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175 lines
7.5 KiB
175 lines
7.5 KiB
from __future__ import annotations |
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import typing |
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from dataclasses import dataclass, field |
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from itertools import chain |
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from functools import partial |
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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_rf, theta_rf, sigma_x, sigma_y, sigma, x, y, theta_grating, phi_grating = sp.symbols(r'k x_0 y_0 \phi_{rf} \theta_{rf} \sigma_x \sigma_y \sigma x y \theta_{grating} \phi_{grating}') |
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defaults = { |
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k: 6, |
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sigma: 1, |
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phi_rf: sp.pi / 2, |
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phi_grating: sp.pi / 2, |
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theta_grating: 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_grating) + k * (y - y0) * sp.sin(theta_grating) + phi_grating) |
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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_rf) + k * y * sp.sin(theta_rf) + phi_rf) |
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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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p = (1 / 2) * sp.exp(-k*k*sigma*sigma) * ( |
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sp.exp(-k*k*sigma*sigma*sp.sin(theta_grating + theta_rf)) * sp.cos(phi_grating + phi_rf + 2 * k / (sigma * sigma) * ( |
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x0 * sp.cos(theta_rf) + y0 * sp.sin(theta_grating) |
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+ x0 * sp.sin(theta_rf) + y0 * sp.cos(theta_grating) |
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)) + |
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sp.exp( k*k*sigma*sigma*sp.sin(theta_grating + theta_rf)) * sp.cos(phi_grating - phi_rf + 2 * k / (sigma * sigma) * ( |
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-x0 * sp.cos(theta_rf) - y0 * sp.sin(theta_rf) |
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+ x0 * sp.sin(theta_rf) + y0 * sp.cos(theta_grating) |
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))) |
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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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phi_split = np.arange(0, 2 * np.pi, np.pi / 100) |
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theta_split = np.arange(0, np.pi, np.pi / 100) |
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# The second option is (the distribution function, the function that takes the size and returns the step and the starting point) |
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Distribution = typing.Union[float, typing.Dict[float, float], typing.Tuple[typing.Callable[[float], float], typing.Callable[[int], typing.Tuple[float, float]]]] |
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def sample_distribution(distribution: Distribution, size: int = 1) -> np.ndarray: |
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if isinstance(distribution, float) or isinstance(distribution, int): |
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return np.array([float(distribution)] * size) |
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if isinstance(distribution, dict): |
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return np.random.choice(list(distribution.keys()), size, p=list(distribution.values())) |
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elif isinstance(distribution, tuple): |
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step, start = distribution[1](size) |
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res = [start] |
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for i in range(size): |
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res.append(res[-1] + step / distribution[0](res[-1])) |
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return np.array(res) |
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else: |
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raise ValueError(f'Unknown distribution type: {type(distribution)}') |
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def get_uniform_dist(start: float, stop: float) -> Distribution: |
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return (lambda _x: 1, lambda size: ((stop - start) / (size - 1 or 1), start)) |
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phi_dist_uni = get_uniform_dist(0, 2 * np.pi) |
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theta_dist_uni = get_uniform_dist(0, np.pi) |
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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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phi_val: float |
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theta_val: float |
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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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@property |
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def sympy_func(self) -> sp.Expr: |
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return receptive_field\ |
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.subs(sigma, self.sigma_val).subs(x0, self.x0_val).subs(y0, self.y0_val)\ |
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.subs(k, self.k_val).subs(phi_rf, self.phi_val).subs(theta_rf, self.theta_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_grating, phi_grating), |
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p.subs(sigma, self.sigma_val).subs(x0, self.x0_val)\ |
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.subs(y0, self.y0_val).subs(k, self.k_val)\ |
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.subs(phi_rf, self.phi_val).subs(theta_rf, self.theta_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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phi_val: float = defaults[phi_grating] |
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theta_val: float = defaults[theta_grating] |
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k_val: float = defaults[k] |
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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_grating, self.phi_val).subs(theta_grating, 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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@property |
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def response_func(self) -> typing.Callable[[float, float], np.ndarray]: |
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""" |
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Use sp.lambdify and the expression to generate the necessary function. |
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:return: a function (phi, theta) -> responses |
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""" |
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return partial( |
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sp.lambdify( |
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(x0, y0, k, sigma, phi_rf, theta_rf, phi_grating, theta_grating, ), |
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p, 'numpy'), |
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0, 0, np.array([cell.k_val for cell in self.cells]).reshape((-1, 1)), |
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np.array([cell.sigma_val for cell in self.cells]).reshape((-1, 1)), |
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np.array([cell.phi_val for cell in self.cells]).reshape((-1, 1)), |
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np.array([cell.theta_val for cell in self.cells]).reshape((-1, 1)), |
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) |
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@classmethod |
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def sample(cls, n_orient: int, n_phases: int, |
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phi_dist: Distribution = phi_dist_uni, |
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theta_dist: Distribution = theta_dist_uni, |
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sigma_dist: Distribution = defaults[sigma], |
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k_val: float = defaults[k], |
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xy_dist: Distribution = get_uniform_dist(-5, 5)): |
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return cls(cells=[ |
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Cell(phi_val=phi_val, theta_val=theta_val, sigma_val=sigma_val, x0_val=x0_val * 0, y0_val=y0_val * 0, k_val=k_val) |
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for phi_val, theta_val, sigma_val, x0_val, y0_val in zip( |
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list(sample_distribution(phi_dist, n_phases)) * n_orient, |
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list(chain(*[[x] * n_phases for x in sample_distribution(theta_dist, n_orient)])), |
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sample_distribution(sigma_dist, n_phases * n_orient), |
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sample_distribution(xy_dist, n_phases * n_orient), |
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sample_distribution(xy_dist, n_phases * n_orient)) |
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]) |
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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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