package gdsc.smlm.function.gaussian.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 SingleCircularErfGaussian2DFunction extends SingleFreeCircularErfGaussian2DFunction { static final int[] gradientIndices; static { gradientIndices = createGradientIndices(1, new SingleCircularErfGaussian2DFunction(1, 1)); } /** * 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 SingleCircularErfGaussian2DFunction(int maxx, int maxy) { super(maxx, maxy); } @Override public ErfGaussian2DFunction copy() { return new SingleCircularErfGaussian2DFunction(maxx, maxy); } 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 s = a[Gaussian2DFunction.X_SD]; final double one_sSqrt2 = ONE_OVER_ROOT2 / s; createDeltaETable(one_sSqrt2, deltaEx, tx); createDeltaETable(one_sSqrt2, deltaEy, ty); } 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 s = a[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 * ONE_OVER_ROOT2PI / s; final double I_ssSqrt2pi = tI * ONE_OVER_ROOT2PI / (s * s); createFirstOrderTables(one_sSqrt2, one_2ss, I_sSqrt2pi, I_ssSqrt2pi, deltaEx, du_dtx, du_dtsx, tx); createFirstOrderTables(one_sSqrt2, one_2ss, I_sSqrt2pi, I_ssSqrt2pi, deltaEy, du_dty, du_dtsy, ty); } 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 s = a[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_sSqrt2pi = ONE_OVER_ROOT2PI / s; 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 * ONE_OVER_ROOT2PI / s; final double I_ssSqrt2pi = tI * ONE_OVER_ROOT2PI / ss; final double I_sssSqrt2pi = I_sSqrt2pi / ss; final double one_sssSqrt2pi = one_sSqrt2pi / ss; final double one_sssssSqrt2pi = one_sssSqrt2pi / ss; createSecondOrderTables(tI, one_sSqrt2, one_2ss, I_sSqrt2pi, I_ssSqrt2pi, I_sssSqrt2pi, ss, one_sssSqrt2pi, one_sssssSqrt2pi, deltaEx, du_dtx, du_dtsx, d2u_dtx2, d2u_dtsx2, tx); createSecondOrderTables(tI, one_sSqrt2, one_2ss, I_sSqrt2pi, I_ssSqrt2pi, I_sssSqrt2pi, ss, one_sssSqrt2pi, one_sssssSqrt2pi, deltaEy, du_dty, du_dtsy, d2u_dty2, d2u_dtsy2, ty); } /** * 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_dtx[x] * deltaEy[y]; duda[3] = du_dty[y] * deltaEx[x]; duda[4] = du_dtsx[x] * deltaEy[y] + du_dtsy[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 duda[0] = 1.0; duda[1] = deltaEx[x] * deltaEy[y]; duda[2] = du_dtx[x] * deltaEy[y]; duda[3] = du_dty[y] * deltaEx[x]; duda[4] = du_dtsx[x] * deltaEy[y] + du_dtsy[y] * deltaEx[x]; d2uda2[0] = 0; d2uda2[1] = 0; d2uda2[2] = d2u_dtx2[x] * deltaEy[y]; d2uda2[3] = d2u_dty2[y] * deltaEx[x]; // Working example of this in GraspJ source code: // https://github.com/isman7/graspj/blob/master/graspj/src/main/java/eu/brede/graspj/opencl/src/functions/psfmodel_derivatives_sigma.cl //@formatter:off d2uda2[4] = d2u_dtsx2[x] * deltaEy[y] + d2u_dtsy2[y] * deltaEx[x] + 2 * du_dtsx[x] * du_dtsy[y] / tI; //@formatter:on return tB + tI * duda[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 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 du_dtsy = this.du_dtsy[y]; for (int x = 0; x < maxx; x++) { duda[1] = deltaEx[x] * deltaEy; duda[2] = du_dtx[x] * deltaEy; duda[3] = du_dty * deltaEx[x]; duda[4] = du_dtsx[x] * deltaEy + du_dtsy * deltaEx[x]; procedure.execute(tB + tI * duda[1], 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++) { final double du_dty = this.du_dty[y]; final double deltaEy = this.deltaEy[y]; final double du_dtsy = this.du_dtsy[y]; final double two_du_dtsy_tI = 2 * this.du_dtsy[y] / tI; final double d2u_dty2 = this.d2u_dty2[y]; final double d2u_dtsy2 = this.d2u_dtsy2[y]; for (int x = 0; x < maxx; x++) { duda[1] = deltaEx[x] * deltaEy; duda[2] = du_dtx[x] * deltaEy; duda[3] = du_dty * deltaEx[x]; duda[4] = du_dtsx[x] * deltaEy + du_dtsy * deltaEx[x]; d2uda2[2] = d2u_dtx2[x] * deltaEy; d2uda2[3] = d2u_dty2 * deltaEx[x]; //@formatter:off d2uda2[4] = d2u_dtsx2[x] * deltaEy + d2u_dtsy2 * deltaEx[x] + du_dtsx[x] * two_du_dtsy_tI; //@formatter:on procedure.execute(tB + tI * duda[1], duda, d2uda2); } } } }