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@minrk
Last active May 22, 2018 09:25
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{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Binder cordon probabilities"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "%matplotlib inline\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.stats import binom\nimport ipywidgets as W",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@W.interact(duration=(0.0, 4.0), interval=(12, 36), nodes=(1, 8))\ndef plotit(duration, interval, nodes=4):\n # probability that any given node is cordoned\n p = 1.0 * duration / interval\n p_inverse = 1 - p\n # n = for number of nodes available\n n = np.arange(0, nodes + 1)\n prob = binom.pmf(n, nodes, p)\n plt.semilogy(n, prob, '-o')\n plt.title(\"Probability that N nodes are cordoned at any given time\")\n plt.xticks(n)\n plt.xlabel(\"cordoned nodes\")\n plt.ylabel(\"P\")\n print(f\"Probability of N/{nodes} nodes cordoned:\")\n for i, p_i in zip(n, prob):\n print(f\"{i}: 1/{1/p_i:.2g}\")\n",
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "interactive(children=(FloatSlider(value=2.0, description='duration', max=4.0), IntSlider(value=24, description='interval', max=36, min=12), IntSlider(value=4, description='nodes', max=8, min=1), Output()), _dom_classes=('widget-interact',))",
"text/html": "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n<p>\n If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n that the widgets JavaScript is still loading. If this message persists, it\n likely means that the widgets JavaScript library is either not installed or\n not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n Widgets Documentation</a> for setup instructions.\n</p>\n<p>\n If you're reading this message in another frontend (for example, a static\n rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n it may mean that your frontend doesn't currently support widgets.\n</p>\n",
"application/vnd.jupyter.widget-view+json": {
"version_major": 2,
"version_minor": 0,
"model_id": "8133cd82aadc45bea43fcbc413cd58f1"
}
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plotit(duration=2, interval=24)",
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": "Probability of N/4 nodes cordoned:\n0: 1/1.4\n1: 1/3.9\n2: 1/29\n3: 1/4.7e+02\n4: 1/2.1e+04\n",
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x11e8525f8>",
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