] * dy_da[2];
beta[0] += dy_da[0] * dy;
beta[1] += dy_da[1] * dy;
beta[2] += dy_da[2] * dy;
ssx += dy * dy;
}
}
// Generate symmetric matrix
alpha[0][1] = alpha[1][0];
alpha[0][2] = alpha[2][0];
alpha[1][2] = alpha[2][1];
return checkGradients(alpha, beta, nparams, ssx);
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.fitting.nonlinear.gradient.GradientCalculator#fisherInformationDiagonal(int, double[],
* gdsc.smlm.function.NonLinearFunction)
*/
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;
}
checkGradients(alpha, nparams);
return alpha;
}
}