import numpy as np
import scipy.stats as stats
[docs]def gauss1D_cart(x, mu=0.0, sigma=1.0):
"""gauss1D_cart
gauss1D_cart takes a 1D array x, a mean and standard deviation,
and produces a gaussian with given parameters, with a peak of height 1.
Parameters
----------
x : numpy.ndarray (1D)
space on which to calculate the gauss
mu : float, optional
mean/mode of gaussian (the default is 0.0)
sigma : float, optional
standard deviation of gaussian (the default is 1.0)
Returns
-------
numpy.ndarray
gaussian values at x
"""
return np.exp(-((x-mu)**2)/(2*sigma**2)).astype('float32')
[docs]def gauss1D_log(x, mu=0.0, sigma=1.0):
"""gauss1D_log
gauss1D_log takes a 1D array x, a mean and standard deviation,
and produces a pRF with given parameters with the distance between mean and x log-scaled
Parameters
----------
x : numpy.ndarray (1D)
space on which to calculate the gauss
mu : float, optional
mean/mode of gaussian (the default is 0.0)
sigma : float, optional
standard deviation of gaussian (the default is 1.0)
Returns
-------
numpy.ndarray
gaussian values at log(x)
"""
return np.exp(-(np.log(x/mu)**2)/(2*sigma**2)).astype('float32')
[docs]def vonMises1D(x, mu=0.0, kappa=1.0):
"""vonMises1D
vonMises1D takes a 1D array x, a mean and kappa (inverse of standard deviation),
and produces a von Mises pRF with given parameters. This shape can be thought of
as a circular gaussian shape. Used for orientation or motion direction pRFs,
for instance.
Parameters
----------
x : numpy.ndarray (1D)
space on which to calculate the von Mises.
Assumed to be in the range (0, 2*np.pi)
mu : float, optional
mean/mode of von Mises (the default is 0.0)
kappa : float, optional
dispersion coefficient of the von Mises,
akin to invers of standard deviation of gaussian (the default is 1.0)
Returns
-------
numpy.ndarray
von Mises values at x, peak has y-value of 1
"""
vm = stats.vonmises.pdf(x-mu, kappa)
return vm / np.max(vm)
[docs]def gauss2D_iso_cart(x, y, mu=(0.0, 0.0), sigma=1.0, normalize_RFs=False):
"""gauss2D_iso_cart
gauss2D_iso_cart takes two-dimensional arrays x and y, containing
the x and y coordinates at which to evaluate the 2D isotropic gaussian
function, with a given sigma, and returns a 2D array of Z values.
Parameters
----------
x : numpy.ndarray, 2D or flattened by masking
2D, containing x coordinates
y : numpy.ndarray, 2D or flattened by masking
2D, containing y coordinates
mu : tuple, optional
mean, 2D coordinates of mean/mode of gauss (the default is (0.0,0.0))
sigma : float, optional
standard deviation of gauss (the default is 1.0)
Returns
-------
numpy.ndarray, 2D or flattened by masking
gaussian values evaluated at (x,y)
"""
if normalize_RFs:
return (np.exp(-((x-mu[0])**2 + (y-mu[1])**2)/(2*sigma**2)) /(2*np.pi*sigma**2)).astype('float32')
else:
return (np.exp(-((x-mu[0])**2 + (y-mu[1])**2)/(2*sigma**2))).astype('float32')
[docs]def gauss2D_rot_cart(x, y, mu=(0.0, 0.0), sigma=1.0, theta=0.0, ar=1.0):
"""gauss2D_rot_cart
gauss2D_rot_cart takes two-dimensional arrays x and y, containing
the x and y coordinates at which to evaluate the 2D non-isotropic gaussian
function, with a given sigma, angle of rotation theta, and aspect ratio ar.
it returns a 2D array of Z values. Default is an isotropic gauss.
Parameters
----------
x : numpy.ndarray, 2D
2D, containing x coordinates or flattened by masking
y : numpy.ndarray, 2D
2D, containing y coordinates or flattened by masking
mu : tuple, optional
mean, 2D coordinates of mean/mode of gauss (the default is (0.0,0.0))
sigma : float, optional
standard deviation of gauss (the default is 1.0)
theta : float, optional
angle of rotation of gauss (the default is 0.0)
ar : float, optional
aspect ratio of gauss, multiplies the rotated y parameters (the default is 1.0)
Returns
-------
numpy.ndarray, 2D or flattened by masking
gaussian values evaluated at (x,y)
"""
xr = (x-mu[0]) * np.cos(theta) + (y-mu[1]) * np.sin(theta)
yr = -(x-mu[0]) * np.sin(theta) + (y-mu[1]) * np.cos(theta)
return np.exp(-(xr**2 + ar**2 * yr**2)/(2*sigma**2))
[docs]def gauss2D_logpolar(ecc, polar, mu=(1.0, 0.0), sigma=1.0, kappa=1.0):
"""gauss2D_logpolar
gauss2D_logpolar takes two-dimensional arrays ecc and polar, containing
the eccentricity and polar angle coordinates at which to evaluate the 2D gaussian,
which in this case is a von Mises in the polar angle direction, and a log gauss
in the eccentricity dimension, and returns a 2D array of Z values.
We recommend entering the ecc and polar angles ordered as x and y for easy
visualization.
Parameters
----------
ecc : numpy.ndarray, 2D or flattened by masking
2D, containing eccentricity
polar : numpy.ndarray, 2D or flattened by masking
2D, containing polar angle coordinates (0, 2*np.pi)
mu : tuple, optional
mean, 2D coordinates of mean/mode of gauss (ecc) and von Mises (polar) (the default is (0.0,0.0))
sigma : float, optional
standard deviation of gauss (the default is 1.0)
kappa : float, optional
dispersion coefficient of the von Mises,
akin to inverse of standard deviation of gaussian (the default is 1.0)
Returns
-------
numpy.ndarray, 2D or flattened by masking
values evaluated at (ecc, polar), peak has y-value of 1.
"""
ecc_gauss = np.exp(-(np.log(ecc/mu[0])**2)/(2*sigma**2))
polar_von_mises = stats.vonmises.pdf(polar-mu[1], kappa)
polar_von_mises /= np.max(polar_von_mises)
logpolar_Z = ecc_gauss * polar_von_mises
return logpolar_Z / np.max(logpolar_Z)
