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116 lines
4.5 KiB
116 lines
4.5 KiB
from __future__ import annotations |
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import typing |
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from dataclasses import dataclass, field |
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import matplotlib as mpl |
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import sympy as sp |
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import numpy as np |
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from utils import get_orientation_phase_grid |
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sp.init_printing() |
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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') |
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defaults = { |
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k: 6, |
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sigma: 0.2, |
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phi: sp.pi / 2, |
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theta: 0, |
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sigma: 1, |
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x0: 0, y0: 0 |
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} |
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sigma_x = sigma_y = sigma |
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grating_f = sp.cos(k * (x - x0) * sp.cos(theta) + k * (y - y0) * sp.sin(theta) + phi) |
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receptive_field = 1 / (2 * sp.pi * sigma * sigma) * sp.exp(-(x ** 2 + y ** 2) / (2 * sigma ** 2)) * sp.cos( |
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k * x * sp.cos(theta) + k * y * sp.sin(theta) + phi) |
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receptive_field = receptive_field.subs(theta, 0).subs(phi, 0) |
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# p = sp.cosh(k ** 2 * sigma ** 2 * sp.cos(theta)) * sp.exp(k ** 2 * (1 + sp.cos(theta) ** 2) / 2) * sp.cos( |
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# phi - k * (x0 * sp.cos(theta) + y0 * sp.sin(theta))) |
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p = sp.cosh(k ** 2 * sigma ** 2 * sp.cos(theta) * 4) * sp.exp(-4 * k ** 2 * sigma ** 2) * sp.cos( |
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phi - k * (x0 * sp.cos(theta) + y0 * sp.sin(theta))) |
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sigma_split = np.arange(0.1, 1, 0.05) |
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k_split = np.arange(0.2, 6, 0.2) |
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xy_split = np.arange(-1, 1, 0.05) |
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def sigmoid(x): |
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return 1 / (1 + np.exp(-x)) |
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@dataclass |
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class Cell: |
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sigma_val: float = defaults[sigma] |
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x0_val: float = defaults[x0] |
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y0_val: float = defaults[y0] |
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k_val: float = defaults[k] |
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@classmethod |
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def random(cls, sigma_dist: np.ndarray = np.ones(len(sigma_split)), |
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k_val: float = defaults[k], |
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xy_dist: np.ndarray = np.ones(len(xy_split))): |
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return cls( |
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sigma_val=np.random.choice(sigma_split, p=sigma_dist / np.sum(sigma_dist)), |
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x0_val=np.random.choice(xy_split, p=xy_dist / np.sum(xy_dist)), |
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y0_val=np.random.choice(xy_split, p=xy_dist / np.sum(xy_dist)), |
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k_val=k_val |
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) |
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@property |
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def sympy_func(self) -> sp.Expr: |
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return receptive_field.subs(sigma, self.sigma_val).subs(x0, self.x0_val).subs(y0, self.y0_val).subs(k, |
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self.k_val) |
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def get_tuning_function(self) -> typing.Callable[[np.ndarray, np.ndarray], np.ndarray]: |
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""" |
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Get the tuning sympy function as a numpy lambda function of theta and phi. |
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:return: a function (theta, phi) -> value |
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""" |
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return sp.lambdify( |
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(theta, phi), |
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p.subs(sigma, self.sigma_val).subs(x0, self.x0_val).subs(y0, self.y0_val).subs(k, self.k_val), |
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'numpy') |
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def get_value(self, theta_deg: float, phi_deg: float) -> float: |
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return float(self.get_tuning_function()(theta_deg * np.pi / 180, phi_deg * np.pi / 180)) |
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def get_tuning_plot(self, theta_step_deg: float, phi_step_deg: float) -> np.ndarray: |
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grid = get_orientation_phase_grid(theta_step_deg, phi_step_deg) |
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return self.get_tuning_function()(grid[:, :, 0], grid[:, :, 1]) |
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@dataclass |
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class Grating: |
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k_val: float = defaults[k] |
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phi_val: float = defaults[phi] |
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theta_val: float = defaults[theta] |
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@property |
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def sympy_func(self) -> sp.Expr: |
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return grating_f.subs(k, self.k_val).subs(phi, self.phi_val).subs(theta, self.theta_val) |
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@dataclass |
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class Population: |
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cells: typing.List[Cell] = field(default_factory=list) |
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@classmethod |
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def random(cls, n: int, sigma_dist: np.ndarray = np.ones(len(sigma_split)), |
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k_val: float = defaults[k], |
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xy_dist: np.ndarray = np.ones(len(xy_split))): |
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return cls(cells=[Cell.random(sigma_dist, k_val, xy_dist) for _ in range(n)]) |
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def get_response(self, phi_deg: float, theta_deg: float, coef: float = 4, use_sigmoid: bool = True) -> np.ndarray: |
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return (sigmoid if use_sigmoid else (lambda x: x))(np.array([cell.get_value(theta_deg, phi_deg) for cell in self.cells]) * coef) |
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def sample_responses( |
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self, n: int, noise_sigma: float = 0, coef: float = 2, use_sigmoid: bool = True, |
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custom_grid: typing.Optional[np.ndarray] = None |
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) -> np.ndarray: |
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return np.array([ |
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np.array([self.get_response(phi_deg, theta_deg % 180, coef=coef, use_sigmoid=use_sigmoid), np.ones(len(self.cells)) * phi_deg, |
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np.ones(len(self.cells)) * theta_deg]).swapaxes(0, 1) |
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for phi_deg, theta_deg in (np.random.uniform(0, 360, (n, 2)) if custom_grid is None else custom_grid) |
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]) + np.random.normal( |
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0, [noise_sigma, 0, 0], |
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(n if custom_grid is None else len(custom_grid), len(self.cells), 3))
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