1. 利用数组进行数据处理
# -*- coding: utf-8 -*-
import matplotlib.pyplot as plt
import numpy as np
import pylab
points = np.arange(-5, 5, 0.01) # 生成100个点
xs, ys = np.meshgrid(points, points) # xs, ys互为转置矩阵
print (xs)
print (ys)
z = np.sqrt(xs ** 2 + ys ** 2)
print (z)
# 画图
plt.imshow(z, cmap = plt.cm.gray);
plt.colorbar()
plt.title("Image plot of $\sqrt{x^2 + y^2}$ for a grid of values")
pylab.show()
image.png
1.1 将条件逻辑表述为数组运算
import numpy as np
import numpy.random as np_random
print ('更多where的例子')
arr = np_random.randn(4, 4)
print (arr)
[[-0.24957277 -1.00358211 -0.73089612 0.2547624 ]
[ 0.37150224 -0.13316825 -0.60619815 -1.92511077]
[-0.42200075 -0.48937521 -1.25945836 -0.73708106]
[-0.52699294 1.2829272 0.5382728 -0.33665592]]
print (np.where(arr > 0, 2, -2))
[[-2 -2 -2 2]
[ 2 -2 -2 -2]
[-2 -2 -2 -2]
[-2 2 2 -2]]
print (np.where(arr > 0, 2, arr))
[[-0.24957277 -1.00358211 -0.73089612 2. ]
[ 2. -0.13316825 -0.60619815 -1.92511077]
print ('where嵌套')
cond_1 = np.array([True, False, True, True, False])
cond_2 = np.array([False, True, False, True, False])
# 传统代码如下
result = []
for i in range(len(cond_1)):
if cond_1[i] and cond_2[i]:
result.append(0)
elif cond_1[i]:
result.append(1)
elif cond_2[i]:
result.append(2)
else:
result.append(3)
print (result)
[1, 2, 1, 0, 3]
# np版本代码
result = np.where(cond_1 & cond_2, 0, \
np.where(cond_1, 1, np.where(cond_2, 2, 3)))
print (result)
[1 2 1 0 3]
1.2 数学和统计方法
image.png
import numpy as np
import numpy.random as np_random
print ('求和，求平均')
arr = np.random.randn(5, 4)
print (arr)
[[ 0.91340516 -0.28913556 -0.70409556 0.79581511]
[ 0.03067817 -1.48720141 -0.12093709 -0.46505081]
[ 1.19378156 -1.6550555 1.66422768 -0.21638596]
[ 0.05186091 -0.26038421 1.10220866 0.15916608]
[ 1.27671635 -1.88666043 1.97051236 0.2858806 ]]
print (arr.mean())
0.117967306233
print (arr.sum())
2.35934612466
print (arr.mean(axis = 1)) # 对每一行的元素求平均
[ 0.17899729 -0.51062779 0.24664195 0.26321286 0.41161222]
print (arr.sum(0)) # 对每一列元素求和，axis可以省略。
[ 3.46644215 -5.57843711 3.91191605 0.55942504]
'''
cumsum:
- 按列操作：a[i][j] += a[i - 1][j]
- 按行操作：a[i][j] *= a[i][j - 1]
cumprod:
- 按列操作：a[i][j] += a[i - 1][j]
- 按行操作：a[i][j] *= a[i][j - 1]
'''
print ('cunsum和cumprod函数演示')
arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
print (arr.cumsum(0)) # 累加
[[ 0 1 2]
[ 3 5 7]
[ 9 12 15]]
print (arr.cumprod(1)) # 累乘
[[ 0 0 0]
[ 3 12 60]
[ 6 42 336]]
1.3 布尔型数组的方法
import numpy as np
import numpy.random as np_random
print ('对正数求和')
arr = np_random.randn(100)
47
print ((arr > 0).sum())
print ('对数组逻辑操作')
bools = np.array([False, False, True, False])
print (bools.any()) # 有一个为True则返回True
True
print (bools.all()) # 有一个为False则返回False
False
1.4 排序
import numpy.random as np_random
print ('一维数组排序')
arr = np_random.randn(5)
arr.sort()
print (arr)
[-0.95478899 -0.84025039 -0.81146653 -0.59203327 -0.08063988]
print ('二维数组排序')
arr = np_random.randn(3, 2)
print (arr)
[[ 0.22553826 -0.55803348]
[-1.26086564 0.52919879]
[-0.44668631 -0.53374782]]
arr.sort(1) # 对每一行元素做排序
print (arr)
[[-0.55803348 0.22553826]
[-1.26086564 0.52919879]
[-0.53374782 -0.44668631]]
1.5 去重以及其它集合运算
image.png
import numpy as np
import numpy.random as np_random
print ('用unique函数去重')
names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
print (sorted(set(names))) # 传统Python做法
['Bob', 'Joe', 'Will']
print (np.unique(names))
['Bob' 'Joe' 'Will']
ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])
print (np.unique(ints))
[1 2 3 4]
print ('查找数组元素是否在另一数组')
values = np.array([6, 0, 0, 3, 2, 5, 6])
print (np.in1d(values, [2, 3, 6]))
[ True False False True True False True]
1.6 数组文件的输入输出
import numpy as np
print ('读取csv文件做为数组')
arr = np.loadtxt('array_ex.txt', delimiter = ',')
print (arr)
print ('数组文件读写')
arr = np.arange(10)
np.save('some_array', arr)
print (np.load('some_array.npy'))
print ('多个数组压缩存储')
np.savez('array_archive.npz', a = arr, b = arr)
arch = np.load('array_archive.npz')
print (arch['b'])
image.png
2 线性代数
-
常用的numpy.linalg函数 I
image.png
image.png
# -*- coding: utf-8 -*-
import numpy as np
import numpy.random as np_random
from numpy.linalg import inv, qr
print ('矩阵乘法')
x = np.array([[1., 2., 3.], [4., 5., 6.]])
y = np.array([[6., 23.], [-1, 7], [8, 9]])
print (x.dot(y))
[[ 28. 64.]
[ 67. 181.]]
print (np.dot(x, np.ones(3)))
[ 6. 15.]
x = np_random.randn(5, 5)
print ('矩阵求逆')
mat = x.T.dot(x)
print (inv(mat)) # 矩阵求逆
[[ 1.56337148 2.0598732 0.71214902]
[ 2.0598732 3.70889345 1.32647939]
[ 0.71214902 1.32647939 0.67314987]]
print (mat.dot(inv(mat))) # 与逆矩阵相乘，得到单位矩阵。
[[ 1.00000000e+00 -1.11022302e-16 -2.77555756e-17]
[ 2.22044605e-16 1.00000000e+00 0.00000000e+00]
[ -4.44089210e-16 0.00000000e+00 1.00000000e+00]]
print ('矩阵消元')
print (mat)
q, r = qr(mat)
print (q)
print (r)
3. 随机数生成
- numpy.random 函数
image.png
image.png
print ('正态分布随机数')
samples = np.random.normal(size=(4, 4))
print (samples)
print ('批量按正态分布生成0到1的随机数')
N = 10
print (np.random.normal(size = N))
image.png
4. 高级应用 数组重塑
import numpy as np
print ("将一维数组转换为二维数组")
arr = np.arange(8)
print (arr.reshape((4, 2)))
[[0 1]
[2 3]
[4 5]
[6 7]]
print (arr.reshape((4, 2)).reshape((2, 4))) # 支持链式操作
[[0 1 2 3]
[4 5 6 7]]
print ("维度大小自动推导")
arr = np.arange(15)
print (arr.reshape((5, -1)))
[[ 0 1 2]
[ 3 4 5]
[ 6 7 8]
[ 9 10 11]
[12 13 14]]
print ("获取维度信息并应用")
other_arr = np.ones((3, 5))
print (other_arr.shape)
print (arr.reshape(other_arr.shape))
(3, 5)
[[ 0 1 2 3 4]
[ 5 6 7 8 9]
[10 11 12 13 14]]
print ("高维数组拉平")
arr = np.arange(15).reshape((5, 3))
print (arr.ravel())
[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14]
4.1 数组的合并和拆分
- 数组连接函数
image.png
# -*- coding: utf-8 -*-
import numpy as np
import numpy.random as np_random
print ('连接两个二维数组')
arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([[7, 8, 9], [10, 11, 12]])
print (np.concatenate([arr1, arr2], axis = 0)) # 按行连接
[[ 1 2 3]
[ 4 5 6]
[ 7 8 9]
[10 11 12]]
print (np.concatenate([arr1, arr2], axis = 1)) # 按列连接
[[ 1 2 3 7 8 9]
[ 4 5 6 10 11 12]]
# 所谓堆叠，参考叠盘子。。。连接的另一种表述
print ('垂直stack与水平stack')
print (np.vstack((arr1, arr2))) # 垂直堆叠
[[ 1 2 3]
[ 4 5 6]
[ 7 8 9]
[10 11 12]]
print (np.hstack((arr1, arr2))) # 水平堆叠
[[ 1 2 3 7 8 9]
[ 4 5 6 10 11 12]]
print ('拆分数组')
arr = np_random.randn(5, 5)
print (arr)
[[ 0.05528194 -1.40691043 1.25390116 0.01343898 -0.56362107]
[-0.67196856 -2.01689483 0.530919 -0.01049739 -0.08576697]
[-0.00469774 0.60896671 0.49864293 -1.16233372 1.09303811]
[-1.6787031 0.1201058 0.83891825 -0.97806989 1.01268929]
[ 0.23928598 0.50982453 -0.77814664 0.71755991 -0.66536248]]
print ('水平拆分')
first, second, third = np.split(arr, [1, 3], axis = 0)
print ('first')
print (first)
[[ 0.05528194 -1.40691043 1.25390116 0.01343898 -0.56362107]]
print ('second')
print (second)
[[-0.67196856 -2.01689483 0.530919 -0.01049739 -0.08576697]
[-0.00469774 0.60896671 0.49864293 -1.16233372 1.09303811]]
print ('third')
print (third)
[[-1.6787031 0.1201058 0.83891825 -0.97806989 1.01268929]
[ 0.23928598 0.50982453 -0.77814664 0.71755991 -0.66536248]]
print ('垂直拆分')
first, second, third = np.split(arr, [1, 3], axis = 1)
print ('first')
print (first)
[[ 0.05528194]
[-0.67196856]
[-0.00469774]
[-1.6787031 ]
[ 0.23928598]]
print ('second')
print (second)
[[-1.40691043 1.25390116]
[-2.01689483 0.530919 ]
[ 0.60896671 0.49864293]
[ 0.1201058 0.83891825]
[ 0.50982453 -0.77814664]]
print ('third')
print (third)
[[ 0.01343898 -0.56362107]
[-0.01049739 -0.08576697]
[-1.16233372 1.09303811]
[-0.97806989 1.01268929]
[ 0.71755991 -0.66536248]]
# 堆叠辅助类
arr = np.arange(6)
arr1 = arr.reshape((3, 2))
arr2 = np_random.randn(3, 2)
print ('r_用于按行堆叠')
[[ 0. 1. ]
[ 2. 3. ]
[ 4. 5. ]
[-0.1285436 1.78124128]
[-1.18281363 -0.5240686 ]
[ 0.14317738 1.4884177 ]]
print (np.r_[arr1, arr2])
print ('c_用于按列堆叠')
print (np.c_[np.r_[arr1, arr2], arr])
[[ 0. 1. 0. ]
[ 2. 3. 1. ]
[ 4. 5. 2. ]
[-0.1285436 1.78124128 3. ]
[-1.18281363 -0.5240686 4. ]
[ 0.14317738 1.4884177 5. ]]
print ('切片直接转为数组')
print (np.c_[1:6, -10:-5])
[[ 1 -10]
[ 2 -9]
[ 3 -8]
[ 4 -7]
[ 5 -6]]
4.2 元素的重复操作
import numpy as np
import numpy.random as np_random
print ('Repeat: 按元素')
arr = np.arange(3)
print (arr.repeat(3))
[0 0 0 1 1 1 2 2 2]
print (arr.repeat([2, 3, 4])) # 3个元素，分别复制2, 3, 4次。长度要匹配！
[0 0 1 1 1 2 2 2 2]
print ('Repeat，指定轴')
arr = np_random.randn(2, 2)
print (arr)
[[-0.24003754 0.87388196]
[ 0.63967445 0.53702917]]
print (arr.repeat(2, axis = 0)) # 按行repeat
[[-0.24003754 0.87388196]
[-0.24003754 0.87388196]
[ 0.63967445 0.53702917]
[ 0.63967445 0.53702917]]
print (arr.repeat(2, axis = 1)) # 按列repeat
[[-0.24003754 -0.24003754 0.87388196 0.87388196]
[ 0.63967445 0.63967445 0.53702917 0.53702917]]
print (arr.repeat(2, axis = 0)) # 按行repeat
[[-0.24003754 0.87388196]
[-0.24003754 0.87388196]
[ 0.63967445 0.53702917]
[ 0.63967445 0.53702917]]
print ('Tile: 参考贴瓷砖')
print (np.tile(arr, 2))
[[-0.24003754 0.87388196 -0.24003754 0.87388196]
[ 0.63967445 0.53702917 0.63967445 0.53702917]]
print (np.tile(arr, (2, 3))) # 指定每个轴的tile次数
[[-0.24003754 0.87388196 -0.24003754 0.87388196 -0.24003754 0.87388196]
[ 0.63967445 0.53702917 0.63967445 0.53702917 0.63967445 0.53702917]
[-0.24003754 0.87388196 -0.24003754 0.87388196 -0.24003754 0.87388196]
[ 0.63967445 0.53702917 0.63967445 0.53702917 0.63967445 0.53702917]]
4.3 花式索引的等价函数
# -*- coding: utf-8 -*-
import numpy as np
import numpy.random as np_random
print ('Fancy Indexing例子代码')
arr = np.arange(10) * 100
inds = [7, 1, 2, 6]
print (arr[inds])
[700 100 200 600]
print ('使用take')
print (arr.take(inds))
[700 100 200 600]
print ('使用put更新内容')
arr.put(inds, 50)
print (arr)
[ 0 50 50 300 400 500 50 50 800 900]
[ 0 10 20 300 400 500 60 70 800 900]
arr.put(inds, [70, 10, 20, 60])
print (arr)
[[-0.93008115 0.61977807 -0.25993519 -1.09063511]
[ 0.73107853 -1.25725762 0.75042044 0.89568034]]
arr.put(inds, [70, 10, 20, 60])
print (arr)
[[-0.25993519 -0.93008115 -0.25993519 0.61977807]
[ 0.75042044 0.73107853 0.75042044 -1.25725762]]