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 single peak.
* <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 SingleFreeCircularGaussian2DFunction extends Gaussian2DFunction
{
private static final int[] gradientIndices;
static
{
gradientIndices = createGradientIndices(1, new SingleFreeCircularGaussian2DFunction(1, 1));
}
protected double background;
protected double x0pos;
protected double x1pos;
protected double n;
protected double height;
protected double aa;
protected double bb;
protected double cc;
protected double nx;
protected double ax;
protected double bx;
protected double cx;
protected double ny;
protected double ay;
protected double by;
protected double cy;
/**
* Constructor
*
* @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 SingleFreeCircularGaussian2DFunction(int maxx, int maxy)
{
super(maxx, maxy);
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.Gaussian2DFunction#copy()
*/
@Override
public Gaussian2DFunction copy()
{
return new SingleFreeCircularGaussian2DFunction(maxx, maxy);
}
/*
* (non-Javadoc)
*
* @see gdsc.fitting.function.NonLinearFunction#initialise(double[])
*/
public void initialise(double[] a)
{
background = a[BACKGROUND];
x0pos = a[X_POSITION];
x1pos = a[Y_POSITION];
// Precalculate multiplication factors
final double theta = a[SHAPE];
final double sx = a[X_SD];
final double sy = a[Y_SD];
final double sx2 = sx * sx;
final double sy2 = sy * sy;
final double sx3 = sx2 * sx;
final double sy3 = sy2 * sy;
final double cosSqt = Math.cos(theta) * Math.cos(theta);
final double sinSqt = Math.sin(theta) * Math.sin(theta);
final double sin2t = Math.sin(2 * theta);
n = ONE_OVER_TWO_PI / (sx * sy);
height = a[SIGNAL] * 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 ) )
aa = -0.5 * (cosSqt / sx2 + sinSqt / sy2);
bb = -0.25 * (-sin2t / sx2 + sin2t / sy2);
cc = -0.5 * (sinSqt / sx2 + cosSqt / sy2);
// For the x-width gradient
nx = -1 / sx;
ax = cosSqt / sx3;
bx = -0.5 * sin2t / sx3;
cx = sinSqt / sx3;
// For the y-width gradient
ny = -1 / sy;
ay = sinSqt / sy3;
by = 0.5 * sin2t / sy3;
cy = cosSqt / sy3;
}
/**
* 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 + 2b(x-x0)(y-y0) + c(y-y0)^2 ) )<br/>
* Where: <br/>
* a = cos(r)^2/(2*sx^2) + sin(r)^2 /(2*sy^2) <br/>
* b = -sin(2r)^2/(4*sx^2) + sin(2r)^2/(4*sy^2) <br/>
* c = sin(r)^2/(2*sx^2) + cos(r)^2/(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)
{
// First parameter is the background level
dyda[0] = 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;
return background + gaussian(x0, x1, dyda);
}
private double gaussian(final int x0, final int x1, final double[] dy_da)
{
final double dx = x0 - x0pos;
final double dy = x1 - x1pos;
final double dx2 = dx * dx;
final double dxy = dx * dy;
final double dy2 = dy * dy;
// Calculate gradients
final double exp = FastMath.exp(aa * dx2 + bb * dxy + cc * dy2);
dy_da[1] = n * exp;
final double y = height * exp;
dy_da[2] = y * (-2.0 * aa * dx - bb * dy);
dy_da[3] = y * (-2.0 * cc * dy - bb * dx);
dy_da[4] = y * (nx + ax * dx2 + bx * dxy + cx * dy2);
dy_da[5] = y * (ny + ay * dx2 + by * dxy + cy * dy2);
return y;
}
/*
* (non-Javadoc)
*
* @see gdsc.fitting.function.NonLinearFunction#eval(int)
*/
public double eval(final int x)
{
// Unpack the predictor into the dimensions
final int x1 = x / maxx;
final int x0 = x % maxx;
final double dx = x0 - x0pos;
final double dy = x1 - x1pos;
return background + height * FastMath.exp(aa * dx * dx + bb * dx * dy + cc * dy * dy);
}
@Override
public int getNPeaks()
{
return 1;
}
@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 true;
}
@Override
public int getParametersPerPeak()
{
return 5;
}
/*
* (non-Javadoc)
*
* @see gdsc.fitting.function.NonLinearFunction#gradientIndices()
*/
public int[] gradientIndices()
{
return gradientIndices;
}
}