Topology in neuroscience
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import numpy as np
import sympy as sp
def eval_func(func: sp.Expr, sub_1: sp.Expr, sub_2: sp.Expr, grid: np.ndarray) -> np.ndarray:
# return np.array([[float(func.subs(sub_1, x_).subs(sub_2, y_)) for x_, y_ in line] for line in grid])
func = sp.lambdify([sub_1, sub_2], func, 'numpy')
return func(grid[:, :, 0], grid[:, :, 1])
def get_orientation_phase_grid(step_phase: float, step_orientation: float) -> np.ndarray:
"""
Returns a grid of x and y values for plotting.
:param step_phase: step for the phase (phi) - in degrees
:param step_orientation: step for the orientation (theta) - in degrees
:return: numpy array of shape (n_orientation, n_phase). Each element is a tuple (theta, phi)
"""
# phase <-> phi
# orientation <-> theta
step_phase *= np.pi / 180
step_orientation *= np.pi / 180
phi = np.arange(0, 2 * np.pi, step_phase)
theta = np.arange(0, np.pi, step_orientation)
return np.array(np.meshgrid(theta, phi)).T.reshape(-1, len(phi), 2)
def get_spatial_grid(step_x: float, step_y: float, size: float = 1) -> np.ndarray:
"""
Returns a grid of x and y values for plotting.
:param step_x: step for the x-coordinate
:param step_y: step for the y-coordinate
:param size: size of the grid
:return: numpy array of shape (2 * size / step_x, 2 * size / step_y). Each element is a tuple (x, y)
"""
x = np.arange(-size, size, step_x)
y = np.arange(-size, size, step_y)
return np.array(np.meshgrid(x, y)).T.reshape(-1, len(x), 2)