基本概率分布图的绘制
原文地址：https://github.com/AsuraDong/Blog/blob/master/Articles/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/%E5%9F%BA%E6%9C%AC%E6%A6%82%E7%8E%87%E5%88%86%E5%B8%83%E5%9B%BE%E7%9A%84%E7%BB%98%E5%88%B6.md
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import math
import time
from scipy import stats
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
mpl.rcParams['font.sans-serif'] = ['FangSong']
mpl.rcParams['axes.unicode_minus']=False
一、绘图介绍
Bar柱状图(和之后的直方图不同)
x = np.arange(0,10,0.1)
y = np.sin(x)
plt.bar(x,y,width=0.04,linewidth=0.2)
plt.plot(x,y,'r--',linewidth=2)
plt.title('Sin曲线')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
屁股线
f(x) = x**x when x>0 and (-x)**(-x) when x<0
def f(x):
y = np.ones(x.shape)
i = x>0
y[i] = np.power(x[i],x[i])
i = x<0
y[i] = np.power(-x[i],-x[i])
return y
x = np.linspace(-1.3,1.3,101)
y = f(x)
plt.plot(x,y,'g-',label='x^x',linewidth = 2)
plt.grid()
plt.legend(loc='upper left')
plt.show()
心形线
t = np.linspace(0,2*np.pi,100)
x = 16*np.sin(t)**3
y = 13*np.cos(t)-5*np.cos(2*t)-2*np.cos(3*t)-np.cos(4*t)
plt.plot(x,y,'r-',linewidth = 2)
plt.grid(True)
plt.show()
胸型线
x = np.arange(1,0,-0.001)
y = (-3 * x * np.log(x) + np.exp(-(40 * (x - 1 / np.e)) ** 4) / 25) / 2 #注意这里在1/e取极值，给它一个智力的波动
plt.figure(figsize=(5,7))
plt.plot(y,x,'r-',linewidth = 2) #注意这里是y，x
plt.grid(True)
plt.title('胸型线',fontsize = 20)
plt.show()
渐开线
t = np.linspace(0, 50, num=1000)
x = t*np.sin(t) + np.cos(t)
y = np.sin(t) - t*np.cos(t)
plt.plot(x, y, 'r-', linewidth=2)
plt.grid()
plt.show()
正态分布概率密度函数
######## 高斯分布/正态分布###############
mu = 0
sigma = 1
x = np.linspace(mu-3*sigma,mu+3*sigma,51)
y = np.exp(-(x-mu)**2/(2*sigma**2))/(np.sqrt(2*np.pi)*sigma)
plt.figure()
#plt.plot(x,y,'ro-',linewidth=2)
plt.plot(x,y,'ro-',x,y,'g*',linewidth=2,markersize = 3)
plt.xlabel('X',fontsize = 15)
plt.ylabel('Y',fontsize=15)
plt.title(r'Normal distribution',fontsize =18)
#plt.grid(True)
plt.savefig('NormalDistribution.png')
plt.show()
损失函数：Logistic损失(-1,1)/SVM Hinge损失/ 0/1损失
plt.figure(figsize=(10,8))
x = np.linspace(start=-2, stop=3, num=1001, dtype=np.float)
y_logit = np.log(1 + np.exp(-x)) / math.log(2) #Logistic损失（取对数）
y_boost = np.exp(-x)
y_01 = x < 0
y_hinge = 1.0 - x
y_hinge[y_hinge < 0] = 0
plt.plot(x, y_logit, 'r-', label='Logistic Loss', linewidth=2)
plt.plot(x, y_01, 'g-', label='0/1 Loss', linewidth=2)
plt.plot(x, y_hinge, 'b-', label='Hinge Loss', linewidth=2)
plt.plot(x, y_boost, 'm--', label='Adaboost Loss', linewidth=2)
plt.grid()
plt.legend(loc='upper right')
plt.savefig('1.png')
plt.show()
二、概率分布
均匀分布（散点图）
x = np.random.rand(10000) #每个的概率
t = np.arange(len(x))
plt.plot(t,x,'g.',label="Uniform Distribution")
plt.legend(loc="upper left")
plt.grid()
plt.show()
概率分布（直方图）
x = np.random.rand(10000)
#x = [1,2,1]
plt.hist(x,25,color="m",alpha=0.37,label="Uniform Distribution")#直方图
plt.legend(loc="upper left")
plt.grid()
plt.show()
中心极限定理
TIMES = 1000
SIZE = 10000
resultArr = np.zeros(SIZE)
for i in range(TIMES):
resultArr += np.random.uniform(-5,5,SIZE)
resultArr = resultArr / TIMES
plt.hist(resultArr,bins=30,color='g',alpha = 0.3,label="Uniform Distribution")
plt.legend(loc="upper right")
plt.grid()
plt.show()
其他的中心极限定理
lamda = 7
p = stats.poisson(lamda)
y = p.rvs(size=1000)
mx = 30
r = (0, mx)
bins = r[1] - r[0]
plt.figure(figsize=(15, 8), facecolor='w')
plt.subplot(121)
plt.hist(y, bins=bins, range=r, color='g', alpha=0.8, normed=True)
t = np.arange(0, mx+1)
plt.plot(t, p.pmf(t), 'ro-', lw=2)
plt.grid(True)
N = 1000
M = 10000
plt.subplot(122)
a = np.zeros(M, dtype=np.float)
p = stats.poisson(lamda)
for i in np.arange(N):
a += p.rvs(size=M)
a /= N
plt.hist(a, bins=20, color='g', alpha=0.8, normed=True)
plt.grid(b=True)
plt.show()
Possion分布
x = np.random.poisson(lam=5, size=10000)
print (x)
pillar = 15
a = plt.hist(x, bins=pillar, normed=True, range=[0, pillar], color='g', alpha=0.5)
plt.grid()
plt.show()
print (a[1])
print('-'*10)
print (a[0].sum())
[5 4 4 ..., 4 2 3]
[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
15.]
----------
1.0
size = 1000
lamda = 5
p = np.random.poisson(lam=lamda, size=size)
plt.figure()
plt.hist(p, bins=range(3 * lamda), histtype='bar', align='left', color='r', rwidth=0.8, normed=True)
plt.grid(b=True, ls=':')
# plt.xticks(range(0, 15, 2))
plt.title('Numpy.random.poisson', fontsize=13)
plt.figure()
r = stats.poisson(mu=lamda)
p = r.rvs(size=size)
plt.hist(p, bins=range(3 * lamda), color='r', align='left', rwidth=0.8, normed=True)
plt.grid(b=True, ls=':')
plt.title('scipy.stats.poisson', fontsize=13)
plt.show()
插值
rv = np.random.poisson(5)
x1 = a[1]
y1 = rv.pmf(x1)
itp = BarycentricInterpolator(x1, y1) # 重心插值
x2 = np.linspace(x.min(), x.max(), 50)
y2 = itp(x2)
cs = sp.interpolate.CubicSpline(x1, y1) # 三次样条插值
plt.plot(x2, cs(x2), 'm--', linewidth=5, label='CubicSpine') # 三次样条插值
plt.plot(x2, y2, 'g-', linewidth=3, label='BarycentricInterpolator') # 重心插值
plt.plot(x1, y1, 'r-', linewidth=1, label='Actural Value') # 原始值
plt.legend(loc='upper right')
plt.grid()
plt.show()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-44-28524b0e3309> in <module>()
1 rv = np.random.poisson(5)
2 x1 = a[1]
----> 3 y1 = rv.pmf(x1)
4 itp = BarycentricInterpolator(x1, y1) # 重心插值
5 x2 = np.linspace(x.min(), x.max(), 50)
AttributeError: 'int' object has no attribute 'pmf'
三、 绘制3D图像
x, y = np.mgrid[-3:3:7j, -3:3:7j]
print (x)
print (y)
u = np.linspace(-3, 3, 101)
x, y = np.meshgrid(u, u) #注意meshgrid的用法
print (x)
print (y)
z = x*y*np.exp(-(x**2 + y**2)/2) / math.sqrt(2*math.pi)
# z = x*y*np.exp(-(x**2 + y**2)/2) / math.sqrt(2*math.pi)
fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')
# ax.plot_surface(x, y, z, rstride=5, cstride=5, cmap=cm.coolwarm, linewidth=0.1) #
ax.plot_surface(x, y, z, rstride=3, cstride=3, cmap=cm.gist_heat, linewidth=0.5)
plt.show()
[[-3. -3. -3. -3. -3. -3. -3.]
[-2. -2. -2. -2. -2. -2. -2.]
[-1. -1. -1. -1. -1. -1. -1.]
[ 0. 0. 0. 0. 0. 0. 0.]
[ 1. 1. 1. 1. 1. 1. 1.]
[ 2. 2. 2. 2. 2. 2. 2.]
[ 3. 3. 3. 3. 3. 3. 3.]]
[[-3. -2. -1. 0. 1. 2. 3.]
[-3. -2. -1. 0. 1. 2. 3.]
[-3. -2. -1. 0. 1. 2. 3.]
[-3. -2. -1. 0. 1. 2. 3.]
[-3. -2. -1. 0. 1. 2. 3.]
[-3. -2. -1. 0. 1. 2. 3.]
[-3. -2. -1. 0. 1. 2. 3.]]
[[-3. -2.94 -2.88 ..., 2.88 2.94 3. ]
[-3. -2.94 -2.88 ..., 2.88 2.94 3. ]
[-3. -2.94 -2.88 ..., 2.88 2.94 3. ]
...,
[-3. -2.94 -2.88 ..., 2.88 2.94 3. ]
[-3. -2.94 -2.88 ..., 2.88 2.94 3. ]
[-3. -2.94 -2.88 ..., 2.88 2.94 3. ]]
[[-3. -3. -3. ..., -3. -3. -3. ]
[-2.94 -2.94 -2.94 ..., -2.94 -2.94 -2.94]
[-2.88 -2.88 -2.88 ..., -2.88 -2.88 -2.88]
...,
[ 2.88 2.88 2.88 ..., 2.88 2.88 2.88]
[ 2.94 2.94 2.94 ..., 2.94 2.94 2.94]
[ 3. 3. 3. ..., 3. 3. 3. ]]
cmaps = [('Perceptually Uniform Sequential',
['viridis', 'inferno', 'plasma', 'magma']),
('Sequential', ['Blues', 'BuGn', 'BuPu',
'GnBu', 'Greens', 'Greys', 'Oranges', 'OrRd',
'PuBu', 'PuBuGn', 'PuRd', 'Purples', 'RdPu',
'Reds', 'YlGn', 'YlGnBu', 'YlOrBr', 'YlOrRd']),
('Sequential (2)', ['afmhot', 'autumn', 'bone', 'cool',
'copper', 'gist_heat', 'gray', 'hot',
'pink', 'spring', 'summer', 'winter']),
('Diverging', ['BrBG', 'bwr', 'coolwarm', 'PiYG', 'PRGn', 'PuOr',
'RdBu', 'RdGy', 'RdYlBu', 'RdYlGn', 'Spectral',
'seismic']),
('Qualitative', ['Accent', 'Dark2', 'Paired', 'Pastel1',
'Pastel2', 'Set1', 'Set2', 'Set3']),
('Miscellaneous', ['gist_earth', 'terrain', 'ocean', 'gist_stern',
'brg', 'CMRmap', 'cubehelix',
'gnuplot', 'gnuplot2', 'gist_ncar',
'nipy_spectral', 'jet', 'rainbow',
'gist_rainbow', 'hsv', 'flag', 'prism'])]
