Numpy基础教程
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代码又不会打,模型又写不好,卷积又不会卷积,只有搬运整理基础教程才能维持得了生活这样子
Numpy简介
Numpy是Python中用于科学计算的核心库。它提供了高性能的多维数组对象,以及相关工具。
1. 数组Arrays
一个numpy数组是一个由不同数值组成的网格。网格中的数据都是同一种数据类型,可以通过非负整型数的元组来访问。维度的数量被称为数组的阶,数组的大小是一个由整型数构成的元组,可以描述数组不同维度上的大小。
我们可以从列表创建数组,然后利用方括号访问其中的元素:
import numpy as np a = np.array([1, 2, 3]) # Create a rank 1 array print type(a) # Prints "<type '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 # 显示一下矩阵b print b.shape # Prints "(2, 3)" print b[0, 0], b[0, 1], b[1, 0] # Prints "1 2 4"
Numpy还提供了很多其他创建数组的方法:
p { color: red } 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]]"
2. 访问数组
Numpy提供了多种访问数组的方法。
2.1 切片
和Python列表类似,numpy数组可以使用切片语法。因为数组可以是多维的,所以你必须为每个维度指定好切片。
p { color: red } 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"
你可以同时使用整型和切片语法来访问数组。但是,这样做会产生一个比原数组低阶的新数组。需要注意的是,这里和MATLAB中的情况是不同的:
p { color: red } 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)"
2.2 整型数组访问
当我们使用切片语法访问数组时,得到的总是原数组的一个子集。整型数组访问允许我们利用其它数组的数据构建一个新的数组:
p { color: red } 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]"
整型数组访问语法还有个有用的技巧,可以用来选择或者更改矩阵中每行中的一个元素:
p { color: red } 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]])
2.3 布尔型数组访问
布尔型数组访问可以让你选择数组中任意元素。通常,这种访问方式用于选取数组中满足某些条件的元素,举例如下:
p { color: red } 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]"
为了教程的简洁,有很多数组访问的细节我们没有详细说明,可以查看文档。
3. 数据类型
每个Numpy数组都是数据类型相同的元素组成的网格。Numpy提供了很多的数据类型用于创建数组。当你创建数组的时候,Numpy会尝试猜测数组的数据类型,你也可以通过参数直接指定数据类型,例子如下:
p { color: red } 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"
更多细节查看文档。
4. 数组计算
基本数学计算函数会对数组中元素逐个进行计算,既可以利用操作符重载,也可以使用函数方式:
p { color: red } 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)
和MATLAB不同,*是元素逐个相乘,而不是矩阵乘法。在Numpy中使用dot来进行矩阵乘法:
p { color: red } 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提供了很多计算数组的函数,其中最常用的一个是sum:
p { color: red } 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]"
想要了解更多函数,可以查看文档。
除了计算,我们还常常改变数组或者操作其中的元素。其中将矩阵转置是常用的一个,在Numpy中,使用T来转置矩阵:
p { color: red } 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还提供了更多操作数组的方法,请查看文档。