amgen/model/sym_model.py

from __future__ import annotations
import typing
from dataclasses import dataclass, field
from functools import partial

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_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}')
defaults = {
    k: 6,
    sigma: 1,
    phi_rf: sp.pi / 2,
    phi_grating: sp.pi / 2,
    theta_grating: 0,
    sigma: 1,
    x0: 0, y0: 0
}
sigma_x = sigma_y = sigma
grating_f = sp.cos(k * (x - x0) * sp.cos(theta_grating) + k * (y - y0) * sp.sin(theta_grating) + phi_grating)
receptive_field = 1 / (2 * sp.pi * sigma * sigma) * sp.exp(-(x ** 2 + y ** 2) / (2 * sigma ** 2)) * sp.cos(
    k * x * sp.cos(theta_rf) + k * y * sp.sin(theta_rf) + phi_rf)
# 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)))

# p = sp.cosh(k ** 2 * sigma ** 2 * sp.cos(theta) * 4) * sp.exp(-4 * k ** 2 * sigma ** 2) * sp.cos(
#     phi - k * (x0 * sp.cos(theta) + y0 * sp.sin(theta)))

p = (1 / 2) * sp.exp(-k*k*sigma*sigma) * (
    sp.exp(-k*k*sigma*sigma*sp.sin(theta_grating + theta_rf)) * sp.cos(phi_grating + phi_rf + 2 * k / (sigma * sigma) * (
        x0 * sp.cos(theta_rf) + y0 * sp.sin(theta_grating) 
        + x0 * sp.sin(theta_rf) + y0 * sp.cos(theta_grating)
    )) + 
    sp.exp( k*k*sigma*sigma*sp.sin(theta_grating + theta_rf)) * sp.cos(phi_grating - phi_rf + 2 * k / (sigma * sigma) * (
        -x0 * sp.cos(theta_rf) - y0 * sp.sin(theta_rf)
        + x0 * sp.sin(theta_rf) + y0 * sp.cos(theta_grating)
)))

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)
phi_split = np.arange(0, 2 * np.pi, np.pi / 100)
theta_split = np.arange(0, np.pi, np.pi / 100)

# The second option is (the distribution function, the function that takes the size and returns the step and the starting point)
Distribution = typing.Union[float, typing.Dict[float, float], typing.Tuple[typing.Callable[[float], float], typing.Callable[[int], typing.Tuple[float, float]]]]


def sample_distribution(distribution: Distribution, size: int = 1) -> np.ndarray:
    if isinstance(distribution, float) or isinstance(distribution, int):
        return np.array([float(distribution)] * size)
    if isinstance(distribution, dict):
        return np.random.choice(list(distribution.keys()), size, p=list(distribution.values()))
    elif isinstance(distribution, tuple):
        step, start = distribution[1](size)
        res = [start]
        for i in range(size):
            res.append(res[-1] + step / distribution[0](res[-1]))
        return np.array(res)
    else:
        raise ValueError(f'Unknown distribution type: {type(distribution)}')


def get_uniform_dist(start: float, stop: float) -> Distribution:
    return (lambda _x: 1, lambda size: ((stop - start) / (size - 1 or 1), start))

phi_dist_uni = get_uniform_dist(0, 2 * np.pi)
theta_dist_uni = get_uniform_dist(0, np.pi)


def sigmoid(x):
    return 1 / (1 + np.exp(-x))


@dataclass
class Cell:
    phi_val: float
    theta_val: float
    sigma_val: float = defaults[sigma]
    x0_val: float = defaults[x0]
    y0_val: float = defaults[y0]
    k_val: float = defaults[k]

    @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).subs(phi_rf, self.phi_val).subs(theta_rf, self.theta_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_grating, phi_grating),
            p.subs(sigma, self.sigma_val).subs(x0, self.x0_val)\
                .subs(y0, self.y0_val).subs(k, self.k_val)\
                .subs(phi_rf, self.phi_val).subs(theta_rf, self.theta_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:
    phi_val: float = defaults[phi_grating]
    theta_val: float = defaults[theta_grating]
    k_val: float = defaults[k]

    @property
    def sympy_func(self) -> sp.Expr:
        return grating_f.subs(k, self.k_val).subs(phi_grating, self.phi_val).subs(theta_grating, self.theta_val)


@dataclass
class Population:
    cells: typing.List[Cell] = field(default_factory=list)

    @property
    def response_func(self) -> typing.Callable[[float, float], np.ndarray]:
        """
        Use sp.lambdify and the expression to generate the necessary function.
        :return: a function (phi, theta) -> responses
        """
        return partial(
            sp.lambdify(
                (x0, y0, k, sigma, phi_rf, theta_rf, phi_grating, theta_grating, ),
                p, 'numpy'),
                0, 0, np.array([cell.k_val for cell in self.cells]).reshape((-1, 1)),
                np.array([cell.sigma_val for cell in self.cells]).reshape((-1, 1)),
                np.array([cell.phi_val for cell in self.cells]).reshape((-1, 1)),
                np.array([cell.theta_val for cell in self.cells]).reshape((-1, 1)),
                )

    @classmethod
    def random(cls, n: int, 
               phi_dist: Distribution = phi_dist_uni,
               theta_dist: Distribution = theta_dist_uni,
               sigma_dist: Distribution = defaults[sigma],
               k_val: float = defaults[k],
               xy_dist: Distribution = get_uniform_dist(-5, 5)):
        return cls(cells=[
            Cell(phi_val=phi_val, theta_val=theta_val, sigma_val=sigma_val, x0_val=x0_val, y0_val=y0_val, k_val=k_val) 
            for phi_val, theta_val, sigma_val, x0_val, y0_val in zip(
                sample_distribution(phi_dist, n),
                sample_distribution(theta_dist, n),
                sample_distribution(sigma_dist, n),
                sample_distribution(xy_dist, n),
                sample_distribution(xy_dist, n))
        ])

    def get_response(self, phi_deg: float, theta_deg: float, coef: float = 4, use_sigmoid: bool = True) -> np.ndarray:
        return (sigmoid if use_sigmoid else (lambda x: x))(np.array([cell.get_value(theta_deg, phi_deg) for cell in self.cells]) * coef)

    def sample_responses(
            self, n: int, noise_sigma: float = 0, coef: float = 2, use_sigmoid: bool = True,
            custom_grid: typing.Optional[np.ndarray] = None
    ) -> np.ndarray:
        return np.array([
            np.array([self.get_response(phi_deg, theta_deg % 180, coef=coef, use_sigmoid=use_sigmoid), np.ones(len(self.cells)) * phi_deg,
                      np.ones(len(self.cells)) * theta_deg]).swapaxes(0, 1)
            for phi_deg, theta_deg in (np.random.uniform(0, 360, (n, 2)) if custom_grid is None else custom_grid)
        ]) + np.random.normal(
            0, [noise_sigma, 0, 0],
            (n if custom_grid is None else len(custom_grid), len(self.cells), 3))