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Genome Damage and Stability Centre SMLM Package Software for single molecule localisation microscopy (SMLM)
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/*-
 * #%L
 * Genome Damage and Stability Centre SMLM Package
 *
 * Software for single molecule localisation microscopy (SMLM)
 * %%
 * Copyright (C) 2011 - 2023 Alex Herbert
 * %%
 * 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.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public
 * License along with this program.  If not, see
 * .
 * #L%
 */

package uk.ac.sussex.gdsc.smlm.function.gaussian;

import uk.ac.sussex.gdsc.smlm.utils.StdMath;

/**
 * Evaluates a 2-dimensional Gaussian function for a single peak.
 *
 * 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.
 *
 * 
Data should be packed in descending dimension order, e.g. Y,X : Index for [x,y] = MaxX*y + x.
 */
public class SingleFixedGaussian2DFunction extends Gaussian2DFunction {
  private static final int[] gradientIndices;

  static {
    gradientIndices = createGradientIndices(1, new SingleFixedGaussian2DFunction(1, 1));
  }

  /** The background. */
  protected double background;
  /** The x0 position. */
  protected double x0pos;
  /** The x1 position. */
  protected double x1pos;

  /** The amplitude./height normalisation: 1/(2*pi*sx*sx). */
  protected double norm;
  /** The amplitude./height. */
  protected double height;
  /** x0 position pre-factor. */
  protected double aa;
  /** x0 position gradient pre-factor. */
  protected double aa2;

  /**
   * 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 SingleFixedGaussian2DFunction(int maxx, int maxy) {
    super(maxx, maxy);
  }

  @Override
  public Gaussian2DFunction copy() {
    return new SingleFixedGaussian2DFunction(maxx, maxy);
  }

  @Override
  public void initialise(double[] a) {
    background = a[BACKGROUND];
    x0pos = a[X_POSITION];
    x1pos = a[Y_POSITION];

    final double sx = a[X_SD];
    final double sx2 = sx * sx;

    norm = ONE_OVER_TWO_PI / sx2;
    height = a[SIGNAL] * norm;

    // All prefactors are negated since the Gaussian uses the exponential to the negative:
    // A * exp( -( a(x-x0)^2 + 2b(x-x0)(y-y0) + c(y-y0)^2 ) )

    aa = -0.5 / sx2;
    aa2 = -2.0 * aa;
  }

  /**
   * Evaluates a 2-dimensional fixed circular Gaussian function for a single peak.
   *
   * 
{@inheritDoc}
   */
  @Override
  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);
  }

  /**
   * Evaluates a 2-dimensional fixed circular Gaussian function for a single peak.
   *
   * {@inheritDoc}
   */
  @Override
  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 * StdMath.exp(aa * (dx * dx + dy * dy));
  }

  private double gaussian(final int x0, final int x1, final double[] dyDa) {
    final double dx = x0 - x0pos;
    final double dy = x1 - x1pos;

    // Calculate gradients

    final double exp = StdMath.exp(aa * (dx * dx + dy * dy));
    dyDa[1] = norm * exp;
    final double y = height * exp;
    final double yaa2 = y * aa2;
    dyDa[2] = yaa2 * dx;
    dyDa[3] = yaa2 * dy;

    return y;
  }

  @Override
  public int getNPeaks() {
    return 1;
  }

  @Override
  public boolean evaluatesBackground() {
    return true;
  }

  @Override
  public boolean evaluatesSignal() {
    return true;
  }

  @Override
  public boolean evaluatesAngle() {
    return false;
  }

  @Override
  public boolean evaluatesPosition() {
    return true;
  }

  @Override
  public boolean evaluatesSD0() {
    return false;
  }

  @Override
  public boolean evaluatesSD1() {
    return false;
  }

  @Override
  public int getGradientParametersPerPeak() {
    return 3;
  }

  @Override
  public int[] gradientIndices() {
    return gradientIndices;
  }
}