Add python files with models

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

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))
+        ])

utils.py

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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)