python的numpy的用法总结

本文总结Numpy的用法，建议先学习python的container 基础。numpy可以理解列表或数组。

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。

1、创建一维数组

1. import numpy as np
3. a = np.array([1, 2, 3]) # Create a rank 1 array
4. print type(a) # Prints ""
5. print a.shape # Prints "(3,)"
6. print a[0], a[1], a[2] # Prints "1 2 3"
7. a[0] = 5 # Change an element of the array
8. print a # Prints "[5, 2, 3]"

2、创建二维数组

1. b = np.array([[1,2,3],[4,5,6]]) # Create a rank 2 array
2. print b # 显示一下矩阵b
3. print b.shape # Prints "(2, 3)"
4. print b[0, 0], b[0, 1], b[1, 0] # Prints "1 2 4"

3、Numpy还提供了很多其他创建数组的方法

1. import numpy as np
2. #创建2行2列，值均为0的数组
3. a = np.zeros((2,2)) # Create an array of all zeros
4. print a # Prints "[[ 0. 0.]
5. # [ 0. 0.]]"
6. #创建1行2列，值均为1的数组
7. b = np.ones((1,2)) # Create an array of all ones
8. print b # Prints "[[ 1. 1.]]"
10. #创建2行2列，值均为7的数组
11. c = np.full((2,2), 7) # Create a constant array
12. print c # Prints "[[ 7. 7.]
13. # [ 7. 7.]]"
14. #创建2行2列，斜线为1的数组
15. d = np.eye(2) # Create a 2x2 identity matrix
16. print d # Prints "[[ 1. 0.]
17. # [ 0. 1.]]"
18. #创建2行2列的随机数组
19. e = np.random.random((2,2)) # Create an array filled with random values
20. print e # Might print "[[ 0.91940167 0.08143941]

4、数组切片

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。

1. import numpy as np
3. # 创建2维表，形状 3行4列
4. # [[ 1 2 3 4]
5. # [ 5 6 7 8]
6. # [ 9 10 11 12]]
7. a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
9. # 使用切片得到2行2列的子数组b
10. # :2指取0至1行，1:3指取1至2列
11. # [[2 3]
12. # [6 7]]
13. b = a[:2, 1:3]
15. # 0指取0行，1指取1列
16. print a[0, 1] # Prints "2"
17. b[0, 0] = 77 # b[0, 0] is the same piece of data as a[0, 1]
19. #当子数组更新，父数组也相应更新
20. print a[0, 1] # Prints "77"

5、整型和切片语法

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

1. # [[ 1 2 3 4]
2. # [ 5 6 7 8]
3. # [ 9 10 11 12]]
4. a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
6. # Two ways of accessing the data in the middle row of the array.
7. # Mixing integer indexing with slices yields an array of lower rank,
8. # while using only slices yields an array of the same rank as the
9. # original array:
10. row_r1 = a[1, :] # Rank 1 view of the second row of a
11. row_r2 = a[1:2, :] # Rank 2 view of the second row of a
12. print row_r1, row_r1.shape # Prints "[5 6 7 8] (4,)"
13. print row_r2, row_r2.shape # Prints "[[5 6 7 8]] (1, 4)"
15. # We can make the same distinction when accessing columns of an array:
16. col_r1 = a[:, 1]
17. col_r2 = a[:, 1:2]
18. print col_r1, col_r1.shape # Prints "[ 2 6 10] (3,)"
19. print col_r2, col_r2.shape # Prints "[[ 2]
20. # [ 6]
21. # [10]] (3, 1)"

6、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：

1. import numpy as np
3. a = np.array([[1,2], [3, 4], [5, 6]])
5. # An example of integer array indexing.
6. # The returned array will have shape (3,) and
7. # [0, 1, 2]指第0,1,2行，[0, 1, 0]指第0,1,0列
8. print a[[0, 1, 2], [0, 1, 0]] # Prints "[1 4 5]"
10. # The above example of integer array indexing is equivalent to this:
11. print np.array([a[0, 0], a[1, 1], a[2, 0]]) # Prints "[1 4 5]"
13. # When using integer array indexing, you can reuse the same
14. # element from the source array:
15. a[[0, 0], [1, 1]] 相当于 a[0, 1]
16. print a[[0, 0], [1, 1]] # Prints "[2 2]"
18. # Equivalent to the previous integer array indexing example
19. print np.array([a[0, 1], a[0, 1]]) # Prints "[2 2]"

7、选择或者更改元素

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：

1. import numpy as np
3. # Create a new array from which we will select elements
4. a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
6. print a # prints "array([[ 1, 2, 3],
7. # [ 4, 5, 6],
8. # [ 7, 8, 9],
9. # [10, 11, 12]])"
11. # Create an array of indices
12. b = np.array([0, 2, 0, 1])
14. # Select one element from each row of a using the indices in b
15. #np.arange(4)指按顺序从0至3数，相当于数组[0,1,2,3],即是指定了第0-3行
16. #b [0, 2, 0, 1] 是取a数组的第0,2,0,1列
17. print a[np.arange(4), b] # Prints "[ 1 6 7 11]"
19. # Mutate one element from each row of a using the indices in b
20. a[np.arange(4), b] += 10
21. #以上指定的元素，均加10
22. print a # prints "array([[11, 2, 3],
23. # [ 4, 5, 16],
24. # [17, 8, 9],
25. # [10, 21, 12]])

8、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：

1. import numpy as np
3. a = np.array([[1,2], [3, 4], [5, 6]])
5. bool_idx = (a > 2) # Find the elements of a that are bigger than 2;
6. # this returns a numpy array of Booleans of the same
7. # shape as a, where each slot of bool_idx tells
8. # whether that element of a is > 2.
10. print bool_idx # Prints "[[False False]
11. # [ True True]
12. # [ True True]]"
14. # We use boolean array indexing to construct a rank 1 array
15. # consisting of the elements of a corresponding to the True values
16. # of bool_idx
17. print a[bool_idx] # Prints "[3 4 5 6]"
19. # We can do all of the above in a single concise statement:
20. print a[a > 2] # Prints "[3 4 5 6]"

有很多数组访问的细节我们没有详细说明，可以查看文档。

9、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：

1. import numpy as np
3. x = np.array([1, 2]) # Let numpy choose the datatype
4. print x.dtype # Prints "int64"
6. x = np.array([1.0, 2.0]) # Let numpy choose the datatype
7. print x.dtype # Prints "float64"
9. x = np.array([1, 2], dtype=np.int64) # Force a particular datatype
10. print x.dtype # Prints "int64"

更多细节查看文档。

10、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：

1. import numpy as np
3. x = np.array([[1,2],[3,4]], dtype=np.float64)
4. y = np.array([[5,6],[7,8]], dtype=np.float64)
6. # Elementwise sum; both produce the array
7. # [[ 6.0 8.0]
8. # [10.0 12.0]]
9. print x + y
10. print np.add(x, y)
12. # Elementwise difference; both produce the array
13. # [[-4.0 -4.0]
14. # [-4.0 -4.0]]
15. print x - y
16. print np.subtract(x, y)
18. # Elementwise product; both produce the array
19. # [[ 5.0 12.0]
20. # [21.0 32.0]]
21. print x * y
22. print np.multiply(x, y)
24. # Elementwise division; both produce the array
25. # [[ 0.2 0.33333333]
26. # [ 0.42857143 0.5 ]]
27. print x / y
28. print np.divide(x, y)
30. # Elementwise square root; produces the array
31. # [[ 1. 1.41421356]
32. # [ 1.73205081 2. ]]
33. print np.sqrt(x)

11、dot矩阵乘法

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，计算矩阵乘法,请将第一个矩阵行元素(或数字)乘以第二个矩阵列元素,然后计算其总和：

1. import numpy as np
3. x = np.array([[1,2],[3,4]])
4. y = np.array([[5,6],[7,8]])
6. v = np.array([9,10])
7. w = np.array([11, 12])
9. # Inner product of vectors; both produce 219
10. print v.dot(w)
11. print np.dot(v, w)
13. # Matrix / vector product; both produce the rank 1 array [29 67]
14. print x.dot(v)
15. print np.dot(x, v)
17. # Matrix / matrix product; both produce the rank 2 array
18. # [[19 22]
19. # [43 50]]
20. #计算过程：1*5+2*7=19,1*6+2*8=22，其他依此类计算
21. print x.dot(y)
22. print np.dot(x, y)

12、sum函数

Numpy提供了很多计算数组的函数，其中最常用的一个是sum：

1. import numpy as np
3. x = np.array([[1,2],[3,4]])
5. print np.sum(x) # Compute sum of all elements; prints "10"
6. #axis=0 列相加；axis=1 行相加。
7. print np.sum(x, axis=0) # Compute sum of each column; prints "[4 6]"
8. 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。

13、T转置矩阵

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：

1. import numpy as np
3. x = np.array([[1,2], [3,4]])
4. print x # Prints "[[1 2]
5. # [3 4]]"
6. print x.T # Prints "[[1 3]
7. # [2 4]]"
9. # Note that taking the transpose of a rank 1 array does nothing:
10. v = np.array([1,2,3])
11. print v # Prints "[1 2 3]"
12. 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。

14、广播Broadcasting

广播是一种强有力的机制，它让Numpy可以让不同大小的矩阵在一起进行数学计算。我们常常会有一个小的矩阵和一个大的矩阵，然后我们会需要用小的矩阵对大的矩阵做一些计算。

举个例子，如果我们想要把一个向量加到矩阵的每一行，我们可以这样做：

1. import numpy as np
3. # We will add the vector v to each row of the matrix x,
4. # storing the result in the matrix y
5. x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
6. v = np.array([1, 0, 1])
7. y = np.empty_like(x) # Create an empty matrix with the same shape as x
9. # Add the vector v to each row of the matrix x with an explicit loop
10. for i in range(4):
11. y[i, :] = x[i, :] + v
13. # Now y is the following
14. # [[ 2 2 4]
15. # [ 5 5 7]
16. # [ 8 8 10]
17. # [11 11 13]]
18. print y

这样是行得通的，但是当x矩阵非常大，利用循环来计算就会变得很慢很慢。我们可以换一种思路：

1. import numpy as np
3. # We will add the vector v to each row of the matrix x,
4. # storing the result in the matrix y
5. x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
6. v = np.array([1, 0, 1])
7. vv = np.tile(v, (4, 1)) # Stack 4 copies of v on top of each other
8. print vv # Prints "[[1 0 1]
9. # [1 0 1]
10. # [1 0 1]
11. # [1 0 1]]"
12. y = x + vv # Add x and vv elementwise
13. print y # Prints "[[ 2 2 4
14. # [ 5 5 7]
15. # [ 8 8 10]
16. # [11 11 13]]"

Numpy广播机制可以让我们不用创建vv，就能直接运算，看看下面例子：

1. import numpy as np
3. # We will add the vector v to each row of the matrix x,
4. # storing the result in the matrix y
5. x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
6. v = np.array([1, 0, 1])
7. y = x + v # Add v to each row of x using broadcasting
8. print y # Prints "[[ 2 2 4]
9. # [ 5 5 7]
10. # [ 8 8 10]
11. # [11 11 13]]"

对两个数组使用广播机制要遵守下列规则：

1. 如果数组的秩不同，使用1来将秩较小的数组进行扩展，直到两个数组的尺寸的长度都一样。

2. 如果两个数组在某个维度上的长度是一样的，或者其中一个数组在该维度上长度为1，那么我们就说这两个数组在该维度上是相容的。

3. 如果两个数组在所有维度上都是相容的，他们就能使用广播。

4. 如果两个输入数组的尺寸不同，那么注意其中较大的那个尺寸。因为广播之后，两个数组的尺寸将和那个较大的尺寸一样。

5. 在任何一个维度上，如果一个数组的长度为1，另一个数组长度大于1，那么在该维度上，就好像是对第一个数组进行了复制。

如果上述解释看不明白，可以读一读文档和这个解释。译者注：强烈推荐阅读文档中的例子。

支持广播机制的函数是全局函数。哪些是全局函数可以在文档中查找。

1. 下面是一些广播机制的使用：
2. import numpy as np
4. # Compute outer product of vectors
5. v = np.array([1,2,3]) # v has shape (3,)
6. w = np.array([4,5]) # w has shape (2,)
7. # To compute an outer product, we first reshape v to be a column
8. # vector of shape (3, 1); we can then broadcast it against w to yield
9. # an output of shape (3, 2), which is the outer product of v and w:
10. # [[ 4 5]
11. # [ 8 10]
12. # [12 15]]
13. print np.reshape(v, (3, 1)) * w
15. # Add a vector to each row of a matrix
16. x = np.array([[1,2,3], [4,5,6]])
17. # x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),
18. # giving the following matrix:
19. # [[2 4 6]
20. # [5 7 9]]
21. print x + v
23. # Add a vector to each column of a matrix
24. # x has shape (2, 3) and w has shape (2,).
25. # If we transpose x then it has shape (3, 2) and can be broadcast
26. # against w to yield a result of shape (3, 2); transposing this result
27. # yields the final result of shape (2, 3) which is the matrix x with
28. # the vector w added to each column. Gives the following matrix:
29. # [[ 5 6 7]
30. # [ 9 10 11]]
31. print (x.T + w).T
33. # Another solution is to reshape w to be a row vector of shape (2, 1);
34. # we can then broadcast it directly against x to produce the same
35. # output.
36. print x + np.reshape(w, (2, 1))
38. # Multiply a matrix by a constant:
39. # x has shape (2, 3). Numpy treats scalars as arrays of shape ();
40. # these can be broadcast together to shape (2, 3), producing the
41. # following array:
42. # [[ 2 4 6]
43. # [ 8 10 12]]
44. print x * 2

广播机制能够让你的代码更简洁更迅速，能够用的时候请尽量使用！

15、SciPy

Numpy提供了高性能的多维数组，以及计算和操作数组的基本工具。SciPy基于Numpy，提供了大量的计算和操作数组的函数，这些函数对于不同类型的科学和工程计算非常有用。

熟悉SciPy的最好方法就是阅读文档。我们会强调对于本课程有用的部分。

1. • 图像操作

SciPy提供了一些操作图像的基本函数。比如，它提供了将图像从硬盘读入到数组的函数，也提供了将数组中数据写入的硬盘成为图像的函数。下面是一个简单的例子：

2. from scipy.misc import imread, imsave, imresize
4. # Read an JPEG image into a numpy array
5. img = imread('assets/cat.jpg')
6. print img.dtype, img.shape # Prints "uint8 (400, 248, 3)"
8. # We can tint the image by scaling each of the color channels
9. # by a different scalar constant. The image has shape (400, 248, 3);
10. # we multiply it by the array [1, 0.95, 0.9] of shape (3,);
11. # numpy broadcasting means that this leaves the red channel unchanged,
12. # and multiplies the green and blue channels by 0.95 and 0.9
13. # respectively.
14. img_tinted = img * [1, 0.95, 0.9]
16. # Resize the tinted image to be 300 by 300 pixels.
17. img_tinted = imresize(img_tinted, (300, 300))
19. # Write the tinted image back to disk
20. imsave('assets/cat_tinted.jpg', img_tinted)

2、点之间的距离

SciPy定义了一些有用的函数，可以计算集合中点之间的距离。

函数scipy.spatial.distance.pdist能够计算集合中所有两点之间的距离：

1. import numpy as np
2. from scipy.spatial.distance import pdist, squareform
4. # Create the following array where each row is a point in 2D space:
5. # [[0 1]
6. # [1 0]
7. # [2 0]]
8. x = np.array([[0, 1], [1, 0], [2, 0]])
9. print x
11. # Compute the Euclidean distance between all rows of x.
12. # d[i, j] is the Euclidean distance between x[i, :] and x[j, :],
13. # and d is the following array:
14. # [[ 0. 1.41421356 2.23606798]
15. # [ 1.41421356 0. 1. ]
16. # [ 2.23606798 1. 0. ]]
17. d = squareform(pdist(x, 'euclidean'))
18. print d

具体细节请阅读文档。

函数scipy.spatial.distance.cdist可以计算不同集合中点的距离，具体请查看文档。

16、Matplotlib

Matplotlib是一个作图库。这里简要介绍matplotlib.pyplot模块，功能和MATLAB的作图功能类似。

绘图。matplotlib库中最重要的函数是Plot。该函数允许你做出2D图形，如下：

1. import numpy as np
2. import matplotlib.pyplot as plt
4. # Compute the x and y coordinates for points on a sine curve
5. x = np.arange(0, 3 * np.pi, 0.1)
6. y = np.sin(x)
8. # Plot the points using matplotlib
9. plt.plot(x, y)
10. plt.show() # You must call plt.show() to make graphics appear.

只需要少量工作，就可以一次画不同的线，加上标签，坐标轴标志等。

1. import numpy as np
2. import matplotlib.pyplot as plt
4. # Compute the x and y coordinates for points on sine and cosine curves
5. x = np.arange(0, 3 * np.pi, 0.1)
6. y_sin = np.sin(x)
7. y_cos = np.cos(x)
9. # Plot the points using matplotlib
10. plt.plot(x, y_sin)
11. plt.plot(x, y_cos)
12. plt.xlabel('x axis label')
13. plt.ylabel('y axis label')
14. plt.title('Sine and Cosine')
15. plt.legend(['Sine', 'Cosine'])
16. plt.show()

绘制多个图像，可以使用subplot函数来在一幅图中画不同的东西：

1. import numpy as np
2. import matplotlib.pyplot as plt
4. # Compute the x and y coordinates for points on sine and cosine curves
5. x = np.arange(0, 3 * np.pi, 0.1)
6. y_sin = np.sin(x)
7. y_cos = np.cos(x)
9. # Set up a subplot grid that has height 2 and width 1,
10. # and set the first such subplot as active.
11. plt.subplot(2, 1, 1)
13. # Make the first plot
14. plt.plot(x, y_sin)
15. plt.title('Sine')
17. # Set the second subplot as active, and make the second plot.
18. plt.subplot(2, 1, 2)
19. plt.plot(x, y_cos)
20. plt.title('Cosine')
22. # Show the figure.
23. plt.show()

你可以使用imshow函数来显示图像，如下所示：

1. import numpy as np
2. from scipy.misc import imread, imresize
3. import matplotlib.pyplot as plt
5. img = imread('assets/cat.jpg')
6. img_tinted = img * [1, 0.95, 0.9]
8. # Show the original image
9. plt.subplot(1, 2, 1)
10. plt.imshow(img)
12. # Show the tinted image
13. plt.subplot(1, 2, 2)
15. # A slight gotcha with imshow is that it might give strange results
16. # if presented with data that is not uint8. To work around this, we
17. # explicitly cast the image to uint8 before displaying it.
18. plt.imshow(np.uint8(img_tinted))
19. plt.show()