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本教程由Justin Johnson贡献。(原文地址:http://cs231n.github.io/python-numpy-tutorial/ )

我们将使用Python编程语言进行本课程中的所有作业。Python是一种很好的通用编程语言,但是在数个流行的库(numpy,scipy,matplotlib)的帮助下,它成为科学计算的强大环境。

我们期望你们中的许多人对Python和numpy有一些经验; 对于其他人来说,本节将作为Python编程语言和Python用于科学计算的快速崩溃课程。

有些人可能在Matlab中有以前的知识,在这种情况下,我们还推荐Matlab用户页面的numpy

您还可以在这里Volodymyr KuleshovIsaac CaswellCS 228创建的本教程IPython笔记本版本

目录: 

目录

 

Python

Python是一种高级,动态类型的multiparadigm编程语言。Python代码通常被称为伪代码,因为它允许您在极少数行代码中表达非常强大的想法,同时非常易读。例如,这里是Python中经典的快速排序算法的实现:

代码块
languagepy
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

目前有两种不同的支持版本的Python,2.7和3.5。有趣的是,Python 3.0引入了许多向后不兼容的语言更改,因此为2.7编写的代码可能无法在3.5之下运行,反之亦然。对于这个类,所有代码将使用Python 3.5。

您可以通过运行在命令行中检查您的Python版本 python --version

基本数据类型

像大多数语言一样,Python有一些基本类型,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熟悉的方式表现。

数字:整数和浮点数与其他语言一样工作:

代码块
languagepy
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" 

Python还有复杂数字的内置类型; 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):

代码块
languagepy
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对字符串有很大的支持:

代码块
languagepy
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"

String对象有一些有用的方法; 例如:

代码块
languagepy
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包括几个内置的容器类型:列表,字典,集和元组。Python包括几个内置的容器类型:列表 ,字典,集合和元组。

清单

列表

列表是与数组相当的Python,但可重新调整大小,并且可以包含不同类型的元素:

代码块
languagepy
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']"

像往常一样,您可以在文档中找到有关列表的所有血清细节 。

切片: 除了一次访问列表元素之外,Python还提供了简洁的语法来访问子列表; 这被称为切片

代码块
languagepy
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:您可以循环遍历列表的元素,如下所示:

代码块
languagepy
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:

代码块
languagepy
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

列表推导: 编程时,我们经常要将一种数据转换为另一种数据。作为一个简单的例子,考虑以下代码来计算平方数:

代码块
languagepy
nums = [0, 1, 2, 3, 4]
squares = []
for x in nums:
    squares.append(x ** 2)
print(squares)   # Prints [0, 1, 4, 9, 16]

您可以使用列表理解使此代码更简单:

代码块
languagepy
nums = [0, 1, 2, 3, 4]
squares = [x ** 2 for x in nums]
print(squares)   # Prints [0, 1, 4, 9, 16]

列表的理解也可以包含条件:

代码块
languagepy
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]"

字典

字典存储(键,值)对,类似于MapJava或Javascript中的对象。你可以这样使用:

代码块
languagepy
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您需要了解的字典 。

循环:在字典中的键迭代很容易:

代码块
languagepy
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"

如果要访问密钥及其对应的值,请使用以下items方法:

代码块
languagepy
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"

词典解读: 这些与列表推导相似,但可以轻松构建字典。例如:

代码块
languagepy
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}"

集合

一组是不同元素的无序集合。作为一个简单的例子,请考虑以下几点:

代码块
languagepy
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,您想了解的有关集的所有内容都可以在文档中找到 。

循环: 迭代一个集合具有与遍历列表相同的语法; 然而,由于集合无序,您不能对您访问集合元素的顺序做出假设:

代码块
languagepy
animals = {'cat', 'dog', 'fish'}
for idx, animal in enumerate(animals):
    print('#%d: %s' % (idx + 1, animal))
# Prints "#1: fish", "#2: dog", "#3: cat"

设置理解: 像列表和字典一样,我们可以使用集合推理轻松构造集合:

代码块
languagepy
from math import sqrt
nums = {int(sqrt(x)) for x in range(30)}
print(nums)  # Prints "{0, 1, 2, 3, 4, 5}"
元组

元组是一个(不可变的)有序的值列表。一个元组在许多方面与列表相似; 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,而列表不能。这里是一个简单的例子:

代码块
languagepy
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"

该文档有关于元组的更多信息。

功能

Python函数使用def关键字定义。例如:

代码块
languagepy
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"

我们经常定义函数来采用可选的关键字参数,如下所示:

代码块
languagepy
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!"

有关文档中 Python函数的更多信息 。

Python中定义类的语法很简单:

代码块
languagepy
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更多关于Python类 的内容

 

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,以及使用这些数组的工具。如果您已经熟悉MATLAB,您可能会发现 本教程对于开始使用Numpy 很有用。

数组

numpy数组是一个值的网格,全部是相同的类型,并且由非负整数的元组索引。维数是数组的等级 ; 阵列的形状是一个整数元组,给出沿着每个维度的数组的大小。

我们可以从嵌套的Python列表初始化numpy数组,并使用方括号来访问元素:

代码块
languagepy
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还提供许多功能来创建数组:

代码块
languagepy
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]]"

您可以在文档中阅读有关数组创建的其他方法 。

数组索引

Numpy提供了几种将数据索引到数组中的方法。

切片: 与Python列表类似,可以对numpy数组进行切片。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:

代码块
languagepy
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"

 

您还可以将整数索引与片段索引进行混合。然而,这样做会产生比原始数组更低的数组。请注意,这与MATLAB处理数组切片的方式截然不同:

代码块
languagepy
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: 当您使用切片索引到numpy数组时,生成的数组视图将始终是原始数组的子阵列。相反,整数数组索引允许您使用另一个数组的数据来构造任意数组。这是一个例子:

代码块
languagepy
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的技巧就是从一个矩阵的每一行中选择一个元素:

代码块
languagepy
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: 布尔数组索引可以让您选取数组的任意元素。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:

代码块
languagepy
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]"

为了简洁起见,我们省略了很多关于numpy数组索引的细节; 如果您想了解更多,请 阅读文档

数据类型

每个numpy数组都是相同类型元素的网格。Numpy提供了一组可用于构造数组的数字数据类型。Numpy尝试在创建数组时猜测数据类型,但构造数组的函数通常还包含可选参数以显式指定数据类型。这是一个例子:

代码块
languagepy
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"

您可以阅读文档中的所有关于numpy数据类型 。

数组数学

基本数学函数在数组上以元素方式运行,并且可以作为运算符重载和numpy模块中的函数使用:

代码块
languagepy
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,*是元素乘法,而不是矩阵乘法。我们使用该dot函数来计算向量的内积,乘以一个向量乘以一个矩阵,并乘以矩阵。dot可用作numpy模块中的函数和数组对象的实例方法:

代码块
languagepy
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提供许多有用的功能,用于对数组执行计算; 其中最有用的是sum

代码块
languagepy
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由numpy提供的数学函数的完整列表 。

除了使用数组来计算数学函数,我们经常需要重新整形或以其他方式处理数组中的数据。这种类型的操作的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:

代码块
languagepy
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]"

Numpy提供了更多的功能来操作数组; 您可以在文档中看到完整列表 。

广播

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。通常我们有一个更小的数组和更大的数组,并且我们想要使用较小的数组多次来对较大的数组执行一些操作。

例如,假设我们要为矩阵的每一行添加一个常量向量。我们可以这样做:

代码块
languagepy
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)

 

这样做 然而,当矩阵x非常大时,在Python中计算显式循环可能很慢。请注意,添加载体v的矩阵的每一行 x等效于形成基质vv通过堆叠的多个副本v垂直,则执行的elementwise求和xvv。我们可以这样实现这个方法:

代码块
languagepy
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广播允许我们在不实际创建多个副本的情况下执行此计算v。考虑这个版本,使用广播:

代码块
languagepy
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]]"

线条y = x + v作品虽然x具有形状(4, 3)v形状, (3,)由于广播; 这条线似乎v实际上具有形状(4, 3),每行是一个副本v,并且总和是以元素方式执行的。

广播两个阵列一起遵循以下规则:

  1. 如果阵列不具有相同的等级,则用1s前缀下级阵列的形状,直到两个形状具有相同的长度。
  2. 如果两个数组在维中具有相同的大小,或者其中一个数组在该维度中具有大小1,则称它们在维度上是兼容的
  3. 如果数组在所有维度上都兼容,则可以一起广播数组。
  4. 广播后,每个阵列的行为就好像其形状等于两个输入数组的形状的元素最大值。
  5. 在其中一个数组的大小为1且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沿着该维度复制一样

如果这个解释没有意义,请从文档 或这个解释中阅读 说明

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:

代码块
languagepy
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快捷,因此您应尽可能地努力使用它。

Numpy文档

这个简要的概述已经涉及到您需要了解的许多重要的事情,关于numpy,但是远未完成。查看 numpy参考 ,了解更多关于numpy的信息。

 

SciPy

Numpy提供了一个高性能的多维数组和基本的工具来计算和操纵这些数组。 SciPy 建立在此基础之上,并提供了大量的功能,可以运行在numpy数组上,并且可用于不同类型的科学和工程应用程序。

熟悉SciPy的最佳方式是 浏览文档。我们将重点介绍SciPy的一些可能对此类有用的部分。

图像操作

SciPy提供了一些基本功能来处理图像。例如,它具有从磁盘读取图像到numpy数组,将numpy数组写入磁盘作为图像并调整图像大小的功能。这是一个简单的例子来展示这些功能:

代码块
languagepy
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)

MATLAB文件

功能scipy.io.loadmatscipy.io.savemat允许您读取和写入MATLAB文件。您可以在文档中阅读它们 。

点之间的距离

SciPy定义了一些有用的函数,用于计算点集合之间的距离。

该函数scipy.spatial.distance.pdist计算给定集合中所有成对点之间的距离:

代码块
languagepy
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)计算两组点之间的所有对之间的距离; 您可以在文档中阅读。

Matplotlib

Matplotlib是一个绘图库。本节简要介绍该matplotlib.pyplot模块,该模块提供了与MATLAB类似的绘图系统。

绘制

matplotlib中最重要的功能是plot允许您绘制2D数据。这是一个简单的例子:

代码块
languagepy
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.

运行此代码生成以下图:

只需一点额外的工作,我们可以轻松地绘制多行,并添加标题,图例和轴标签:

代码块
languagepy
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()

您可以阅读更多关于文档中plot功能 。  

次要情节

您可以使用该subplot功能在同一个图中绘制不同的东西。这是一个例子:

代码块
languagepy
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()

您可以阅读更多关于文档中subplot功能 。  

图片

您可以使用该imshow功能来显示图像。这是一个例子:

代码块
languagepy
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()