5.4 统计分析函数¶
Markdown by 张涛涛
1. 均值和百分位数¶
导入模块，生成数据。
In [30]:
import numpy as np
import matplotlib.pyplot as plt
if __name__=='__main__':
np.random.seed(3)
time = np.arange(30)
y = np.random.rand(30)*10-5+0.3*time
计算平均数和百分位数。
In [31]:
dat = [y,
np.mean(y,axis=0), ## 计算平均数。第一个参数为要计算的数据；axis参数指对哪个维度求值。
np.median(y,axis=0), ## 计算中位数。用法同上。
np.percentile(y,90,axis=0), ##计算百分位数。用法同上，但第二个参数为要计算的百分位数。
np.percentile(y,10,axis=0)]
print(dat[1:5])
[3.8050986699512066, 4.343131393906942, 7.704979080599599, -1.5119811389049338]
2. 方差和标准差¶
In [32]:
var = np.var(y,axis=0) ## 计算方差。用法与np.mean()一致；
std = np.std(y,axis=0) ## 计算标准差，用法同上
print(var,std**2)
13.175594239681516 13.175594239681518
将以上数据的计算结果绘图。
In [33]:
color = ['k','k','grey','gray','gray']
line = ['-','--',':','--','--']
wd = [3,1,1,1,1]
label=['Data','Mean','Median','90th','10th']
marker = ['','.','*','^','v']
xf = [0,30,30,0,0]
yf = [-1*std,-1*std,std,std,-1*std]
yf = np.array(yf)+np.mean(y)
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(2,1,1)
L = []
for i,x in enumerate(dat):
if i>0:
x = np.tile(x,(len(time),))
tmpl, = ax.plot(time,x,
color=color[i],label=label[i],
marker=marker[i],markevery=5,
linestyle=line[i],linewidth=wd[i])
L.append(tmpl)
ax.fill(xf,yf, facecolor='lightgrey')
ax.legend(handles=L,ncol=3,loc='upper left',
frameon=False)
Out[33]:
<matplotlib.legend.Legend at 0x228641a2560>
3. 协方差和相关系数¶
In [34]:
cov = np.cov(y,time) ## 协方差
print(cov)
r = np.corrcoef(y,time) ## 相关系数
print(r)
[[13.62992508 22.98957124] [22.98957124 77.5 ]] [[1. 0.70734825] [0.70734825 1. ]]
4. 线性回归和趋势¶
Numpy库提供的np.linalg.lstsq()函数可以用来作一元和多元线性回归。
In [36]:
import numpy as np
import matplotlib.pyplot as plt
if __name__=='__main__':
np.random.seed(3)
time = np.arange(30)
y = np.random.rand(30)*10-5+0.3*time ##生成带趋势的随机数据
x0 = np.ones(len(time))
x1 = time
x2 = np.sin(4*2*time/30*np.pi)
X = np.vstack([x0,x1,x2]).T
b,*res = np.linalg.lstsq(X,y,rcond=None)
print(X.shape,b.shape)
yh = np.dot(X,b)
(30, 3) (3,)
对原始数据和回归结果绘图。
In [41]:
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(3,1,1)
ax.plot(y,color='k',label='Data',
linewidth=3,linestyle='-')
ax.plot(yh,color='gray',label='Regression',
linewidth=3,linestyle='--')
ax.legend(loc='lower right')
ax.text(-0.5,10,'(a)',fontsize=11)
Out[41]:
Text(-0.5, 10, '(a)')
np.linalg.lstsq()函数做一元线性回归则得到线性趋势。此外，np.polyfit()和np.polyval()函数也可快速得到线性趋势。
In [44]:
X = np.vstack([x0,x1]).T
b,*res = np.linalg.lstsq(X,y,rcond=None)
yh1 = np.dot(X,b)
pf = np.polyfit(time,y,1)
yt = np.polyval(pf,time)
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(3,1,2)
ax.plot(y,color='k',label='Data',
linewidth=3,linestyle='-')
ax.plot(yh1,color='gray',label='Trend',
linewidth=3,linestyle='--')
ax.legend(loc='lower right')
ax.text(-0.5,10,'(b)',fontsize=11)
Out[44]:
Text(-0.5, 10, '(b)')
In [47]:
fig = plt.figure(figsize=(8,6))
for i,x in enumerate([[y,yh],
[y,yh1],
[yh1,yt]]):
ax = fig.add_subplot(3,3,7+i)
ax.scatter(x[0],x[1],20,marker='o',
edgecolor='k',facecolor='none')
ax.plot([-5,12],[-5,12],'--k',
linewidth=0.5)
ax.set_xlim([-5,12])
ax.set_ylim([-5,12])
ax.text(-4,9,'('+chr(ord('c')+i)+')',
fontsize=11)
上图从左至右分别为：“原始数据与回归量”，“原始数据与趋势”，“线性回归与拟合”的数据结果。表明使用回归函数和拟合函数的结果是一致的。
通常在对气象数据进行处理时需要做“去趋势”，将原始数据y减去yt即可，也可使用scipy.signal.detrend()函数。
5. 显著性检验¶
对统计分析结果进行物理意义解释前，需要先进行显著性检验。气象上一般用Student's t检验。也可以构建随机分布检验，需要用到Scipy.stats模块。
In [52]:
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
def ttest(dat,mu):
m = np.mean(dat)
t = (m-mu)/np.std(dat)*np.sqrt(len(dat))
p = stats.t(len(dat)-1).cdf(t)
ta = stats.t(len(dat)-1).ppf(0.975)
print(t,ta,p)
return t,p,ta
if __name__=='__main__':
np.random.seed(3)
time = np.arange(30)
dat = np.random.rand(30)*10-5+0.3*time
t,p,ta = ttest(dat,0)
x = np.linspace(-10,10,501)
y = stats.t(len(x)-1).pdf(x)
fig = plt.figure(figsize=(11,8.5))
for i,mu in enumerate([2,3]):
t,p,ta = ttest(dat,mu)
ax = fig.add_subplot(2,2,i+1)
ax.plot(x,y,'-k')
msk = x>=ta
pa = stats.t(len(y)-1).pdf(ta)
ax.fill(np.hstack((ta,ta,x[msk])),
np.hstack(( 0,pa,y[msk])),
color='lightgray')
ax.plot([t,t],[0,0.5],':k',linewidth=1)
ax.set_ylim([0,0.5])
ax.set_xlim([-5,5])
ax.text(-4.5,0.45,'('+chr(ord('a')+i)+')',
fontsize=20)
plt.show()
5.741712524032624 2.045229642132703 0.9999983788365278 2.723807853452162 2.045229642132703 0.9945923325554527 1.2148555181619316 2.045229642132703 0.882889779282764
对相关系数做t检验
In [50]:
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
def ttest(r,n):
t = r/np.sqrt(1-r**2)*np.sqrt(n-2)
p = stats.t(n-2).cdf(t)
ta = stats.t(n-2).ppf(0.975)
return t,p,ta
if __name__=='__main__':
np.random.seed(3)
time = np.arange(30)
dat = np.random.rand(30)*10-5+0.3*time
x2 = np.sin(4*2*time/30*np.pi)
for x in [time,x2]:
r = np.corrcoef(dat,x)[0,1]
t,p,ta = ttest(r,30)
print('r=','%6.3f' %(r),
't=','%6.3f' %(t),
'p=','%6.3f' %(p),
'ta=','%6.3f' %(ta))
r= 0.707 t= 5.295 p= 1.000 ta= 2.048 r= -0.259 t= -1.420 p= 0.083 ta= 2.048
当不知道相关系数的t分布公式，可以使用随机分布进行显著性检验
Monte Carlo检验
In [51]:
R = []
for i in range(10000):
x = np.random.rand(30)
tmp = np.corrcoef(dat,x)[0,1]
R.append(tmp)
R = np.array(R)
for r in [0.707,-0.259]:
msk = R>=np.abs(r)
p = np.sum(msk)/len(msk)
print('r=','%6.3f' %(r),
'p=','%6.3f' %(p))
r= 0.707 p= 0.000 r= -0.259 p= 0.085
6. 谱分析和滤波¶
6.1 谱分析 ——在气象上常用来提取数据的周期特征。
In [53]:
import numpy as np
from scipy.signal import detrend
import matplotlib.pyplot as plt
def specx_anal(dat,smooth=0): ##子函数输入参数为一维序列dat和滑动平均窗口长度
dat = detrend(dat) ## 对数据做去趋势
frq = np.fft.fftfreq(len(dat)) ## 计算频率
p = np.fft.fft(dat) ## 快速傅里叶变换，得到谱结果
p = np.abs(p)**2 ##p.real**2+p.imag**2
n = len(p)
if smooth:
wgt = np.ones(smooth)
wgt[[0,-1]] = 0.5
p0 = p.copy()
half = smooth//2
for i in range(half,n-half):
p0[i]=np.average(
p[i-half:i+half+1],
weights=wgt)
p = p0
df = frq.copy()
df[1:] = frq[1:]-frq[:-1]
df[0] = df[1]
p = p*df*2
return frq,p
if __name__=='__main__':
## 生成随机数据
np.random.seed(3)
n = 128
time = np.arange(n)
dat = np.random.rand(n)*10-5+0.3*time
x1 = np.sin(12*2*time/n*np.pi)
x2 = np.sin( 4*2*time/n*np.pi)
dat = dat+5*x2+3*x1
## 调用谱分析
frq, p = specx_anal(dat,smooth=3)
msk = frq>0
frq = frq[msk]
p = p[msk]
fig = plt.figure(figsize=(11,8.5))
ax = fig.add_subplot(2,1,1)
ax.plot(time,dat)
ax = fig.add_subplot(2,1,2)
ax.plot(1/frq,p,'-k',linewidth=2)
for k in [4,12]:
ax.plot([n/k,n/k],[0,1500],
linestyle='--',
color='gray',linewidth=1)
ax.set_xlim([0,128])
ax.set_ylim([0,1500])
ax.text(2,1300,'(b)',fontsize=20)
plt.show()
也可使用Scipy.signal.periodogram()函数进行谱分析
In [55]:
import numpy as np
from scipy.signal import periodogram,detrend
from scipy import stats
import matplotlib.pyplot as plt
def specx_ci(dat,smooth=0,a=0.05):
frq, p=periodogram(dat,fs=1,
detrend='linear',
scaling='density')
n = len(p)
df = 2
if smooth:
wgt = np.ones(smooth)
wgt[[0,-1]] = 0.5
wgt = wgt/np.sum(wgt)
wgtsq = np.sum(wgt**2)
df = df/wgtsq
p0 = p.copy()
half = smooth//2
for i in range(half,n-half):
p0[i]=np.average(p[i-half:i+half+1],
weights=wgt)
p = p0
dat = detrend(dat)
phi = np.corrcoef(dat[1:],dat[:-1])[0,1]
n = len(dat)
mkov = 1./(1+phi**2-2*phi*np.cos(2*np.pi*frq))
S = np.sum(p)/np.sum(mkov)*mkov
Sa = S/df*stats.chi2(df).ppf(1-a)
return frq,p,Sa
if __name__=='__main__':
np.random.seed(3)
n = 128
time = np.arange(n)
dat = np.random.rand(n)*10-5+0.3*time
x1 = np.sin(12*2*time/n*np.pi)
x2 = np.sin( 4*2*time/n*np.pi)
dat = dat+5*x2+3*x1
frq, p, Sa = specx_ci(dat,smooth=3, a=0.05)
fig = plt.figure(figsize=(11,8.5))
ax = fig.add_subplot(2,2,1)
ax.plot(1/frq,p,'-k',linewidth=2)
ax.plot(1/frq,Sa,'-r',linewidth=2)
ax.set_xlim([0,128])
ax.set_ylim([0,800])
plt.show()
C:\Users\ttzhang\AppData\Local\Temp\ipykernel_14472\750116768.py:41: RuntimeWarning: divide by zero encountered in divide ax.plot(1/frq,p,'-k',linewidth=2) C:\Users\ttzhang\AppData\Local\Temp\ipykernel_14472\750116768.py:42: RuntimeWarning: divide by zero encountered in divide ax.plot(1/frq,Sa,'-r',linewidth=2)
6.2 滤波
a) Scipy.signal.savgol_filter()函数
In [63]:
from scipy import signal
import numpy as np
import matplotlib.pyplot as plt
if __name__=='__main__':
## 生成数据
np.random.seed(3)
n = 128
time = np.arange(n)
dat = np.random.rand(n)*10-5+0.3*time
x1 = np.sin(12*2*time/n*np.pi)
x2 = np.sin( 4*2*time/n*np.pi)
dat = dat+5*x2+3*x1
dat = signal.detrend(dat)
## 平滑 ——savgol_filter()函数第一个参数为数据，参数2表示几点平滑，
## 参数3表示平滑阶数，参数mode为边界处理方式。
dats = signal.savgol_filter(dat,5,1, mode='mirror')
##绘图
fig = plt.figure(figsize=(11,8.5))
ax = fig.add_subplot(3,1,1)
ax.plot(time,dat,linestyle='--',color='gray',linewidth=2)
ax.plot(time,dats,color='k',linewidth=3)
b) Butterworth滤波器
In [66]:
##构造滤波器
##参数1为滤波阶数，常用3，数越大滤波效果越强
##参数2为Nyquist频率，常用半周期的倒数表示
##参数3为滤波方式，有low,high,band
sos = signal.butter(3, 2/20, btype='low', output='sos')
##使用sosfiltfilt函数进行滤波
datf = signal.sosfiltfilt(sos,dat,axis=-1)
fig = plt.figure(figsize=(11,8.5))
ax = fig.add_subplot(3,1,2)
ax.plot(time,dat,linestyle='--',color='gray',linewidth=2)
ax.plot(time,datf,color='k', linewidth=3)
## 带通滤波
sos = signal.butter(3,[2/60,2/10],btype='band',output='sos')
datf = signal.sosfiltfilt(sos,dat,axis=-1)
ax = fig.add_subplot(3,1,3)
dat = signal.detrend(dat)
ax.plot(time,dat,linestyle='--', color='gray',linewidth=2)
ax.plot(time,datf,color='k', linewidth=3)
plt.show()
7. EOF分解¶
EOF常用来提取气象要素的时空变化特征，其核心思想就是求解矩阵的特征值和特征向量。
In [71]:
import numpy as np
import xarray as xr
from scipy.stats import binned_statistic_2d
import matplotlib.pyplot as plt
## 生成数据的子函数
def crdat():
lon = np.arange(0,360,2.5)
lat = np.arange(-90,91,2.5)
x,y = np.meshgrid(lon,lat)
m, n = (1,2)
A = 100*np.sin(n*y/180*np.pi)**2
dat = []
for i in range(100):
tmp = A*np.sin(m*x/180*np.pi-2*np.pi*i/100)
dat.append(tmp)
dat = xr.DataArray(dat,dims=('time','lat','lon'),
coords={'time':np.arange(100),
'lat':lat,
'lon':lon})
return dat
## 计算EOF的子函数
def caleof(dat):
m = dat.shape
dat = dat - np.tile(np.mean(dat,0),(m[0],1,1)) ##求距平场
X = dat.reshape(m[0],-1) ##将三维数据转成“时间×格点”的二维形状
print(X.shape)
A = np.dot(X,X.T) ##得到“时间×时间”形状的A矩阵
lmd, u = np.linalg.eigh(A) ##计算A矩阵的特征值和特征向量
lmd = lmd[::-1] ## 把上述结果从大到小排列
u = u[:,::-1]
V = np.dot(X.T,u)
V = V/np.tile(np.sqrt(np.abs(lmd)),
(X.shape[1],1))
Z = np.dot(X,V) ## 求时间系数
V = V*np.tile(np.std(Z,0),(X.shape[1],1))##特征向量
Z = Z/np.tile(np.std(Z,0),(m[0],1))
V = V.reshape(m[1],m[2],-1)
ro = lmd/np.sum(lmd) ##计算解释方差
return ro,V,Z
if __name__=='__main__':
dat = crdat()
dat = dat.loc[:,10:80,100:280]
ro,V,Z = caleof(dat.to_numpy())
levels = list(range(-100,100,20))
levels.remove(0)
fig = plt.figure(figsize=(11,8.5))
for i in range(2):
ax = fig.add_subplot(2,2,i+1)
c = ax.contour(dat['lon'],dat['lat'],
V[:,:,i],levels=levels,
colors='k')
ax.text(105,15,
'('+chr(ord('a')+i)+') '+ \
'EOF'+str(i+1)+' '+ \
'%6.2f' %(ro[i]*100)+'%',
backgroundcolor='w',
fontsize=15)
ax.clabel(c)
ax = fig.add_subplot(4,2,i+5)
ax.plot(Z[:,i],'-k')
ax.text(-0.5,1,
'('+chr(ord('c')+i)+') '+ \
'PC'+str(i+1),
fontsize=15)
plt.show()
(100, 2117)
8. SVD分解¶
SVD分解用于探讨两个气象要素场之间的联系。
In [72]:
import numpy as np
import xarray as xr
from scipy.stats import binned_statistic_2d
import matplotlib.pyplot as plt
def crdat():
lon = np.arange(0,360,2.5)
lat = np.arange(-90,91,2.5)
x,y = np.meshgrid(lon,lat)
m, n = (1,2)
A = 100*np.sin(n*y/180*np.pi)**2
B = 150*np.cos(n*y/180*np.pi)**2
dat = []
for i in range(100):
tmp = A*np.sin(m*x/180*np.pi-2*np.pi*i/100)+ \
B*np.sin(np.random.sample(x.shape)*np.pi)
dat.append(tmp)
dat = xr.DataArray(dat,dims=('time','lat','lon'),
coords={'time':np.arange(100),
'lat':lat,
'lon':lon})
return dat
## 计算非齐次场
def calcor(dat,T):
m = dat.shape
T = np.tile(T,(m[1],1)).T
fnc = lambda x: (x -
np.tile(np.mean(x,0),(x.shape[0],1)))/ \
np.tile(np.std(x,0) ,(x.shape[0],1))
dat = fnc(dat)
T = fnc(T)
r = np.mean(dat*T,0)
return r
## 计算 SVD
def calsvd(dat0,dat1):
m = dat0.shape
n = dat1.shape
X = dat0.reshape(m[0],-1)
Y = dat1.reshape(n[0],-1)
A = np.dot(X.T,Y)
u,s,v = np.linalg.svd(A,full_matrices=False) ##计算SVD
Tu = np.dot(X,u) ## 左场时间序列
Tv = np.dot(Y,v.T) ## 右场时间序列
ro = s/np.sum(s) ## 各模态解释率
rlft = calcor(X,Tv[:,0])
rrgt = calcor(Y,Tu[:,0])
rlft = rlft.reshape(m[1],m[2])
rrgt = rrgt.reshape(m[1],m[2])
r = np.corrcoef(Tv[:,0],Tu[:,0])[0,1]
return r,ro,rlft,rrgt
def smth9(dat):
tmp = dat.copy()
tmp[1:-1,1:-1] = dat[1:-1,1:-1]*1.0+ \
dat[:-2,1:-1]*0.5+dat[2:,1:-1]*0.5+ \
dat[1:-1,:-2]*0.5+dat[1:-1,2:]*0.5+ \
dat[ :-2,:-2]*0.3+dat[2:, 2:]*0.3+ \
dat[2:, :-2]*0.3+dat[ :-2,2:]*0.3
tmp[1:-1,1:-1] = tmp[1:-1,1:-1]/(1+0.5*4+0.3*4)
return tmp
if __name__=='__main__':
dat = crdat()
dat0 = dat.loc[:,10:80,100:280]
dat1 = dat.loc[:,-80:-10,0:180]
r,ro,rlft, rrgt = calsvd(dat0.to_numpy(),
dat1.to_numpy())
print(r,ro[0])
fig = plt.figure(figsize=(11,8.5))
levels = list(np.arange(-1,1,0.2))
rlft = smth9(rlft)
rrgt = smth9(rrgt)
ax = fig.add_subplot(2,2,1)
c = ax.contour(dat0['lon'],dat0['lat'],rlft,
levels=levels,colors='k')
ax.clabel(c,colors='gray')
ax = fig.add_subplot(2,2,2)
c = ax.contour(dat1['lon'],dat1['lat'],rrgt,
levels=levels,colors='k')
ax.clabel(c,colors='gray')
plt.show()
0.7504128176668776 0.46596437957082554
9. 聚类分析¶
聚类分析是气象上常用的统计方法之一，用于将具有相同特性的数值聚在一起，特别是在进行天气/气候的分型时使用非常方便，本小节仅介绍目前最常用的方法之一，K-means方法的使用。该方法仅需确定聚类的k值，即类别的个数。
In [3]:
import matplotlib.pyplot as plt
import numpy as np
from sklearn.cluster import KMeans
def crdat():
x0 = np.arange(100)*360/100
y0 = np.arange(100)*360/100
x, y = np.meshgrid(x0,y0)
V = []
for i in range(2):
for j in range(2):
c = np.sin(0.5*(j+1)*x/180*np.pi)* \
np.sin(0.5*(i+1)*y/180*np.pi)
c = c/np.sqrt(np.sum(c**2))
V.append(c.flatten())
n = 250
X = []
for i in range(4):
theta = np.random.rand(n)*2*np.pi
z = 100*np.sin(theta)
z = z.reshape(-1,1)
v = V[i].reshape(1,-1)
X.append(np.dot(z,v))
X = np.array(X)
X = X.reshape(-1,len(y0),len(x0))
I = np.arange(X.shape[0])
np.random.shuffle(I)
X = X[I]
V = np.reshape(V,(4,len(y0),len(x0)))
return x,y,X,V
In [10]:
x,y,X,V = crdat()
fig = plt.figure(figsize=(11,8.5))
for i in range(4):
ax = fig.add_subplot(2,2,i+1)
h = ax.contourf(x,y,V[i],levels=np.linspace(-0.02,0.02,11),
cmap='bwr')
cax = fig.add_axes([0.1,0.05,0.8,0.02])
plt.colorbar(h,cax=cax,orientation='horizontal')
plt.show()
In [11]:
F = X.reshape(X.shape[0],-1)
print(F.shape)
(1000, 10000)
In [14]:
model = KMeans(n_clusters=8,init='k-means++')
kmeans = model.fit(F)
lb = kmeans.labels_
print(lb)
[2 4 2 5 4 1 1 3 4 0 6 1 1 1 6 4 1 1 5 4 1 4 1 1 6 1 7 1 3 4 7 1 2 1 1 7 3 0 4 5 5 1 1 1 6 6 2 4 2 1 1 6 2 6 1 5 1 6 7 0 1 2 1 0 2 7 3 0 5 1 7 3 2 1 0 5 5 3 1 1 5 5 3 1 1 0 3 7 2 1 1 1 3 1 2 3 2 5 4 6 1 6 5 4 5 1 3 1 1 7 0 0 2 1 5 3 7 0 1 7 1 0 1 2 1 7 6 4 1 0 6 1 4 2 1 1 5 5 7 0 0 5 0 0 7 1 3 1 0 1 2 1 1 4 0 1 2 7 0 1 3 2 1 2 0 0 1 4 7 0 7 4 1 0 2 5 5 1 3 0 6 1 2 4 3 5 1 5 6 1 7 0 5 1 1 7 1 1 6 1 6 7 2 4 2 7 3 3 1 3 4 0 2 7 1 0 3 2 1 1 7 3 2 7 0 4 5 1 3 4 0 5 1 7 5 0 0 3 1 2 3 6 1 1 3 1 0 0 0 1 4 5 3 7 4 4 2 5 4 0 4 1 7 6 1 6 0 4 0 7 1 4 1 1 1 0 0 4 3 3 3 0 1 6 0 1 5 4 1 0 6 4 7 5 1 1 3 5 1 7 7 6 7 1 0 5 7 2 1 0 7 1 1 7 1 3 6 6 1 1 3 4 1 1 3 2 1 3 7 3 2 0 5 5 2 2 2 1 2 5 0 2 4 5 1 4 1 6 0 1 7 1 6 4 5 1 4 1 7 6 4 1 1 1 2 3 0 1 0 7 5 1 1 6 1 6 1 4 1 4 3 1 3 1 1 6 3 6 1 1 1 1 6 1 4 6 1 0 3 2 1 6 4 2 1 1 7 7 3 6 4 2 1 1 3 6 1 1 2 0 7 0 5 1 7 1 0 0 3 2 1 7 6 5 7 1 1 6 7 2 4 1 2 4 1 6 1 5 6 1 0 5 0 1 4 3 6 6 0 1 2 4 1 2 1 6 1 4 2 6 4 1 1 5 1 1 5 2 1 5 5 4 3 2 1 1 3 2 1 4 1 1 1 4 2 1 1 2 1 1 1 7 5 1 0 2 5 6 3 4 4 0 2 4 5 2 1 4 4 7 1 0 1 1 4 0 3 5 0 6 4 0 1 7 0 7 0 3 1 4 2 1 7 1 3 1 3 1 2 5 7 7 6 1 5 1 3 5 6 1 7 4 1 6 1 2 0 5 1 1 1 4 2 1 1 5 6 7 1 5 6 6 1 4 7 5 1 0 7 2 1 0 6 2 7 4 1 5 3 0 4 5 0 0 3 4 4 2 1 7 6 1 1 1 2 1 1 3 1 0 2 4 0 1 3 4 6 5 1 4 4 7 5 0 5 7 1 2 6 1 1 5 1 1 7 0 7 1 1 1 5 5 1 2 1 5 3 1 1 3 1 2 0 1 7 1 0 1 7 2 1 5 5 5 1 5 5 6 7 4 2 1 7 1 2 6 0 1 7 2 3 1 1 4 3 2 6 4 7 4 1 1 0 1 3 2 6 1 0 4 3 0 5 2 6 1 1 6 7 6 1 3 4 7 1 2 4 1 1 4 6 4 7 2 7 1 1 7 5 2 6 6 4 2 1 1 6 4 1 5 5 6 6 1 3 1 7 6 4 2 3 7 4 1 1 3 4 7 6 2 1 5 3 6 1 5 0 2 1 0 1 7 1 1 4 1 4 3 2 5 3 1 1 6 1 5 1 5 3 2 3 6 1 1 5 1 5 2 1 1 1 6 1 5 7 6 1 2 0 7 6 1 1 1 7 1 2 5 7 7 3 3 1 1 7 1 1 0 1 2 2 6 1 2 1 7 0 1 0 1 1 1 5 1 0 4 7 1 7 1 0 1 7 5 2 4 4 1 1 3 1 1 2 1 1 2 1 6 5 0 5 5 1 2 1 5 7 7 3 1 0 3 4 5 2 1 2 6 1 2 3 1 3 1 1 1 3 6 5 2 3 7 0 1 1 4 4 1 1 1 1 6 4 1 5 5 5 7 1 1 0 1 6 7 1 1 5 5 1 6 5 2 7 0 2 0 1 7 2 2 2 2 1 3 7 1 1 2 0 4 5 3 1 1 0 0 7 4 5 6 1 0 3 5 1 1 7 1 1 1 0 4 2 7 7 3 0 6 1 5 1 6 4 1 2 6 1 3 7 0]
C:\ProgramData\Anaconda3\envs\mete\Lib\site-packages\sklearn\cluster\_kmeans.py:1429: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=4. warnings.warn(
In [19]:
fig = plt.figure(figsize=(11,8.5))
for i in range(8):
msk = lb==i
ax = fig.add_subplot(3,3,i+1)
h = ax.contourf(x,y,np.mean(X[msk],0),levels=np.linspace(-2,2,21),
extend='both',cmap='bwr')
cax = fig.add_axes([0.1,0.05,0.8,0.02])
plt.colorbar(h,cax=cax,orientation='horizontal')
plt.show()
