这篇教程由Justin Johnson创作。
我们将使用Python编程语言来完成本课程的所有作业。Python是一门伟大的通用编程语言，在一些常用库（numpy, scipy, matplotlib）的帮助下，它又会变成一个强大的科学计算环境。
我们期望你们中大多数人对于Python语言和Numpy库比较熟悉，而对于没有Python经验的同学，这篇教程可以帮助你们快速了解Python编程环境和如何使用Python作为科学计算工具。
一部分同学对于Matlab有一定经验。对于这部分同学，我们推荐阅读 numpy for Matlab users页面。
你们还可以查看本教程的IPython notebook版。该教程是由Volodymyr Kuleshov和Isaac Caswell为课程CS 228创建的。
内容列表：
· Python
· 基本数据类型
· 容器· 列表· 字典 · 集合· 元组
· 函数
· 类
· Numpy· 数组· 访问数组· 数据类· 数组计算· 广播
· SciP· 图像操作· MATLAB文件· 点之间的距离
· Matplotlib· 绘制图形· 绘制多个图形· 图像
Python
Python是一种高级的，动态类型的多范型编程语言。很多时候，大家会说Python看起来简直和伪代码一样，这是因为你能够通过很少行数的代码表达出很有力的思想。举个例子，下面是用Python实现的经典的quicksort算法例子：
1def quicksort(arr):
2 if len(arr) <= 1:
3 return arr
4 pivot = arr[len(arr) / 2]
5 left = [x for x in arr if x < pivot]
6 middle = [x for x in arr if x == pivot]
7 right = [x for x in arr if x > pivot]
8 return quicksort(left) + middle + quicksort(right)
9print quicksort([3,6,8,10,1,2,1])
10# Prints "[1, 1, 2, 3, 6, 8, 10]"
Python版本
Python有两个支持的版本，分别是2.7和3.4。这有点让人迷惑，3.0向语言中引入了很多不向后兼容的变化，2.7下的代码有时候在3.4下是行不通的。在这个课程中，我们使用的是2.7版本。
如何查看版本呢？使用python --version命令。
基本数据类型
和大多数编程语言一样，Python拥有一系列的基本数据类型，比如整型、浮点型、布尔型和字符串等。这些类型的使用方式和在其他语言中的使用方式是类似的。
数字：整型和浮点型的使用与其他语言类似。
1x = 3
2print type(x) # Prints "<type 'int'>"
3print x # Prints "3"
4print x + 1 # Addition; prints "4"
5print x - 1 # Subtraction; prints "2"
6print x * 2 # Multiplication; prints "6"
7print x ** 2 # Exponentiation; prints "9"
8x += 1
9print x # Prints "4"
10x *= 2
11print x # Prints "8"
12y = 2.5
13print type(y) # Prints "<type 'float'>"
14print y, y + 1, y * 2, y ** 2 # Prints "2.5 3.5 5.0 6.25"
需要注意的是，Python中没有 x++ 和 x-- 的操作符。
Python也有内置的长整型和复杂数字类型，具体细节可以查看文档。
布尔型：Python实现了所有的布尔逻辑，但用的是英语，而不是我们习惯的操作符（比如&&和||等）。
1t = True
2f = False
3print type(t) # Prints "<type 'bool'>"
4print t and f # Logical AND; prints "False"
5print t or f # Logical OR; prints "True"
6print not t # Logical NOT; prints "False"
7print t != f # Logical XOR; prints "True"
字符串：Python对字符串的支持非常棒。
1hello = 'hello' # String literals can use single quotes
2world = "world" # or double quotes; it does not matter.
3print hello # Prints "hello"
4print len(hello) # String length; prints "5"
5hw = hello + ' ' + world # String concatenation
6print hw # prints "hello world"
7hw12 = '%s %s %d' % (hello, world, 12) # sprintf style string formatting
8print hw12 # prints "hello world 12"
字符串对象有一系列有用的方法，比如：
1s = "hello"
2print s.capitalize() # Capitalize a string; prints "Hello"
3print s.upper() # Convert a string to uppercase; prints "HELLO"
4print s.rjust(7) # Right-justify a string, padding with spaces; prints " hello"
5print s.center(7) # Center a string, padding with spaces; prints " hello "
6print s.replace('l', '(ell)') # Replace all instances of one substring with another;
7 # prints "he(ell)(ell)o"
8print ' world '.strip() # Strip leading and trailing whitespace; prints "world"
如果想详细查看字符串方法，请看文档。
容器Containers
译者注：有知友建议container翻译为复合数据类型，供读者参考。
Python有以下几种容器类型：列表（lists）、字典（dictionaries）、集合（sets）和元组（tuples）。
列表Lists
列表就是Python中的数组，但是列表长度可变，且能包含不同类型元素。
1xs = [3, 1, 2] # Create a list
2print xs, xs[2] # Prints "[3, 1, 2] 2"
3print xs[-1] # Negative indices count from the end of the list; prints "2"
4xs[2] = 'foo' # Lists can contain elements of different types
5print xs # Prints "[3, 1, 'foo']"
6xs.append('bar') # Add a new element to the end of the list
7print xs # Prints
8x = xs.pop() # Remove and return the last element of the list
9print x, xs # Prints "bar [3, 1, 'foo']"
列表的细节，同样可以查阅文档。
切片Slicing：为了一次性地获取列表中的元素，Python提供了一种简洁的语法，这就是切片。
1nums = range(5) # range is a built-in function that creates a list of integers
2print nums # Prints "[0, 1, 2, 3, 4]"
3print nums[2:4] # Get a slice from index 2 to 4 (exclusive); prints "[2, 3]"
4print nums[2:] # Get a slice from index 2 to the end; prints "[2, 3, 4]"
5print nums[:2] # Get a slice from the start to index 2 (exclusive); prints "[0, 1]"
6print nums[:] # Get a slice of the whole list; prints ["0, 1, 2, 3, 4]"
7print nums[:-1] # Slice indices can be negative; prints ["0, 1, 2, 3]"
8nums[2:4] = [8, 9] # Assign a new sublist to a slice
9print nums # Prints "[0, 1, 8, 8, 4]"
在Numpy数组的内容中，我们会再次看到切片语法。
循环Loops：我们可以这样遍历列表中的每一个元素：
1animals = ['cat', 'dog', 'monkey']
2for animal in animals:
3 print animal
4# Prints "cat", "dog", "monkey", each on its own line.
如果想要在循环体内访问每个元素的指针，可以使用内置的
enumerate函数
1animals = ['cat', 'dog', 'monkey']
2for idx, animal in enumerate(animals):
3 print '#%d: %s' % (idx + 1, animal)
4# Prints "#1: cat", "#2: dog", "#3: monkey", each on its own line
列表推导List comprehensions：在编程的时候，我们常常想要将一种数据类型转换为另一种。下面是一个简单例子，将列表中的每个元素变成它的平方。
1nums = [0, 1, 2, 3, 4]
2squares = []
3for x in nums:
4 squares.append(x ** 2)
5print squares # Prints [0, 1, 4, 9, 16]
使用列表推导，你就可以让代码简化很多：
1nums = [0, 1, 2, 3, 4]
2squares = [x ** 2 for x in nums]
3print squares # Prints [0, 1, 4, 9, 16]
列表推导还可以包含条件：
1nums = [0, 1, 2, 3, 4]
2even_squares = [x ** 2 for x in nums if x % 2 == 0]
3print even_squares # Prints "[0, 4, 16]"
字典Dictionaries
字典用来储存（键, 值）对，这和Java中的Map差不多。你可以这样使用它：
1d = {'cat': 'cute', 'dog': 'furry'} # Create a new dictionary with some data
2print d['cat'] # Get an entry from a dictionary; prints "cute"
3print 'cat' in d # Check if a dictionary has a given key; prints "True"
4d['fish'] = 'wet' # Set an entry in a dictionary
5print d['fish'] # Prints "wet"
6# print d['monkey'] # KeyError: 'monkey' not a key of d
7print d.get('monkey', 'N/A') # Get an element with a default; prints "N/A"
8print d.get('fish', 'N/A') # Get an element with a default; prints "wet"
9del d['fish'] # Remove an element from a dictionary
10print d.get('fish', 'N/A') # "fish" is no longer a key; prints "N/A"
想要知道字典的其他特性，请查阅文档。
循环Loops：在字典中，用键来迭代更加容易。
1d = {'person': 2, 'cat': 4, 'spider': 8}
2for animal in d:
3 legs = d[animal]
4 print 'A %s has %d legs' % (animal, legs)
5# Prints "A person has 2 legs", "A spider has 8 legs", "A cat has 4 legs"
如果你想要访问键和对应的值，那就使用
iteritems方法：
1d = {'person': 2, 'cat': 4, 'spider': 8}
2for animal, legs in d.iteritems():
3 print 'A %s has %d legs' % (animal, legs)
4# Prints "A person has 2 legs", "A spider has 8 legs", "A cat has 4 legs"
字典推导Dictionary comprehensions：和列表推导类似，但是允许你方便地构建字典。
1nums = [0, 1, 2, 3, 4]
2even_num_to_square = {x: x ** 2 for x in nums if x % 2 == 0}
3print even_num_to_square # Prints "{0: 0, 2: 4, 4: 16}"
集合Sets
集合是独立不同个体的无序集合。示例如下：
1def sign(x):
2 if x > 0:
3 return 'positive'
4 elif x < 0:
5 return 'negative'
6 else:
7 return 'zero'
8for x in [-1, 0, 1]:
9 print sign(x)
10# Prints "negative", "zero", "positive"
我们常常使用可选参数来定义函数：
1def hello(name, loud=False):
2 if loud:
3 print 'HELLO, %s' % name.upper()
4 else:
5 print 'Hello, %s!' % name
6hello('Bob') # Prints "Hello, Bob"
7hello('Fred', loud=True) # Prints "HELLO, FRED!"
函数还有很多内
容，可以查看文档。类Classes
Python对于类的定义是简单直接的：
1class Greeter(object):
2 # Constructor
3 def __init__(self, name):
4 self.name = name # Create an instance variable
5 # Instance method
6 def greet(self, loud=False):
7 if loud:
8 print 'HELLO, %s!' % self.name.upper()
9 else:
10 print 'Hello, %s' % self.name
11g = Greeter('Fred') # Construct an instance of the Greeter class
12g.greet() # Call an instance method; prints "Hello, Fred"
13g.greet(loud=True) # Call an instance method; prints "HELLO, FRED!"
更多类的信息请查阅文档。
Numpy
Numpy是Python中用于科学计算的核心库。它提供了高性能的多维数组对象，以及相关工具。
数组Arrays
一个numpy数组是一个由不同数值组成的网格。网格中的数据都是同一种数据类型，可以通过非负整型数的元组来访问。维度的数量被称为数组的阶，数组的大小是一个由整型数构成的元组，可以描述数组不同维度上的大小。
我们可以从列表创建数组，然后利用方括号访问其中的元素：
1import numpy as np
2a = np.array([1, 2, 3]) # Create a rank 1 array
3print type(a) # Prints "<type 'numpy.ndarray'>"
4print a.shape # Prints "(3,)"
5print a[0], a[1], a[2] # Prints "1 2 3"
6a[0] = 5 # Change an element of the array
7print a # Prints "[5, 2, 3]"
8b = np.array([[1,2,3],[4,5,6]]) # Create a rank 2 array
9print b # 显示一下矩阵b
10print b.shape # Prints "(2, 3)"
11print b[0, 0], b[0, 1], b[1, 0] # Prints "1 2 4"
Numpy还提供了很多其他创建数组的方法：
1import numpy as np
2a = np.zeros((2,2)) # Create an array of all zeros
3print a # Prints "[[ 0. 0.]
4 # [ 0. 0.]]"
5b = np.ones((1,2)) # Create an array of all ones
6print b # Prints "[[ 1. 1.]]"
7c = np.full((2,2), 7) # Create a constant array
8print c # Prints "[[ 7. 7.]
9 # [ 7. 7.]]"
10d = np.eye(2) # Create a 2x2 identity matrix
11print d # Prints "[[ 1. 0.]
12 # [ 0. 1.]]"
13e = np.random.random((2,2)) # Create an array filled with random values
14print e # Might print "[[ 0.91940167 0.08143941]
15 # [ 0.68744134 0.87236687]]"
其他数组相关方法，请查看文档。
访问数组
Numpy提供了多种访问数组的方法。
切片：和Python列表类似，numpy数组可以使用切片语法。因为数组可以是多维的，所以你必须为每个维度指定好切片。
1import numpy as np
2# Create the following rank 2 array with shape (3, 4)
3# [[ 1 2 3 4]
4# [ 5 6 7 8]
5# [ 9 10 11 12]]
6a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
7# Use slicing to pull out the subarray consisting of the first 2 rows
8# and columns 1 and 2; b is the following array of shape (2, 2):
9# [[2 3]
10# [6 7]]
11b = a[:2, 1:3]
12# A slice of an array is a view into the same data, so modifying it
13# will modify the original array.
14print a[0, 1] # Prints "2"
15b[0, 0] = 77 # b[0, 0] is the same piece of data as a[0, 1]
16print a[0, 1] # Prints "77"
你可以同时使用整型和切片语法来访问数组。但是，这样做会产生一个比原数组低阶的新数组。需要注意的是，这里和MATLAB中的情况是不同的：
1import numpy as np
2# Create the following rank 2 array with shape (3, 4)
3# [[ 1 2 3 4]
4# [ 5 6 7 8]
5# [ 9 10 11 12]]
6a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
7# Two ways of accessing the data in the middle row of the array.
8# Mixing integer indexing with slices yields an array of lower rank,
9# while using only slices yields an array of the same rank as the
10# original array:
11row_r1 = a[1, :] # Rank 1 view of the second row of a
12row_r2 = a[1:2, :] # Rank 2 view of the second row of a
13print row_r1, row_r1.shape # Prints "[5 6 7 8] (4,)"
14print row_r2, row_r2.shape # Prints "[[5 6 7 8]] (1, 4)"
15# We can make the same distinction when accessing columns of an array:
16col_r1 = a[:, 1]
17col_r2 = a[:, 1:2]
18print col_r1, col_r1.shape # Prints "[ 2 6 10] (3,)"
19print col_r2, col_r2.shape # Prints "[[ 2]
20 # [ 6]
21 # [10]] (3, 1)"
整型数组访问：当我们使用切片语法访问数组时，得到的总是原数组的一个子集。整型数组访问允许我们利用其它数组的数据构建一个新的数组：
1import numpy as np
2a = np.array([[1,2], [3, 4], [5, 6]])
3# An example of integer array indexing.
4# The returned array will have shape (3,) and
5print a[[0, 1, 2], [0, 1, 0]] # Prints "[1 4 5]"
6# The above example of integer array indexing is equivalent to this:
7print np.array([a[0, 0], a[1, 1], a[2, 0]]) # Prints "[1 4 5]"
8# When using integer array indexing, you can reuse the same
9# element from the source array:
10print a[[0, 0], [1, 1]] # Prints "[2 2]"
11# Equivalent to the previous integer array indexing example
12print np.array([a[0, 1], a[0, 1]]) # Prints "[2 2]"
整型数组访问语法还有个有用的技巧，可以用来选择或者更改矩阵中每行中的一个元素：
1import numpy as np
2# Create a new array from which we will select elements
3a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
4print a # prints "array([[ 1, 2, 3],
5 # [ 4, 5, 6],
6 # [ 7, 8, 9],
7 # [10, 11, 12]])"
8# Create an array of indices
9b = np.array([0, 2, 0, 1])
10# Select one element from each row of a using the indices in b
11print a[np.arange(4), b] # Prints "[ 1 6 7 11]"
12# Mutate one element from each row of a using the indices in b
13a[np.arange(4), b] += 10
14print a # prints "array([[11, 2, 3],
15 # [ 4, 5, 16],
16 # [17, 8, 9],
17 # [10, 21, 12]])
布尔型数组访问：布尔型数组访问可以让你选择数组中任意元素。通常，这种访问方式用于选取数组中满足某些条件的元素，举例如下：
1import numpy as np
2a = np.array([[1,2], [3, 4], [5, 6]])
3bool_idx = (a > 2) # Find the elements of a that are bigger than 2;
4 # this returns a numpy array of Booleans of the same
5 # shape as a, where each slot of bool_idx tells
6 # whether that element of a is > 2.
7print bool_idx # Prints "[[False False]
8 # [ True True]
9 # [ True True]]"
10# We use boolean array indexing to construct a rank 1 array
11# consisting of the elements of a corresponding to the True values
12# of bool_idx
13print a[bool_idx] # Prints "[3 4 5 6]"
14# We can do all of the above in a single concise statement:
15print a[a > 2] # Prints "[3 4 5 6]"
为了教程的简介，有很多数组访问的细节我们没有详细说明，可以查看文档。
数据类型
每个Numpy数组都是数据类型相同的元素组成的网格。Numpy提供了很多的数据类型用于创建数组。当你创建数组的时候，Numpy会尝试猜测数组的数据类型，你也可以通过参数直接指定数据类型，例子如下：
1import numpy as np
2x = np.array([1, 2]) # Let numpy choose the datatype
3print x.dtype # Prints "int64"
4x = np.array([1.0, 2.0]) # Let numpy choose the datatype
5print x.dtype # Prints "float64"
6x = np.array([1, 2], dtype=np.int64) # Force a particular datatype
7print x.dtype # Prints "int64"
数组计算
基本数学计算函数会对数组中元素逐个进行计算，既可以利用操作符重载，也可以使用函数方式：
1import numpy as np
2x = np.array([[1,2],[3,4]], dtype=np.float64)
3y = np.array([[5,6],[7,8]], dtype=np.float64)
4# Elementwise sum; both produce the array
5# [[ 6.0 8.0]
6# [10.0 12.0]]
7print x + y
8print np.add(x, y)
9# Elementwise difference; both produce the array
10# [[-4.0 -4.0]
11# [-4.0 -4.0]]
12print x - y
13print np.subtract(x, y)
14# Elementwise product; both produce the array
15# [[ 5.0 12.0]
16# [21.0 32.0]]
17print x * y
18print np.multiply(x, y)
19# Elementwise division; both produce the array
20# [[ 0.2 0.33333333]
21# [ 0.42857143 0.5 ]]
22print x / y
23print np.divide(x, y)
24# Elementwise square root; produces the array
25# [[ 1. 1.41421356]
26# [ 1.73205081 2. ]]
27print np.sqrt(x)
和MATLAB不同，*是元素逐个相乘，而不是矩阵乘法。在Numpy中使用dot来进行矩阵乘法：
1import numpy as np
2x = np.array([[1,2],[3,4]])
3y = np.array([[5,6],[7,8]])
4v = np.array([9,10])
5w = np.array([11, 12])
6# Inner product of vectors; both produce 219
7print v.dot(w)
8print np.dot(v, w)
9# Matrix / vector product; both produce the rank 1 array [29 67]
10print x.dot(v)
11print np.dot(x, v)
12# Matrix / matrix product; both produce the rank 2 array
13# [[19 22]
14# [43 50]]
15print x.dot(y)
16print np.dot(x, y)
Numpy提供了很多计算数组的函数，其中最常用的一个是sum：
1import numpy as np
2x = np.array([[1,2],[3,4]])
3print np.sum(x) # Compute sum of all elements; prints "10"
4print np.sum(x, axis=0) # Compute sum of each column; prints "[4 6]"
5print np.sum(x, axis=1) # Compute sum of each row; prints "[3 7]"
想要了解更多函数，可以查看文档。
除了计算，我们还常常改变数组或者操作其中的元素。其中将矩阵转置是常用的一个，在Numpy中，使用T来转置矩阵：
1import numpy as np
2x = np.array([[1,2], [3,4]])
3print x # Prints "[[1 2]
4 # [3 4]]"
5print x.T # Prints "[[1 3]
6 # [2 4]]"
7# Note that taking the transpose of a rank 1 array does nothing:
8v = np.array([1,2,3])
9print v # Prints "[1 2 3]"
10print v.T # Prints "[1 2 3]"
Numpy还提供了更多操作数组的方法，请查看文档。
广播Broadcasting
广播是一种强有力的机制，它让Numpy可以让不同大小的矩阵在一起进行数学计算。我们常常会有一个小的矩阵和一个大的矩阵，然后我们会需要用小的矩阵对大的矩阵做一些计算。
举个例子，如果我们想要把一个向量加到矩阵的每一行，我们可以这样做：
1import numpy as np
2# We will add the vector v to each row of the matrix x,
3# storing the result in the matrix y
4x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
5v = np.array([1, 0, 1])
6y = np.empty_like(x) # Create an empty matrix with the same shape as x
7# Add the vector v to each row of the matrix x with an explicit loop
8for i in range(4):
9 y[i, :] = x[i, :] + v
10# Now y is the following
11# [[ 2 2 4]
12# [ 5 5 7]
13# [ 8 8 10]
14# [11 11 13]]
15print y
这样是行得通的，但是当x矩阵非常大，利用循环来计算就会变得很慢很慢。我们可以换一种思路：
1import numpy as np
2# We will add the vector v to each row of the matrix x,
3# storing the result in the matrix y
4x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
5v = np.array([1, 0, 1])
6vv = np.tile(v, (4, 1)) # Stack 4 copies of v on top of each other
7print vv # Prints "[[1 0 1]
8 # [1 0 1]
9 # [1 0 1]
10 # [1 0 1]]"
11y = x + vv # Add x and vv elementwise
12print y # Prints "[[ 2 2 4
13 # [ 5 5 7]
14 # [ 8 8 10]
15 # [11 11 13]]"
Numpy广播机制可以让我们不用创建vv，就能直接运算，看看下面例子：
1import numpy as np
2# We will add the vector v to each row of the matrix x,
3# storing the result in the matrix y
4x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
5v = np.array([1, 0, 1])
6y = x + v # Add v to each row of x using broadcasting
7print y # Prints "[[ 2 2 4]
8 # [ 5 5 7]
9 # [ 8 8 10]
10 # [11 11 13]]"
对两个数组使用广播机制要遵守下列规则：
- 如果数组的秩不同，使用1来将秩较小的数组进行扩展，直到两个数组的尺寸的长度都一样。
- 如果两个数组在某个维度上的长度是一样的，或者其中一个数组在该维度上长度为1，那么我们就说这两个数组在该维度上是相容的。
- 如果两个数组在所有维度上都是相容的，他们就能使用广播。
- 如果两个输入数组的尺寸不同，那么注意其中较大的那个尺寸。因为广播之后，两个数组的尺寸将和那个较大的尺寸一样。
- 在任何一个维度上，如果一个数组的长度为1，另一个数组长度大于1，那么在该维度上，就好像是对第一个数组进行了复制。
如果上述解释看不明白，可以读一读文档和这个解释。译者注：强烈推荐阅读文档中的例子。
支持广播机制的函数是全局函数。哪些是全局函数可以在文档中查找。
下面是一些广播机制的使用：
1import numpy as np
2# Compute outer product of vectors
3v = np.array([1,2,3]) # v has shape (3,)
4w = np.array([4,5]) # w has shape (2,)
5# To compute an outer product, we first reshape v to be a column
6# vector of shape (3, 1); we can then broadcast it against w to yield
7# an output of shape (3, 2), which is the outer product of v and w:
8# [[ 4 5]
9# [ 8 10]
10# [12 15]]
11print np.reshape(v, (3, 1)) * w
12# Add a vector to each row of a matrix
13x = np.array([[1,2,3], [4,5,6]])
14# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),
15# giving the following matrix:
16# [[2 4 6]
17# [5 7 9]]
18print x + v
19# Add a vector to each column of a matrix
20# x has shape (2, 3) and w has shape (2,).
21# If we transpose x then it has shape (3, 2) and can be broadcast
22# against w to yield a result of shape (3, 2); transposing this result
23# yields the final result of shape (2, 3) which is the matrix x with
24# the vector w added to each column. Gives the following matrix:
25# [[ 5 6 7]
26# [ 9 10 11]]
27print (x.T + w).T
28# Another solution is to reshape w to be a row vector of shape (2, 1);
29# we can then broadcast it directly against x to produce the same
30# output.
31print x + np.reshape(w, (2, 1))
32# Multiply a matrix by a constant:
33# x has shape (2, 3). Numpy treats scalars as arrays of shape ();
34# these can be broadcast together to shape (2, 3), producing the
35# following array:
36# [[ 2 4 6]
37# [ 8 10 12]]
38print x * 2
广播机制能够让你的代码更简洁更迅速，能够用的时候请尽量使用！
Numpy文档
这篇教程涉及了你需要了解的numpy中的一些重要内容，但是numpy远不止如此。可以查阅numpy文献来学习更多。
SciPy
Numpy提供了高性能的多维数组，以及计算和操作数组的基本工具。SciPy基于Numpy，提供了大量的计算和操作数组的函数，这些函数对于不同类型的科学和工程计算非常有用。
熟悉SciPy的最好方法就是阅读文档。我们会强调对于本课程有用的部分。
图像操作
SciPy提供了一些操作图像的基本函数。比如，它提供了将图像从硬盘读入到数组的函数，也提供了将数组中数据写入的硬盘成为图像的函数。下面是一个简单的例子：
1from scipy.misc import imread, imsave, imresize
2# Read an JPEG image into a numpy array
3img = imread('assets/cat.jpg')
4print img.dtype, img.shape # Prints "uint8 (400, 248, 3)"
5# We can tint the image by scaling each of the color channels
6# by a different scalar constant. The image has shape (400, 248, 3);
7# we multiply it by the array [1, 0.95, 0.9] of shape (3,);
8# numpy broadcasting means that this leaves the red channel unchanged,
9# and multiplies the green and blue channels by 0.95 and 0.9
10# respectively.
11img_tinted = img * [1, 0.95, 0.9]
12# Resize the tinted image to be 300 by 300 pixels.
13img_tinted = imresize(img_tinted, (300, 300))
14# Write the tinted image back to disk
15imsave('assets/cat_tinted.jpg', img_tinted)
译者注：如果运行这段代码出现类似ImportError: cannot import name imread的报错，那么请利用pip进行Pillow的下载，可以解决问题。命令：pip install Pillow。
左边是原始图片，右边是变色和变形的图片。 MATLAB文件
函数scipy.io.loadmat和scipy.io.savemat能够让你读和写MATLAB文件。具体请查看文档。
点之间的距离
SciPy定义了一些有用的函数，可以计算集合中点之间的距离。
函数scipy.spatial.distance.pdist能够计算集合中所有两点之间的距离：
1import numpy as np
2from scipy.spatial.distance import pdist, squareform
3# Create the following array where each row is a point in 2D space:
4# [[0 1]
5# [1 0]
6# [2 0]]
7x = np.array([[0, 1], [1, 0], [2, 0]])
8print x
9# Compute the Euclidean distance between all rows of x.
10# d[i, j] is the Euclidean distance between x[i, :] and x[j, :],
11# and d is the following array:
12# [[ 0. 1.41421356 2.23606798]
13# [ 1.41421356 0. 1. ]
14# [ 2.23606798 1. 0. ]]
15d = squareform(pdist(x, 'euclidean'))
16print d
函数scipy.spatial.distance.cdist可以计算不同集合中点的距离，具体请查看文档。
Matplotlib
Matplotlib是一个作图库。这里简要介绍matplotlib.pyplot模块，功能和MATLAB的作图功能类似。
绘图
matplotlib库中最重要的函数是Plot。该函数允许你做出2D图形，如下：
1import numpy as np
2import matplotlib.pyplot as plt
3# Compute the x and y coordinates for points on a sine curve
4x = np.arange(0, 3 * np.pi, 0.1)
5y = np.sin(x)
6# Plot the points using matplotlib
7plt.plot(x, y)
8plt.show() # You must call plt.show() to make graphics appear.
运行上面代码会产生下面的作图：
只需要少量工作，就可以一次画不同的线，加上标签，坐标轴标志等。
1import numpy as np
2import matplotlib.pyplot as plt
3# Compute the x and y coordinates for points on sine and cosine curves
4x = np.arange(0, 3 * np.pi, 0.1)
5y_sin = np.sin(x)
6y_cos = np.cos(x)
7# Plot the points using matplotlib
8plt.plot(x, y_sin)
9plt.plot(x, y_cos)
10plt.xlabel('x axis label')
11plt.ylabel('y axis label')
12plt.title('Sine and Cosine')
13plt.legend(['Sine', 'Cosine'])
14plt.show()
可以在文档中阅读更多关于plot的内容。
绘制多个图像
可以使用subplot函数来在一幅图中画不同的东西：
1import numpy as np
2import matplotlib.pyplot as plt
3# Compute the x and y coordinates for points on sine and cosine curves
4x = np.arange(0, 3 * np.pi, 0.1)
5y_sin = np.sin(x)
6y_cos = np.cos(x)
7# Set up a subplot grid that has height 2 and width 1,
8# and set the first such subplot as active.
9plt.subplot(2, 1, 1)
10# Make the first plot
11plt.plot(x, y_sin)
12plt.title('Sine')
13# Set the second subplot as active, and make the second plot.
14plt.subplot(2, 1, 2)
15plt.plot(x, y_cos)
16plt.title('Cosine')
17# Show the figure.
18plt.show()
关于subplot的更多细节，可以阅读文档。
图像
你可以使用imshow函数来显示图像，如下所示：
1import numpy as np
2from scipy.misc import imread, imresize
3import matplotlib.pyplot as plt
4img = imread('assets/cat.jpg')
5img_tinted = img * [1, 0.95, 0.9]
6# Show the original image
7plt.subplot(1, 2, 1)
8plt.imshow(img)
9# Show the tinted image
10plt.subplot(1, 2, 2)
11# A slight gotcha with imshow is that it might give strange results
12# if presented with data that is not uint8. To work around this, we
13# explicitly cast the image to uint8 before displaying it.
14plt.imshow(np.uint8(img_tinted))
15plt.show()
