机器学习笔记--数学库

代码 【随机生成10行两列个0到1之间的小数】

import numpy as np
data = np.random.rand(10,2)

print(data)

初始数据

[[0.85482143 0.87208392]
 [0.15226363 0.52549581]
 [0.85199583 0.63840434]
 [0.37461595 0.7699527 ]
 [0.62885774 0.50949107]
 [0.13442721 0.33380331]
 [0.72998008 0.01574827]
 [0.20302876 0.19834324]
 [0.78084008 0.34859342]
 [0.1350378  0.55653729]]

python行索引【0,1,2,3】行

print(data[[0,1,2,3]])

[[0.85733026 0.51441212]
 [0.9297203  0.32537354]
 [0.55053671 0.98026599]
 [0.01811309 0.78720568]]

python列索引【0】列 

print(data[:,0])

[0.85733026 0.9297203  0.55053671 0.01811309 0.72665786 0.51680252
 0.89344144 0.80729948 0.05969606 0.71608088]

代码【利用随机数据绘制扇形】

import numpy as np
import matplotlib.pyplot as plt
data = np.random.rand(10000,2) #随机生成10000行两列个数据

x = data[:,0]
y = data[:,1]
idx = x**2+y**2 < 1 #索引条件圆形中x和y都大于0的数据
plt.plot(x[idx],y[idx],'go',markersize=1)
plt.show()

效果

代码【用随机数据绘制圆形图案】

import numpy as np
import matplotlib.pyplot as plt
data = 2*np.random.rand(10000,2) - 1 #定义域转为[-1,1]

x = data[:,0]
y = data[:,1]
idx = x**2+y**2 < 1 #圆形
plt.plot(x[idx],y[idx],'go',markersize=1)
plt.show()

效果

代码【利用随机数据绘制圆环】

import numpy as np
import matplotlib.pyplot as plt
data = 2*np.random.rand(10000,2) - 1

x = data[:,0]
y = data[:,1]
idx = x**2+y**2 < 1
hole = x**2 + y**2 < 0.25
idx = np.logical_and(idx,~hole) #numpy中的逻辑与，大圆和不包含小圆区域取相同的部分
plt.plot(x[idx],y[idx],'go',markersize=1)
plt.show()

效果 

代码【利用随机数据绘制直方图】【均匀分布】

 

import numpy as np
import matplotlib.pyplot as plt

p = np.random.rand(10000)
np.set_printoptions(edgeitems=5000, suppress=True)
plt.hist(p,bins=20,color='g') #分成20份
plt.show()

效果

import numpy as np
import matplotlib.pyplot as plt

p = np.random.rand(10000)
np.set_printoptions(edgeitems=5000, suppress=True)
plt.hist(p,bins=20, color='g', edgecolor='k')
plt.show()

效果

代码【利用随机数据绘制直方图】【高斯分布】【验证中心极限定理】

import numpy as np
import matplotlib.pyplot as plt

N = 10000
times = 100
z = np.zeros(N)
for i in range(times):
    z += np.random.rand(N)
z /= times
plt.hist(z, bins = 20, color = 'm', edgecolor='k')
plt.show()

效果

代码【pandas的dataframe类型】

import numpy as np
import pandas as pd

d = np.random.rand(3,4)
print(d)
print(type(d))
data = pd.DataFrame(data=d,columns = list('abcd'))
print('='*50)
print(data)
print(type(data))
print(data['b'])
data.to_csv('./data.dsv', index=False, header=True)
print('文件保存成功')

效果

代码【产生100个随机数据，范围为[-4,2]，散点图显示】

import numpy as np
import matplotlib.pyplot as plt

# [-4,2]
d = np.random.rand(100)*6-4
print(d)
plt.plot(d,'r.')
plt.show()

效果

代码【圆周率的演算模拟】

import numpy as np

if __name__=='__main__':
    a = np.arange(1,10000)
    print(a)
    print(np.sqrt(6*np.sum(1/(a**2))))

 效果

[   1    2    3 ... 9997 9998 9999]
3.141497154397623

代码【自然对数e的演算模拟】

import numpy as np

if __name__=='__main__':
    x = np.arange(1,20)
    print(np.sum(1/x.cumprod()) + 1) #cumprod求阶乘

效果

2.7182818351251554

代码【实线，虚线绘制图形】

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,1,100)
print(x)
y = x**x
plt.plot(x,y,'r-',linewidth=2)
plt.show()

效果

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,1,100)
print(x)
y = x**x
plt.plot(x,y,'r--',linewidth=2)
plt.show()

效果

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,1,100)
print(x)
y = x**x
plt.plot(x,y,'r:',linewidth=2)
plt.show()

效果

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,1,100)
print(x)
y = x**x
plt.plot(x,y,'r.',linewidth=2)
plt.show()