package gdsc.smlm.function.gaussian.erf;
import gdsc.smlm.function.Gradient1Procedure;
import gdsc.smlm.function.Gradient2Procedure;
import gdsc.smlm.function.gaussian.AstimatismZModel;
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 SingleAstigmatismErfGaussian2DFunction extends SingleFreeCircularErfGaussian2DFunction
{
static final int[] gradientIndices;
static
{
gradientIndices = createGradientIndices(1, new SingleAstigmatismErfGaussian2DFunction(1, 1, null));
}
protected final AstimatismZModel zModel;
// Required for the z-depth gradients
protected double dtsx_dtz, d2tsx_dtz2, dtsy_dtz, d2tsy_dtz2;
/**
* 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)
* @param zModel
* the z model
*/
public SingleAstigmatismErfGaussian2DFunction(int maxx, int maxy, AstimatismZModel zModel)
{
super(maxx, maxy);
this.zModel = zModel;
}
@Override
public ErfGaussian2DFunction copy()
{
return new SingleAstigmatismErfGaussian2DFunction(maxx, maxy, zModel);
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.erf.SingleFreeCircularErfGaussian2DFunction#initialise0(double[])
*/
public void initialise0(double[] a)
{
tB = a[Gaussian2DFunction.BACKGROUND];
tI = a[Gaussian2DFunction.SIGNAL];
// Pre-compute the offset by 0.5
final double tx = a[Gaussian2DFunction.X_POSITION] + 0.5;
final double ty = a[Gaussian2DFunction.Y_POSITION] + 0.5;
final double tsx = a[Gaussian2DFunction.X_SD];
final double tsy = a[Gaussian2DFunction.Y_SD];
final double tz = a[ErfGaussian2DFunction.Z_POSITION];
final double sx = tsx * zModel.getSx(tz);
final double sy = tsy * zModel.getSy(tz);
createDeltaETable(ONE_OVER_ROOT2 / sx, deltaEx, tx);
createDeltaETable(ONE_OVER_ROOT2 / sy, deltaEy, ty);
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.erf.SingleFreeCircularErfGaussian2DFunction#initialise1(double[])
*/
public void initialise1(double[] a)
{
create1Arrays();
tB = a[Gaussian2DFunction.BACKGROUND];
tI = a[Gaussian2DFunction.SIGNAL];
// Pre-compute the offset by 0.5
final double tx = a[Gaussian2DFunction.X_POSITION] + 0.5;
final double ty = a[Gaussian2DFunction.Y_POSITION] + 0.5;
final double tsx = a[Gaussian2DFunction.X_SD];
final double tsy = a[Gaussian2DFunction.Y_SD];
final double tz = a[ErfGaussian2DFunction.Z_POSITION];
// We can pre-compute part of the derivatives for position and sd in arrays
// since the Gaussian is XY separable
final double[] ds_dz = new double[1];
final double sx = tsx * zModel.getSx(tz, ds_dz);
dtsx_dtz = tsx * ds_dz[0];
final double sy = tsy * zModel.getSy(tz, ds_dz);
dtsy_dtz = tsy * ds_dz[0];
createFirstOrderTables(tI, deltaEx, du_dtx, du_dtsx, tx, sx);
createFirstOrderTables(tI, deltaEy, du_dty, du_dtsy, ty, sy);
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.gaussian.erf.SingleFreeCircularErfGaussian2DFunction#initialise2(double[])
*/
public void initialise2(double[] a)
{
create2Arrays();
tB = a[Gaussian2DFunction.BACKGROUND];
tI = a[Gaussian2DFunction.SIGNAL];
// Pre-compute the offset by 0.5
final double tx = a[Gaussian2DFunction.X_POSITION] + 0.5;
final double ty = a[Gaussian2DFunction.Y_POSITION] + 0.5;
final double tsx = a[Gaussian2DFunction.X_SD];
final double tsy = a[Gaussian2DFunction.Y_SD];
final double tz = a[ErfGaussian2DFunction.Z_POSITION];
// We can pre-compute part of the derivatives for position and sd in arrays
// since the Gaussian is XY separable
final double[] ds_dz = new double[2];
final double sx = tsx * zModel.getSx2(tz, ds_dz);
dtsx_dtz = tsx * ds_dz[0];
d2tsx_dtz2 = tsx * ds_dz[1];
final double sy = tsy * zModel.getSy2(tz, ds_dz);
dtsy_dtz = tsy * ds_dz[0];
d2tsy_dtz2 = tsy * ds_dz[1];
createSecondOrderTables(tI, deltaEx, du_dtx, du_dtsx, d2u_dtx2, d2u_dtsx2, tx, sx);
createSecondOrderTables(tI, deltaEy, du_dty, du_dtsy, d2u_dty2, d2u_dtsy2, ty, sy);
}
/**
* 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
final int y = i / maxx;
final int x = i % maxx;
// Return in order of Gaussian2DFunction.createGradientIndices().
// Use pre-computed gradients
duda[0] = 1.0;
duda[1] = deltaEx[x] * deltaEy[y];
duda[2] = du_dtsx[x] * deltaEy[y] * dtsx_dtz + du_dtsy[y] * deltaEx[x] * dtsy_dtz;
duda[3] = du_dtx[x] * deltaEy[y];
duda[4] = du_dty[y] * deltaEx[x];
return tB + tI * duda[1];
}
/**
* 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
final int y = i / maxx;
final int x = i % maxx;
// Return in order of Gaussian2DFunction.createGradientIndices().
// Use pre-computed gradients
final double du_dsx = du_dtsx[x] * deltaEy[y];
final double du_dsy = du_dtsy[y] * deltaEx[x];
duda[0] = 1.0;
duda[1] = deltaEx[x] * deltaEy[y];
duda[2] = du_dsx * dtsx_dtz + du_dsy * dtsy_dtz;
duda[3] = du_dtx[x] * deltaEy[y];
duda[4] = du_dty[y] * deltaEx[x];
d2uda2[0] = 0;
d2uda2[1] = 0;
//@formatter:off
d2uda2[2] =
d2u_dtsx2[x] * deltaEy[y] * dtsx_dtz * dtsx_dtz +
du_dsx * d2tsx_dtz2 +
d2u_dtsy2[y] * deltaEx[x] * dtsy_dtz * dtsy_dtz +
du_dsy * d2tsy_dtz2 +
// Add the equivalent term we add in the circular version.
// Note: this is not in the Smith, et al (2010) paper but is
// in the GraspJ source code and it works in JUnit tests.
2 * du_dtsx[x] * dtsx_dtz * du_dtsy[y] * dtsy_dtz / tI;
//@formatter:on
d2uda2[3] = d2u_dtx2[x] * deltaEy[y];
d2uda2[4] = d2u_dty2[y] * deltaEx[x];
return tB + tI * duda[1];
}
@Override
public boolean evaluatesBackground()
{
return true;
}
@Override
public boolean evaluatesSignal()
{
return true;
}
@Override
public boolean evaluatesShape()
{
return true;
}
@Override
public boolean evaluatesPosition()
{
return true;
}
@Override
public boolean evaluatesSD0()
{
return false;
}
@Override
public boolean evaluatesSD1()
{
return false;
}
@Override
public int getParametersPerPeak()
{
return 4;
}
/*
* (non-Javadoc)
*
* @see gdsc.fitting.function.NonLinearFunction#gradientIndices()
*/
public int[] gradientIndices()
{
return gradientIndices;
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.GradientFunction#getNumberOfGradients()
*/
public int getNumberOfGradients()
{
return 5;
}
/*
* (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++)
{
final double du_dty = this.du_dty[y];
final double deltaEy = this.deltaEy[y];
final double deltaEy_by_dtsx_dtz = deltaEy * dtsx_dtz;
final double du_dtsy_by_dtsy_dtz = this.du_dtsy[y] * dtsy_dtz;
for (int x = 0; x < maxx; x++)
{
duda[1] = deltaEx[x] * deltaEy;
duda[2] = du_dtsx[x] * deltaEy_by_dtsx_dtz + du_dtsy_by_dtsy_dtz * deltaEx[x];
duda[3] = du_dtx[x] * deltaEy;
duda[4] = du_dty * deltaEx[x];
procedure.execute(tB + tI * duda[1], duda);
}
}
}
/*
* (non-Javadoc)
*
* @see gdsc.smlm.function.Gradient2Function#forEach(gdsc.smlm.function.Gradient2Procedure)
*/
public void forEach(Gradient2Procedure procedure)
{
final double[] duda = new double[getNumberOfGradients()];
final double[] d2uda2 = new double[getNumberOfGradients()];
duda[0] = 1.0;
final double dtsx_dtz_2 = dtsx_dtz * dtsx_dtz;
final double dtsy_dtz_2 = dtsy_dtz * dtsy_dtz;
final double two_dtsx_dtz_by_dtsy_dtz_tI = 2 * dtsx_dtz * dtsy_dtz / tI;
for (int y = 0; y < maxy; y++)
{
final double du_dty = this.du_dty[y];
final double deltaEy = this.deltaEy[y];
final double du_dtsy = this.du_dtsy[y];
final double d2u_dty2 = this.d2u_dty2[y];
final double deltaEy_by_dtsx_dtz_2 = deltaEy * dtsx_dtz_2;
final double d2u_dtsy2_by_dtsy_dtz_2 = this.d2u_dtsy2[y] * dtsy_dtz_2;
final double two_dtsx_dtz_by_du_dtsy_by_dtsy_dtz_tI = two_dtsx_dtz_by_dtsy_dtz_tI * du_dtsy;
for (int x = 0; x < maxx; x++)
{
final double du_dsx = du_dtsx[x] * deltaEy;
final double du_dsy = du_dtsy * deltaEx[x];
duda[1] = deltaEx[x] * deltaEy;
duda[2] = du_dsx * dtsx_dtz + du_dsy * dtsy_dtz;
duda[3] = du_dtx[x] * deltaEy;
duda[4] = du_dty * deltaEx[x];
//@formatter:off
d2uda2[2] =
d2u_dtsx2[x] * deltaEy_by_dtsx_dtz_2 +
du_dsx * d2tsx_dtz2 +
//d2u_dtsy2[y] * deltaEx[x] * dtsy_dtz_2 +
d2u_dtsy2_by_dtsy_dtz_2 * deltaEx[x] +
du_dsy * d2tsy_dtz2 +
// Add the equivalent term we add in the circular version.
// Note: this is not in the Smith, et al (2010) paper but is
// in the GraspJ source code and it works in JUnit tests.
//2 * du_dtsx[x] * dtsx_dtz * du_dtsy * dtsy_dtz / tI;
two_dtsx_dtz_by_du_dtsy_by_dtsy_dtz_tI * du_dtsx[x];
//@formatter:on
d2uda2[3] = d2u_dtx2[x] * deltaEy;
d2uda2[4] = d2u_dty2 * deltaEx[x];
procedure.execute(tB + tI * duda[1], duda, d2uda2);
}
}
}
}