Topology in neuroscience
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import typing
import matplotlib as mpl
import numpy as np
import matplotlib.pyplot as plt
import sympy as sp
from utils import eval_func, get_orientation_phase_grid, get_spatial_grid
sp.init_printing()
AxOrImg = typing.Union[mpl.axes.Axes, mpl.image.AxesImage]
# %%
def plot_spatial(func: sp.Expr, ax: AxOrImg, step_x: float = 0.05, step_y: float = 0.05, size: float = 1,
title: str = None, show: bool = False,
patch: typing.Optional[typing.Tuple[float, float, float]] = None
):
"""
Plots a spatial map of the function.
:param func: function to plot
:param ax: axes to plot on or the image on axes
:param step_x: step for the x-coordinate
:param step_y: step for the y-coordinate
:param size: size of the grid
:param title: title of the plot
:param show: whether to show the plot
:param patch: optional circle to plot - a tuple (x, y, radius)
"""
grid = get_spatial_grid(step_x, step_y, size)
image: np.ndarray = eval_func(func, x, y, grid)
if isinstance(ax, mpl.image.AxesImage):
ax.set_data(image)
return ax
img = ax.imshow(image, extent=[-size, size, -size, size], vmin=-size, vmax=size, cmap='gray')
ax.invert_yaxis()
if patch is not None:
ax.add_patch(plt.Circle(patch[:2], radius=patch[2], color='b', fill=False))
ax.set_title(title)
if show:
plt.show()
return img
def normalize(img):
return (img - img.min()) / (img.max() - img.min())
def plot_tuning_curve(func: typing.Union[sp.Expr, typing.Callable], ax: AxOrImg, step_phase: float = 20,
step_orientation: float = 15, title: str = None, show: bool = False):
"""
Plots a tuning curve of the function.
:param func: function to plot - sympy or a function of (theta, phi)
:param ax: axes to plot on or image to update
:param step_phase: step for the phase (phi) - in degrees
:param step_orientation: step for the orientation (theta) - in degrees
:param title: title of the plot
:param show: whether to show the plot
"""
grid = get_orientation_phase_grid(step_phase, step_orientation)
if isinstance(func, sp.Expr):
image: np.ndarray = eval_func(func, theta, phi, grid)
else:
image = np.array([[func(theta_val, phi_val) for theta_val, phi_val in line] for line in grid])
image = normalize(image)
if isinstance(ax, mpl.image.AxesImage):
ax.set_data(image)
return ax
img = ax.imshow(image, extent=[0, 360, 0, 180], cmap='viridis')
ax.set_title(title)
if show:
plt.show()
return img