253 lines
6.7 KiB
Text
253 lines
6.7 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 人工智能与机器学习-实验1\n",
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"\n",
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"## Part.II Numpy练习\n",
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"\n",
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"|学号 |姓名 |\n",
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"|----------|--------|\n",
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"|***REMOVED***|***REMOVED***|\n",
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"|2020113874|何一涛|"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 1. 数组\n",
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"\n",
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"创建一个长度为10全为0的一维数组，然后让第5个元素等于1。"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"a = np.zeros(10)\n",
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"a[4] = 1\n",
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"print(a)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 2. 向量内积\n",
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"\n",
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"随机生成2个长度为$10^6$的向量，分别用numpy函数和for循环计算其内积。并比较耗时情况。"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"250517.08615769504\n",
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"numpy:0.9500980377197266ms\n",
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"250517.08615771346\n",
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"for:450.66380500793457ms\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"import time\n",
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"a = np.random.rand(1000000)\n",
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"b = np.random.rand(1000000)\n",
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"tic = time.time()\n",
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"c = np.dot(a,b)\n",
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"toc = time.time()\n",
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"print(c)\n",
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"print(\"numpy:\" + str(1000*(toc-tic)) + \"ms\")\n",
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"c = 0\n",
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"tic = time.time()\n",
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"for i in range(1000000):\n",
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" c += a[i]*b[i]\n",
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"toc = time.time()\n",
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"print(c)\n",
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"print(\"for:\" + str(1000*(toc-tic)) + \"ms\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 3. 矩阵乘法\n",
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"\n",
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"生成一个$4\\times5$和一个$5\\times4$的矩阵，并计算它们的乘积。"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[0.832603 0.01479218 0.74726877 0.11899442 0.5139687 ]\n",
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" [0.85742314 0.20950708 0.31393951 0.69463518 0.58622781]\n",
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" [0.92412297 0.93890447 0.27295923 0.44996205 0.98461149]\n",
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" [0.56097043 0.81885742 0.31026755 0.65530345 0.51932541]]\n",
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"[[0.54243804 0.59199752 0.2088532 0.09047042]\n",
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" [0.96482797 0.66663309 0.7223203 0.96680344]\n",
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" [0.1848234 0.88155844 0.98424619 0.99646051]\n",
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" [0.76723488 0.42095062 0.55842772 0.58467868]\n",
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" [0.56045915 0.6447964 0.05470569 0.317023 ]]\n",
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"[[0.98337534 1.54301691 1.01463973 1.0667643 ]\n",
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" [1.58676566 1.59441744 1.05937409 1.184938 ]\n",
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" [2.35467111 2.23789856 1.44499002 1.83856268]\n",
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" [1.94552528 1.76219908 1.40836713 1.69937482]]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"a = np.random.rand(4,5)\n",
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"b = np.random.rand(5,4)\n",
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"c = np.dot(a,b)\n",
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"print(a)\n",
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"print(b)\n",
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"print(c)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 4. 函数\n",
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"\n",
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"函数$f$定义如下，其中$x$是任意实数:\n",
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"$$\n",
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"f(x)=\\frac{\\sin(x+1)(x+1)}{2e^x}\n",
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"$$，\n",
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"\n",
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"生成一个数组$a\\in \\mathbb{R}^5$，计算$b = f(a)$。"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[0.89379618 0.03735883 0.51341215 0.49607132 0.15340217]\n",
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"[0.36734363 0.43023904 0.45210542 0.45422143 0.45221582]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"def f(x):\n",
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" return np.sin(x+1)*(x+1)/(2*np.exp(x))\n",
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"a = np.random.rand(5)\n",
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"b = f(a)\n",
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"print(a)\n",
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"print(b)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 5. 平均值\n",
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"\n",
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"随机生成一个5行10列的矩阵，然后每行元素减去该行的平均值"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[0.39753532 0.54410703 0.60167078 0.24255209 0.67574439 0.01004289\n",
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" 0.55770556 0.10702142 0.48778556 0.51648967]\n",
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" [0.98453781 0.66164632 0.66346184 0.5019827 0.74216596 0.37279722\n",
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" 0.02415767 0.21952032 0.94425462 0.83570665]\n",
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" [0.366748 0.38391583 0.21428393 0.56555728 0.73883924 0.38754266\n",
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" 0.7720652 0.68972519 0.69671146 0.43759293]\n",
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" [0.93430798 0.57475894 0.23919737 0.31449016 0.56069848 0.23824185\n",
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" 0.61332708 0.8877036 0.895658 0.39875045]\n",
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" [0.80075957 0.85481337 0.10696488 0.91660988 0.95048433 0.62219214\n",
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" 0.61386599 0.1400393 0.68407094 0.08965478]]\n",
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"[[-0.01653016 0.13004156 0.18760531 -0.17151338 0.26167892 -0.40402258\n",
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" 0.14364009 -0.30704405 0.07372009 0.10242419]\n",
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" [ 0.3895147 0.06662321 0.06843873 -0.09304041 0.14714285 -0.22222589\n",
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" -0.57086544 -0.37550279 0.34923151 0.24068354]\n",
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" [-0.15855017 -0.14138234 -0.31101425 0.0402591 0.21354107 -0.13775551\n",
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" 0.24676703 0.16442702 0.17141329 -0.08770524]\n",
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" [ 0.36859459 0.00904555 -0.32651602 -0.25122323 -0.00501491 -0.32747154\n",
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" 0.04761369 0.32199021 0.32994461 -0.16696294]\n",
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" [ 0.22281405 0.27686785 -0.47098064 0.33866436 0.37253881 0.04424662\n",
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" 0.03592048 -0.43790622 0.10612542 -0.48829074]]\n",
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"[[ 0.00000000e+00]\n",
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" [ 6.66133815e-17]\n",
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" [-3.33066907e-17]\n",
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" [ 1.11022302e-17]\n",
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" [-3.33066907e-17]]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"a = np.random.rand(5,10)\n",
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"b = a - np.mean(a,axis=1,keepdims=True)\n",
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"print(a)\n",
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"print(b)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.10.7 ('.venv': venv)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.7"
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},
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"vscode": {
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"interpreter": {
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"hash": "1f0d395e06aa83586067b19165efc9b683889967164248deef4bbf1fa27cfb00"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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