Commit bc09d956 authored by Pierre-antoine Comby's avatar Pierre-antoine Comby

un llyod max qui marche

parent 8cae2bbf
Pipeline #1195 passed with stage
in 3 minutes and 14 seconds
#!/usr/bin/env python3
import numpy as np
from sipy import integrate
from scipy import norm
M = 8
X = np.random.normal(0,1,1000)
from scipy import integrate
from scipy.stats import norm
import matplotlib.pyplot as plt
def ddp(x):
mean = 0,
sigma = 1
return norm.pdf(x,mean,sigma)
def init_thres_vec(M,X):
step = (np.max(X)-np.min(X))/M
thres_intervals = np.array([])
mid = np.mean(X)
for i in range(int(M/2)):
thres_intervals = np.append(thres_vec,mid+(i+1)*step)
thres_intervals = np.insert(thtres_vec,0,mid-(1+1)*step)
return thres_intervals
def quant(x,thres,intervals):
thres= np.append(thres, np.inf)
thres= np.insert(thres, 0, -np.inf)
x_hat_q = np.zeros(np.shape(x))
for i in range(len(thres)-1):
if i == 0:
x_hat_q = np.where(np.logical_and(x > thres[i], x <= thres[i+1]),
np.full(np.size(x_hat_q), intervals[i]), x_hat_q)
elif i == range(len(thres))[-1]-1:
x_hat_q = np.where(np.logical_and(x > thres[i], x <= thres[i+1]),
np.full(np.size(x_hat_q), intervals[i]), x_hat_q)
else:
x_hat_q = np.where(np.logical_and(x > thres[i], x < thres[i+1]),
np.full(np.size(x_hat_q), intervals[i]), x_hat_q)
return x_hat_q
def quant(centroids, X):
bornes = (centroids[:-1]+centroids[1:])/2
bornes = np.insert(bornes,0,-np.inf)
bornes = np.append(bornes,np.inf)
xquant =np.zeros(len(X))
for k in range(len(X)):
for i in range(len(bornes)):
if X[k]>=bornes[i] and X[k] <bornes[i+1]:
xquant[k] = centroids[i]
return xquant
def llyodMax(X,M,maxiter=1000,eps=1e-6):
#répartition uniforme des bornes
step = (np.max(X)-np.min(X))/(M-2)
Xmin = np.min(X)
bornes = np.array([i*step+Xmin for i in range(M-1)])
bornes = np.insert(bornes,0,-np.inf)
bornes = np.append(bornes,np.inf)
centroids = np.zeros(M)
for it in range(maxiter):
old_centroids = centroids.copy()
for i in range(M):
centroids[i] = integrate.quad(lambda x: x*ddp(x),bornes[i],bornes[i+1])[0]\
/integrate.quad(lambda x: ddp(x),bornes[i],bornes[i+1])[0]
bornes[1:-1] = (centroids[:-1]+centroids[1:])/2
err = np.linalg.norm(centroids-old_centroids)
print(err)
if err < eps :
break
return centroids
M = 4
X = np.random.normal(0,1,1000)
centroids = llyodMax(X,M)
bornes = (centroids[:-1]+centroids[1:])/2
bornes = np.insert(bornes,0,-np.inf)
bornes = np.append(bornes,np.inf)
def LlyodMax(X,intervals, max_iter=1000,eps=1e-5):
err_min = np.inf
for i in range(max_iter):
for j in range(len(x_hat_q)):
centroids[i] = integrate.quad(lambda x : x*ddp(x),
intervals[j],intervals[j+1])[0]/
integrate.quad(lambda x : ddp(x),
intervals[j],intervals[j+1])[0]
intervals = 0.5*(centroids[1:]+centroids[:-1])
x_hat = quant(X,centroids,intervals)
err = np.linalg.norm(X-x_hat)
if err < err_min:
err_min =err
intervals_min = intervals
centroids_min = centroids
if err_min< 1e-5:
break
best_x_hat = quant(X,centroids_min,intervals_min)
return best_x_hat
print(centroids, bornes)
plt.figure()
plt.plot(X)
plt.plot(quant(bornes,X))
plt.show()
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