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@ohtaman
Last active October 17, 2020 00:49
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Shredder_DevFest2020_Routing
Demos for DevFest 2020
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Shredder_DevFest2020_MIP",
"provenance": [],
"collapsed_sections": [
"8Lm9Zyn0HGLB",
"elZB_HelnEqv"
],
"toc_visible": true,
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/ohtaman/1ff72de0fc321fa36ccb2df0138deef9/shredder_mip.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "VoAcNcujPflZ",
"outputId": "cbee8297-5c68-4ddd-d18b-883e30b50df0",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 85
}
},
"source": [
"!pip install ortools"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Requirement already satisfied: ortools in /usr/local/lib/python3.6/dist-packages (8.0.8283)\n",
"Requirement already satisfied: protobuf>=3.13.0 in /usr/local/lib/python3.6/dist-packages (from ortools) (3.13.0)\n",
"Requirement already satisfied: six>=1.10 in /usr/local/lib/python3.6/dist-packages (from ortools) (1.15.0)\n",
"Requirement already satisfied: setuptools in /usr/local/lib/python3.6/dist-packages (from protobuf>=3.13.0->ortools) (50.3.0)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "SyIyEo9w-NEx"
},
"source": [
"## シュレッダーの復元問題\n",
"\n",
"Google OR-Tools の使い方のデモとして、以下の問題を解く\n",
"\n",
"> 証券会社 A のシュレッダーは、A4サイズの紙を $N$ 本に裁断できる。\n",
"> 証券取引等監視委員会の検査に先立って、証券会社 A は重要と思われる書類をシュレッダーにかけてしまった。検査官のあなたは、どうやって裁断された文書を復元したらよいだろうか?\n",
"> 裁断された文書はきれいにスキャンされており、手持ちのPC上で復元作業を行うものとする。$N=10, 20, 50, 100, 200$ として考えてみよう。\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "kPPd8c9SRgK1",
"cellView": "form",
"outputId": "e94dfe20-b64d-43d4-f986-48917ba0f850",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 572
}
},
"source": [
"import math\n",
"import random\n",
"\n",
"from urllib.request import urlopen\n",
"from PIL import Image\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"def load_img(url):\n",
" img = Image.open(urlopen(url))\n",
" return np.array(img)\n",
"\n",
"\n",
"def shred(img, bins, shuffle=False):\n",
" width = img.shape[1]//bins\n",
" actual_bins = math.ceil(img.shape[1]/width)\n",
" print(f'bins: {actual_bins}')\n",
" imgs = [img[:, width*i:width*(i + 1)] for i in range(actual_bins)]\n",
" if shuffle:\n",
" random.shuffle(imgs)\n",
" return imgs\n",
"\n",
"\n",
"def sort_imgs(imgs, x):\n",
" left_idx = 0\n",
" sorted = [imgs[left_idx]]\n",
" for _ in range(bins - 1):\n",
" for right_idx in range(bins):\n",
" if left_idx == right_idx:\n",
" continue\n",
" if x[left_idx, right_idx].solution_value() == 1:\n",
" sorted.append(imgs[right_idx])\n",
" left_idx = right_idx\n",
" break\n",
" return sorted\n",
"\n",
"\n",
"bins = 100#@param {type: \"integer\"}\n",
"img_url = \"https://static9.depositphotos.com/1586254/1105/i/450/depositphotos_11056146-stock-photo-two-peeking-from-hole-in.jpg\" #@param [\"https://3.bp.blogspot.com/-uJOnRqlESrA/VGX8Z5GTZ-I/AAAAAAAApGM/5VvrJsL8MuI/s800/chabudai_kaeshi.png\", \"https://pbs.twimg.com/media/EJ3TVioU8AAqEvN.jpg\", \"https://static9.depositphotos.com/1586254/1105/i/450/depositphotos_11056146-stock-photo-two-peeking-from-hole-in.jpg\"] {allow-input: true}\n",
"\n",
"img = load_img(img_url)\n",
"shredded = shred(img, bins, shuffle=True)\n",
"\n",
"print('original')\n",
"plt.imshow(img)\n",
"plt.show()\n",
"print('shredded')\n",
"plt.imshow(np.hstack(shredded))\n",
"plt.show()\n"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"bins: 100\n",
"original\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "stream",
"text": [
"shredded\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "dhK3EiAdqHHU"
},
"source": [
"## 定式化の方針\n",
"\n",
"隣り合う紙片同士の類似度の合計を最大化するすればよさそう<br>\n",
" ⇔ 隣り合う紙片同士の**非**類似度の合計を最**小**化する\n",
"\n",
"**非類似度の定義**\n",
"\n",
"今回は簡単のため、ここでは簡単のため「左側の画像の右端と右側の画像の左端をピクセルごとに比較して、値の異なるチャンネルの数の合計」とする\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "J8sLF5EfrI5i"
},
"source": [
"def disimilarity(left, right):\n",
" return np.sum(left[:, -1] != right[:, 0])"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "WFpheiP5U11N"
},
"source": [
"\n",
"## 定式化1(不完全な定式化)\n",
"\n",
"### 目的関数\n",
"\n",
"隣り合う紙片同士の非類似度の合計を最小化する\n",
"\n",
"- $\\mathrm{Minimize}\\ \\sum_{i,j}C_{ij}x_{ij}$\n",
"\n",
"ここで $C_{i,j}$ は紙片 $i$ の右側と紙片 $j$ の左側の非類似度を表す($C_{i,j}$が小さいほど、$i$ の次に $j$ がきやすい)。\n",
"\n",
"### 制約条件\n",
"\n",
"各紙片が一列に並んでいることを数式で表す\n",
"\n",
"- $\\sum_{i}x_{ij} = 1$: 紙片 $i$ の前にくる紙片は $1$ つである。\n",
"- $\\sum_{j}x_{ij} = 1$: 紙片 $i$ の次にくる紙片は $1$ つである。\n",
"\n",
"### 決定変数\n",
"\n",
"- $x_{ij} \\in \\{0, 1\\}$: 紙片 $i$ の次に紙片 $j$ がくる場合は $1$、それ以外は $0$ となる変数"
]
},
{
"cell_type": "code",
"metadata": {
"id": "VHJ0stNWVEbh",
"outputId": "a713a74c-5f6b-4b1b-c955-893ff4700623",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 68
}
},
"source": [
"from ortools.linear_solver import pywraplp\n",
"\n",
"# 非類似度を計算.\n",
"C = np.array([[\n",
" disimilarity(shredded[i], shredded[j])\n",
" for j in range(bins)\n",
" ] for i in range(bins)\n",
"])\n",
"\n",
"# ソルバーを定義\n",
"solver = pywraplp.Solver('shredder', pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)\n",
"\n",
"# 決定変数を定義\n",
"x = np.array([[\n",
" solver.BoolVar(f'x_{i}_{j}') if i!= j else 0\n",
" for j in range(bins)\n",
" ] for i in range(bins)\n",
"])\n",
"\n",
"# 目的関数を定義\n",
"objective = (C*x).sum()\n",
"solver.Minimize(objective)\n",
"\n",
"# 制約\n",
"for j in range(bins):\n",
" solver.Add(x[:, j].sum() == 1)\n",
"\n",
"for i in range(bins):\n",
" solver.Add(x[i, :].sum() == 1)\n",
"\n",
"# 求解\n",
"%time status = solver.Solve()\n",
"# 最適解が求まったことを確認\n",
"status == pywraplp.Solver.OPTIMAL"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"CPU times: user 307 ms, sys: 21.9 ms, total: 329 ms\n",
"Wall time: 329 ms\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {
"tags": []
},
"execution_count": 4
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "-dcY3lJDDVX_",
"outputId": "cd485eba-6d68-422c-cf13-b24f06675c85",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 286
}
},
"source": [
"plt.imshow(np.hstack(sort_imgs(shredded, x)))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7faee8330e10>"
]
},
"metadata": {
"tags": []
},
"execution_count": 5
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "C7z7erGkyI2y"
},
"source": [
"## 定式化2(部分順回路除去)\n",
"\n",
"上記の制約だけだと、**部分順回路** が発生する可能性がある\n",
"部分順回路を除去するために、 **順番**を表すような変数を導入する\n",
"\n",
"### 変数\n",
"\n",
"- $n_i \\in [0, N - 1]$: 紙片 $i$ の順番(左から数えて何番目か?)\n",
"\n",
"### 制約\n",
"\n",
"- 紙片 $i$ の次が紙片 $j$ ならば$n_i + 1 \\leq n_j $\n",
" - $n_i + 1 - N( 1- x_{ij}) \\leq n_j \\quad (j \\neq 0)$\n",
"\n",
"※ `if` をうまく表現するのがポイント。 $x_{ij} = 1$ の時、上記の制約は $n_i + 1 \\leq n_j$ となる一方で、 $x_{ij} = 0$ のとき、 左辺は $n_i + 1 - N \\leq 0 $ となり、上記の制約はどんな $n_i$、$n_j$でも満たされる。つまり、$x_{ij} = 1$ のときだけ有効な制約となっている。\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "g4PnyIfwyp6c",
"outputId": "2cfa36c8-e6bb-4100-bb91-318eac523c96",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 68
}
},
"source": [
"# ソルバーを定義\n",
"solver = pywraplp.Solver('shredder', pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)\n",
"\n",
"# 決定変数を定義\n",
"x = np.array([[\n",
" solver.BoolVar(f'x_{i}_{j}') if i != j else 0\n",
" for j in range(bins)\n",
" ] for i in range(bins)\n",
"])\n",
"# 順序を表す変数を追加\n",
"n = np.array([\n",
" solver.NumVar(0, bins, f'n_{i}')\n",
" for i in range(bins)\n",
"])\n",
"\n",
"# 目的関数を定義\n",
"objective = (C*x).sum()\n",
"solver.Minimize(objective)\n",
"\n",
"# 制約\n",
"for j in range(bins):\n",
" solver.Add(x[:, j].sum() == 1)\n",
"\n",
"for i in range(bins):\n",
" solver.Add(x[i, :].sum() == 1)\n",
"\n",
"# 追加の制約(部分順回路除去)\n",
"for i in range(bins):\n",
" for j in range(1, bins):\n",
" solver.Add(n[i] + 1 - bins*(1 - x[i, j]) <= n[j])\n",
"\n",
"# 求解\n",
"%time status = solver.Solve()\n",
"# 最適解が求まったことを確認\n",
"status == pywraplp.Solver.OPTIMAL"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"CPU times: user 7.41 s, sys: 178 ms, total: 7.59 s\n",
"Wall time: 7.56 s\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {
"tags": []
},
"execution_count": 6
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "IaKaa5UOFVl0",
"outputId": "592f18ea-bb56-48f7-84f6-2111a811076f",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 286
}
},
"source": [
"plt.imshow(np.hstack(sort_imgs(shredded, x)))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7faeea9c8358>"
]
},
"metadata": {
"tags": []
},
"execution_count": 7
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9elDeuZZACJr"
},
"source": [
"## 補足: どの紙片を端っこにもってくるか\n",
"\n",
"どの紙片を一番端に持ってくるか(端っこらしい紙片はどれか)については、復元したいドキュメントの種類に依存するので今回は省略しています。簡単な方法として、**最もつながりにくい部分を端っことする**ことが考えられます。(ドキュメントの種類によってうまくいったりいかなかったりします。)\n",
"\n",
"宿題: 「**2. 端っこらしさを含めて定式化する**」にチャレンジしてみましょう。\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "JOpJWGHVAuxP"
},
"source": [
"# ぜひ手を動かしてみてください\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "8Lm9Zyn0HGLB"
},
"source": [
"### 解答例"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Z9MfhsDMHVWh"
},
"source": [
"紙片に加えて「端っこ」を表す特別なノード(紙片)を用意し、そのインデックスを $\\mathrm{bins}$ とします。この「端っこノード」との類似度をすべて $0$ としておくと、他の紙片とつながりにくい紙片は自然と端っこにつながろうとするはずです。"
]
},
{
"cell_type": "code",
"metadata": {
"id": "vNIQE4ItA1IL",
"outputId": "a06b67ad-08fb-47bc-bd8a-59d2fa9c16ec",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 68
}
},
"source": [
"# ソルバーを定義\n",
"solver = pywraplp.Solver('shredder', pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)\n",
"\n",
"# 決定変数を定義\n",
"x = np.array([[\n",
" solver.BoolVar(f'x_{i}_{j}') if i != j else 0\n",
" for j in range(bins + 1)\n",
" ] for i in range(bins + 1)\n",
"])\n",
"# 順序を表す変数を追加\n",
"n = np.array([\n",
" solver.NumVar(0, bins, f'n_{i}')\n",
" for i in range(bins + 1)\n",
"])\n",
"\n",
"# 目的関数を定義\n",
"objective = (C*x[:-1,:-1]).sum()\n",
"solver.Minimize(objective)\n",
"\n",
"# 制約\n",
"for j in range(bins + 1):\n",
" solver.Add(x[:, j].sum() == 1)\n",
"\n",
"for i in range(bins + 1):\n",
" solver.Add(x[i, :].sum() == 1)\n",
"\n",
"# 追加の制約(部分順回路除去)\n",
"for i in range(bins + 1):\n",
" for j in range(bins):\n",
" solver.Add(n[i] + 1 - (bins + 1)*(1 - x[i, j]) <= n[j])\n",
"\n",
"# 求解\n",
"%time status = solver.Solve()\n",
"# 最適解が求まったことを確認\n",
"status == pywraplp.Solver.OPTIMAL"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"CPU times: user 4.48 s, sys: 180 ms, total: 4.66 s\n",
"Wall time: 4.64 s\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "H94TkSZeBOLw",
"outputId": "496e0957-2d4b-41ff-bc94-33c6a860104c",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 286
}
},
"source": [
"left_idx = bins\n",
"sorted = []\n",
"for _ in range(bins):\n",
" for right_idx in range(bins):\n",
" if left_idx == right_idx:\n",
" continue\n",
" if x[left_idx, right_idx].solution_value() == 1:\n",
" sorted.append(shredded[right_idx])\n",
" left_idx = right_idx\n",
" break\n",
"\n",
"plt.imshow(np.hstack(sorted))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7faee80966d8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 10
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "elZB_HelnEqv"
},
"source": [
"## 速度計測"
]
},
{
"cell_type": "code",
"metadata": {
"id": "QxvCjzjqLrhA"
},
"source": [
"def solve(costs):\n",
" bins = len(costs)\n",
" # ソルバーを定義\n",
" solver = pywraplp.Solver('shredder', pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)\n",
"\n",
" # 決定変数を定義\n",
" x = np.array([[\n",
" solver.BoolVar(f'x_{i}_{j}') if i != j else 0\n",
" for j in range(bins)\n",
" ] for i in range(bins)\n",
" ])\n",
" # 順序を表す変数を追加\n",
" n = np.array([\n",
" solver.NumVar(0, bins, f'n_{i}')\n",
" for i in range(bins)\n",
" ])\n",
"\n",
" # 目的関数を定義\n",
" objective = (costs*x).sum()\n",
" solver.Minimize(objective)\n",
"\n",
" # 制約\n",
" for j in range(bins):\n",
" solver.Add(x[:, j].sum() == 1)\n",
"\n",
" for i in range(bins):\n",
" solver.Add(x[i, :].sum() == 1)\n",
"\n",
" # 追加の制約(部分順回路除去)\n",
" for i in range(bins):\n",
" for j in range(1, bins):\n",
" solver.Add(n[i] + 1 - bins*(1 - x[i, j]) <= n[j])\n",
"\n",
" # time limit を設定\n",
" solver.SetTimeLimit(10*60*1000)\n",
" # 求解\n",
" %time status = solver.Solve()\n",
" # 最適解が求まったことを確認\n",
" assert status == pywraplp.Solver.OPTIMAL"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "JdWfApUUnjWG",
"outputId": "8097d542-7a53-4c50-f443-a012193f66e0",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
}
},
"source": [
"for n in (10, 20, 30, 50, 100, 200):\n",
" print(f' ---- n = {n} ----')\n",
" shredded = shred(img, n, shuffle=False)\n",
" costs = np.array([[\n",
" disimilarity(shredded[i], shredded[j])\n",
" for j in range(n)\n",
" ] for i in range(n)\n",
" ])\n",
" idx = np.array(list(range(n)))\n",
" for i in range(5):\n",
" np.random.shuffle(idx)\n",
" solve(costs[idx][:, idx])"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
" ---- n = 10 ----\n",
"bins: 10\n",
"CPU times: user 15 ms, sys: 51 µs, total: 15 ms\n",
"Wall time: 15.1 ms\n",
"CPU times: user 14 ms, sys: 1 ms, total: 15 ms\n",
"Wall time: 15 ms\n",
"CPU times: user 14.8 ms, sys: 8 µs, total: 14.8 ms\n",
"Wall time: 14.7 ms\n",
"CPU times: user 15.5 ms, sys: 9 µs, total: 15.5 ms\n",
"Wall time: 15.4 ms\n",
"CPU times: user 15 ms, sys: 3 µs, total: 15 ms\n",
"Wall time: 14.9 ms\n",
" ---- n = 20 ----\n",
"bins: 20\n",
"CPU times: user 79.2 ms, sys: 2.05 ms, total: 81.3 ms\n",
"Wall time: 80.9 ms\n",
"CPU times: user 85.3 ms, sys: 18 µs, total: 85.3 ms\n",
"Wall time: 85 ms\n",
"CPU times: user 78.7 ms, sys: 1.01 ms, total: 79.7 ms\n",
"Wall time: 79.5 ms\n",
"CPU times: user 82.2 ms, sys: 1.03 ms, total: 83.2 ms\n",
"Wall time: 83.1 ms\n",
"CPU times: user 79.5 ms, sys: 0 ns, total: 79.5 ms\n",
"Wall time: 79.4 ms\n",
" ---- n = 30 ----\n",
"bins: 31\n",
"CPU times: user 175 ms, sys: 11 µs, total: 175 ms\n",
"Wall time: 175 ms\n",
"CPU times: user 172 ms, sys: 17 µs, total: 172 ms\n",
"Wall time: 172 ms\n",
"CPU times: user 177 ms, sys: 1.01 ms, total: 178 ms\n",
"Wall time: 178 ms\n",
"CPU times: user 170 ms, sys: 4.98 ms, total: 175 ms\n",
"Wall time: 175 ms\n",
"CPU times: user 177 ms, sys: 1.96 ms, total: 179 ms\n",
"Wall time: 179 ms\n",
" ---- n = 50 ----\n",
"bins: 50\n",
"CPU times: user 728 ms, sys: 15.1 ms, total: 743 ms\n",
"Wall time: 741 ms\n",
"CPU times: user 711 ms, sys: 11 ms, total: 722 ms\n",
"Wall time: 719 ms\n",
"CPU times: user 710 ms, sys: 9.02 ms, total: 719 ms\n",
"Wall time: 717 ms\n",
"CPU times: user 705 ms, sys: 12 ms, total: 717 ms\n",
"Wall time: 715 ms\n",
"CPU times: user 708 ms, sys: 14 ms, total: 723 ms\n",
"Wall time: 719 ms\n",
" ---- n = 100 ----\n",
"bins: 100\n",
"CPU times: user 6.96 s, sys: 230 ms, total: 7.19 s\n",
"Wall time: 7.17 s\n",
"CPU times: user 6.31 s, sys: 182 ms, total: 6.5 s\n",
"Wall time: 6.47 s\n",
"CPU times: user 6.24 s, sys: 198 ms, total: 6.44 s\n",
"Wall time: 6.42 s\n",
"CPU times: user 6.88 s, sys: 292 ms, total: 7.17 s\n",
"Wall time: 7.16 s\n",
"CPU times: user 5.89 s, sys: 183 ms, total: 6.07 s\n",
"Wall time: 6.05 s\n",
" ---- n = 200 ----\n",
"bins: 200\n",
"CPU times: user 47.7 s, sys: 775 ms, total: 48.4 s\n",
"Wall time: 48.2 s\n",
"CPU times: user 46.2 s, sys: 335 ms, total: 46.6 s\n",
"Wall time: 46.4 s\n",
"CPU times: user 41.8 s, sys: 292 ms, total: 42 s\n",
"Wall time: 41.9 s\n",
"CPU times: user 25.8 s, sys: 197 ms, total: 26 s\n",
"Wall time: 26 s\n",
"CPU times: user 1min 16s, sys: 1.1 s, total: 1min 17s\n",
"Wall time: 1min 16s\n"
],
"name": "stdout"
}
]
}
]
}
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