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Add python files with models

master
Lev 2 years ago
parent
commit
e41b428d56
  1. 146
      PopulationSampling.ipynb
  2. 560
      TuningCurvesFull.ipynb
  3. 78
      plotting_utils.py
  4. 103
      sym_model.py
  5. 37
      utils.py

146
PopulationSampling.ipynb

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560
TuningCurvesFull.ipynb

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78
plotting_utils.py

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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

103
sym_model.py

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from __future__ import annotations
import typing
from dataclasses import dataclass, field
import matplotlib as mpl
import sympy as sp
import numpy as np
from utils import get_orientation_phase_grid
sp.init_printing()
k, x0, y0, phi, theta, sigma_x, sigma_y, sigma, x, y = sp.symbols(r'k x_0 y_0 \phi \theta \sigma_x \sigma_y \sigma x y')
defaults = {
k: 6,
sigma: 0.2,
phi: sp.pi / 2,
theta: 0,
sigma: 1,
x0: 0, y0: 0
}
sigma_x = sigma_y = sigma
grating_f = sp.cos(k * (x - x0) * sp.cos(theta) + k * (y - y0) * sp.sin(theta) + phi)
receptive_field = 1 / (2 * sp.pi * sigma * sigma) * sp.exp(-(x ** 2 + y ** 2) / (2 * sigma ** 2)) * sp.cos(
k * x * sp.cos(theta) + k * y * sp.sin(theta) + phi)
receptive_field = receptive_field.subs(theta, 0).subs(phi, 0)
p = sp.cosh(k ** 2 * sigma ** 2 * sp.cos(theta)) * sp.exp(k ** 2 * (1 + sp.cos(theta) ** 2) / 2) * sp.cos(
phi - k * (x0 * sp.cos(theta) + y0 * sp.sin(theta)))
sigma_split = np.arange(0.1, 1, 0.05)
k_split = np.arange(0.2, 6, 0.2)
xy_split = np.arange(-1, 1, 0.05)
@dataclass
class Cell:
sigma_val: float = defaults[sigma]
x0_val: float = defaults[x0]
y0_val: float = defaults[y0]
k_val: float = defaults[k]
@classmethod
def random(cls, sigma_dist: np.ndarray = np.ones(len(sigma_split)),
k_val: float = defaults[k],
xy_dist: np.ndarray = np.ones(len(xy_split))):
return cls(
sigma_val=np.random.choice(sigma_split, p=sigma_dist / np.sum(sigma_dist)),
x0_val=np.random.choice(xy_split, p=xy_dist / np.sum(xy_dist)),
y0_val=np.random.choice(xy_split, p=xy_dist / np.sum(xy_dist)),
k_val=k_val
)
@property
def sympy_func(self) -> sp.Expr:
return receptive_field.subs(sigma, self.sigma_val).subs(x0, self.x0_val).subs(y0, self.y0_val).subs(k,
self.k_val)
def get_tuning_function(self) -> typing.Callable[[np.ndarray, np.ndarray], np.ndarray]:
"""
Get the tuning sympy function as a numpy lambda function of theta and phi.
:return: a function (theta, phi) -> value
"""
return sp.lambdify(
(theta, phi),
p.subs(sigma, self.sigma_val).subs(x0, self.x0_val).subs(y0, self.y0_val).subs(k, self.k_val),
'numpy')
def get_value(self, theta_deg: float, phi_deg: float) -> float:
return float(self.get_tuning_function()(theta_deg * np.pi / 180, phi_deg * np.pi / 180))
def get_tuning_plot(self, theta_step_deg: float, phi_step_deg: float) -> np.ndarray:
grid = get_orientation_phase_grid(theta_step_deg, phi_step_deg)
return self.get_tuning_function()(grid[:, :, 0], grid[:, :, 1])
@dataclass
class Grating:
k_val: float = defaults[k]
phi_val: float = defaults[phi]
theta_val: float = defaults[theta]
@property
def sympy_func(self) -> sp.Expr:
return grating_f.subs(k, self.k_val).subs(phi, self.phi_val).subs(theta, self.theta_val)
@dataclass
class Population:
cells: typing.List[Cell] = field(default_factory=list)
@classmethod
def random(cls, n: int, sigma_dist: np.ndarray = np.ones(len(sigma_split)),
k_val: float = defaults[k],
xy_dist: np.ndarray = np.ones(len(xy_split))):
return cls(cells=[Cell.random(sigma_dist, k_val, xy_dist) for _ in range(n)])
def get_response(self, phi_deg: float, theta_deg: float) -> typing.List[float]:
return [cell.get_value(theta_deg, phi_deg) for cell in self.cells]
def sample_responses(self, n: int) -> np.ndarray:
return np.array([
self.get_response(phi_deg, theta_deg % 180)
for phi_deg, theta_deg in np.random.uniform(0, 360, (n, 2))
])

37
utils.py

@ -0,0 +1,37 @@
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)
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