package gdsc.smlm.fitting.nonlinear.gradient;
import gdsc.smlm.function.Gradient1Function;
/*-----------------------------------------------------------------------------
* GDSC SMLM Software
*
* Copyright (C) 2017 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 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).
* <p>
* Note that the Hessian matrix is scaled by 1/2 and the gradient vector is scaled by -1/2 for convenience in solving
* the non-linear model. See Numerical Recipes in C++, 2nd Ed. Equation 15.5.8 for Nonlinear Models.
*/
public class LSQLVMGradientProcedureLinear extends BaseLSQLVMGradientProcedure
{
/**
* The scaled Hessian curvature matrix (size n*n)
*/
public final double[] alpha;
/**
* @param y
* Data to fit
* @param b
* Baseline pre-computed y-values
* @param func
* Gradient function
*/
public LSQLVMGradientProcedureLinear(final double[] y, final double[] b, final Gradient1Function func)
{
super(y, b, func);
alpha = new double[n * n];
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.Gradient1Procedure#execute(double, double[])
*/
public void execute(double value, double[] dy_da)
{
final double dy = y[++yi] - value;
// Compute:
// - the scaled Hessian matrix (the square matrix of second-order partial derivatives of a function;
// that is, it describes the local curvature of a function of many variables.)
// - the scaled gradient vector of the function's partial first derivatives with respect to the parameters
for (int i = 0, index = 0; i < n; i++, index += i)
{
final double wgt = dy_da[i];
for (int k = i; k < n; k++)
{
//System.out.printf("alpha[%d] += dy_da[%d] * dy_da[%d];\n", index, i, k);
alpha[index++] += wgt * dy_da[k];
}
beta[i] += wgt * dy;
}
//if (true) throw new RuntimeException();
this.value += dy * dy;
}
protected void initialiseGradient()
{
for (int i = 0, index = 0; i < n; i++, index += i)
{
beta[i] = 0;
for (int k = i; k < n; k++)
{
//System.out.printf("alpha[%d] = 0;\n", index);
alpha[index++] = 0;
}
}
//if (true) throw new RuntimeException();
}
protected void finishGradient()
{
// Generate symmetric matrix
// Adapted from org.ejml.alg.dense.misc.TransposeAlgs.square()
for (int i = 0, index = 1; i < n; i++, index += i + 1)
{
for (int k = i + 1, indexOther = (i + 1) * n + i; k < n; k++, index++, indexOther += n)
// for (int i = 0, index = 1, indexEnd = n; i < n; i++, index += i + 1, indexEnd += n)
// {
// for (int indexOther = (i + 1) * n + i; index < indexEnd; index++, indexOther += n)
{
//System.out.printf("alpha[%d] = alpha[%d];\n", indexOther, index);
alpha[indexOther] = alpha[index];
}
}
//throw new RuntimeException();
}
protected boolean checkGradients()
{
for (int i = 0, index = 0; i < n; i++, index += i)
{
if (Double.isNaN(beta[i]))
return true;
for (int k = i; k < n; k++)
{
if (Double.isNaN(alpha[index++]))
return true;
}
}
return false;
}
@Override
public void getAlphaMatrix(double[][] alpha)
{
toMatrix(this.alpha, alpha);
}
@Override
public double[] getAlphaLinear()
{
return alpha;
}
@Override
public void getAlphaLinear(double[] alpha)
{
System.arraycopy(this.alpha, 0, alpha, 0, alpha.length);
}
}