翻译自：http://cs231n.github.io/python-numpy-tutorial/
Numpy
Numpy是python科学计算的一个核心库。它提供了高性能多维数据对象以及操作这些数组的工具。
Arrays
numpy数据是一个相同数据类型的值网格，用一个非负整数的元组来索引。
rank：维数
shape：是一个整数元组，元素表示每一维的大小
我们可以用python的lists初始化一个numpy数组，用方括号取元素。注意shape的输出，如：
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也提供了很多创建数组的函数
如：np.zeros(shape),np.ones(shape)
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]]"
可在此链接中找到更多的创建数组的方法：https://docs.scipy.org/doc/numpy/user/basics.creation.html#arrays-creation
Array indexing
numpy提供了索引数组的几种方式
切片：类似于Python lists，numpy数组也可以切片。因为数组很可能是多维的，你必须为数组的每一维指定一个切片。
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]]
#注意：下标是含头不含尾的
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"
也可以将切片索引和整数索引整合在一起。然而，这样做的话将会产生一个更低rank的数组。示例如下：
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 ，使用切片索引和整数索引相结合
row_r2 = a[1:2, :] # Rank 2 view of the second row of a，只使用切片索引
print(row_r1, row_r1.shape) # Prints "[5 6 7 8] (4,)" ，rank比原始数组低
print(row_r2, row_r2.shape) # Prints "[[5 6 7 8]] (1, 4)"，rank和原始数组一样
# 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
当你使用切片来索引numpy数组时，结果数组是原始数组的一个子数组。与之相反，整数数组索引允许你构建一个全新的数组，通过来自其他数组的元素。示例如下：
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]"
整数索引的一个有用的技巧是从矩阵每一行选择或者改变一个元素
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]])
boolean数组索引
一般用来选择满足情况的元素
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]"