Matplotlib_plots/6-Histograms_and_Binnings.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "%matplotlib inline\r\n",
    "import numpy as np\r\n",
    "import matplotlib.pyplot as plt\r\n",
    "plt.style.use('seaborn-white')\r\n",
    "\r\n",
    "data = np.random.randn(1000)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "plt.hist(data);"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "plt.hist(data, bins=30, density=True, alpha=0.5, histtype = 'stepfilled', color='steelblue', edgecolor='none');"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "x1 = np.random.normal(0, 0.8, 1000)\r\n",
    "x2 = np.random.normal(-2, 1, 1000)\r\n",
    "x3 = np.random.normal(3, 2, 1000)\r\n",
    "\r\n",
    "kwargs = dict(histtype='stepfilled', alpha=0.3, density=True, bins=40)\r\n",
    "\r\n",
    "plt.hist(x1, **kwargs)\r\n",
    "plt.hist(x2, **kwargs)\r\n",
    "plt.hist(x3, **kwargs);"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<!-- Created with matplotlib (https://matplotlib.org/) -->\r\n<svg height=\"244.485312pt\" version=\"1.1\" viewBox=\"0 0 366.6 244.485312\" width=\"366.6pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-08-20T00:04:22.448617</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.3.4, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n 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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "counts, bin_edges = np.histogram(data, bins=5)\r\n",
    "print(counts)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[  5 162 546 265  22]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "mean = [0, 0]\r\n",
    "cov = [[1, 1], [1, 2]]\r\n",
    "x, y = np.random.multivariate_normal(mean, cov, 10000).T"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "plt.hist2d(x, y, bins=30, cmap='Blues')\r\n",
    "cb = plt.colorbar()\r\n",
    "cb.set_label('counts in bin')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ],
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "counts, xedges, yedges = np.histogram2d(x, y, bins=30)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "plt.hexbin(x, y, gridsize=30, cmap='Blues')\r\n",
    "cb = plt.colorbar(label='count in bin')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ],
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"
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "from scipy.stats import gaussian_kde\r\n",
    "\r\n",
    "data = np.vstack([x, y])\r\n",
    "kde = gaussian_kde(data)\r\n",
    "\r\n",
    "xgrid = np.linspace(-3.5, 3.5, 40)\r\n",
    "ygrid = np.linspace(-6, 6, 40)\r\n",
    "Xgrid, Ygrid = np.meshgrid(xgrid, ygrid)\r\n",
    "Z = kde.evaluate(np.vstack([Xgrid.ravel(), Ygrid.ravel()]))\r\n",
    "\r\n",
    "plt.imshow(Z.reshape(Xgrid.shape),\r\n",
    "           origin='lower', aspect='auto',\r\n",
    "           extent=[-3.5, 3.5, -6, 6],\r\n",
    "           cmap='Blues')\r\n",
    "cb = plt.colorbar()\r\n",
    "cb.set_label(\"density\")"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ],
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"
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 ],
 "metadata": {
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  "language_info": {
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   "codemirror_mode": {
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   "pygments_lexer": "ipython3",
   "nbconvert_exporter": "python",
   "file_extension": ".py"
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  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.6.10 64-bit ('lab': conda)"
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  "interpreter": {
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}