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Test.py
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Test.py
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from random import random
import matplotlib.pyplot as pl
import math
import numpy as np
import copy
from scipy import signal
import Mes_Fonctions_v2 as MesFonctions
# import Kernel_Estimation_v6 as MonImage
import opkpy_v3
# -----------------------------------------------------------------------------------
# Quelle image importe-t-on ?
# --> "essaie" pour une simple image 9x9
# --> nom de l'image sinon ("test", "chat", etc)
ImageImportee = "essaie"
# -----------------------------------------------------------------------------------
# -----------------------------------------------------------------------------------
# On importe une image
if ImageImportee == "essaie":
NbLigne, NbColonne, image_vraie, latent, kernel_vrai, kernel = MesFonctions.mon_image("create")
floue = MesFonctions.conv(image_vraie, kernel_vrai)
# else :
# NbLigne, NbColonne, image_vraie, kernel_vrai, floue, kernel, inutile = MonImage.Ouverture("ImageImportee")
# -----------------------------------------------------------------------------------
# -----------------------------------------------------------------------------------
# On declare certains parametres
size = NbLigne * NbColonne
regularization = "Tikhonov"
dt = 10
# On fait les conversions en vecteur
floue_v = floue.reshape(size)
kernel_v = kernel.reshape(size)
# On cree la matrice bruit
noise = np.asarray([np.around(random(), decimals=5) for i in range(size)])
C_noise = np.zeros((size, size))
for i in range(0, size):
C_noise[i, i] = noise[i] * noise[i]
C_noise_inv = np.linalg.inv(C_noise)
# -----------------------------------------------------------------------------------
# -----------------------------------------------------------------------------------
# La fonction que l'on souhaite optimiser
def phi(entry):
# Likelihood fonction
A = MesFonctions.matrice_A(entry[0:size].reshape((NbLigne, NbColonne)), methode="3")
x_ = (
floue.reshape(size) - MesFonctions.conv_matrices(A, entry[size:2 * size].reshape((NbLigne, NbColonne)),
"vecteur",
"coin"))
likelihood = np.dot(np.dot(x_, C_noise_inv), x_.transpose())
# Regularization term
image_ = entry[0:size] # /sum(sum(im))
PSF_ = entry[size:2 * size] # /sum(sum(PSF))
if regularization == "spectral":
fy_ = np.fft(image_)
y_ = 0
for i in range(0, size):
y_ = y_ + i * i * abs(fy_[i]) * abs(fy_[i])
regularization_im = y_
fz_ = np.fft(PSF_)
z_ = 0
for i in range(0, size):
z_ = z_ + i * i * abs(fz_[i]) * abs(fz_[i])
regularization_PSF = z_
elif regularization == "Tikhonov":
y_ = sum(image_ * image_)
regularization_im = math.sqrt(y_)
z_ = sum(PSF_ * PSF_)
regularization_PSF = math.sqrt(z_)
t_ = likelihood + regularization_im + regularization_PSF
return t_
# -----------------------------------------------------------------------------------
# -----------------------------------------------------------------------------------
# On cree le gradient, un vecteur de taille "NombreDeParametres
def grad(entry):
l = 0
Retour = np.zeros(2 * size)
phi_originel = phi(entry)
for i in range(0, 2 * size):
entry_dt = copy.deepcopy(entry)
entry_dt[i] = entry[i] + dt
Retour[i] = (phi(entry_dt) - phi_originel) / dt
l += 1
return Retour
# -----------------------------------------------------------------------------------
# -----------------------------------------------------------------------------------
# Calcul le gradient et retourne la valeur de la fonction au point x
def fg(x, gx):
legradient = grad(x)
gx[0:size] = legradient[0:size]
gx[size:2 * size] = legradient[size:2 * size]
return phi(x)
# -----------------------------------------------------------------------------------
########################## FONCTION DE DEFLOUTAGE D'IMAGE #########################
## On definit notre premier point x (ici l'image floue et un kernel quelconque)
# x = np.concatenate((floue_v, kernel_v), axis=0)
# g = np.concatenate((floue_v, kernel_v), axis=0)
# f = np.array([fg(x,g)], dtype="double")
#
## On execute la fonction de minimisation
# pl.matshow(x[0:size].reshape((NbLigne,NbColonne)),cmap=pl.cm.gray)
# pl.matshow(x[size:2*size].reshape((NbLigne,NbColonne)),cmap=pl.cm.gray)
# opkpy.opk_minimize(x, fg, g, algorithm="nlcg", linesearch="Armijo")
# pl.matshow(x[0:size].reshape((NbLigne,NbColonne)),cmap=pl.cm.gray)
# pl.matshow(x[size:2*size].reshape((NbLigne,NbColonne)),cmap=pl.cm.gray)
##################################################################################
############################ FONCTION DE ROSENBROCK ##############################
def Rosenbrock(x):
return (x[0] - 1) * (x[0] - 1) + 10 * (x[0] * x[0] - x[1] * x[1]) * (x[0] * x[0] - x[1] * x[1])
def fg_Rosen(x, gx):
gx[0] = 2 * (x[0] - 1) + 40 * x[0] * (x[0] * x[0] - x[1] * x[1])
gx[1] = -40 * x[1] * (x[0] * x[0] - x[1] * x[1])
return Rosenbrock(x)
x = np.array([-1.2, 1.0], dtype="float64")
g = np.array([12, 4], dtype="float64")
f = fg_Rosen(x, g)
#x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="nlcg", linesearch="nonmonotone",
# nlcg="FletcherReeves", limited=1, verbose=0)
#print"FletcherReeves :" + str(x_out) + "\n \n"
#x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="nlcg", linesearch="nonmonotone",
# nlcg="HestenesStiefel", limited=1, verbose=0)
#print"HestenesStiefel :" + str(x_out) + "\n \n"
#x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="nlcg", linesearch="nonmonotone",
# nlcg="PolakRibierePolyak", limited=1)
#print"PolakRibierePolyak :" + str(x_out) + "\n \n"
#x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="nlcg", linesearch="nonmonotone",
# nlcg="Fletcher", limited=1)
#print"Fletcher :" + str(x_out) + "\n \n"
#x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="nlcg", linesearch="nonmonotone",
# nlcg="LiuStorey", limited=1)
#print"LiuStorey :" + str(x_out) + "\n \n"
#x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="nlcg", linesearch="nonmonotone",
# nlcg="DaiYuan", limited=1)
#print"DaiYuan :" + str(x_out) + "\n \n"
#x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="nlcg", linesearch="nonmonotone",
# nlcg="PerryShanno", limited=1)
#print"PerryShanno :" + str(x_out) + "\n \n"
x_out = opkpy_v3.opk_minimize(x, fg_Rosen, g, algorithm="vmlmb", linesearch="nonmonotone",
nlcg="HagerZhang", limited=0)
print("HagerZhang :" + str(x_out) + "\n \n")
##############################################################################
################################# PARAMETRES #################################
# x, f, g
# bl, bu ---> only for vmlmb
###### algorithm
###### linesearch
# autostep
###### nlcg ---> only for nlcg
###### vmlmb ---> only for vmlmb
# delta, epsilon
# gatol, grtol
# maxiter, maxeval
# mem ---> only for vmlmb
# powell
# verbose
###### limited
##############################################################################
################################# RESULTATS ##################################
"""
--> NLCG
--> quadratic
--> FletcherReeves
--> nonlimited OK
--> limited OK
--> HestenesStiefel
--> nonlimited CONVERGE
--> limited CONVERGE
--> PolakRibierePolyak
--> nonlimited CONVERGE
--> limited CONVERGE
--> Fletcher
--> nonlimited OK
--> limited OK
--> LiuStorey
--> nonlimited CONVERGE
--> limited CONVERGE
--> DaiYuan
--> nonlimited CONVERGE
--> limited CONVERGE
--> PerryShanno
--> nonlimited CONVERGE
--> limited CONVERGE
--> HagerZhang
--> nonlimited CONVERGE
--> limited CONVERGE
--> Armijo
--> FletcherReeves
--> nonlimited OK
--> limited OK
--> HestenesStiefel
--> nonlimited OK
--> limited OK
--> PolakRibierePolyak
--> nonlimited CONVERGE
--> limited OK
--> Fletcher
--> nonlimited OK
--> limited OK
--> LiuStorey
--> nonlimited OK
--> limited OK
--> DaiYuan
--> nonlimited CONVERGE
--> limited CONVERGE
--> PerryShanno
--> nonlimited CONVERGE
--> limited CONVERGE
--> HagerZhang
--> nonlimited CONVERGE
--> limited CONVERGE
--> cubic
--> FletcherReeves
--> nonlimited CONVERGE
--> limited CONVERGE
--> HestenesStiefel
--> nonlimited CONVERGE
--> limited CONVERGE
--> PolakRibierePolyak
--> nonlimited CONVERGE
--> limited CONVERGE
--> Fletcher
--> nonlimited CONVERGE
--> limited CONVERGE
--> LiuStorey
--> nonlimited CONVERGE
--> limited CONVERGE
--> DaiYuan
--> nonlimited CONVERGE
--> limited CONVERGE
--> PerryShanno
--> nonlimited CONVERGE
--> limited CONVERGE
--> HagerZhang
--> nonlimited CONVERGE
--> limited CONVERGE
--> nonmonotone
--> FletcherReeves
--> nonlimited CONVERGE
--> limited CONVERGE
--> HestenesStiefel
--> nonlimited OK
--> limited CONVERGE
--> PolakRibierePolyak
--> nonlimited OK
--> limited OK
--> Fletcher
--> nonlimited CONVERGE
--> limited CONVERGE
--> LiuStorey
--> nonlimited OK
--> limited OK
--> DaiYuan
--> nonlimited CONVERGE
--> limited CONVERGE
--> PerryShanno
--> nonlimited CONVERGE
--> limited CONVERGE
--> HagerZhang
--> nonlimited CONVERGE
--> limited CONVERGE
"""
##############################################################################