package gdsc.smlm.function.gaussian;
import org.apache.commons.math3.util.FastMath;
/*-----------------------------------------------------------------------------
* 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.
*---------------------------------------------------------------------------*/
/**
* Evaluates an 2-dimensional Gaussian function for a configured number of peaks.
* <p>
* The single parameter x in the {@link #eval(int, double[])} function is assumed to be a linear index into
* 2-dimensional
* data. The dimensions of the data must be specified to allow unpacking to coordinates.
* <p>
* Data should be packed in descending dimension order, e.g. Y,X : Index for [x,y] = MaxX*y + x.
*/
public class CircularGaussian2DFunction extends MultiPeakGaussian2DFunction
{
protected static final int PARAMETERS_PER_PEAK = 4;
protected final double[][] peakFactors;
protected double[] a;
/**
* Constructor
*
* @param npeaks
* The number of peaks
* @param maxx
* The maximum x value of the 2-dimensional data (used to unpack a linear index into coordinates)
* @param maxy
* The maximum y value of the 2-dimensional data (used to unpack a linear index into coordinates)
*/
public CircularGaussian2DFunction(int npeaks, int maxx, int maxy)
{
super(npeaks, maxx, maxy);
peakFactors = new double[npeaks][5];
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.Gaussian2DFunction#copy()
*/
@Override
public Gaussian2DFunction copy()
{
return new CircularGaussian2DFunction(npeaks, maxx, maxy);
}
protected static final int N = 0;
protected static final int HEIGHT = 1;
protected static final int AA = 2;
protected static final int AA2 = 3;
protected static final int AX = 4;
/*
* (non-Javadoc)
*
* @see gdsc.fitting.function.NonLinearFunction#initialise(double[])
*/
public void initialise(double[] a)
{
this.a = a;
// Precalculate multiplication factors
for (int j = 0; j < npeaks; j++)
{
final double sx = a[j * 6 + X_SD];
final double sx2 = sx * sx;
peakFactors[j][N] = ONE_OVER_TWO_PI / sx2;
peakFactors[j][HEIGHT] = a[j * 6 + SIGNAL] * peakFactors[j][N];
// All prefactors are negated since the Gaussian uses the exponential to the negative:
// (A/2*pi*sx*sy) * exp( -( a(x-x0)^2 + 2b(x-x0)(y-y0) + c(y-y0)^2 ) )
peakFactors[j][AA] = -0.5 / sx2;
peakFactors[j][AA2] = -2.0 * peakFactors[j][AA];
// For the x-width gradient
peakFactors[j][AX] = -2 / sx;
}
}
/**
* Produce an output predicted value for a given set of input
* predictors (x) and coefficients (a).
* <p>
* Evaluates an 2-dimensional elliptical Gaussian function for a single peak.
* <p>
* The first coefficient is the Gaussian background level (B). The coefficients are then packed for each peak:
* Amplitude; Angle; position[N]; sd[N]. Amplitude (A) is the volume of the Gaussian. Angle (r) is the rotation
* angle of the ellipse. Position (x,y) is the position of the Gaussian in each of the N-dimensions. SD (sx,sy) is
* the standard deviation in each of the N-dimensions.
* <p>
* The equation per peak is:<br/>
* y_peak = A/(2*pi*sx*sy) * exp( -( a(x-x0)^2 + c(y-y0)^2 ) )<br/>
* Where: <br/>
* a = 1/(2*sx^2) <br/>
* c = 1/(2*sy^2)
*
* @param x
* Input predictor
* @param dyda
* Partial gradient of function with respect to each coefficient
* @return The predicted value
*
* @see gdsc.smlm.function.NonLinearFunction#eval(int, double[])
*/
public double eval(final int x, final double[] dyda)
{
// Track the position of the parameters
int apos = 0;
int dydapos = 0;
// First parameter is the background level
double y_fit = a[BACKGROUND];
dyda[dydapos++] = 1.0; // Gradient for a constant background is 1
// Unpack the predictor into the dimensions
final int x1 = x / maxx;
final int x0 = x % maxx;
for (int j = 0; j < npeaks; j++)
{
y_fit += gaussian(x0, x1, dyda, apos, dydapos, peakFactors[j]);
apos += 6;
dydapos += PARAMETERS_PER_PEAK;
}
return y_fit;
}
protected double gaussian(final int x0, final int x1, final double[] dy_da, final int apos, final int dydapos,
final double[] factors)
{
final double dx = x0 - a[apos + X_POSITION];
final double dy = x1 - a[apos + Y_POSITION];
// Calculate gradients
final double aadx2dy2 = factors[AA] * (dx * dx + dy * dy);
final double exp = FastMath.exp(aadx2dy2);
dy_da[dydapos] = factors[N] * exp;
final double y = factors[HEIGHT] * exp;
final double yaa2 = y * factors[AA2];
dy_da[dydapos + 1] = yaa2 * dx;
dy_da[dydapos + 2] = yaa2 * dy;
dy_da[dydapos + 3] = factors[AX] * y * (1 + aadx2dy2);
return y;
}
/*
* (non-Javadoc)
*
* @see gdsc.fitting.function.NonLinearFunction#eval(int)
*/
public double eval(final int x)
{
// Track the position of the parameters
int apos = 0;
// First parameter is the background level
double y_fit = a[BACKGROUND];
// Unpack the predictor into the dimensions
final int x1 = x / maxx;
final int x0 = x % maxx;
for (int j = 0; j < npeaks; j++, apos += 6)
{
y_fit += gaussian(x0, x1, apos, peakFactors[j]);
}
return y_fit;
}
protected double gaussian(final int x0, final int x1, final int apos, final double[] factors)
{
final double dx = x0 - a[apos + X_POSITION];
final double dy = x1 - a[apos + Y_POSITION];
return factors[HEIGHT] * FastMath.exp(factors[AA] * (dx * dx + dy * dy));
}
@Override
public boolean evaluatesBackground()
{
return true;
}
@Override
public boolean evaluatesSignal()
{
return true;
}
@Override
public boolean evaluatesShape()
{
return false;
}
@Override
public boolean evaluatesPosition()
{
return true;
}
@Override
public boolean evaluatesSD0()
{
return true;
}
@Override
public boolean evaluatesSD1()
{
return false;
}
@Override
public int getParametersPerPeak()
{
return PARAMETERS_PER_PEAK;
}
}