amgen/TuningCurves.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Tuning Curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Import everything**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import typing\n",
    "\n",
    "import matplotlib as mpl\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import ipywidgets as widgets\n",
    "import sympy as sp\n",
    "sp.init_printing()\n",
    "AxOrImg = typing.Union[mpl.axes.Axes, mpl.image.AxesImage]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "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",
    "defaults = {\n",
    "    k: 6,\n",
    "    sigma: 0.2,\n",
    "    phi: sp.pi / 2,\n",
    "    theta: 0,\n",
    "    sigma: 1,\n",
    "    x0: 0, y0: 0\n",
    "}\n",
    "sigma_x = sigma_y = sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Formulas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "cos(\\phi + k⋅(x - x₀)⋅cos(\\theta) + k⋅(y - y₀)⋅sin(\\theta))",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle \\cos{\\left(\\phi + k \\left(x - x_{0}\\right) \\cos{\\left(\\theta \\right)} + k \\left(y - y_{0}\\right) \\sin{\\left(\\theta \\right)} \\right)}$"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grating_f = sp.cos(k * (x - x0) * sp.cos(theta) + k * (y - y0) * sp.sin(theta) + phi)\n",
    "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",
    "receptive_field = receptive_field.subs(theta, 0).subs(phi, 0)\n",
    "grating_f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "    2    2         \n - x  - y          \n ─────────         \n         2         \n 2⋅\\sigma          \nℯ         ⋅cos(k⋅x)\n───────────────────\n              2    \n    2⋅π⋅\\sigma     ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle \\frac{e^{\\frac{- x^{2} - y^{2}}{2 \\sigma^{2}}} \\cos{\\left(k x \\right)}}{2 \\pi \\sigma^{2}}$"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "receptive_field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "int1 = sp.Integral(grating_f * receptive_field, (x, -1, 1), (y, -1, 1)).subs(defaults)\n",
    "# int1.evalf(2).doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "  2 ⎛   2            ⎞                                                        \n k ⋅⎝cos (\\theta) + 1⎠                                                        \n ─────────────────────                                                        \n           2                                                               ⎛  \nℯ                     ⋅cos(\\phi - k⋅(x₀⋅cos(\\theta) + y₀⋅sin(\\theta)))⋅cosh⎝\\s\n\n                     \n                     \n                     \n    2  2            ⎞\nigma ⋅k ⋅cos(\\theta)⎠",
      "image/png": "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
      "text/latex": "$\\displaystyle e^{\\frac{k^{2} \\left(\\cos^{2}{\\left(\\theta \\right)} + 1\\right)}{2}} \\cos{\\left(\\phi - k \\left(x_{0} \\cos{\\left(\\theta \\right)} + y_{0} \\sin{\\left(\\theta \\right)}\\right) \\right)} \\cosh{\\left(\\sigma^{2} k^{2} \\cos{\\left(\\theta \\right)} \\right)}$"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Plot stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def get_orientation_phase_grid(step_phase: float, step_orientation: float) -> np.ndarray:\n",
    "    \"\"\"\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",
    "    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": [
    {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3)\n",
    "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",
    "val = get_value()\n",
    "line = ax[2].plot([val, val])[0]\n",
    "ax[2].set(ylim=[-0.2, 0.2])\n",
    "\n",
    "@widgets.interact(\n",
    "    k_val=widgets.FloatSlider(min=0, max=10, step=0.2, value=defaults[k], description='k'),\n",
    "    phi_val=widgets.FloatSlider(min=0, max=360, step=10, value=90, description='phi'),\n",
    "    theta_val=widgets.FloatSlider(min=0, max=180, step=10, value=0, description='theta'),\n",
    "    x0_val=widgets.FloatSlider(min=-1, max=1, step=0.05, value=0, 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=defaults[sigma], description='sigma'),\n",
    ")\n",
    "def plot_stuff(k_val, phi_val, theta_val, x0_val, y0_val, sigma_val):\n",
    "    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",
    "    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": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<IPython.core.display.Javascript object>",
      "application/javascript": "/* Put everything inside the global mpl namespace */\n/* global mpl */\nwindow.mpl = {};\n\nmpl.get_websocket_type = function () {\n    if (typeof WebSocket !== 'undefined') {\n        return WebSocket;\n    } else if (typeof MozWebSocket !== 'undefined') {\n        return MozWebSocket;\n    } else {\n        alert(\n            'Your browser does not have WebSocket support. ' +\n                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n                'Firefox 4 and 5 are also supported but you ' +\n                'have to enable WebSockets in about:config.'\n        );\n    }\n};\n\nmpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n    this.id = figure_id;\n\n    this.ws = websocket;\n\n    this.supports_binary = this.ws.binaryType !== undefined;\n\n    if (!this.supports_binary) {\n        var warnings = document.getElementById('mpl-warnings');\n        if (warnings) {\n            warnings.style.display = 'block';\n            warnings.textContent =\n                'This browser does not support binary websocket messages. ' +\n                'Performance may be slow.';\n        }\n    }\n\n    this.imageObj = new Image();\n\n    this.context = undefined;\n    this.message = undefined;\n    this.canvas = undefined;\n    this.rubberband_canvas = undefined;\n    this.rubberband_context = undefined;\n    this.format_dropdown = undefined;\n\n    this.image_mode = 'full';\n\n    this.root = document.createElement('div');\n    this.root.setAttribute('style', 'display: inline-block');\n    this._root_extra_style(this.root);\n\n    parent_element.appendChild(this.root);\n\n    this._init_header(this);\n    this._init_canvas(this);\n    this._init_toolbar(this);\n\n    var fig = this;\n\n    this.waiting = false;\n\n    this.ws.onopen = function () {\n        fig.send_message('supports_binary', { value: fig.supports_binary });\n        fig.send_message('send_image_mode', {});\n        if (fig.ratio !== 1) {\n            fig.send_message('set_device_pixel_ratio', {\n                device_pixel_ratio: fig.ratio,\n            });\n        }\n        fig.send_message('refresh', {});\n    };\n\n    this.imageObj.onload = function () {\n        if (fig.image_mode === 'full') {\n            // Full images could contain transparency (where diff images\n            // almost always do), so we need to clear the canvas so that\n            // there is no ghosting.\n            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n        }\n        fig.context.drawImage(fig.imageObj, 0, 0);\n    };\n\n    this.imageObj.onunload = function () {\n        fig.ws.close();\n    };\n\n    this.ws.onmessage = this._make_on_message_function(this);\n\n    this.ondownload = ondownload;\n};\n\nmpl.figure.prototype._init_header = function () {\n    var titlebar = document.createElement('div');\n    titlebar.classList =\n        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n    var titletext = document.createElement('div');\n    titletext.classList = 'ui-dialog-title';\n    titletext.setAttribute(\n        'style',\n        'width: 100%; text-align: center; padding: 3px;'\n    );\n    titlebar.appendChild(titletext);\n    this.root.appendChild(titlebar);\n    this.header = titletext;\n};\n\nmpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._init_canvas = function () {\n    var fig = this;\n\n    var canvas_div = (this.canvas_div = document.createElement('div'));\n    canvas_div.setAttribute(\n        'style',\n        'border: 1px solid #ddd;' +\n            'box-sizing: content-box;' +\n            'clear: both;' +\n            'min-height: 1px;' +\n            'min-width: 1px;' +\n            'outline: 0;' +\n            'overflow: hidden;' +\n            'position: relative;' +\n            'resize: both;'\n    );\n\n    function on_keyboard_event_closure(name) {\n        return function (event) {\n            return fig.key
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<IPython.core.display.HTML object>",
      "text/html": "<div id='4106d5b0-666f-49c4-a240-3744f7c3f5c3'></div>"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "interactive(children=(FloatSlider(value=0.8, description='k', max=10.0, step=0.2), FloatSlider(value=0.8, desc…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "75bac2ab8604428a9d0928978ef62b80"
      }
     },
     "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",
    "    k_val=widgets.FloatSlider(min=0, max=10, step=0.2, value=DEF_K, description='k'),\n",
    "    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",
    ")\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,
   "outputs": [],
   "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()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "data": {
      "text/plain": "  2 ⎛   2            ⎞                                                        \n k ⋅⎝cos (\\theta) + 1⎠                                                        \n ─────────────────────                                                        \n           2                                                               ⎛  \nℯ                     ⋅cos(\\phi - k⋅(x₀⋅cos(\\theta) + y₀⋅sin(\\theta)))⋅cosh⎝\\s\n\n                     \n                     \n                     \n    2  2            ⎞\nigma ⋅k ⋅cos(\\theta)⎠",
      "image/png": "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
      "text/latex": "$\\displaystyle e^{\\frac{k^{2} \\left(\\cos^{2}{\\left(\\theta \\right)} + 1\\right)}{2}} \\cos{\\left(\\phi - k \\left(x_{0} \\cos{\\left(\\theta \\right)} + y_{0} \\sin{\\left(\\theta \\right)}\\right) \\right)} \\cosh{\\left(\\sigma^{2} k^{2} \\cos{\\left(\\theta \\right)} \\right)}$"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.5"
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}