源鏈接為：http://cs231n.github.io/python-numpy-tutorial/。

這篇指導書是由Justin Johnson編寫的。

在這門課程中我們將使用Python語言完成所有變成任務！Python本身就是一種很棒的通用編程語言，但是在一些流行的庫幫助下（numpy，scipy，matplotlib）它已經成為科學計算的強大環境。
我們希望你們中的許多人都有一些Python和numpy的使用經驗; 對你們其他人來說，這個section將作為Python用于科學計算和使用的快速速成課程。
你們中的一些人可能已經掌握了Matlab的知識，在這種情況下我們也推薦使用numpy。

你也可以閱讀由Volodymyr Kuleshov和Isaac Caswell（CS 228）編寫的Notebook版筆記。

本教程使用的Python版本為Python3.

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目錄

Arrays

Array indexing

Datatypes

Array math

Broadcasting

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原文共分為4部分，分別介紹了Python、Numpy、Scipy和Matplotlib的使用。本次翻譯為第二部分：Numpy的使用指導！

Numpy是Python中科學計算的核心庫。 它提供了一個高性能的多維數組對象，以及用于處理這些數組的工具。 如果您已經熟悉MATLAB，那么您可能會發現本教程對Numpy入門非常有用。

Arrays

numpy數組是一個值網格，所有類型都相同，并且由非負整數元組索引。 數組的形狀是一個整數元組，并且給出了每個維度的數組大小。

我們可以從嵌套的Python列表初始化numpy數組，并使用方括號訪問元素：

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"

Numpy還提供了創建數組的函數：

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]]"

你可以在這篇文檔看到更多關于創建數組的方法。

Array indexing

Numpy提供了幾種索引數組的方法。

切片：與Python列表類似，可以切割numpy數組。 由于數組可能是多維的，因此必須為數組的每個維指定一個切片：

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"#這里也對原始數組進行了修改

您還可以將整數索引與切片索引混合使用。 但是，這樣做會產生比原始數組更低級別的數組。 請注意，這與MATLAB處理數組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)"

整數數組索引：使用切片索引到numpy數組時，生成的數組視圖將始終是原始數組的子數組。 相反，整數數組索引允許您使用另一個數組中的數據構造任意數組。 這是一個例子：

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]"# 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改變一個元素：

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]])

布爾數組索引：布爾數組索引允許您選擇數組的任意元素。 通常，這種類型的索引用于選擇滿足某些條件的數組元素。 這是一個例子：

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]"

為簡潔起見，我們遺漏了很多關于numpy數組索引的細節; 如果你想了解更多，你應該閱讀文檔。

Datatypes

每個numpy數組都是相同類型的元素。 Numpy提供了一組可用于構造數組的大量數值數據類型。 Numpy在創建數組時嘗試猜測數據類型，但構造數組的函數通常還包含一個可選參數來顯式指定數據類型。 這是一個例子：

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"

你可以在這篇文檔看到更多關于數組數據類型的細節。

Array math

基本數學函數在數組上以元素方式運行，既可以作為運算符重載，也可以作為numpy模塊中的函數：

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))

請注意，與MATLAB不同，*是元素乘法，而不是矩陣乘法。 我們使用點函數來計算向量的內積，將向量乘以矩陣，并乘以矩陣。 dot既可以作為numpy模塊中的函數使用，也可以作為數組對象的實例方法：

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 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提供了許多用于在數組上執行計算的有用函數; 其中最有用的是sum：

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; prints "[4 6]" print(np.sum(x, axis=1)) # Compute sum of each row; prints "[3 7]"

您可以在文檔中找到numpy提供的完整數學函數列表。

除了使用數組計算數學函數之外，我們經常需要重新整形或以其他方式操縱數組中的數據。 這種操作的最簡單的例子是轉置矩陣; 要轉置矩陣，只需使用數組對象的T屬性：

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提供了很多操作素組的方法，可以看這篇文檔！

Broadcasting

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。 我們經常有一個較小的數組和一個較大的數組，我們希望多次使用較小的數組來對較大的數組執行某些操作。

例如，假設我們想要向矩陣的每一行添加一個常量向量。 我們可以這樣做：

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)

這有效; 但是當矩陣x非常大時，在Python中計算顯式循環可能會很慢。 注意，將向量v添加到矩陣x的每一行等同于通過垂直堆疊v的多個副本來形成矩陣w，然后執行x和w的元素求和。 我們可以像這樣實現這種方法：

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廣播允許我們執行此計算而不實際創建v的多個副本。考慮此版本，使用廣播：

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]]"

支持廣播的功能稱為通用功能。您可以在文檔中找到所有通用功能的列表。

以下是廣播的一些應用：

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)

廣播通常會使您的代碼更簡潔，更快速，因此您應該盡可能地使用它。

Numpy文檔
這個簡短的概述涉及了許多關于numpy需要了解的重要事項，但還遠未完成。 查看numpy參考資料，了解有關numpy的更多信息。

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