NumPy入门(4)_广播_布尔掩码_排序等

代码来自于《Python数据科学手册》的代码复现。
来自和鲸科技（科赛）的K-lab项目

import numpy as np
a = np.array([0, 1, 2])
b = np.array([5, 5, 5])
a + b

array([5, 6, 7])

a + 5

array([5, 6, 7])

M = np.ones((3, 3))
print(M)

[[1. 1. 1.]
 [1. 1. 1.]
 [1. 1. 1.]]

M + a

array([[1., 2., 3.],
       [1., 2., 3.],
       [1., 2., 3.]])

a = np.arange(3)
b = np.arange(3)[:, np.newaxis]
print(a)
print(b)

[0 1 2]
[[0]
 [1]
 [2]]

a + b

array([[0, 1, 2],
       [1, 2, 3],
       [2, 3, 4]])

M = np.ones((2, 3))
a = np.arange(3)
M + a

array([[1., 2., 3.],
       [1., 2., 3.]])

a = np.arange(3).reshape((3, 1))
b = np.arange(3)
a + b

array([[0, 1, 2],
       [1, 2, 3],
       [2, 3, 4]])

a 

array([[0],
       [1],
       [2]])

print(M)
print(a)

[[1. 1.]
 [1. 1.]
 [1. 1.]]
[0 1 2]

```python
a[:, np.newaxis].shape

(3, 1)

M + a[:, np.newaxis]

array([[1., 1.],
       [2., 2.],
       [3., 3.]])

广播规则对于任意二进制通用函数都是适用的

np.logaddexp(M, a[:, np.newaxis])
array([[1.31326169, 1.31326169],
       [1.69314718, 1.69314718],
       [2.31326169, 2.31326169]])
X = np.random.random((10, 3))
Xmean = X.mean(0)
Xmean

array([0.44962305, 0.53916304, 0.40801379])

X_centered = X -Xmean
X_centered.mean(0)

array([-1.11022302e-17,  6.66133815e-17,  5.55111512e-17])

x = np.linspace(0, 5, 50)
y = np.linspace(0, 5, 50)[:, np.newaxis]
z = np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)
%matplotlib inline
import matplotlib.pyplot as plt

plt.imshow(z, origin='lower', extent=[0, 5, 0, 5], cmap='viridis')
plt.colorbar();

比较、掩码和布尔逻辑
示例：统计下雨天数

import numpy as ny
import pandas as pd

# 利用Pandas抽取降雨量，放入一个NumPy数组
rainfall = pd.read_csv('/home/kesci/input/Handbook6828/Seattle2014.csv')['PRCP'].values
inches = rainfall / 254
inches.shape
(365,)
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn; seaborn.set()

plt.hist(inches, 40);

类比操作

x = np.array([1, 2, 3, 4, 5])
x < 3

array([ True,  True, False, False, False])

x > 3

array([False, False, False,  True,  True])

(2 * x)  == (x ** 2)

array([False,  True, False, False, False])

np.equal(x, 2)

array([False,  True, False, False, False])

rng = np.random.RandomState(0)
x = rng.randint(10, size=(3, 4))
x

array([[5, 0, 3, 3],
       [7, 9, 3, 5],
       [2, 4, 7, 6]])

x < 6

array([[ True,  True,  True,  True],
       [False, False,  True,  True],
       [ True,  True, False, False]])

np.less(x, 6)

array([[ True,  True,  True,  True],
       [False, False,  True,  True],
       [ True,  True, False, False]])

操作布尔数组

print(x)

[[5 0 3 3]
 [7 9 3 5]
 [2 4 7 6]]

统计记录个数

# 有多少个值小于6？
np.count_nonzero(x < 6)

8

np.sum(x < 6)

8

# 每行有多少值小于6
np.sum(x < 6, axis=1)

array([4, 2, 2])

有没有值大于8

np.any(x > 8)

True

有没有值小于0

np.any(x < 0)

False

是否所有的值都小于10？

np.all(x < 10)

True

是否所有的值都等于6

np.all(x == 6)

False

是否所有的行都等于8

np.all(x < 8, axis=1)

array([ True, False,  True])

统计降水量在0.5英寸和1英寸之间的天数

np.sum((inches > 0.5) & (inches < 1))
29
np.sum(~((inches <= 0.5) | (inches >= 1)))
29
print("Number days without rain:       ", np.sum(inches == 0))
print("Number days with rain:          ", np.sum(inches != 0))
print("Days with more than 0.5 inches: ", np.sum(inches > 0.5))
print("Rainy day with < 0.2 inches:    ", np.sum((inches > 0) & (inches < 0.2)))

Number days without rain:        215
Number days with rain:           150
Days with more than 0.5 inches:  37
Rainy day with < 0.2 inches:     75

将布尔数组作为掩码

x < 5

array([[False,  True,  True,  True],
       [False, False,  True, False],
       [ True,  True, False, False]])    

x[x < 5]

array([0, 3, 3, 3, 2, 4])

为所有下雨天创建一个掩码

rainy = (inches > 0)

构建一个包含整个夏季日期的掩码（6.21是172天）

summer = (np.arange(365) - 172 < 90) & (np.arange(365) - 172 > 0)
print("Median precip on rainy days in 2014:    ", np.median(inches[rainy]))
print("Median precip on summer days in 2014:   ", np.median(inches[summer]))
print("Maximum precip on summer days in 2014:  ", np.max(inches[summer]))
print("Median precip non-summer rainy days:    ", np.median(inches[rainy & ~summer]))

Median precip on rainy days in 2014:     0.19488188976377951
Median precip on summer days in 2014:    0.0
Maximum precip on summer days in 2014:   0.8503937007874016
Median precip non-summer rainy days:     0.20078740157480315

索引

import numpy as np
rand = np.random.RandomState(42)
x = rand.randint(100, size=10)
print(x)

[51 92 14 71 60 20 82 86 74 74]

[x[3], x[7], x[2]]

[71, 86, 14]

ind = [3, 7, 4]
x[ind]

array([71, 86, 60])

ind = np.array([[3, 7], [4, 5]])
x[ind]

array([[71, 86],
       [60, 20]])

X = np.arange(12).reshape((3, 4))
X

array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

row = np.array([0, 1, 2])
col = np.array([2, 1, 3])
X[row, col]

array([ 2,  5, 11])

X[row[:, np.newaxis], col]

array([[ 2,  1,  3],
       [ 6,  5,  7],
       [10,  9, 11]])

row[:, np.newaxis] * col

array([[0, 0, 0],
       [2, 1, 3],
       [4, 2, 6]])

组合索引

print(X)

[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]

X[2, [2, 0, 1]]

array([10,  8,  9])

X[1:, [2, 0, 1]]

array([[ 6,  4,  5],
       [10,  8,  9]])

mask = np.array([1, 0, 1, 0], dtype=bool)
X[row[:, np.newaxis], mask]

array([[ 0,  2],
       [ 4,  6],
       [ 8, 10]])

用索引修改值

x = np.arange(10)
i = np.array([2, 1, 8, 4])
x[i] = 99
print(x)

[ 0 99 99  3 99  5  6  7 99  9]

x[i] -= 10
print(x)

[ 0 89 89  3 89  5  6  7 89  9]

x = np.zeros(10)
x[[0, 0]] = [4, 6]
print(x)

[6. 0. 0. 0. 0. 0. 0. 0. 0. 0.]

i = [2, 3, 3, 4, 4, 4, 4]
x[i] += 1
print(x)

[6. 0. 1. 1. 1. 0. 0. 0. 0. 0.]

累加

x = np.zeros(10)
np.add.at(x, i, 1)
print(x)

[0. 0. 1. 2. 4. 0. 0. 0. 0. 0.]

数组的排序
选择排序

import numpy as np

def selection_sort(x):
    for i in range(len(x)):
        swap = i + np.argmin(x[i:])
        (x[i], x[swap]) = (x[swap], x[i])
    return x
    
x = np.array([2, 1, 4, 3, 5])
selection_sort(x)

array([1, 2, 3, 4, 5])

def bogosort(x):
    while np.any(x[:-1] > x[1:]):
        np.random.shuffle(x)
    return x

x = np.array([2, 1, 4, 3, 5])
bogosort(x)

array([1, 2, 3, 4, 5])

NumPy中的快速排序

x = np.array([2, 1, 4, 3, 5])
np.sort(x)

array([1, 2, 3, 4, 5])

x.sort()
print(x)

[1 2 3 4 5]

返回索引值

x = np.array([2, 1, 4, 3, 5])
i = np.argsort(x)
print(i)

[1 0 3 2 4]

x[i]

array([1, 2, 3, 4, 5])

沿着行或列排序

rand = np.random.RandomState(42)
X = rand.randint(0, 10, (4, 6))
print(X)

[[6 3 7 4 6 9]
 [2 6 7 4 3 7]
 [7 2 5 4 1 7]
 [5 1 4 0 9 5]]

对X的每一个行排序

np.sort(X, axis=0)

array([[2, 1, 4, 0, 1, 5],
       [5, 2, 5, 4, 3, 7],
       [6, 3, 7, 4, 6, 7],
       [7, 6, 7, 4, 9, 9]])

对X的每一列排序

np.sort(X, axis=1)

array([[3, 4, 6, 6, 7, 9],
       [2, 3, 4, 6, 7, 7],
       [1, 2, 4, 5, 7, 7],
       [0, 1, 4, 5, 5, 9]])

部分排序

找到第三小的，放在最左边右边则任意排序

x = np.array([7, 2, 3, 1, 6, 5, 4])
np.partition(x, 3)

array([2, 1, 3, 4, 6, 5, 7])

np.partition(X, 2, axis=1)

array([[3, 4, 6, 7, 6, 9],
       [2, 3, 4, 7, 6, 7],
       [1, 2, 4, 5, 7, 7],
       [0, 1, 4, 5, 9, 5]])