{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# python与numpy基础" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "寒小阳(2016年6月)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Python介绍" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "如果你问我没有编程基础，想学习一门语言，我一定会首推给你Python
\n", "类似伪代码的书写方式，让你能够集中精力去解决问题，而不是花费大量的时间在开发和debug上
\n", "同时得益于Numpy/Scipy这样的科学计算库，使得其有非常高效和简易的科学计算能力。
\n", "而活跃的社区提供的各种可视化的库，也使得 机器学习/数据挖掘 的全过程(数据采集，数据清洗，数据处理，建模，可视化)可以非常流畅地完成。
\n", "而近年来极其热门的深度学习开源框架，基本都有python接口，google的Tensorflow更是python主导。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这个教程里面的内容包括：\n", "\n", "* 基本Python语法: 基本数据类型 (Containers, Lists, Dictionaries, Sets, Tuples), 函数, 类\n", "* Numpy: Arrays/数组, Array indexing/数组取值, Datatypes, Array math, Broadcasting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 基本python语法" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Python确实经常被人像伪代码，下面是一个快排程序，你可以感受一下:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 1, 2, 3, 6, 8, 9, 10]\n" ] } ], "source": [ "def quicksort(arr):\n", " if len(arr) <= 1:\n", " return arr\n", " pivot = arr[len(arr) / 2]\n", " left = [x for x in arr if x < pivot]\n", " middle = [x for x in arr if x == pivot]\n", " right = [x for x in arr if x > pivot]\n", " return quicksort(left) + middle + quicksort(right)\n", "\n", "print quicksort([3,6,9, 8,10,1,2,1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 基本数据类型" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 数值型" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "整型和浮点型以及基本的运算大家应该都知道：" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4 \n" ] } ], "source": [ "x = 4\n", "print x, type(x)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5\n", "3\n", "8\n", "16\n" ] } ], "source": [ "print x + 1 # 加;\n", "print x - 1 # 减;\n", "print x * 2 # 乘;\n", "print x ** 2 # 指数;" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5\n", "10\n" ] } ], "source": [ "x += 1\n", "print x # 自加\n", "x *= 2\n", "print x # 自乘" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "2.5 3.5 5.0 6.25\n" ] } ], "source": [ "y = 2.5\n", "print type(y) # 输出类型\n", "print y, y + 1, y * 2, y ** 2 # 连续输出" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "不过需要提醒一句，用习惯C++和Java的同学，Python真的没有(x++)和(x--)这俩操作" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 布尔型" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "用于指定真假的类型，布尔型，包含真（True）和假（False）:" ] }, { "cell_type": "code", "execution_count": 139, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "t, f = True, False\n", "print type(t) # Prints \"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "看看逻辑与或非这些操作" ] }, { "cell_type": "code", "execution_count": 140, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "False\n", "True\n", "False\n", "True\n" ] } ], "source": [ "print t and f # Logical AND;\n", "print t or f # Logical OR;\n", "print not t # Logical NOT;\n", "print t != f # Logical XOR;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 字符串型" ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "hello 5\n" ] } ], "source": [ "hello = 'hello' # 实在想不出的时候就用hello world\n", "world = \"world\"\n", "print hello, len(hello) # 字符串长度" ] }, { "cell_type": "code", "execution_count": 143, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "hello world\n" ] } ], "source": [ "hw = hello + ' ' + world # 字符串拼接\n", "print hw" ] }, { "cell_type": "code", "execution_count": 144, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "hello world 12\n" ] } ], "source": [ "hw12 = '%s %s %d' % (hello, world, 12) # 类似sprintf的格式化输出\n", "print hw12 # prints \"hello world 12\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我能说什么，你面试的时候面试官最爱让你写的字符串操作，都是它自带的:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hello\n", "HELLO\n", " hello\n", " hello \n", "he(ell)(ell)o\n", "world\n" ] } ], "source": [ "s = \"hello\"\n", "print s.capitalize() # 首字母大写\n", "print s.upper() # 全大写\n", "print s.rjust(7) # 靠右对齐\n", "print s.center(7) # 居中输出\n", "print s.replace('l', '(ell)') # 字符串替换\n", "print ' world '.strip() # 去掉两侧空白" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "其他你想要的字符串操作看[这里](https://docs.python.org/2/library/stdtypes.html#string-methods)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 容器" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "内置的容器用得非常非常多，包括: lists, dictionaries, sets, and tuples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Lists/列表" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "和你学数据结构里面数组长得一样的容器，但是操作可多多了:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3, 1, 2] 2\n", "2\n" ] } ], "source": [ "xs = [3, 1, 2] # 建一个列表\n", "print xs, xs[2]\n", "print xs[-1] # 用-1表示最后一个元素，输出来" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3, 1, 'Hanxiaoyang']\n" ] } ], "source": [ "xs[2] = 'Hanxiaoyang' # 有意思的是，Python的list居然可以有不同类型的元素\n", "print xs" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3, 1, 'Hanxiaoyang', 'happy']\n" ] } ], "source": [ "xs.append('happy') # 可以用append在尾部添加元素\n", "print xs " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "happy [3, 1, 'Hanxiaoyang']\n" ] } ], "source": [ "x = xs.pop() # 也可以把最后一个元素“弹射”出来\n", "print x, xs " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "关于list更多的操作和内容可以看[这里](https://docs.python.org/2/tutorial/datastructures.html#more-on-lists)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 列表切片" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这是大家最爱python list的原因之一，取东西太方便啦:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 1, 2, 3, 4]\n", "[2, 3]\n", "[2, 3, 4]\n", "[0, 1]\n", "[0, 1, 2, 3, 4]\n", "[0, 1, 2, 3]\n", "[0, 1, 8, 9, 4]\n" ] } ], "source": [ "nums = range(5) # 0-4\n", "print nums # 输出 \"[0, 1, 2, 3, 4]\"\n", "print nums[2:4] # 下标2到4(不包括)的元素，注意下标从0开始\n", "print nums[2:] # 下标2到结尾的元素; prints \"[2, 3, 4]\"\n", "print nums[:2] # 直到下标2的元素; prints \"[0, 1]\"\n", "print nums[:] # Get a slice of the whole list; prints [\"0, 1, 2, 3, 4]\"\n", "print nums[:-1] # 直到倒数第一个元素; prints [\"0, 1, 2, 3]\"\n", "nums[2:4] = [8, 9] # 也可以直接这么赋值\n", "print nums # Prints \"[0, 1, 8, 8, 4]\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 循环" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可以对list立面的元素做一个循环:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "喵星人\n", "汪星人\n", "火星人\n" ] } ], "source": [ "animals = ['喵星人', '汪星人', '火星人']\n", "for animal in animals:\n", " print animal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "又要输出元素，又要输出下标怎么办，用 `enumerate` 函数:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "#1: 喵星人\n", "#2: 汪星人\n", "#3: 火星人\n" ] } ], "source": [ "animals = ['喵星人', '汪星人', '火星人']\n", "for idx, animal in enumerate(animals):\n", " print '#%d: %s' % (idx + 1, animal)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### List comprehensions:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "如果对list里面的元素都做一样的操作，然后生成一个list，用它最快了，这绝对会成为你最爱的python操作之一:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 1, 4, 9, 16]\n" ] } ], "source": [ "# 求一个list里面的元素的平方，然后输出，很out的for循环写法\n", "nums = [0, 1, 2, 3, 4]\n", "squares = []\n", "for x in nums:\n", " squares.append(x ** 2)\n", "print squares" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "用list comprehension可以这么写:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 1, 4, 9, 16]\n" ] } ], "source": [ "nums = [0, 1, 2, 3, 4]\n", "# 对每个x完成一个操作以后返回来，组成新的list\n", "squares = [x ** 2 for x in nums]\n", "print squares" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "你甚至可以加条件，去筛出你想要的元素，去做你想要的操作:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 4, 16]\n" ] } ], "source": [ "nums = [0, 1, 2, 3, 4]\n", "# 把所有的偶数取出来，平方后返回\n", "even_squares = [x ** 2 for x in nums if x % 2 == 0]\n", "print even_squares" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 字典" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "存储键值对(key => value)的数据结构, 类似Java中的`Map`，这真的是我使用频度相当高的数据结构:" ] }, { "cell_type": "code", "execution_count": 158, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cute\n", "True\n" ] } ], "source": [ "d = {'cat': 'cute', 'dog': 'furry'} # 建立字典\n", "print d['cat'] # 根据key取value\n", "print 'cat' in d # 查一个元素是否在字典中" ] }, { "cell_type": "code", "execution_count": 159, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "wet\n" ] } ], "source": [ "d['fish'] = 'wet' # 设定键值对\n", "print d['fish'] # 这时候肯定是输出修改后的内容" ] }, { "cell_type": "code", "execution_count": 161, "metadata": { "collapsed": false }, "outputs": [ { "ename": "KeyError", "evalue": "'monkey'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mprint\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'monkey'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# KeyError: 'monkey' not a key of d\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mKeyError\u001b[0m: 'monkey'" ] } ], "source": [ "print d['monkey'] # 不是d的键，肯定输不出东西" ] }, { "cell_type": "code", "execution_count": 162, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N/A\n", "wet\n" ] } ], "source": [ "print d.get('monkey', 'N/A') # 可以默认输出'N/A'（取不到key对应的value值的时候）\n", "print d.get('fish', 'N/A') " ] }, { "cell_type": "code", "execution_count": 163, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N/A\n" ] } ], "source": [ "del d['fish'] # 删除字典中的键值对\n", "print d.get('fish', 'N/A') # 这会儿就没有了" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "同样的，你其他想了解的字典相关的操作和内容可以看 [这里](https://docs.python.org/2/library/stdtypes.html#dict)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "你可以这样循环python字典取出你想要的内容:" ] }, { "cell_type": "code", "execution_count": 164, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A person has 2 legs\n", "A spider has 8 legs\n", "A cat has 4 legs\n" ] } ], "source": [ "d = {'person': 2, 'cat': 4, 'spider': 8}\n", "for animal in d:\n", " legs = d[animal]\n", " print 'A %s has %d legs' % (animal, legs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "用iteritems函数可以同时取出键值对:" ] }, { "cell_type": "code", "execution_count": 165, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A person has 2 legs\n", "A spider has 8 legs\n", "A cat has 4 legs\n" ] } ], "source": [ "d = {'person': 2, 'cat': 4, 'spider': 8}\n", "for animal, legs in d.iteritems():\n", " print 'A %s has %d legs' % (animal, legs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dictionary comprehensions: 和list comprehension有点像啦，但是生成的是字典:" ] }, { "cell_type": "code", "execution_count": 166, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{0: 0, 2: 4, 4: 16}\n" ] } ], "source": [ "nums = [0, 1, 2, 3, 4]\n", "even_num_to_square = {x: x ** 2 for x in nums if x % 2 == 0}\n", "print even_num_to_square" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "你可以理解成没有相同元素的列表（当然，显然和list是不同的）:" ] }, { "cell_type": "code", "execution_count": 167, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n", "False\n" ] } ], "source": [ "animals = {'cat', 'dog'}\n", "print 'cat' in animals # Check if an element is in a set; prints \"True\"\n", "print 'fish' in animals # prints \"False\"\n" ] }, { "cell_type": "code", "execution_count": 170, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n", "2\n" ] } ], "source": [ "animals.add('fish') # 添加元素\n", "print 'fish' in animals\n", "print len(animals) # 元素个数" ] }, { "cell_type": "code", "execution_count": 171, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3\n", "2\n" ] } ], "source": [ "animals.add('cat') # 如果元素已经在set里了，操作不会怎么样\n", "print len(animals) \n", "animals.remove('cat') # 删除一个元素\n", "print len(animals) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "循环的方式和list很像啦:" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "#1: fish\n", "#2: dog\n", "#3: cat\n" ] } ], "source": [ "animals = {'cat', 'dog', 'fish'}\n", "for idx, animal in enumerate(animals):\n", " print '#%d: %s' % (idx + 1, animal)\n", "# Prints \"#1: fish\", \"#2: dog\", \"#3: cat\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set comprehensions: 熟悉的感觉:" ] }, { "cell_type": "code", "execution_count": 172, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "set([0, 1, 2, 3, 4, 5])\n" ] } ], "source": [ "from math import sqrt\n", "print {int(sqrt(x)) for x in range(30)}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 元组" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "和list很像，但是可以作为字典的key或者set的元素出现，但是一整个list不可以作为字典的key或者set的元素的:" ] }, { "cell_type": "code", "execution_count": 173, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "5\n", "1\n" ] } ], "source": [ "d = {(x, x + 1): x for x in range(10)} # Create a dictionary with tuple keys\n", "t = (5, 6) # Create a tuple\n", "print type(t)\n", "print d[t] \n", "print d[(1, 2)]" ] }, { "cell_type": "code", "execution_count": 176, "metadata": { "collapsed": false }, "outputs": [ { "ename": "TypeError", "evalue": "'tuple' object does not support item assignment", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment" ] } ], "source": [ "t[0] = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 函数" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "用 `def` 就可以定义一个函数，就像下面这样:" ] }, { "cell_type": "code", "execution_count": 178, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "negative\n", "zero\n", "positive\n" ] } ], "source": [ "def sign(x):\n", " if x > 0:\n", " return 'positive'\n", " elif x < 0:\n", " return 'negative'\n", " else:\n", " return 'zero'\n", "\n", "for x in [-1, 0, 1]:\n", " print sign(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "函数名字后面接的括号里，可以有多个参数，你自己可以试试:" ] }, { "cell_type": "code", "execution_count": 179, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hello, Bob!\n", "HELLO, FRED\n" ] } ], "source": [ "def hello(name, loud=False):\n", " if loud:\n", " print 'HELLO, %s' % name.upper()\n", " else:\n", " print 'Hello, %s!' % name\n", "\n", "hello('Bob')\n", "hello('Fred', loud=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 类" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Python的类，怎么说呢，比较简单粗暴:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hello, Fred\n", "HELLO, FRED!\n" ] } ], "source": [ "class Greeter:\n", "\n", " # 构造函数\n", " def __init__(self, name):\n", " self.name = name # Create an instance variable\n", "\n", " # 类的成员函数\n", " def greet(self, loud=False):\n", " if loud:\n", " print 'HELLO, %s!' % self.name.upper()\n", " else:\n", " print 'Hello, %s' % self.name\n", "\n", "g = Greeter('Fred') # 构造一个类\n", "g.greet() # 调用函数; prints \"Hello, Fred\"\n", "g.greet(loud=True) # 调用函数; prints \"HELLO, FRED!\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numpy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们要开始接触高效计算库Numpy了，你要是之前在实验室用MATLAB之类的语法，你会发现Numpy和它们长得不要太像，爱MATLAB的同学，参考文档可以看[这里](http://wiki.scipy.org/NumPy_for_Matlab_Users)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "python里面调用一个包，用import对吧, 所以我们import `numpy` 包:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Arrays/数组" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "看你数组的维度啦，我自己的话比较简单粗暴，一般直接把1维数组就看做向量/vector，2维数组看做2维矩阵，3维数组看做3维矩阵..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可以调用np.array去从list初始化一个数组:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " (3,) 1 2 3\n", "[5 2 3]\n" ] } ], "source": [ "a = np.array([1, 2, 3]) # 1维数组\n", "print type(a), a.shape, a[0], a[1], a[2]\n", "a[0] = 5 # 重新赋值\n", "print a " ] }, { "cell_type": "code", "execution_count": 198, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3]\n", " [4 5 6]]\n" ] } ], "source": [ "b = np.array([[1,2,3],[4,5,6]]) # 2维数组\n", "print b" ] }, { "cell_type": "code", "execution_count": 199, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2, 3)\n", "1 2 4\n" ] } ], "source": [ "print b.shape #可以看形状的（非常常用！！！） \n", "print b[0, 0], b[0, 1], b[1, 0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "有一些内置的创建数组的函数:" ] }, { "cell_type": "code", "execution_count": 186, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0.]\n", " [ 0. 0.]]\n" ] } ], "source": [ "a = np.zeros((2,2)) # 创建2x2的全0数组\n", "print a" ] }, { "cell_type": "code", "execution_count": 187, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1. 1.]]\n" ] } ], "source": [ "b = np.ones((1,2)) # 创建1x2的全0数组\n", "print b" ] }, { "cell_type": "code", "execution_count": 188, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 7. 7.]\n", " [ 7. 7.]]\n" ] } ], "source": [ "c = np.full((2,2), 7) # 定值数组\n", "print c " ] }, { "cell_type": "code", "execution_count": 190, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1. 0.]\n", " [ 0. 1.]]\n" ] } ], "source": [ "d = np.eye(2) # 对角矩阵（对角元素为1）\n", "print d" ] }, { "cell_type": "code", "execution_count": 192, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.09477679 0.79267634]\n", " [ 0.78291274 0.38962829]]\n" ] } ], "source": [ "e = np.random.random((2,2)) # 2x2的随机数组(矩阵)\n", "print e" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Array indexing/数组取值" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numpy提供了蛮多种取值的方式的." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可以像list一样切片（多维数组可以从各个维度同时切片）:" ] }, { "cell_type": "code", "execution_count": 203, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 3]\n", " [6 7]]\n" ] } ], "source": [ "import numpy as np\n", "\n", "# 创建一个如下格式的3x4数组\n", "# [[ 1 2 3 4]\n", "# [ 5 6 7 8]\n", "# [ 9 10 11 12]]\n", "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n", "\n", "# 在两个维度上分别按照[:2]和[1:3]进行切片，取需要的部分\n", "# [[2 3]\n", "# [6 7]]\n", "b = a[:2, 1:3]\n", "print b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "虽然，怎么说呢，不建议你这样去赋值，但是你确实可以修改切片出来的对象，然后完成对原数组的赋值." ] }, { "cell_type": "code", "execution_count": 202, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2\n", "77\n" ] } ], "source": [ "print a[0, 1] \n", "b[0, 0] = 77 # b[0, 0]改了，很遗憾a[0, 1]也被修改了\n", "print a[0, 1] " ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 3 4]\n", " [ 5 6 7 8]\n", " [ 9 10 11 12]]\n" ] } ], "source": [ "# 创建3x4的2维数组/矩阵\n", "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n", "print a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "你就放心大胆地去取你想要的数咯:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[5 6 7 8] (4,)\n", "[[5 6 7 8]] (1, 4)\n", "[[5 6 7 8]] (1, 4)\n" ] } ], "source": [ "row_r1 = a[1, :] # 第2行，但是得到的是1维输出（列向量）\n", "row_r2 = a[1:2, :] # 1x2的2维输出\n", "row_r3 = a[[1], :] # 同上\n", "print row_r1, row_r1.shape \n", "print row_r2, row_r2.shape\n", "print row_r3, row_r3.shape" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2 6 10] (3,)\n", "\n", "[[ 2]\n", " [ 6]\n", " [10]] (3, 1)\n" ] } ], "source": [ "# 试试在第2个维度上切片也一样的:\n", "col_r1 = a[:, 1]\n", "col_r2 = a[:, 1:2]\n", "print col_r1, col_r1.shape\n", "print\n", "print col_r2, col_r2.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "下面这个高级了，更自由地取值和组合，但是要看清楚一点:" ] }, { "cell_type": "code", "execution_count": 220, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 4 5]\n", "[1 4 5]\n" ] } ], "source": [ "a = np.array([[1,2], [3, 4], [5, 6]])\n", "\n", "# 其实意思就是取(0,0),(1,1),(2,0)的元素组起来\n", "print a[[0, 1, 2], [0, 1, 0]]\n", "\n", "# 下面这个比较直白啦\n", "print np.array([a[0, 0], a[1, 1], a[2, 0]])" ] }, { "cell_type": "code", "execution_count": 221, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2 2]\n", "[2 2]\n" ] } ], "source": [ "# 再来试试\n", "print a[[0, 0], [1, 1]]\n", "\n", "# 还是一样\n", "print np.array([a[0, 1], a[0, 1]])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 3]\n", " [ 4 5 6]\n", " [ 7 8 9]\n", " [10 11 12]]\n" ] } ], "source": [ "# 再来熟悉一下\n", "# 先创建一个2维数组\n", "a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n", "print a" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1 6 7 11]\n" ] } ], "source": [ "# 用下标生成一个向量\n", "b = np.array([0, 2, 0, 1])\n", "\n", "# 你能看明白下面做的事情吗？\n", "print a[np.arange(4), b] # Prints \"[ 1 6 7 11]\"" ] }, { "cell_type": "code", "execution_count": 218, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[21 2 3]\n", " [ 4 5 26]\n", " [27 8 9]\n", " [10 31 12]]\n" ] } ], "source": [ "# 既然可以取出来，我们当然可以对这些元素操作咯\n", "a[np.arange(4), b] += 10\n", "print a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "比较fashion的取法之一，用条件判定去取（但是很好用）:" ] }, { "cell_type": "code", "execution_count": 223, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[False False]\n", " [ True True]\n", " [ True True]]\n" ] } ], "source": [ "import numpy as np\n", "\n", "a = np.array([[1,2], [3, 4], [5, 6]])\n", "\n", "bool_idx = (a > 2) # 就是判定一下是否大于2\n", "\n", "print bool_idx # 返回一个布尔型的3x2数组" ] }, { "cell_type": "code", "execution_count": 225, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3 4 5 6]\n", "[3 4 5 6]\n" ] } ], "source": [ "# 用刚才的布尔型数组作为下标就可以去除符合条件的元素啦\n", "print a[bool_idx]\n", "\n", "# 其实一句话也可以完成是不是？\n", "print a[a > 2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "那个，真的，其实还有很多细节，其他的方式去取值，你可以看看官方文档。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们一起来来总结一下，看下面切片取值方式（对应颜色是取出来的结果）：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](http://old.sebug.net/paper/books/scipydoc/_images/numpy_intro_02.png)\n", "![](http://old.sebug.net/paper/books/scipydoc/_images/numpy_intro_03.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Datatypes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们可以用dtype来看numpy数组中元素的类型:" ] }, { "cell_type": "code", "execution_count": 226, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "int64 float64 int64\n" ] } ], "source": [ "x = np.array([1, 2]) # numpy构建数组的时候自己会确定类型\n", "y = np.array([1.0, 2.0])\n", "z = np.array([1, 2], dtype=np.int64)# 指定用int64构建\n", "\n", "print x.dtype, y.dtype, z.dtype" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "更多的内容可以读读[文档](http://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 数学运算" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "下面这些运算才是你在科学运算中经常经常会用到的，比如逐个元素的运算如下:" ] }, { "cell_type": "code", "execution_count": 227, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 6. 8.]\n", " [ 10. 12.]]\n", "[[ 6. 8.]\n", " [ 10. 12.]]\n" ] } ], "source": [ "x = np.array([[1,2],[3,4]], dtype=np.float64)\n", "y = np.array([[5,6],[7,8]], dtype=np.float64)\n", "\n", "# 逐元素求和有下面2种方式\n", "print x + y\n", "print np.add(x, y)" ] }, { "cell_type": "code", "execution_count": 228, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-4. -4.]\n", " [-4. -4.]]\n", "[[-4. -4.]\n", " [-4. -4.]]\n" ] } ], "source": [ "# 逐元素作差\n", "print x - y\n", "print np.subtract(x, y)" ] }, { "cell_type": "code", "execution_count": 229, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 5. 12.]\n", " [ 21. 32.]]\n", "[[ 5. 12.]\n", " [ 21. 32.]]\n" ] } ], "source": [ "# 逐元素相乘\n", "print x * y\n", "print np.multiply(x, y)" ] }, { "cell_type": "code", "execution_count": 230, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.2 0.33333333]\n", " [ 0.42857143 0.5 ]]\n", "[[ 0.2 0.33333333]\n", " [ 0.42857143 0.5 ]]\n" ] } ], "source": [ "# 逐元素相除\n", "# [[ 0.2 0.33333333]\n", "# [ 0.42857143 0.5 ]]\n", "print x / y\n", "print np.divide(x, y)" ] }, { "cell_type": "code", "execution_count": 231, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1. 1.41421356]\n", " [ 1.73205081 2. ]]\n" ] } ], "source": [ "# 逐元素求平方根！！！\n", "# [[ 1. 1.41421356]\n", "# [ 1.73205081 2. ]]\n", "print np.sqrt(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "那如果我要做矩阵的乘法运算怎么办！！！恩，别着急，照着下面写就可以了:" ] }, { "cell_type": "code", "execution_count": 232, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "219\n", "219\n" ] } ], "source": [ "x = np.array([[1,2],[3,4]])\n", "y = np.array([[5,6],[7,8]])\n", "\n", "v = np.array([9,10])\n", "w = np.array([11, 12])\n", "\n", "# 求向量内积\n", "print v.dot(w)\n", "print np.dot(v, w)" ] }, { "cell_type": "code", "execution_count": 233, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[29 67]\n", "[29 67]\n" ] } ], "source": [ "# 矩阵的乘法\n", "print x.dot(v)\n", "print np.dot(x, v)" ] }, { "cell_type": "code", "execution_count": 234, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[19 22]\n", " [43 50]]\n", "[[19 22]\n", " [43 50]]\n" ] } ], "source": [ "# 矩阵的乘法\n", "# [[19 22]\n", "# [43 50]]\n", "print x.dot(y)\n", "print np.dot(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "你猜你做科学运算会最常用到的矩阵内元素的运算是什么？对啦，是求和，用 `sum`可以完成:" ] }, { "cell_type": "code", "execution_count": 235, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10\n", "[4 6]\n", "[3 7]\n" ] } ], "source": [ "x = np.array([[1,2],[3,4]])\n", "\n", "print np.sum(x) # 数组/矩阵中所有元素求和; prints \"10\"\n", "print np.sum(x, axis=0) # 按行去求和; prints \"[4 6]\"\n", "print np.sum(x, axis=1) # 按列去求和; prints \"[3 7]\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我想说最基本的运算就是上面这个样子，更多的运算可能得查查[文档](http://docs.scipy.org/doc/numpy/reference/routines.math.html).\n", "\n", "其实除掉基本运算，我们经常还需要做一些操作，比如矩阵的变形，转置和重排等等:" ] }, { "cell_type": "code", "execution_count": 236, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2]\n", " [3 4]]\n", "[[1 3]\n", " [2 4]]\n" ] } ], "source": [ "# 转置和数学公式一直，简单粗暴\n", "print x\n", "print x.T" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 2 3]\n", "[1 2 3]\n", "[[1 2 3]]\n", "[[1]\n", " [2]\n", " [3]]\n" ] } ], "source": [ "# 需要说明一下，1维的vector转置还是自己\n", "v = np.array([1,2,3])\n", "print v \n", "print v.T\n", "\n", "# 2维的就不一样了\n", "w = np.array([[1,2,3]])\n", "print w \n", "print w.T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Broadcasting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这个没想好哪个中文词最贴切，我们暂且叫它“传播吧”:
\n", "作用是什么呢，我们设想一个场景，如果要用小的矩阵去和大的矩阵做一些操作，但是希望小矩阵能循环和大矩阵的那些块做一样的操作，那急需要Broadcasting啦" ] }, { "cell_type": "code", "execution_count": 238, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2 2 4]\n", " [ 5 5 7]\n", " [ 8 8 10]\n", " [11 11 13]]\n" ] } ], "source": [ "# 我们要做一件事情，给x的每一行都逐元素加上一个向量，然后生成y\n", "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n", "v = np.array([1, 0, 1])\n", "y = np.empty_like(x) # 生成一个和x维度一致的空数组/矩阵\n", "\n", "# 比较粗暴的方式是，用for循环逐个相加\n", "for i in range(4):\n", " y[i, :] = x[i, :] + v\n", "\n", "print y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这种方法当然可以啦，问题是不高效嘛，如果你的x矩阵行数非常多，那就很慢的咯:
\n", "咱们调整一下，先生成好要加的内容" ] }, { "cell_type": "code", "execution_count": 240, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 0 1]\n", " [1 0 1]\n", " [1 0 1]\n", " [1 0 1]]\n" ] } ], "source": [ "vv = np.tile(v, (4, 1)) # 重复4遍v，叠起来\n", "print vv # Prints \"[[1 0 1]\n", " # [1 0 1]\n", " # [1 0 1]\n", " # [1 0 1]]\"" ] }, { "cell_type": "code", "execution_count": 241, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2 2 4]\n", " [ 5 5 7]\n", " [ 8 8 10]\n", " [11 11 13]]\n" ] } ], "source": [ "y = x + vv # 这样求和大家都能看明白对吧\n", "print y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numpy broadcasting allows us to perform this computation without actually creating multiple copies of v. Consider this version, using broadcasting:" ] }, { "cell_type": "code", "execution_count": 242, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2 2 4]\n", " [ 5 5 7]\n", " [ 8 8 10]\n", " [11 11 13]]\n" ] } ], "source": [ "import numpy as np\n", "\n", "# 因为broadcasting的存在，你上面的操作可以简单地汇总成一个求和操作\n", "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n", "v = np.array([1, 0, 1])\n", "y = x + v # Add v to each row of x using broadcasting\n", "print y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "当操作两个array时，numpy会逐个比较它们的shape，在下述情况下，两arrays会兼容和输出broadcasting结果：
\n", "\n", "1. 相等\n", "2. 其中一个为1，（进而可进行拷贝拓展已至，shape匹配）\n", "\n", "比如求和的时候有：\n", "```python\n", "Image (3d array): 256 x 256 x 3\n", "Scale (1d array): 3\n", "Result (3d array): 256 x 256 x 3\n", "\n", "A (4d array): 8 x 1 x 6 x 1\n", "B (3d array): 7 x 1 x 5\n", "Result (4d array): 8 x 7 x 6 x 5\n", "\n", "A (2d array): 5 x 4\n", "B (1d array): 1\n", "Result (2d array): 5 x 4\n", "\n", "A (2d array): 15 x 3 x 5\n", "B (1d array): 15 x 1 x 5\n", "Result (2d array): 15 x 3 x 5\n", "```\n", "\n", "下面是一些 broadcasting 的例子:" ] }, { "cell_type": "code", "execution_count": 243, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 4 5]\n", " [ 8 10]\n", " [12 15]]\n" ] } ], "source": [ "# 我们来理解一下broadcasting的这种用法\n", "v = np.array([1,2,3]) # v 形状是 (3,)\n", "w = np.array([4,5]) # w 形状是 (2,)\n", "# 先把v变形成3x1的数组/矩阵，然后就可以broadcasting加在w上了:\n", "print np.reshape(v, (3, 1)) * w" ] }, { "cell_type": "code", "execution_count": 244, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 4 6]\n", " [5 7 9]]\n" ] } ], "source": [ "# 那如果要把一个矩阵的每一行都加上一个向量呢\n", "x = np.array([[1,2,3], [4,5,6]])\n", "v = np.array([1,2,3])\n", "# 恩，其实是一样的啦\n", "print x + v" ] }, { "cell_type": "code", "execution_count": 245, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 5 6 7]\n", " [ 9 10 11]]\n" ] } ], "source": [ "x = np.array([[1,2,3], [4,5,6]]) # 2x3的\n", "w = np.array([4,5]) # w 形状是 (2,)\n", "\n", "# 自己算算看？\n", "print (x.T + w).T" ] }, { "cell_type": "code", "execution_count": 246, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 5 6 7]\n", " [ 9 10 11]]\n" ] } ], "source": [ "# 上面那个操作太复杂了，其实我们可以直接这么做嘛\n", "print x + np.reshape(w, (2, 1))" ] }, { "cell_type": "code", "execution_count": 247, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2 4 6]\n", " [ 8 10 12]]\n" ] } ], "source": [ "# broadcasting当然可以逐元素运算了\n", "print x * 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "总结一下broadcasting，可以看看下面的图：
\n", "![](http://www.astroml.org/_images/fig_broadcast_visual_1.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "更多的numpy细节和用法可以查看一下官网[numpy指南](http://docs.scipy.org/doc/numpy/reference/)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }