package gdsc.smlm.function.gaussian.erf;
import org.apache.commons.math3.util.FastMath;
import gdsc.smlm.function.Erf;
import gdsc.smlm.function.Gradient1Procedure;
import gdsc.smlm.function.Gradient2Procedure;
import gdsc.smlm.function.gaussian.Gaussian2DFunction;
/*-----------------------------------------------------------------------------
* 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.
*---------------------------------------------------------------------------*/
/**
* Evaluates a 2-dimensional Gaussian function for a single peak.
*/
public class MultiFixedErfGaussian2DFunction extends MultiFreeCircularErfGaussian2DFunction
{
/**
* 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 MultiFixedErfGaussian2DFunction(int nPeaks, int maxx, int maxy)
{
super(nPeaks, maxx, maxy);
}
@Override
protected void create1Arrays()
{
if (du_dtx != null)
return;
du_dtx = new double[deltaEx.length];
du_dty = new double[deltaEy.length];
}
@Override
protected void create2Arrays()
{
if (d2u_dtx2 != null)
return;
d2u_dtx2 = new double[deltaEx.length];
d2u_dty2 = new double[deltaEy.length];
create1Arrays();
}
@Override
protected int[] createGradientIndices()
{
return replicateGradientIndices(SingleFixedErfGaussian2DFunction.gradientIndices);
}
@Override
public ErfGaussian2DFunction copy()
{
return new MultiFixedErfGaussian2DFunction(nPeaks, maxx, maxy);
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.erf.SingleFreeCircularErfGaussian2DFunction#initialise0(double[])
*/
public void initialise0(double[] a)
{
tB = a[Gaussian2DFunction.BACKGROUND];
for (int n = 0, i = 0; n < nPeaks; n++, i += 6)
{
tI[n] = a[i + Gaussian2DFunction.SIGNAL];
// Pre-compute the offset by 0.5
final double tx = a[i + Gaussian2DFunction.X_POSITION] + 0.5;
final double ty = a[i + Gaussian2DFunction.Y_POSITION] + 0.5;
final double s = a[i + Gaussian2DFunction.X_SD];
final double one_sSqrt2 = ONE_OVER_ROOT2 / s;
createDeltaETable(n, maxx, one_sSqrt2, deltaEx, tx);
createDeltaETable(n, maxy, one_sSqrt2, deltaEy, ty);
}
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.erf.SingleFreeCircularErfGaussian2DFunction#initialise1(double[])
*/
public void initialise1(double[] a)
{
create1Arrays();
tB = a[Gaussian2DFunction.BACKGROUND];
for (int n = 0, i = 0; n < nPeaks; n++, i += 6)
{
tI[n] = a[i + Gaussian2DFunction.SIGNAL];
// Pre-compute the offset by 0.5
final double tx = a[i + Gaussian2DFunction.X_POSITION] + 0.5;
final double ty = a[i + Gaussian2DFunction.Y_POSITION] + 0.5;
final double s = a[i + Gaussian2DFunction.X_SD];
// We can pre-compute part of the derivatives for position and sd in arrays
// since the Gaussian is XY separable
final double one_sSqrt2 = ONE_OVER_ROOT2 / s;
final double one_2ss = 0.5 / (s * s);
final double I_sSqrt2pi = tI[n] * ONE_OVER_ROOT2PI / s;
createFirstOrderTables(n, maxx, one_sSqrt2, one_2ss, I_sSqrt2pi, deltaEx, du_dtx, tx);
createFirstOrderTables(n, maxy, one_sSqrt2, one_2ss, I_sSqrt2pi, deltaEy, du_dty, ty);
}
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.erf.SingleFreeCircularErfGaussian2DFunction#initialise2(double[])
*/
public void initialise2(double[] a)
{
create2Arrays();
tB = a[Gaussian2DFunction.BACKGROUND];
for (int n = 0, i = 0; n < nPeaks; n++, i += 6)
{
tI[n] = a[i + Gaussian2DFunction.SIGNAL];
// Pre-compute the offset by 0.5
final double tx = a[i + Gaussian2DFunction.X_POSITION] + 0.5;
final double ty = a[i + Gaussian2DFunction.Y_POSITION] + 0.5;
final double s = a[i + Gaussian2DFunction.X_SD];
// We can pre-compute part of the derivatives for position and sd in arrays
// since the Gaussian is XY separable
final double ss = s * s;
final double one_sSqrt2 = ONE_OVER_ROOT2 / s;
final double one_2ss = 0.5 / ss;
final double I_sSqrt2pi = tI[n] * ONE_OVER_ROOT2PI / s;
final double I_sssSqrt2pi = I_sSqrt2pi / ss;
createSecondOrderTables(n, maxx, one_sSqrt2, one_2ss, I_sSqrt2pi, I_sssSqrt2pi, deltaEx, du_dtx, d2u_dtx2,
tx);
createSecondOrderTables(n, maxy, one_sSqrt2, one_2ss, I_sSqrt2pi, I_sssSqrt2pi, deltaEy, du_dty, d2u_dty2,
ty);
}
}
/**
* Creates the first order derivatives.
*
* @param n
* the peak number
* @param max
* the maximum for the dimension
* @param one_sSqrt2
* one over (s times sqrt(2))
* @param one_2ss
* one over (2 * s^2)
* @param I_sSqrt2pi
* the intensity over (s * sqrt(2*pi))
* @param deltaE
* the delta E for dimension 0 (difference between the error function at the start and end of each pixel)
* @param du_dx
* the first order x derivative for dimension 0
* @param u
* the mean of the Gaussian for dimension 0
*/
protected static void createFirstOrderTables(int n, int max, double one_sSqrt2, double one_2ss, double I_sSqrt2pi,
double[] deltaE, double[] du_dx, double u)
{
// For documentation see SingleFreeCircularErfGaussian2DFunction.createSecondOrderTables(...)
double x_u_p12 = -u;
double erf_x_minus = 0.5 * Erf.erf(x_u_p12 * one_sSqrt2);
double exp_x_minus = FastMath.exp(-(x_u_p12 * x_u_p12 * one_2ss));
for (int i = 0, j = n * max; i < max; i++, j++)
{
x_u_p12 += 1.0;
final double erf_x_plus = 0.5 * Erf.erf(x_u_p12 * one_sSqrt2);
deltaE[j] = erf_x_plus - erf_x_minus;
erf_x_minus = erf_x_plus;
final double exp_x_plus = FastMath.exp(-(x_u_p12 * x_u_p12 * one_2ss));
du_dx[j] = I_sSqrt2pi * (exp_x_minus - exp_x_plus);
exp_x_minus = exp_x_plus;
}
}
/**
* Creates the first and second order derivatives.
*
* @param n
* the peak number
* @param max
* the maximum for the dimension
* @param one_sSqrt2
* one over (s times sqrt(2))
* @param one_2ss
* one over (2 * s^2)
* @param I_sSqrt2pi
* the intensity over (s * sqrt(2*pi))
* @param I_sssSqrt2pi
* the intensity over (s^3 * sqrt(2*pi))
* @param deltaE
* the delta E for dimension 0 (difference between the error function at the start and end of each pixel)
* @param du_dx
* the first order x derivative for dimension 0
* @param d2u_dx2
* the second order x derivative for dimension 0
* @param u
* the mean of the Gaussian for dimension 0
*/
protected static void createSecondOrderTables(int n, int max, double one_sSqrt2, double one_2ss, double I_sSqrt2pi,
double I_sssSqrt2pi, double[] deltaE, double[] du_dx, double[] d2u_dx2, double u)
{
// For documentation see SingleFreeCircularErfGaussian2DFunction.createSecondOrderTables(...)
double x_u_p12 = -u;
double erf_x_minus = 0.5 * Erf.erf(x_u_p12 * one_sSqrt2);
double exp_x_minus = FastMath.exp(-(x_u_p12 * x_u_p12 * one_2ss));
for (int i = 0, j = n * max; i < max; i++, j++)
{
double x_u_m12 = x_u_p12;
x_u_p12 += 1.0;
final double erf_x_plus = 0.5 * Erf.erf(x_u_p12 * one_sSqrt2);
deltaE[j] = erf_x_plus - erf_x_minus;
erf_x_minus = erf_x_plus;
final double exp_x_plus = FastMath.exp(-(x_u_p12 * x_u_p12 * one_2ss));
du_dx[j] = I_sSqrt2pi * (exp_x_minus - exp_x_plus);
d2u_dx2[j] = I_sssSqrt2pi * (x_u_m12 * exp_x_minus - x_u_p12 * exp_x_plus);
exp_x_minus = exp_x_plus;
}
}
/**
* Evaluates an 2-dimensional Gaussian function for a single peak.
*
* @param i
* Input predictor
* @param duda
* 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 i, final double[] duda)
{
// Unpack the predictor into the dimensions
int yy = i / maxx;
int xx = i % maxx;
// Return in order of Gaussian2DFunction.createGradientIndices().
// Use pre-computed gradients
duda[0] = 1.0;
double I = tB;
for (int n = 0, a = 1; n < nPeaks; n++, xx += maxx, yy += maxy)
{
duda[a] = deltaEx[xx] * deltaEy[yy];
I += tI[n] * duda[a++];
duda[a++] = du_dtx[xx] * deltaEy[yy];
duda[a++] = du_dty[yy] * deltaEx[xx];
}
return I;
}
/**
* Evaluates an 2-dimensional Gaussian function for a single peak.
*
* @param i
* Input predictor
* @param duda
* Partial first gradient of function with respect to each coefficient
* @param d2uda2
* Partial second gradient of function with respect to each coefficient
* @return The predicted value
*/
public double eval(final int i, final double[] duda, final double[] d2uda2)
{
// Unpack the predictor into the dimensions
int yy = i / maxx;
int xx = i % maxx;
// Return in order of Gaussian2DFunction.createGradientIndices().
// Use pre-computed gradients
duda[0] = 1.0;
d2uda2[0] = 0;
double I = tB;
for (int n = 0, a = 1; n < nPeaks; n++, xx += maxx, yy += maxy)
{
duda[a] = deltaEx[xx] * deltaEy[yy];
I += tI[n] * duda[a];
d2uda2[a++] = 0;
duda[a] = du_dtx[xx] * deltaEy[yy];
d2uda2[a++] = d2u_dtx2[xx] * deltaEy[yy];
duda[a] = du_dty[yy] * deltaEx[xx];
d2uda2[a++] = d2u_dty2[yy] * deltaEx[xx];
}
return I;
}
@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 false;
}
@Override
public boolean evaluatesSD1()
{
return false;
}
@Override
public int getParametersPerPeak()
{
return 3;
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.GradientFunction#forEach(gdsc.smlm.function.GradientFunction.Gradient1Procedure)
*/
public void forEach(Gradient1Procedure procedure)
{
final double[] duda = new double[getNumberOfGradients()];
duda[0] = 1.0;
for (int y = 0; y < maxy; y++)
{
for (int x = 0; x < maxx; x++)
{
double I = tB;
for (int n = 0, xx = x, yy = y, a = 1; n < nPeaks; n++, xx += maxx, yy += maxy)
{
duda[a] = deltaEx[xx] * deltaEy[yy];
I += tI[n] * duda[a++];
duda[a++] = du_dtx[xx] * deltaEy[yy];
duda[a++] = du_dty[yy] * deltaEx[xx];
}
procedure.execute(I, duda);
}
}
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.GradientFunction#forEach(gdsc.smlm.function.GradientFunction.Gradient2Procedure)
*/
public void forEach(Gradient2Procedure procedure)
{
final double[] duda = new double[getNumberOfGradients()];
final double[] d2uda2 = new double[getNumberOfGradients()];
duda[0] = 1.0;
for (int y = 0; y < maxy; y++)
{
for (int x = 0; x < maxx; x++)
{
double I = tB;
for (int n = 0, xx = x, yy = y, a = 1; n < nPeaks; n++, xx += maxx, yy += maxy)
{
duda[a] = deltaEx[xx] * deltaEy[yy];
I += tI[n] * duda[a++];
duda[a] = du_dtx[xx] * deltaEy[yy];
d2uda2[a++] = d2u_dtx2[xx] * deltaEy[yy];
duda[a] = du_dty[yy] * deltaEx[xx];
d2uda2[a++] = d2u_dty2[yy] * deltaEx[xx];
}
procedure.execute(I, duda, d2uda2);
}
}
}
}