functions.py

"""
Created on Thu Oct 25 15:54:19 2018
General function script to load from
@author: alexschw
"""
import itertools
import numpy as np


def Gaussian2D(Amp, Shape, Sig):
    """
    Computes a 2D gaussian with given amplitude, shape and width (sigma)
    """
    Sig = np.array(Sig)
    # If one or both of the shape values are zero replace it by 6*sigma
    Shape += (Shape == np.zeros(2)) * np.ceil(3 * Sig).astype('int')
    # Decrease even shape values by 1
    Shape -= (Shape % 2 == 0)
    # Calculate the center of the shape
    G_Center = (Shape - 1) // 2
    # gauss = Amp * exp(-((x - cx)^2 / (2*sx^2) + (y - cy)^2 / (2*sy^2)))
    gauss = np.array(np.meshgrid(*map(np.arange, Shape)))
    gauss = 0.5 * (gauss - G_Center[:, None, None])**2 / Sig[:, None, None]**2
    gauss = Amp * np.exp(-np.sum(gauss, axis=0))
    return gauss.transpose()


def Gabor(Amp, Shape, Sig, theta, freq):
    """
    Compute a 2D Gabor with given Amplitude, Shape, Width(Sig)
    Orientation in degree(theta) and Frequency (freq).
    """
    # convert degree to radians
    theta = theta * np.pi / 180
    Sig = np.array(Sig)
    halfSDsq = 1.0 / (2 * Sig**2)
    # If one or both of the shape values are zero replace it by 6*sigma
    Shape += (Shape == np.zeros(2)) * np.ceil(3 * Sig).astype('int')
    # Decrease even shape values by 1
    Shape -= (Shape % 2 == 0)
    # Calculate the center of the shape
    G_cen = (Shape - 1) // 2
    # gauss = Amp * exp(-((x - cx)^2 / (2*sx^2) + (y - cy)^2 / (2*sy^2)))
    grid = np.array(np.meshgrid(*map(np.arange, Shape))) - G_cen[:, None, None]

    x_th = grid[0, :, :] * np.cos(theta) + grid[1, :, :] * np.sin(theta)
    y_th = -grid[0, :, :] * np.sin(theta) + grid[1, :, :] * np.cos(theta)

    Gaussian = np.exp(-halfSDsq[0] * x_th * x_th - halfSDsq[1] * y_th * y_th)
    gabor = Amp * Gaussian * np.cos(np.pi * freq * y_th / Shape[0])
    return gabor


def positive(Arr):
    """
    Removes values smaller than zero from the given Array
    """
    A = np.array(Arr)  # To avoid overwriting the input, a new array is created
    A[A < 0] = 0
    return A


def normpdf(x, mu, sigma):
    """
    Defines a normal probability density function
    """
    return np.exp(-0.5 * ((x - mu) / sigma)**2) / (np.sqrt(2.0 * np.pi) * sigma)


def rangeX(iterations):
    """
    Multidimensional iterator using all possible combinations within the given
    boundaries e.g. rangeX((2,3)) => 00 01 02 10 11 12
    """
    if not isinstance(iterations, (tuple)):
        raise AttributeError
    return itertools.product(*map(range, iterations))
  


if __name__ == '__main__':
    G, co, gab = Gabor(1.0, [200, 200], [20, 10], 30, 3)