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617 lines
76 KiB
617 lines
76 KiB
{ |
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"cells": [ |
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{ |
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"cell_type": "markdown", |
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"metadata": { |
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"pycharm": { |
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"name": "#%% md\n" |
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} |
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}, |
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"source": [ |
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"# Tuning Curves" |
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] |
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}, |
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{ |
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"cell_type": "markdown", |
|
"metadata": { |
|
"pycharm": { |
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"name": "#%% md\n" |
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} |
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}, |
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"source": [ |
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"**Import everything**" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 1, |
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"metadata": { |
|
"pycharm": { |
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"name": "#%%\n" |
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} |
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}, |
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"outputs": [], |
|
"source": [ |
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"%matplotlib inline\n", |
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"import typing\n", |
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"\n", |
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"import matplotlib as mpl\n", |
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"import numpy as np\n", |
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"import matplotlib.pyplot as plt\n", |
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"\n", |
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"import ipywidgets as widgets\n", |
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"import sympy as sp\n", |
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"sp.init_printing()\n", |
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"AxOrImg = typing.Union[mpl.axes.Axes, mpl.image.AxesImage]" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 2, |
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"metadata": { |
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"pycharm": { |
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"name": "#%%\n" |
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} |
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}, |
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"outputs": [], |
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"source": [ |
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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')\n", |
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"defaults = {\n", |
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" k: 6,\n", |
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" sigma: 0.2,\n", |
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" phi: sp.pi / 2,\n", |
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" theta: 0,\n", |
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" sigma: 1,\n", |
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" x0: 0, y0: 0\n", |
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"}\n", |
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"sigma_x = sigma_y = sigma" |
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] |
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}, |
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{ |
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"cell_type": "markdown", |
|
"metadata": { |
|
"pycharm": { |
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"name": "#%% md\n" |
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} |
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}, |
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"source": [ |
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"#### Formulas" |
|
] |
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}, |
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{ |
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"cell_type": "code", |
|
"execution_count": 3, |
|
"metadata": { |
|
"pycharm": { |
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"name": "#%%\n" |
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} |
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}, |
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"outputs": [ |
|
{ |
|
"data": { |
|
"image/png": "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", |
|
"text/latex": [ |
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"$\\displaystyle \\cos{\\left(\\phi + k \\left(x - x_{0}\\right) \\cos{\\left(\\theta \\right)} + k \\left(y - y_{0}\\right) \\sin{\\left(\\theta \\right)} \\right)}$" |
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], |
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"text/plain": [ |
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"cos(\\phi + k⋅(x - x₀)⋅cos(\\theta) + k⋅(y - y₀)⋅sin(\\theta))" |
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] |
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}, |
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"execution_count": 3, |
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"metadata": {}, |
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"output_type": "execute_result" |
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} |
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], |
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"source": [ |
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"grating_f = sp.cos(k * (x - x0) * sp.cos(theta) + k * (y - y0) * sp.sin(theta) + phi)\n", |
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"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)\n", |
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"receptive_field = receptive_field.subs(theta, 0).subs(phi, 0)\n", |
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"grating_f" |
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] |
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}, |
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{ |
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"cell_type": "code", |
|
"execution_count": 4, |
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"metadata": { |
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"pycharm": { |
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"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [ |
|
{ |
|
"data": { |
|
"image/png": "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", |
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"text/latex": [ |
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"$\\displaystyle \\frac{e^{\\frac{- x^{2} - y^{2}}{2 \\sigma^{2}}} \\cos{\\left(k x \\right)}}{2 \\pi \\sigma^{2}}$" |
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], |
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"text/plain": [ |
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" 2 2 \n", |
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" - x - y \n", |
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" ───────── \n", |
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" 2 \n", |
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" 2⋅\\sigma \n", |
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"ℯ ⋅cos(k⋅x)\n", |
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"───────────────────\n", |
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" 2 \n", |
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" 2⋅π⋅\\sigma " |
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] |
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}, |
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"execution_count": 4, |
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"metadata": {}, |
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"output_type": "execute_result" |
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} |
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], |
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"source": [ |
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"receptive_field" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 5, |
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"metadata": { |
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"pycharm": { |
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"name": "#%%\n" |
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} |
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}, |
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"outputs": [], |
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"source": [ |
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"int1 = sp.Integral(grating_f * receptive_field, (x, -1, 1), (y, -1, 1)).subs(defaults)\n", |
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"# int1.evalf(2).doit()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 5, |
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"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
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} |
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}, |
|
"outputs": [], |
|
"source": [] |
|
}, |
|
{ |
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"cell_type": "code", |
|
"execution_count": 6, |
|
"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [ |
|
{ |
|
"data": { |
|
"image/png": "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", |
|
"text/latex": [ |
|
"$\\displaystyle e^{- 4 \\sigma^{2} k^{2}} \\cos{\\left(\\phi - k \\left(x_{0} \\cos{\\left(\\theta \\right)} + y_{0} \\sin{\\left(\\theta \\right)}\\right) \\right)} \\cosh{\\left(4 \\sigma^{2} k^{2} \\cos{\\left(\\theta \\right)} \\right)}$" |
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], |
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"text/plain": [ |
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" 2 2 \n", |
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" -4⋅\\sigma ⋅k ⎛ 2 \n", |
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"ℯ ⋅cos(\\phi - k⋅(x₀⋅cos(\\theta) + y₀⋅sin(\\theta)))⋅cosh⎝4⋅\\sigma ⋅\n", |
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"\n", |
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" \n", |
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" 2 ⎞\n", |
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"k ⋅cos(\\theta)⎠" |
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] |
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}, |
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"execution_count": 6, |
|
"metadata": {}, |
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"output_type": "execute_result" |
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} |
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], |
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"source": [ |
|
"# p = sp.cos(phi) * sp.cos(k*x0*sp.cos(theta) + k*y0*sp.sin(theta)) * sp.exp(k**2 * (sigma_x **2 * (1 + sp.cos(theta))**2 + sigma_y**2 * sp.sin(theta) **2) / 2)\n", |
|
"# 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)))\n", |
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"\n", |
|
"p = sp.cosh(k ** 2 * sigma ** 2 * sp.cos(theta) * 4) * sp.exp(-4 * k ** 2 * sigma ** 2) * sp.cos(\n", |
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" phi - k * (x0 * sp.cos(theta) + y0 * sp.sin(theta)))\n", |
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"p" |
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] |
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}, |
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{ |
|
"cell_type": "markdown", |
|
"metadata": { |
|
"pycharm": { |
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"name": "#%% md\n" |
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} |
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}, |
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"source": [ |
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"#### Plot stuff" |
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] |
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}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 7, |
|
"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
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} |
|
}, |
|
"outputs": [], |
|
"source": [ |
|
"def get_orientation_phase_grid(step_phase: float, step_orientation: float) -> np.ndarray:\n", |
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" \"\"\"\n", |
|
" Returns a grid of x and y values for plotting.\n", |
|
" :param step_phase: step for the phase (phi) - in degrees\n", |
|
" :param step_orientation: step for the orientation (theta) - in degrees\n", |
|
" :return: numpy array of shape (n_orientation, n_phase). Each element is a tuple (theta, phi)\n", |
|
" \"\"\"\n", |
|
" # phase <-> phi\n", |
|
" # orientation <-> theta\n", |
|
" step_phase *= np.pi / 180\n", |
|
" step_orientation *= np.pi / 180\n", |
|
" phi = np.arange(0, 2 * np.pi, step_phase)\n", |
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" theta = np.arange(0, np.pi, step_orientation)\n", |
|
" return np.array(np.meshgrid(theta, phi)).T.reshape(-1, len(phi), 2)\n", |
|
"\n", |
|
"\n", |
|
"def get_spatial_grid(step_x: float, step_y: float, size: float = 1) -> np.ndarray:\n", |
|
" \"\"\"\n", |
|
" Returns a grid of x and y values for plotting.\n", |
|
" :param step_x: step for the x-coordinate\n", |
|
" :param step_y: step for the y-coordinate\n", |
|
" :param size: size of the grid\n", |
|
" :return: numpy array of shape (2 * size / step_x, 2 * size / step_y). Each element is a tuple (x, y)\n", |
|
" \"\"\"\n", |
|
" x = np.arange(-size, size, step_x)\n", |
|
" y = np.arange(-size, size, step_y)\n", |
|
" return np.array(np.meshgrid(x, y)).T.reshape(-1, len(x), 2)" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 8, |
|
"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [], |
|
"source": [ |
|
"def eval_func(func: sp.Expr, sub_1: sp.Expr, sub_2: sp.Expr, grid: np.ndarray) -> np.ndarray:\n", |
|
" # return np.array([[float(func.subs(sub_1, x_).subs(sub_2, y_)) for x_, y_ in line] for line in grid])\n", |
|
" func = sp.lambdify([sub_1, sub_2], func, 'numpy')\n", |
|
" return func(grid[:, :, 0], grid[:, :, 1])\n", |
|
"\n", |
|
"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,\n", |
|
" patch: typing.Optional[typing.Tuple[float, float, float]] = None\n", |
|
" ):\n", |
|
" \"\"\"\n", |
|
" Plots a spatial map of the function.\n", |
|
"\n", |
|
" :param func: function to plot\n", |
|
" :param ax: axes to plot on or the image on axes\n", |
|
" :param step_x: step for the x-coordinate\n", |
|
" :param step_y: step for the y-coordinate\n", |
|
" :param size: size of the grid\n", |
|
" :param title: title of the plot\n", |
|
" :param show: whether to show the plot\n", |
|
" :param patch: optional circle to plot - a tuple (x, y, radius)\n", |
|
" \"\"\"\n", |
|
" grid = get_spatial_grid(step_x, step_y, size)\n", |
|
" image: np.ndarray = eval_func(func, x, y, grid)\n", |
|
" if isinstance(ax, mpl.image.AxesImage):\n", |
|
" ax.set_data(image)\n", |
|
" return ax\n", |
|
" img = ax.imshow(image, extent=[-size, size, -size, size], vmin=-size, vmax=size, cmap='gray')\n", |
|
" ax.invert_yaxis()\n", |
|
" if patch is not None:\n", |
|
" ax.add_patch(plt.Circle(patch[:2], radius=patch[2], color='b', fill=False))\n", |
|
" ax.set_title(title)\n", |
|
" if show:\n", |
|
" plt.show()\n", |
|
" return img\n", |
|
"\n", |
|
"def normalize(img):\n", |
|
" return (img - img.min()) / (img.max() - img.min())\n", |
|
"\n", |
|
"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):\n", |
|
" \"\"\"\n", |
|
" Plots a tuning curve of the function.\n", |
|
"\n", |
|
" :param func: function to plot - sympy or a function of (theta, phi)\n", |
|
" :param ax: axes to plot on or image to update\n", |
|
" :param step_phase: step for the phase (phi) - in degrees\n", |
|
" :param step_orientation: step for the orientation (theta) - in degrees\n", |
|
" :param title: title of the plot\n", |
|
" :param show: whether to show the plot\n", |
|
" \"\"\"\n", |
|
" grid = get_orientation_phase_grid(step_phase, step_orientation)\n", |
|
" if isinstance(func, sp.Expr):\n", |
|
" image: np.ndarray = eval_func(func, theta, phi, grid)\n", |
|
" else:\n", |
|
" image = np.array([[func(theta_val, phi_val) for theta_val, phi_val in line] for line in grid])\n", |
|
" image = normalize(image)\n", |
|
" if isinstance(ax, mpl.image.AxesImage):\n", |
|
" ax.set_data(image)\n", |
|
" return ax\n", |
|
" img = ax.imshow(image, extent=[0, 360, 0, 180], cmap='viridis')\n", |
|
" ax.set_title(title)\n", |
|
" if show:\n", |
|
" plt.show()\n", |
|
" return img" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 9, |
|
"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [], |
|
"source": [ |
|
"def plot_gratings(ax: typing.Union[plt.Axes, mpl.image.AxesImage], k_val: float, phi_val: float, theta_val: float, x0_val: float = 0, y0_val: float = 0):\n", |
|
" phi_val *= np.pi / 180\n", |
|
" theta_val *= np.pi / 180\n", |
|
" return plot_spatial(\n", |
|
" # grating_f.evalf(subs={k: k_val, x0: x0_val, y0: y0_val, theta: theta_val, phi: phi_val}),\n", |
|
" grating_f.subs(k, k_val).subs(x0, x0_val).subs(y0, y0_val).subs(theta, theta_val).subs(phi, phi_val),\n", |
|
" ax, step_x=0.05, step_y=0.05, size=1, title='Grating', show=False)\n", |
|
"\n", |
|
"def plot_receptive_field(ax: plt.Axes, k_val: float, phi_val: float, theta_val: float, sigma_val: float = 1):\n", |
|
" phi_val *= np.pi / 180\n", |
|
" theta_val *= np.pi / 180\n", |
|
" return plot_spatial(\n", |
|
" receptive_field.subs(k, k_val).subs(theta, theta_val).subs(phi, phi_val).subs(sigma, sigma_val),\n", |
|
" ax, step_x=0.05, step_y=0.05, size=1, title='Receptive field', show=False)" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 10, |
|
"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [], |
|
"source": [ |
|
"def get_value(k_val: float = defaults[k], phi_val: float = 90, theta_val: float = 0, x0_val: float = 0, y0_val: float = 0, sigma_val: float = defaults[sigma]):\n", |
|
" phi_val *= np.pi / 180\n", |
|
" theta_val *= np.pi / 180\n", |
|
" grid_size = 0.05\n", |
|
" grid = get_spatial_grid(grid_size, grid_size, 1)\n", |
|
" subs = {\n", |
|
" k: k_val,\n", |
|
" x0: x0_val,\n", |
|
" y0: y0_val,\n", |
|
" theta: theta_val,\n", |
|
" phi: phi_val,\n", |
|
" sigma: sigma_val\n", |
|
" }\n", |
|
" grating_img = eval_func(grating_f.subs(subs), x, y, grid)\n", |
|
" rf_img = eval_func(receptive_field.subs(subs), x, y, grid)\n", |
|
" return np.sum(grating_img * rf_img) * grid_size ** 2" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 11, |
|
"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [ |
|
{ |
|
"data": { |
|
"image/png": 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", |
|
"text/plain": [ |
|
"<Figure size 432x288 with 3 Axes>" |
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] |
|
}, |
|
"metadata": { |
|
"needs_background": "light" |
|
}, |
|
"output_type": "display_data" |
|
}, |
|
{ |
|
"data": { |
|
"application/vnd.jupyter.widget-view+json": { |
|
"model_id": "1aeab1cd8fc64df8a7107f5cafb3bdc6", |
|
"version_major": 2, |
|
"version_minor": 0 |
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}, |
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"text/plain": [ |
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"interactive(children=(FloatSlider(value=6.0, description='k', max=10.0, step=0.2), FloatSlider(value=90.0, des…" |
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] |
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}, |
|
"metadata": {}, |
|
"output_type": "display_data" |
|
} |
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], |
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"source": [ |
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"fig, ax = plt.subplots(1, 3)\n", |
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"img_gr = plot_gratings(ax[0], defaults[k], 90, 0, 0, 0)\n", |
|
"img_rf = plot_receptive_field(ax[1], defaults[k], 90, 90, defaults[sigma])\n", |
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"val = get_value()\n", |
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"line = ax[2].plot([val, val])[0]\n", |
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"ax[2].set(ylim=[-0.2, 0.2])\n", |
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"\n", |
|
"@widgets.interact(\n", |
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" k_val=widgets.FloatSlider(min=0, max=10, step=0.2, value=defaults[k], description='k'),\n", |
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" phi_val=widgets.FloatSlider(min=0, max=360, step=10, value=90, description='phi'),\n", |
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" theta_val=widgets.FloatSlider(min=0, max=180, step=10, value=0, description='theta'),\n", |
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" x0_val=widgets.FloatSlider(min=-1, max=1, step=0.05, value=0, description='x0'),\n", |
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" y0_val=widgets.FloatSlider(min=-1, max=1, step=0.05, value=0, description='y0'),\n", |
|
" sigma_val=widgets.FloatSlider(min=0, max=1, step=0.05, value=defaults[sigma], description='sigma'),\n", |
|
")\n", |
|
"def plot_stuff(k_val, phi_val, theta_val, x0_val, y0_val, sigma_val):\n", |
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" plot_gratings(img_gr, k_val, phi_val, theta_val, x0_val, y0_val)\n", |
|
" plot_receptive_field(img_rf, k_val, phi_val, theta_val, sigma_val)\n", |
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" val = get_value(k_val, phi_val, theta_val, x0_val, y0_val, sigma_val)\n", |
|
" line.set_ydata([val, val])\n", |
|
" fig.canvas.draw_idle()" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 14, |
|
"metadata": { |
|
"pycharm": { |
|
"name": "#%%\n" |
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} |
|
}, |
|
"outputs": [ |
|
{ |
|
"data": { |
|
"image/png": 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", |
|
"text/plain": [ |
|
"<Figure size 432x288 with 2 Axes>" |
|
] |
|
}, |
|
"metadata": { |
|
"needs_background": "light" |
|
}, |
|
"output_type": "display_data" |
|
}, |
|
{ |
|
"data": { |
|
"application/vnd.jupyter.widget-view+json": { |
|
"model_id": "a746cf33796443a2a12fcb48948c7aed", |
|
"version_major": 2, |
|
"version_minor": 0 |
|
}, |
|
"text/plain": [ |
|
"interactive(children=(FloatSlider(value=0.8, description='k', max=10.0, step=0.2), FloatSlider(value=0.8, desc…" |
|
] |
|
}, |
|
"metadata": {}, |
|
"output_type": "display_data" |
|
} |
|
], |
|
"source": [ |
|
"fig, ax = plt.subplots(1, 2)\n", |
|
"DEF_K, DEF_SIGMA, DEF_X = 0.8, 0.05, 0.8\n", |
|
"get_tuning_curve_func = lambda k_val, x0_val, y0_val, sigma_val: lambda theta_val, phi_val: get_value(k_val, phi_val * 180 / np.pi, theta_val * 180 / np.pi, x0_val, y0_val, sigma_val)\n", |
|
"left_img = plot_tuning_curve(get_tuning_curve_func(DEF_K, DEF_X, 0, DEF_SIGMA), ax[0], title='Tuning Curve')\n", |
|
"right_img = plot_tuning_curve(p.subs({k: defaults[k], x0: defaults[x0], y0: defaults[y0], sigma: defaults[sigma]}), ax[1], title='Tuning Curve')\n", |
|
"\n", |
|
"@widgets.interact(\n", |
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" k_val=widgets.FloatSlider(min=0, max=10, step=0.2, value=DEF_K, description='k'),\n", |
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" x0_val=widgets.FloatSlider(min=-1, max=1, step=0.05, value=DEF_X, description='x0'),\n", |
|
" y0_val=widgets.FloatSlider(min=-1, max=1, step=0.05, value=0, description='y0'),\n", |
|
" sigma_val=widgets.FloatSlider(min=0, max=1, step=0.05, value=DEF_SIGMA, description='sigma'),\n", |
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")\n", |
|
"def plot_tuning_curves(k_val, x0_val, y0_val, sigma_val):\n", |
|
" plot_tuning_curve(get_tuning_curve_func(k_val, x0_val, y0_val, sigma_val), left_img, title='Tuning Curve - Numeric')\n", |
|
" plot_tuning_curve(p.subs({k: k_val, x0: x0_val, y0: y0_val, sigma: sigma_val}), right_img, title='Tuning Curve - Analytic')\n", |
|
" fig.canvas.draw_idle()" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 13, |
|
"metadata": { |
|
"collapsed": false, |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [ |
|
{ |
|
"data": { |
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"image/png": 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", |
|
"text/plain": [ |
|
"<Figure size 432x288 with 1 Axes>" |
|
] |
|
}, |
|
"metadata": { |
|
"needs_background": "light" |
|
}, |
|
"output_type": "display_data" |
|
} |
|
], |
|
"source": [ |
|
"# %matplotlib inline\n", |
|
"func_1 = get_tuning_curve_func(DEF_K, DEF_X, 0, DEF_SIGMA)\n", |
|
"func_2 = p.subs({k: DEF_K, x0: DEF_X, y0: 0, sigma: DEF_SIGMA})\n", |
|
"grid = get_orientation_phase_grid(15, 15)\n", |
|
"img_1 = np.array([[func_1(theta, phi) for theta, phi in line] for line in grid])\n", |
|
"img_2 = eval_func(func_2, theta, phi, grid)\n", |
|
"plt.plot(np.mean(img_2, axis=1))\n", |
|
"plt.show()" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 14, |
|
"metadata": { |
|
"collapsed": false, |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [ |
|
{ |
|
"data": { |
|
"image/png": 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", |
|
"text/latex": [ |
|
"$\\displaystyle e^{\\frac{k^{2} \\left(\\cos^{2}{\\left(\\theta \\right)} + 1\\right)}{2}} \\cos{\\left(\\phi - k \\left(x_{0} \\cos{\\left(\\theta \\right)} + y_{0} \\sin{\\left(\\theta \\right)}\\right) \\right)} \\cosh{\\left(\\sigma^{2} k^{2} \\cos{\\left(\\theta \\right)} \\right)}$" |
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], |
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"text/plain": [ |
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" 2 ⎛ 2 ⎞ \n", |
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" k ⋅⎝cos (\\theta) + 1⎠ \n", |
|
" ───────────────────── \n", |
|
" 2 ⎛ \n", |
|
"ℯ ⋅cos(\\phi - k⋅(x₀⋅cos(\\theta) + y₀⋅sin(\\theta)))⋅cosh⎝\\s\n", |
|
"\n", |
|
" \n", |
|
" \n", |
|
" \n", |
|
" 2 2 ⎞\n", |
|
"igma ⋅k ⋅cos(\\theta)⎠" |
|
] |
|
}, |
|
"execution_count": 14, |
|
"metadata": {}, |
|
"output_type": "execute_result" |
|
} |
|
], |
|
"source": [ |
|
"p" |
|
] |
|
}, |
|
{ |
|
"cell_type": "code", |
|
"execution_count": 14, |
|
"metadata": { |
|
"collapsed": false, |
|
"pycharm": { |
|
"name": "#%%\n" |
|
} |
|
}, |
|
"outputs": [], |
|
"source": [] |
|
} |
|
], |
|
"metadata": { |
|
"kernelspec": { |
|
"display_name": "Python 3.10.5 64-bit", |
|
"language": "python", |
|
"name": "python3" |
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}, |
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"language_info": { |
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"codemirror_mode": { |
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"name": "ipython", |
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"version": 3 |
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}, |
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"file_extension": ".py", |
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"mimetype": "text/x-python", |
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"name": "python", |
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"nbconvert_exporter": "python", |
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"pygments_lexer": "ipython3", |
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"version": "3.10.5" |
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}, |
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"vscode": { |
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"interpreter": { |
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"hash": "e7370f93d1d0cde622a1f8e1c04877d8463912d04d973331ad4851f04de6915a" |
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} |
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} |
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}, |
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"nbformat": 4, |
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"nbformat_minor": 1 |
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}
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