Python Numpy学习手册（翻译自斯坦福大学 CS231n: Convolutional Neural Networks for Visual Recognition）
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Python Numpy学习手册（翻译自斯坦福大学 CS231n: Convolutional Neural Networks for Visual Recognition）
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1、Python簡介
Python是一種高級的動態類型化多范例編程語言，也類似偽代碼，舉個例子，對數據排序
def quicksort(arr):if len(arr) <= 1:return arrpivot = 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的官方中文學習文檔：https://docs.python.org/zh-cn/3.8/c-api/index.html
2、Python數據類型
Python包含整數、浮點數、布爾和字符串，
2.1 數字型
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"2.2 布爾型
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"Python布爾計算通過英文字母 and or not in來表達，和matlab通過 && ||有區別
2.3 字符型
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" 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"更多字符串使用學習：https://docs.python.org/3.5/library/stdtypes.html#string-methods
3?Containers
3.1 list
list類似數組，但可以包含不同類似的數據
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']"list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]"list的循環
animals = ['cat', 'dog', 'monkey'] for animal in animals:print(animal) # Prints "cat", "dog", "monkey", each on its own line.如果想提取每次循環的數據索引，可以用enumerate函數
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列表推導式，把列表的數據轉換為另外的數據，比如把list的數據都平方
常規for做法
nums = [0, 1, 2, 3, 4] squares = [] for x in nums:squares.append(x ** 2) print(squares) # Prints [0, 1, 4, 9, 16] nums = [0, 1, 2, 3, 4] squares = [x ** 2 for x in nums] print(squares) # Prints [0, 1, 4, 9, 16]加入判斷條件
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]"3.2 字典
字典存儲key和value，類似Java的map，更多資料見：https://docs.python.org/3.5/library/stdtypes.html#dict
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"字段遍歷：通過for遍歷字典的key
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"如果要同時獲得key和value通過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"同list的推導式，字典也可以做
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}"3.3 集合
Python集合:無序的不重復元素序列
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"集合遍歷同list一樣
animals = {'cat', 'dog', 'fish'} for idx, animal in enumerate(animals):print('#%d: %s' % (idx + 1, animal)) # Prints "#1: fish", "#2: dog", "#3: cat"集合推導式
from math import sqrt nums = {int(sqrt(x)) for x in range(30)} print(nums) # Prints "{0, 1, 2, 3, 4, 5}"3.4 元組
元組可以配合字典和集合使用，見下例
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"4 函數
Python函數用過def 關鍵字定義
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"同時函數可以定義初始入參，如下例的loud默認為False
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!"5 類
class Greeter(object):# Constructordef __init__(self, name):self.name = name # Create an instance variable# Instance methoddef 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!"6 Numpy
numpy是python的核心科學計算庫，類似matlab 對數據進行運算
6.1 numpy的數組
import numpy as npa = 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" import numpy as npa = 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]]"6.2 數組索引
數組索引同list，由于數組是多維，索引必須指明每個維度
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"數組切片的時候和matlab有差異，通過mix interger（ex:1）和only slice(ex：1:2)切出來的數組有區別
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)"?
import numpy as npa = 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]" ## 上下2個方法相同，都得到shape(3,) # 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]"整數數組索引的一個有用技巧是從矩陣的每一行中選擇或更改一個元素：
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] += 10print(a) # prints "array([[11, 2, 3],# [ 4, 5, 16],# [17, 8, 9],# [10, 21, 12]])數組的布爾運算用于提取滿足某種條件的數
import numpy as npa = 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]"6.3 數組數據類型
Numpy提供了大量的數值型數據類型，在你創建數組的時候，numpy回去猜測你的數據類型，當然你也可以指定數據類型
import numpy as npx = 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"6.4 數組數值計算
import numpy as npx = 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))matlab 的*是矩陣相乘 .*是點乘，在numpy里面是通過dot實現矩陣相乘
import numpy as npx = 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，w變量轉為[2,1]，v是[1,2] print(v.dot(w)) print(np.dot(v, w))# Matrix / vector product; both produce the rank 1 array [29 67], v是[2,1] 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sum函數運算
import numpy as npx = 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（列）; prints "[4 6]" print(np.sum(x, axis=1)) # Compute sum of each row（行）; prints "[3 7]"更多的函數見：https://docs.scipy.org/doc/numpy/reference/routines.math.html
矩陣轉置通過T
import numpy as npx = 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的Broadcasting功能，廣播是一種強大的機制，允許numpy在執行算術運算時使用不同形狀的數組。 通常，我們有一個較小的數組和一個較大的數組，并且我們想多次使用較小的數組對較大的數組執行某些操作。舉個例子，我們想把矩陣的每一行加上一個常數行。
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)然而當x很大的時候，這種循環計算在python里面就會很慢，現在我們可以等效一個矩陣vv是v在每一行的復制得到，然后x和vv相加，計算過程如下
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]]"然而numpy的broadcasting 運行我們不用創造vv來實現該功能
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]]"x是4*3的矩陣，v是1*3矩陣，由于numpy的broadcasting功能，y = x+v實現了v為4*3矩陣，v中的每一行是原始v的復制行
Broadcasting 實現2個矩陣運算遵循下面規定：
1）如果2個矩陣rank不一致，追加低rank的矩陣知道2個矩陣rank一致
2）2個矩陣兼容的條件是他們有相同的dimension或者其中一個矩陣在dimension為1
3）如果數組在所有dimension一直，則數組可以broadcast?
4）broadcast 后，每個數組的行為就好像它們的形狀等于兩個輸入數組的形狀的元素最大值一樣。
5）在一個數組的大小為1而另一個數組的大小大于1的任何維度中，第一個數組的行為就像是沿著該維度復制的一樣
換句話說，矩陣dimension為（x,y）和(y,)或者（x,y）和(x,1)可以Broadcasting
更多資料見：https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html
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)7 Numpy的SciPy和圖片處理
SciPy參考資料：https://docs.scipy.org/doc/scipy/reference/index.html
scipy自1.3.0后移除了imread、imsave、imresize等方法
這里imread、imsave使用imageio中的imwrite、imread代替。
imresize使用np.array(Image.fromarray(np.uint8(img_tinted)).resize())代替,其中img_tinted是np.ndarray類型的三維數組
8 Numpy和matlab配合使用
scipy.io.loadmat和scipy.io.savemat可以讀取matlab的數據
9?scipy應用
9.1 計算點直接距離
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)10?Matplotlib
10.1 繪圖
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()subplot
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()imshow
from imageio import imwrite,imread import numpy as np import matplotlib.pyplot as plt from PIL import Image img = imread(r'Desktop\20200109215359.jpg') print(img.dtype,img.shape) img_tinted=img*[1, 0.5, 0.5] img_tinted = np.array(Image.fromarray(np.uint8(img_tinted)).resize((300,300))) imwrite(r'Desktop\1.jpg', img_tinted) plt.subplot(1, 2, 1) plt.imshow(img) 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()?
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總結
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