04.07_numpy_fancy_indexing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fancy indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:44.995013Z",
     "start_time": "2019-10-18T00:47:44.882880Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[51 92 14 71 60 20 82 86 74 74]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "rand = np.random.RandomState(42)\n",
    "\n",
    "x = rand.randint(100, size=10)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.005651Z",
     "start_time": "2019-10-18T00:47:44.996763Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[71, 82, 14]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# suppose we want to access three different elements \n",
    "# we could do it like this\n",
    "[x[3], x[6], x[2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.011397Z",
     "start_time": "2019-10-18T00:47:45.007949Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([71, 82, 14])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Alternatively, we can pass a sigle list or array of indices to obtain the same result\n",
    "index = [3,6,2]\n",
    "x[index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.015476Z",
     "start_time": "2019-10-18T00:47:45.012648Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[71 60]\n",
      " [20 92]]\n"
     ]
    }
   ],
   "source": [
    "# using fancy indexing\n",
    "# the shape fo the result reflects the shape of the index arrays \n",
    "index =np.array([[3,4],\n",
    "                 [5,1]])\n",
    "print(x[index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.020011Z",
     "start_time": "2019-10-18T00:47:45.016779Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# multiple dimensions  also works\n",
    "x = np.arange(12).reshape((3,4))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.024134Z",
     "start_time": "2019-10-18T00:47:45.021357Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 9 11  6]\n"
     ]
    }
   ],
   "source": [
    "row = np.array([2,2,1])\n",
    "col = np.array([1,3,2])\n",
    "print(x[row,col]) # Equivalently [x[2,1],x[2,3],x[1,2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.028620Z",
     "start_time": "2019-10-18T00:47:45.025861Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9 11 10]\n",
      " [ 9 11 10]\n",
      " [ 5  7  6]]\n"
     ]
    }
   ],
   "source": [
    "print(x[row[:,np.newaxis], col])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.032351Z",
     "start_time": "2019-10-18T00:47:45.029892Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.036488Z",
     "start_time": "2019-10-18T00:47:45.033543Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  8,  9])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2, [2,0,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:47:45.042263Z",
     "start_time": "2019-10-18T00:47:45.037634Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6,  4,  5],\n",
       "       [10,  8,  9]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[1:,[2, 0,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:48:05.163333Z",
     "start_time": "2019-10-18T00:48:05.152567Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2]\n",
      " [2]\n",
      " [1]] [ True False  True False]\n",
      "[[ 8 10]\n",
      " [ 8 10]\n",
      " [ 4  6]]\n"
     ]
    }
   ],
   "source": [
    "mask = np.array([1,0,1,0],dtype=bool)\n",
    "# print(x[row[:,np.newaxis]])\n",
    "print(row[:,np.newaxis],mask)\n",
    "print(x[row[:,np.newaxis],mask])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T00:48:30.031237Z",
     "start_time": "2019-10-18T00:48:30.028116Z"
    }
   },
   "source": [
    "### example: selecting random points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:11:52.645002Z",
     "start_time": "2019-10-18T01:11:52.636298Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2)\n",
      "[[ 5.86501323e-01  2.65750974e+00]\n",
      " [ 8.91568728e-02 -4.10108912e-01]\n",
      " [ 1.08760627e+00  1.12826476e+00]\n",
      " [ 5.96401368e-01  1.15404786e+00]\n",
      " [ 9.97906065e-01  2.35994742e+00]\n",
      " [-3.55226165e-01 -1.08865240e+00]\n",
      " [-3.03399728e-01 -1.60611376e+00]\n",
      " [-9.73621269e-01 -2.21867838e+00]\n",
      " [-2.35151244e+00 -3.06392323e+00]\n",
      " [ 5.98644067e-01  9.80839233e-01]\n",
      " [-4.67325254e-04  6.43655246e-01]\n",
      " [-9.75217525e-01 -3.06097819e+00]\n",
      " [-3.00206653e-01 -8.71889611e-01]\n",
      " [-1.14870280e+00 -1.13938864e+00]\n",
      " [ 8.61065030e-01  2.71343135e-01]\n",
      " [-3.68613042e-01 -1.79122424e+00]\n",
      " [-1.68961962e-01  4.43965779e-01]\n",
      " [-2.35830450e-01 -6.79446032e-01]\n",
      " [ 1.64178663e+00  8.24801146e-01]\n",
      " [-5.48363884e-01 -1.59766047e+00]\n",
      " [-1.55045915e+00 -3.31231706e+00]\n",
      " [ 9.16611489e-02  1.37606145e+00]\n",
      " [-9.79685051e-01 -2.60224726e+00]\n",
      " [-8.90276868e-01 -2.75037960e+00]\n",
      " [-3.66163830e-01 -2.65509702e-01]\n",
      " [-9.62889757e-01 -1.65189111e+00]\n",
      " [-1.11204807e-01  9.15337643e-01]\n",
      " [ 3.32713201e-01  1.87329944e-01]\n",
      " [-2.30259914e-01  1.54393170e+00]\n",
      " [ 1.91215901e-01  1.85969192e+00]\n",
      " [ 8.62321110e-01  2.60993237e+00]\n",
      " [-8.94885987e-01 -4.05642558e-01]\n",
      " [ 9.60738294e-01  1.31208373e+00]\n",
      " [-5.29450524e-01  5.23761879e-01]\n",
      " [ 1.80740008e+00  1.56176782e+00]\n",
      " [-4.18584971e-01  1.72026864e-02]\n",
      " [ 6.12144957e-01  2.39564383e+00]\n",
      " [ 1.01314248e+00  2.28730850e+00]\n",
      " [-2.40964450e-01 -1.86704293e+00]\n",
      " [-6.32646685e-01 -2.12266356e-01]\n",
      " [-1.62086361e-01 -1.17131111e+00]\n",
      " [-1.65506871e+00 -3.28305040e+00]\n",
      " [ 1.38809812e+00  4.28661584e+00]\n",
      " [ 4.52659364e-01  1.30557523e+00]\n",
      " [-7.20949699e-01 -2.33541426e+00]\n",
      " [ 9.44182133e-01  3.90904768e+00]\n",
      " [-1.04254340e+00 -2.61136765e+00]\n",
      " [-6.47100429e-01 -1.96205995e+00]\n",
      " [-3.43721564e-02 -2.39157870e-01]\n",
      " [ 1.66405563e-01  7.90644878e-01]\n",
      " [ 1.21248750e+00  2.65489464e+00]\n",
      " [-9.93951836e-01 -4.10066133e-01]\n",
      " [ 8.79453934e-01  2.68663218e+00]\n",
      " [ 1.36007608e-01 -1.70299430e+00]\n",
      " [-7.16152641e-01 -7.76131715e-01]\n",
      " [-5.11726592e-01 -1.32625949e+00]\n",
      " [-3.72870401e-01 -7.16350203e-01]\n",
      " [ 1.48687457e+00  3.79888117e+00]\n",
      " [ 6.08852603e-01  7.07006190e-01]\n",
      " [-2.77516816e+00 -5.34402713e+00]\n",
      " [ 9.29968496e-01  2.62033887e+00]\n",
      " [-7.74469082e-01 -3.48920806e+00]\n",
      " [-1.18603725e-01 -1.52039371e-01]\n",
      " [ 1.03223028e+00  2.90284662e+00]\n",
      " [-1.60838202e+00 -2.25067874e+00]\n",
      " [-7.26955719e-01  9.52734718e-01]\n",
      " [ 1.76499513e+00  4.64664137e+00]\n",
      " [ 1.27027841e+00  3.16433636e+00]\n",
      " [ 2.88205360e-01  1.24442949e+00]\n",
      " [ 4.33312955e-01  1.52071181e-01]\n",
      " [-3.71029882e-02  2.00210455e+00]\n",
      " [ 2.41613952e-01 -1.25906316e+00]\n",
      " [-4.34361982e-01 -1.25935909e+00]\n",
      " [-3.18008463e-01  1.19700198e-01]\n",
      " [-7.64505966e-01 -2.77525287e+00]\n",
      " [ 2.36465339e-01 -2.02284626e-02]\n",
      " [-4.62529672e-01 -1.36808998e+00]\n",
      " [ 7.64055952e-02 -1.08086034e-01]\n",
      " [-5.54300049e-01  5.06902256e-01]\n",
      " [-2.35308682e+00 -5.27269258e+00]\n",
      " [ 7.02983786e-01 -2.99517944e-02]\n",
      " [ 7.51034592e-01  1.67597980e+00]\n",
      " [ 8.94031191e-01  1.49823040e+00]\n",
      " [-1.46648786e+00 -3.50925192e+00]\n",
      " [ 1.48787918e-01 -3.70532794e-01]\n",
      " [-1.00655915e+00 -2.66014220e+00]\n",
      " [ 1.08614243e+00  9.11187425e-01]\n",
      " [ 2.67714258e-01  4.87761185e-02]\n",
      " [-2.26197823e+00 -3.46507695e+00]\n",
      " [ 1.57067982e+00  2.57734661e+00]\n",
      " [ 5.67570238e-01  4.86962713e-01]\n",
      " [-7.58733264e-02 -5.36709131e-01]\n",
      " [-6.48020244e-01 -4.64647559e-01]\n",
      " [ 6.02361625e-01  2.53143847e+00]\n",
      " [-1.49001739e-01  1.96577906e+00]\n",
      " [-1.45431255e+00 -3.63341835e+00]\n",
      " [ 1.33218310e+00  1.96615658e+00]\n",
      " [-7.95492857e-01 -1.95339736e+00]\n",
      " [-1.69983525e+00 -1.71792508e+00]\n",
      " [ 1.18249455e+00  1.52330235e+00]]\n"
     ]
    }
   ],
   "source": [
    "mean = [0,0]\n",
    "cov = [[1,2],\n",
    "       [2,5]]\n",
    "X = rand.multivariate_normal(mean, cov,100)\n",
    "print(X.shape)\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:09:26.087462Z",
     "start_time": "2019-10-18T01:09:25.989904Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "seaborn.set()\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:18:57.559797Z",
     "start_time": "2019-10-18T01:18:57.548102Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[36 86 46 68 15 10 78 66  9 18  3 70 48 22 58 21 89 79 88  5]\n",
      "[[ 6.12144957e-01  2.39564383e+00]\n",
      " [ 1.08614243e+00  9.11187425e-01]\n",
      " [-1.04254340e+00 -2.61136765e+00]\n",
      " [ 2.88205360e-01  1.24442949e+00]\n",
      " [-3.68613042e-01 -1.79122424e+00]\n",
      " [-4.67325254e-04  6.43655246e-01]\n",
      " [-5.54300049e-01  5.06902256e-01]\n",
      " [ 1.76499513e+00  4.64664137e+00]\n",
      " [ 5.98644067e-01  9.80839233e-01]\n",
      " [ 1.64178663e+00  8.24801146e-01]\n",
      " [ 5.96401368e-01  1.15404786e+00]\n",
      " [-3.71029882e-02  2.00210455e+00]\n",
      " [-3.43721564e-02 -2.39157870e-01]\n",
      " [-9.79685051e-01 -2.60224726e+00]\n",
      " [ 6.08852603e-01  7.07006190e-01]\n",
      " [ 9.16611489e-02  1.37606145e+00]\n",
      " [ 1.57067982e+00  2.57734661e+00]\n",
      " [-2.35308682e+00 -5.27269258e+00]\n",
      " [-2.26197823e+00 -3.46507695e+00]\n",
      " [-3.55226165e-01 -1.08865240e+00]]\n"
     ]
    }
   ],
   "source": [
    "# 根据X的维度shape[0], 从中选取20个点， replace不重复\n",
    "indices = np.random.choice(X.shape[0], 20, replace=False)\n",
    "print(indices)\n",
    "# print(indices.shape)\n",
    "selection = X[indices]  # equivalently, x[indices,:]\n",
    "\n",
    "print(selection)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:24:24.239192Z",
     "start_time": "2019-10-18T01:24:24.131521Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.3)\n",
    "plt.scatter(selection[:, 0], selection[:, 1],\n",
    "            facecolor='none', s=200);\n",
    "plt.show()\n",
    "# plt.scatter?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### modifying values with fancy indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:26:27.228302Z",
     "start_time": "2019-10-18T01:26:27.220936Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0 99 99  3 99  5  6  7 99  9]\n",
      "[ 0 89 89  3 89  5  6  7 89  9]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(10)\n",
    "i = np.array([2, 1, 8, 4])\n",
    "x[i] = 99\n",
    "print(x)\n",
    "x[i] -= 10\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:30:08.007515Z",
     "start_time": "2019-10-18T01:30:08.001273Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0.]\n",
      "[6. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "# 重复的索引操作可能带来意想不到的结果\n",
    "\n",
    "x = np.zeros(10)\n",
    "print(x[[0, 0]])\n",
    "x[[0,0]] = [4, 6] # expected [4,6,0,0,0,..]\n",
    "print(x) # result [6, 0,0 ..]\n",
    "# the reason is that, to first assign x[0]=4,followed by x[0]=6\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:34:08.722693Z",
     "start_time": "2019-10-18T01:34:08.716547Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6., 0., 2., 2., 2., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = [2, 3, 3, 4, 4, 4]\n",
    "x[i] += 1 # expected [6, 0, 1, 2, 3, 0..]\n",
    "x  # result  array([6., 0., 1., 1., 1., 0., 0., 0., 0., 0.])\n",
    "# it is not the augmentation that happens multiple times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:35:18.616476Z",
     "start_time": "2019-10-18T01:35:18.601808Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 1. 2. 3. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "i = [2, 3, 3, 4, 4, 4]\n",
    "x = np.zeros(10)\n",
    "np.add.at(x, i, 1)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### example: binning data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:52:33.311621Z",
     "start_time": "2019-10-18T01:52:33.210564Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "x = np.random.randn(100)\n",
    "# compute a histogram by hand\n",
    "bins = np.linspace(-5, 5, 20)\n",
    "# print(bins)\n",
    "counts = np.zeros_like(bins)\n",
    "\n",
    "# find the appropriate bin for each x\n",
    "i = np.searchsorted(bins, x)# ;print(i) 找出x中的所有元素在直方图中的位置\n",
    "np.add.at(counts, i, 1)\n",
    "plt.plot(bins, counts, linestyle='steps')\n",
    "# plt.hist(x, bins, histtype='step')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T01:54:37.450590Z",
     "start_time": "2019-10-18T01:54:14.138609Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NumPy routine:\n",
      "18.7 µs ± 582 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "Custom routine:\n",
      "9.88 µs ± 199 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(\"NumPy routine:\")\n",
    "%timeit counts, edges = np.histogram(x, bins)\n",
    "### 两种方法等价\n",
    "print(\"Custom routine:\")\n",
    "%timeit np.add.at(counts, np.searchsorted(bins, x), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-18T02:00:17.583416Z",
     "start_time": "2019-10-18T02:00:06.252568Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NumPy routine:\n",
      "58.4 ms ± 2.38 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "Custom routine:\n",
      "81.2 ms ± 4.53 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "# numpy 内置的直方图画法更适用与大数据\n",
    "\n",
    "x = np.random.randn(1000000)\n",
    "print(\"NumPy routine:\")\n",
    "%timeit counts, edges = np.histogram(x, bins)\n",
    "\n",
    "print(\"Custom routine:\")\n",
    "%timeit np.add.at(counts, np.searchsorted(bins, x), 1)"
   ]
  }
 ],
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