Python Numpy教程
本教程由Justin Johnson贡献。
在本课程中，我们将使用Python编程语言进行所有作业。Python本身就是一种出色的通用编程语言，但是在一些流行的库（numpy，scipy，matplotlib）的帮助下，Python成为了科学计算的强大环境。
我们希望你们中的许多人都会对Python和numpy有一定的经验；对于其余的人，本节将作为速成课程，内容涉及Python编程语言以及使用Python进行科学计算。
你们中的某些人可能对Matlab有所了解，在这种情况下，我们还建议numpy for Matlab用户页面。
您还可以在此处找到本教程的IPython笔记本版本，该版本由Volodymyr Kuleshov和Isaac Caswell为CS 228创建。
目录：
- Python
- 基本数据类型 Basic data types
- 集装箱Containers
- 职能Functions
- 类Classes
- Numpy
- SciPy的
- Matplotlib
python
Python是一种高级的，动态类型化的多范例编程语言。Python代码通常被称为几乎类似于伪代码，因为它使您可以在很少的代码行中表达非常强大的思想，同时又易于阅读。例如，这是经典的快速排序算法在Python中的实现：
def quicksort(arr):
if len(arr) <= 1:
return arr
pivot = arr[len(arr) // 2]
left = [x for x in arr if x < pivot]
middle = [x for x in arr if x == pivot]
right = [x for x in arr if x > pivot]
return quicksort(left) + middle + quicksort(right)
print(quicksort([3,6,8,10,1,2,1]))
# Prints "[1, 1, 2, 3, 6, 8, 10]"
Python版本versions
当前有两种不同的受支持的Python版本2.7和3.5。令人困惑的是，Python 3.0对该语言进行了许多向后兼容的更改，因此为2.7编写的代码在3.5下可能无法工作，反之亦然。对于此类，所有代码都将使用Python 3.5。
您可以通过运行来在命令行中检查Python版本 python --version。
基本数据类型
像大多数语言一样，Python有许多基本类型，包括整数，浮点数，布尔值和字符串。这些数据类型以其他编程语言所熟悉的方式运行。
数字：整数和浮点数的工作方式与您期望的其他语言一样：
x = 3
print(type(x)) # Prints "<class 'int'>"
print(x) # Prints "3"
print(x + 1) # Addition; prints "4"
print(x - 1) # Subtraction; prints "2"
print(x * 2) # Multiplication; prints "6"
print(x ** 2) # Exponentiation; prints "9"
x += 1
print(x) # Prints "4"
x *= 2
print(x) # Prints "8"
y = 2.5
print(type(y)) # Prints "<class 'float'>"
print(y, y + 1, y * 2, y ** 2) # Prints "2.5 3.5 5.0 6.25"
请注意，与许多语言不同，Python没有一元的增量（x++）或减量（x--）运算符。
Python还具有用于复数的内置类型。您可以在文档中找到所有详细信息 。
布尔： Python中实现所有通常的运营商的布尔逻辑的，但使用英语词语而非符号（&&，||等）：
t = True
f = False
print(type(t)) # Prints "<class 'bool'>"
print(t and f) # Logical AND; prints "False"
print(t or f) # Logical OR; prints "True"
print(not t) # Logical NOT; prints "False"
print(t != f) # Logical XOR; prints "True"
字符串： Python对字符串有很好的支持：
hello = 'hello' # String literals can use single quotes
world = "world" # or double quotes; it does not matter.
print(hello) # Prints "hello"
print(len(hello)) # String length; prints "5"
hw = hello + ' ' + world # String concatenation
print(hw) # prints "hello world"
hw12 = '%s %s %d' % (hello, world, 12) # sprintf style string formatting
print(hw12) # prints "hello world 12"
字符串对象有很多有用的方法。例如：
s = "hello"
print(s.capitalize()) # Capitalize a string; prints "Hello"
print(s.upper()) # Convert a string to uppercase; prints "HELLO"
print(s.rjust(7)) # Right-justify a string, padding with spaces; prints " hello"
print(s.center(7)) # Center a string, padding with spaces; prints " hello "
print(s.replace('l', '(ell)')) # Replace all instances of one substring with another;
# prints "he(ell)(ell)o"
print(' world '.strip()) # Strip leading and trailing whitespace; prints "world"
您可以在文档中找到所有字符串方法的列表。
集装箱
Python包括几种内置的容器类型：列表，字典，集合和元组。
清单Lists
列表与数组的Python等效，但可调整大小，并且可以包含不同类型的元素：
xs = [3, 1, 2] # Create a list
print(xs, xs[2]) # Prints "[3, 1, 2] 2"
print(xs[-1]) # Negative indices count from the end of the list; prints "2"
xs[2] = 'foo' # Lists can contain elements of different types
print(xs) # Prints "[3, 1, 'foo']"
xs.append('bar') # Add a new element to the end of the list
print(xs) # Prints "[3, 1, 'foo', 'bar']"
x = xs.pop() # Remove and return the last element of the list
print(x, xs) # Prints "bar [3, 1, 'foo']"
与往常一样，您可以在文档中找到有关列表的所有详细信息 。
切片slicing： 除了一次访问一个列表元素，Python还提供了简洁的语法来访问子列表。这称为切片：
nums = list(range(5)) # range is a built-in function that creates a list of integers
print(nums) # Prints "[0, 1, 2, 3, 4]"
print(nums[2:4]) # Get a slice from index 2 to 4 (exclusive); prints "[2, 3]"
print(nums[2:]) # Get a slice from index 2 to the end; prints "[2, 3, 4]"
print(nums[:2]) # Get a slice from the start to index 2 (exclusive); prints "[0, 1]"
print(nums[:]) # Get a slice of the whole list; prints "[0, 1, 2, 3, 4]"
print(nums[:-1]) # Slice indices can be negative; prints "[0, 1, 2, 3]"
nums[2:4] = [8, 9] # Assign a new sublist to a slice
print(nums) # Prints "[0, 1, 8, 9, 4]"
我们将在numpy数组的上下文中再次看到切片。
循环loops：您可以像这样循环遍历列表的元素：
animals = ['cat', 'dog', 'monkey']
for animal in animals:
print(animal)
# Prints "cat", "dog", "monkey", each on its own line.
如果要访问循环体内每个元素的索引，请使用内置enumerate函数：
animals = ['cat', 'dog', 'monkey']
for idx, animal in enumerate(animals):
print('#%d: %s' % (idx + 1, animal))
# Prints "#1: cat", "#2: dog", "#3: monkey", each on its own line
列表理解： 编程时，我们经常希望将一种数据类型转换为另一种数据类型。作为一个简单的示例，请考虑以下计算平方数的代码：
nums = [0, 1, 2, 3, 4]
squares = []
for x in nums:
squares.append(x ** 2)
print(squares) # Prints [0, 1, 4, 9, 16]
您可以使用列表推导式 简化此代码：
nums = [0, 1, 2, 3, 4]
squares = [x ** 2 for x in nums]
print(squares) # Prints [0, 1, 4, 9, 16]
列表推导也可以包含条件：
nums = [0, 1, 2, 3, 4]
even_squares = [x ** 2 for x in nums if x % 2 == 0]
print(even_squares) # Prints "[0, 4, 16]"
辞典Dictionaries
字典存储（键，值）对，类似于MapJava中的或Javascript中的对象。您可以像这样使用它：
d = {'cat': 'cute', 'dog': 'furry'} # Create a new dictionary with some data
print(d['cat']) # Get an entry from a dictionary; prints "cute"
print('cat' in d) # Check if a dictionary has a given key; prints "True"
d['fish'] = 'wet' # Set an entry in a dictionary
print(d['fish']) # Prints "wet"
# print(d['monkey']) # KeyError: 'monkey' not a key of d
print(d.get('monkey', 'N/A')) # Get an element with a default; prints "N/A"
print(d.get('fish', 'N/A')) # Get an element with a default; prints "wet"
del d['fish'] # Remove an element from a dictionary
print(d.get('fish', 'N/A')) # "fish" is no longer a key; prints "N/A"
您可以在文档中找到所有需要了解的字典 。
循环loops：很容易遍历字典中的键：
d = {'person': 2, 'cat': 4, 'spider': 8}
for animal in d:
legs = d[animal]
print('A %s has %d legs' % (animal, legs))
# Prints "A person has 2 legs", "A cat has 4 legs", "A spider has 8 legs"
如果要访问键及其相应的值，请使用以下items方法：
d = {'person': 2, 'cat': 4, 'spider': 8}
for animal, legs in d.items():
print('A %s has %d legs' % (animal, legs))
# Prints "A person has 2 legs", "A cat has 4 legs", "A spider has 8 legs"
字典理解： 这些类似于列表理解，但是使您可以轻松构建字典。例如：
nums = [0, 1, 2, 3, 4]
even_num_to_square = {x: x ** 2 for x in nums if x % 2 == 0}
print(even_num_to_square) # Prints "{0: 0, 2: 4, 4: 16}"
Sets集
集合是不同元素的无序集合。作为一个简单的示例，请考虑以下内容：
animals = {'cat', 'dog'}
print('cat' in animals) # Check if an element is in a set; prints "True"
print('fish' in animals) # prints "False"
animals.add('fish') # Add an element to a set
print('fish' in animals) # Prints "True"
print(len(animals)) # Number of elements in a set; prints "3"
animals.add('cat') # Adding an element that is already in the set does nothing
print(len(animals)) # Prints "3"
animals.remove('cat') # Remove an element from a set
print(len(animals)) # Prints "2"
像往常一样，您想要了解的有关集的所有信息都可以在文档中找到 。
循环：loops 在集合上进行迭代与在列表上进行迭代具有相同的语法；但是，由于集合是无序的，因此无法假设访问集合元素的顺序：
animals = {'cat', 'dog', 'fish'}
for idx, animal in enumerate(animals):
print('#%d: %s' % (idx + 1, animal))
# Prints "#1: fish", "#2: dog", "#3: cat"
集的理解： 像列表和字典一样，我们可以使用集的理解轻松地构建集：
from math import sqrt
nums = {int(sqrt(x)) for x in range(30)}
print(nums) # Prints "{0, 1, 2, 3, 4, 5}"
元组
元组是（不可变的）有序值列表。元组在很多方面类似于列表。最重要的区别之一是，元组可以用作字典中的键和集合的元素，而列表则不能。这是一个简单的示例：
d = {(x, x + 1): x for x in range(10)} # Create a dictionary with tuple keys
t = (5, 6) # Create a tuple
print(type(t)) # Prints "<class 'tuple'>"
print(d[t]) # Prints "5"
print(d[(1, 2)]) # Prints "1"
该文档包含有关元组的更多信息。
职能Functions -函数
Python函数是使用def关键字定义的。例如：
def sign(x):
if x > 0:
return 'positive'
elif x < 0:
return 'negative'
else:
return 'zero'
for x in [-1, 0, 1]:
print(sign(x))
# Prints "negative", "zero", "positive"
我们经常会定义函数以采用可选的关键字参数，如下所示：
def hello(name, loud=False):
if loud:
print('HELLO, %s!' % name.upper())
else:
print('Hello, %s' % name)
hello('Bob') # Prints "Hello, Bob"
hello('Fred', loud=True) # Prints "HELLO, FRED!"
文档中有关于Python函数的更多信息 。
类classes
在Python中定义类的语法很简单：
class Greeter(object):
# Constructor
def __init__(self, name):
self.name = name # Create an instance variable
# Instance method
def greet(self, loud=False):
if loud:
print('HELLO, %s!' % self.name.upper())
else:
print('Hello, %s' % self.name)
g = Greeter('Fred') # Construct an instance of the Greeter class
g.greet() # Call an instance method; prints "Hello, Fred"
g.greet(loud=True) # Call an instance method; prints "HELLO, FRED!"
您可以在文档中阅读有关Python类的更多信息 。
Numpy
Numpy是Python中科学计算的核心库。它提供了一个高性能的多维数组对象，以及用于处理这些数组的工具。如果您已经熟悉MATLAB，则可能会发现 本教程对于 Numpy入门很有用。
数组arrays
numpy数组是所有相同类型的值的网格，并由非负整数元组索引。维数是数组的等级。 数组的形状是一个整数元组，给出沿每个维度的数组大小。
我们可以从嵌套的Python列表初始化numpy数组，并使用方括号访问元素：
import numpy as np
a = np.array([1, 2, 3]) # Create a rank 1 array
print(type(a)) # Prints "<class 'numpy.ndarray'>"
print(a.shape) # Prints "(3,)"
print(a[0], a[1], a[2]) # Prints "1 2 3"
a[0] = 5 # Change an element of the array
print(a) # Prints "[5, 2, 3]"
b = np.array([[1,2,3],[4,5,6]]) # Create a rank 2 array
print(b.shape) # Prints "(2, 3)"
print(b[0, 0], b[0, 1], b[1, 0]) # Prints "1 2 4"
Numpy还提供了许多创建数组的功能：
import numpy as np
a = np.zeros((2,2)) # Create an array of all zeros
print(a) # Prints "[[ 0. 0.]
# [ 0. 0.]]"
b = np.ones((1,2)) # Create an array of all ones
print(b) # Prints "[[ 1. 1.]]"
c = np.full((2,2), 7) # Create a constant array
print(c) # Prints "[[ 7. 7.]
# [ 7. 7.]]"
d = np.eye(2) # Create a 2x2 identity matrix
print(d) # Prints "[[ 1. 0.]
# [ 0. 1.]]"
e = np.random.random((2,2)) # Create an array filled with random values
print(e) # Might print "[[ 0.91940167 0.08143941]
# [ 0.68744134 0.87236687]]"
数组索引
Numpy提供了几种索引数组的方法。
切片： 类似于Python列表，可以切片numpy数组。由于数组可能是多维的，因此必须为数组的每个维度指定一个切片：
import numpy as np
# Create the following rank 2 array with shape (3, 4)
# [[ 1 2 3 4]
# [ 5 6 7 8]
# [ 9 10 11 12]]
a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
# Use slicing to pull out the subarray consisting of the first 2 rows
# and columns 1 and 2; b is the following array of shape (2, 2):
# [[2 3]
# [6 7]]
b = a[:2, 1:3]
# A slice of an array is a view into the same data, so modifying it
# will modify the original array.
print(a[0, 1]) # Prints "2"
b[0, 0] = 77 # b[0, 0] is the same piece of data as a[0, 1]
print(a[0, 1]) # Prints "77"
您也可以将整数索引与切片索引混合使用。但是，这样做将产生比原始数组低级的数组。请注意，这与MATLAB处理数组切片的方式完全不同：
import numpy as np
# Create the following rank 2 array with shape (3, 4)
# [[ 1 2 3 4]
# [ 5 6 7 8]
# [ 9 10 11 12]]
a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
# Two ways of accessing the data in the middle row of the array.
# Mixing integer indexing with slices yields an array of lower rank,
# while using only slices yields an array of the same rank as the
# original array:
row_r1 = a[1, :] # Rank 1 view of the second row of a
row_r2 = a[1:2, :] # Rank 2 view of the second row of a
print(row_r1, row_r1.shape) # Prints "[5 6 7 8] (4,)"
print(row_r2, row_r2.shape) # Prints "[[5 6 7 8]] (1, 4)"
# We can make the same distinction when accessing columns of an array:
col_r1 = a[:, 1]
col_r2 = a[:, 1:2]
print(col_r1, col_r1.shape) # Prints "[ 2 6 10] (3,)"
print(col_r2, col_r2.shape) # Prints "[[ 2]
# [ 6]
# [10]] (3, 1)"
整数数组索引： 使用切片索引到numpy数组时，所得的数组视图将始终是原始数组的子数组。相反，整数数组索引使您可以使用另一个数组中的数据构造任意数组。这是一个例子：
import numpy as np
a = np.array([[1,2], [3, 4], [5, 6]])
# An example of integer array indexing.
# The returned array will have shape (3,) and
print(a[[0, 1, 2], [0, 1, 0]]) # Prints "[1 4 5]"
# The above example of integer array indexing is equivalent to this:
print(np.array([a[0, 0], a[1, 1], a[2, 0]])) # Prints "[1 4 5]"
# When using integer array indexing, you can reuse the same
# element from the source array:
print(a[[0, 0], [1, 1]]) # Prints "[2 2]"
# Equivalent to the previous integer array indexing example
print(np.array([a[0, 1], a[0, 1]])) # Prints "[2 2]"
整数数组索引的一个有用技巧是从矩阵的每一行中选择或更改一个元素：
import numpy as np
# Create a new array from which we will select elements
a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
print(a) # prints "array([[ 1, 2, 3],
# [ 4, 5, 6],
# [ 7, 8, 9],
# [10, 11, 12]])"
# Create an array of indices
b = np.array([0, 2, 0, 1])
# Select one element from each row of a using the indices in b
print(a[np.arange(4), b]) # Prints "[ 1 6 7 11]"
# Mutate one element from each row of a using the indices in b
a[np.arange(4), b] += 10
print(a) # prints "array([[11, 2, 3],
# [ 4, 5, 16],
# [17, 8, 9],
# [10, 21, 12]])
布尔数组索引： 布尔数组索引使您可以挑选出数组的任意元素。通常，这种类型的索引用于选择满足某些条件的数组元素。这是一个例子：
import numpy as np
a = np.array([[1,2], [3, 4], [5, 6]])
bool_idx = (a > 2) # Find the elements of a that are bigger than 2;
# this returns a numpy array of Booleans of the same
# shape as a, where each slot of bool_idx tells
# whether that element of a is > 2.
print(bool_idx) # Prints "[[False False]
# [ True True]
# [ True True]]"
# We use boolean array indexing to construct a rank 1 array
# consisting of the elements of a corresponding to the True values
# of bool_idx
print(a[bool_idx]) # Prints "[3 4 5 6]"
# We can do all of the above in a single concise statement:
print(a[a > 2]) # Prints "[3 4 5 6]"
为简便起见，我们省略了有关numpy数组索引的许多详细信息。如果您想了解更多信息，请 阅读文档。
资料类型
每个numpy数组都是相同类型的元素的网格。Numpy提供了大量可用于构造数组的数字数据类型。在创建数组时，Numpy会尝试猜测一个数据类型，但是构造数组的函数通常还包含一个可选参数，以明确指定该数据类型。这是一个例子：
import numpy as np
x = np.array([1, 2]) # Let numpy choose the datatype
print(x.dtype) # Prints "int64"
x = np.array([1.0, 2.0]) # Let numpy choose the datatype
print(x.dtype) # Prints "float64"
x = np.array([1, 2], dtype=np.int64) # Force a particular datatype
print(x.dtype) # Prints "int64"
您可以在文档中阅读有关numpy数据类型的所有信息 。
数组数学array math
基本数学函数在数组上逐元素进行操作，并且可用作运算符重载和numpy模块中的函数：
import numpy as np
x = np.array([[1,2],[3,4]], dtype=np.float64)
y = np.array([[5,6],[7,8]], dtype=np.float64)
# Elementwise sum; both produce the array
# [[ 6.0 8.0]
# [10.0 12.0]]
print(x + y)
print(np.add(x, y))
# Elementwise difference; both produce the array
# [[-4.0 -4.0]
# [-4.0 -4.0]]
print(x - y)
print(np.subtract(x, y))
# Elementwise product; both produce the array
# [[ 5.0 12.0]
# [21.0 32.0]]
print(x * y)
print(np.multiply(x, y))
# Elementwise division; both produce the array
# [[ 0.2 0.33333333]
# [ 0.42857143 0.5 ]]
print(x / y)
print(np.divide(x, y))
# Elementwise square root; produces the array
# [[ 1. 1.41421356]
# [ 1.73205081 2. ]]
print(np.sqrt(x))
请注意，与MATLAB不同，它*是逐元素乘法，而不是矩阵乘法。取而代之的是，我们使用该dot函数来计算向量的内积，将向量乘以矩阵以及将矩阵相乘。dot可作为numpy模块中的函数和数组对象的实例方法使用：
import numpy as np
x = np.array([[1,2],[3,4]])
y = np.array([[5,6],[7,8]])
v = np.array([9,10])
w = np.array([11, 12])
# Inner product of vectors; both produce 219
print(v.dot(w))
print(np.dot(v, w))
# Matrix / vector product; both produce the rank 1 array [29 67]
print(x.dot(v))
print(np.dot(x, v))
# Matrix / matrix product; both produce the rank 2 array
# [[19 22]
# [43 50]]
print(x.dot(y))
print(np.dot(x, y))
Numpy提供了许多有用的函数来对数组执行计算。最有用的之一是sum：
import numpy as np
x = np.array([[1,2],[3,4]])
print(np.sum(x)) # Compute sum of all elements; prints "10"
print(np.sum(x, axis=0)) # Compute sum of each column; prints "[4 6]"
print(np.sum(x, axis=1)) # Compute sum of each row; prints "[3 7]"
您可以在文档中找到numpy提供的数学函数的完整列表 。
除了使用数组计算数学函数外，我们经常需要重整形或以其他方式处理数组中的数据。这种操作最简单的例子是转置矩阵。要转置矩阵，只需使用T数组对象的属性：
import numpy as np
x = np.array([[1,2], [3,4]])
print(x) # Prints "[[1 2]
# [3 4]]"
print(x.T) # Prints "[[1 3]
# [2 4]]"
# Note that taking the transpose of a rank 1 array does nothing:
v = np.array([1,2,3])
print(v) # Prints "[1 2 3]"
print(v.T) # Prints "[1 2 3]"
广播Broadcasting
广播是一种强大的机制，允许numpy在执行算术运算时使用不同形状的数组。通常，我们有一个较小的数组和一个较大的数组，并且我们想多次使用较小的数组对较大的数组执行某些操作。
例如，假设我们要向矩阵的每一行添加一个常数向量。我们可以这样做：
import numpy as np
# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
y = np.empty_like(x) # Create an empty matrix with the same shape as x
# Add the vector v to each row of the matrix x with an explicit loop
for i in range(4):
y[i, :] = x[i, :] + v
# Now y is the following
# [[ 2 2 4]
# [ 5 5 7]
# [ 8 8 10]
# [11 11 13]]
print(y)
这有效；但是，当矩阵x很大时，在Python中计算显式循环可能会很慢。请注意，将向量添加v到矩阵的每一行 x相当于vv通过v垂直堆叠多个副本，然后对x和进行元素求和来形成矩阵vv。我们可以像这样实现这种方法：
import numpy as np
# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
vv = np.tile(v, (4, 1)) # Stack 4 copies of v on top of each other
print(vv) # Prints "[[1 0 1]
# [1 0 1]
# [1 0 1]
# [1 0 1]]"
y = x + vv # Add x and vv elementwise
print(y) # Prints "[[ 2 2 4
# [ 5 5 7]
# [ 8 8 10]
# [11 11 13]]"
Numpy广播使我们无需实际创建的多个副本即可执行此计算v。考虑以下版本，使用广播：
import numpy as np
# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
y = x + v # Add v to each row of x using broadcasting
print(y) # Prints "[[ 2 2 4]
# [ 5 5 7]
# [ 8 8 10]
# [11 11 13]]"
该线y = x + v即使x具有形状(4, 3)并且由于广播而v具有形状也 (3,)可以工作；这条线就像v实际具有shape一样工作(4, 3)，其中每一行都是的副本v，并且总和是按元素进行的。
一起广播两个数组遵循以下规则：
- 如果数组的秩不同，则将低秩数组的形状添加1s，直到两个形状的长度相同。
- 如果两个数组的尺寸相同，或者其中一个数组的尺寸为1，则称这两个数组在尺寸上兼容。
- 如果阵列在所有维度上都兼容，则可以一起广播。
- 广播后，每个数组的行为就好像它们的形状等于两个输入数组的形状的元素最大值一样。
- 在一个数组的大小为1而另一个数组的大小大于1的任何维度中，第一个数组的行为就像是沿着该维度复制的一样
支持广播的功能称为通用功能。您可以在文档中找到所有通用功能的列表 。
以下是广播的一些应用：
import numpy as np
# Compute outer product of vectors
v = np.array([1,2,3]) # v has shape (3,)
w = np.array([4,5]) # w has shape (2,)
# To compute an outer product, we first reshape v to be a column
# vector of shape (3, 1); we can then broadcast it against w to yield
# an output of shape (3, 2), which is the outer product of v and w:
# [[ 4 5]
# [ 8 10]
# [12 15]]
print(np.reshape(v, (3, 1)) * w)
# Add a vector to each row of a matrix
x = np.array([[1,2,3], [4,5,6]])
# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),
# giving the following matrix:
# [[2 4 6]
# [5 7 9]]
print(x + v)
# Add a vector to each column of a matrix
# x has shape (2, 3) and w has shape (2,).
# If we transpose x then it has shape (3, 2) and can be broadcast
# against w to yield a result of shape (3, 2); transposing this result
# yields the final result of shape (2, 3) which is the matrix x with
# the vector w added to each column. Gives the following matrix:
# [[ 5 6 7]
# [ 9 10 11]]
print((x.T + w).T)
# Another solution is to reshape w to be a column vector of shape (2, 1);
# we can then broadcast it directly against x to produce the same
# output.
print(x + np.reshape(w, (2, 1)))
# Multiply a matrix by a constant:
# x has shape (2, 3). Numpy treats scalars as arrays of shape ();
# these can be broadcast together to shape (2, 3), producing the
# following array:
# [[ 2 4 6]
# [ 8 10 12]]
print(x * 2)
广播通常会使您的代码更简洁，更快捷，因此您应努力使用它。
大量文件Numpy Documentation
这个简短的概述触及了您需要了解的有关numpy的许多重要知识，但还远远不够。查看 numpy参考， 以了解有关numpy的更多信息。
SciPy
Numpy提供了高性能的多维数组和基本工具，可以使用这些数组进行计算和操作。 SciPy 以此为基础，并提供了在numpy数组上运行的大量功能，可用于不同类型的科学和工程应用程序。
熟悉SciPy的最佳方法是 浏览文档。我们将重点介绍SciPy的某些部分，这些部分可能对本课程有用。
影像操作Image operations
SciPy提供了一些处理图像的基本功能。例如，它具有将磁盘中的图像读取到numpy数组，将numpy数组作为图像写入磁盘以及调整图像大小的功能。这是一个简单的示例，展示了这些功能：
from scipy.misc import imread, imsave, imresize
# Read an JPEG image into a numpy array
img = imread('assets/cat.jpg')
print(img.dtype, img.shape) # Prints "uint8 (400, 248, 3)"
# We can tint the image by scaling each of the color channels
# by a different scalar constant. The image has shape (400, 248, 3);
# we multiply it by the array [1, 0.95, 0.9] of shape (3,);
# numpy broadcasting means that this leaves the red channel unchanged,
# and multiplies the green and blue channels by 0.95 and 0.9
# respectively.
img_tinted = img * [1, 0.95, 0.9]
# Resize the tinted image to be 300 by 300 pixels.
img_tinted = imresize(img_tinted, (300, 300))
# Write the tinted image back to disk
imsave('assets/cat_tinted.jpg', img_tinted)
左：原始图像(瘦猫)。右：着色和调整大小的图像（肥🐱）。
MATLAB文件
功能scipy.io.loadmat和scipy.io.savemat允许您读取和写入MATLAB文件。您可以在文档中阅读有关它们 的信息。
点之间的距离
SciPy定义了一些有用的函数来计算点集之间的距离。
该函数scipy.spatial.distance.pdist计算给定集中所有对点之间的距离：
import numpy as np
from scipy.spatial.distance import pdist, squareform
# Create the following array where each row is a point in 2D space:
# [[0 1]
# [1 0]
# [2 0]]
x = np.array([[0, 1], [1, 0], [2, 0]])
print(x)
# Compute the Euclidean distance between all rows of x.
# d[i, j] is the Euclidean distance between x[i, :] and x[j, :],
# and d is the following array:
# [[ 0. 1.41421356 2.23606798]
# [ 1.41421356 0. 1. ]
# [ 2.23606798 1. 0. ]]
d = squareform(pdist(x, 'euclidean'))
print(d)
您可以在文档中阅读有关此功能的所有详细信息 。
类似的函数（scipy.spatial.distance.cdist）计算两组点之间所有对之间的距离；您可以在文档中阅读有关 内容。
Matplotlib
Matplotlib是一个绘图库。在本节中，将简要介绍该matplotlib.pyplot模块，该模块提供了类似于MATLAB的绘图系统。
绘制Plotting
matplotlib中最重要的功能是plot，它允许您绘制2D数据。这是一个简单的示例：
import numpy as np
import matplotlib.pyplot as plt
# Compute the x and y coordinates for points on a sine curve
x = np.arange(0, 3 * np.pi, 0.1)
y = np.sin(x)
# Plot the points using matplotlib
plt.plot(x, y)
plt.show() # You must call plt.show() to make graphics appear.
运行此代码将生成以下图：
仅需一点点额外的工作，我们就可以轻松地一次绘制多条线，并添加标题，图例和轴标签：
import numpy as np
import matplotlib.pyplot as plt
# Compute the x and y coordinates for points on sine and cosine curves
x = np.arange(0, 3 * np.pi, 0.1)
y_sin = np.sin(x)
y_cos = np.cos(x)
# Plot the points using matplotlib
plt.plot(x, y_sin)
plt.plot(x, y_cos)
plt.xlabel('x axis label')
plt.ylabel('y axis label')
plt.title('Sine and Cosine')
plt.legend(['Sine', 'Cosine'])
plt.show()
您可以在文档中阅读有关该plot功能的 更多信息。
次要情节Subplots
您可以使用subplot函数在同一图中绘制不同的事物。这是一个例子：
import numpy as np
import matplotlib.pyplot as plt
# Compute the x and y coordinates for points on sine and cosine curves
x = np.arange(0, 3 * np.pi, 0.1)
y_sin = np.sin(x)
y_cos = np.cos(x)
# Set up a subplot grid that has height 2 and width 1,
# and set the first such subplot as active.
plt.subplot(2, 1, 1)
# Make the first plot
plt.plot(x, y_sin)
plt.title('Sine')
# Set the second subplot as active, and make the second plot.
plt.subplot(2, 1, 2)
plt.plot(x, y_cos)
plt.title('Cosine')
# Show the figure.
plt.show()
您可以在文档中阅读有关该subplot功能的 更多信息。
图片Images
您可以使用该imshow功能显示图像。这是一个例子：
import numpy as np
from scipy.misc import imread, imresize
import matplotlib.pyplot as plt
img = imread('assets/cat.jpg')
img_tinted = img * [1, 0.95, 0.9]
# Show the original image
plt.subplot(1, 2, 1)
plt.imshow(img)
# Show the tinted image
plt.subplot(1, 2, 2)
# A slight gotcha with imshow is that it might give strange results
# if presented with data that is not uint8. To work around this, we
# explicitly cast the image to uint8 before displaying it.
plt.imshow(np.uint8(img_tinted))
plt.show()
参考文档
CS231n用于视觉识别的卷积神经网络
http://cs231n.github.io/python-numpy-tutorial/
cs231n -karpathy@cs.stanford.edu
https://twitter.com/cs231n
cs231n
https://github.com/cs231n
cv计算机视觉 视频
https://www.bilibili.com/video/av32078165
