2D k-d tree example

k-d tree example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from scipy import spatial\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.1.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "kdtree 101:\n",
    "'data' - the INPUT  - the original values that are used to construct the kd tree\n",
    "'grid' - the OUTPUT - the location where the oringinal values are projected\n",
    "\n",
    "'''\n",
    "\n",
    "n_data     = 8\n",
    "range_data = 16\n",
    "\n",
    "n_grid     = [20,20]\n",
    "range_grid = [range_data, range_data]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create 2D set of points\n",
    "points = np.random.rand(n_data,2) * range_data\n",
    "\n",
    "## for a function\n",
    "# x = np.linspace(0,data_range, num=n_data)\n",
    "# y = x + np.sin(2*np.pi*x/5)\n",
    "# points = np.c_[(x,y)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build a KDTree\n",
    "tree = spatial.cKDTree(points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build a query grid\n",
    "tmp  = np.array(n_grid) * 1j  # convert to complex for mgrid[]\n",
    "grid = np.mgrid[0:range_grid[0]:tmp[0], 0:range_grid[1]:tmp[1]]\n",
    "test = grid.reshape(len(grid), -1).T\n",
    "\n",
    "# query the tree\n",
    "dd, ii = tree.query(test, k=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# show the nn mapping\n",
    "plt.title(\"Nearest neighbour map with {} points\".format(n_data))\n",
    "plt.imshow( ii.reshape(grid.shape[1],grid.shape[2]).T, \n",
    "            extent=(0,range_grid[0],0,range_grid[1]), \n",
    "            origin='lower', interpolation='none' )\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('index', rotation=90)\n",
    "# show the original data\n",
    "plt.scatter(points[:,0], points[:,1], c='red')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}