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CrankNicolson.py
138 lines (100 loc) · 4.73 KB
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CrankNicolson.py
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import numpy as np
import config
import healpy as hp
import matplotlib.pyplot as plt
import gradientDescent
import utils
def compute_log_likelihood(x_pix, observations):
return -(1/2)*np.sum(((observations - x_pix)**2)*(1/config.noise_covar))
def compute_CN_ratio(x_pix, y_pix, observations):
return compute_log_likelihood(y_pix, observations) - compute_log_likelihood(x_pix, observations)
def crankNicolson(cls_, observations):
accept = 0
history = []
s = hp.synalm(cls_, lmax=config.L_MAX_SCALARS)
#h, s = gradientDescent.gradient_ascent(observations, cls_)
s_pixel = hp.sphtfunc.alm2map(s, nside=config.NSIDE)
for i in range(config.N_CN):
history.append(s)
prop = np.sqrt(1-config.beta_CN**2)*s + config.beta_CN*hp.sphtfunc.synalm(cls_, lmax=config.L_MAX_SCALARS)
prop_pix = hp.sphtfunc.alm2map(prop, nside=config.NSIDE)
r = compute_CN_ratio(s_pixel, prop_pix, observations)
if np.log(np.random.uniform()) < r:
s = prop
s_pixel = prop_pix
accept += 1
print(accept/config.N_CN)
return history, s
#### Second
def flatten_map(s):
s_real = s.real[[i for i in range(len(s)) if i != 0 and i != 1 and i != (config.L_MAX_SCALARS+1)]]
s_imag = s.imag[[i for i in range((config.L_MAX_SCALARS+2),len(s))]]
s_flatten = np.concatenate((s_real, s_imag))
return s_flatten
def unflat_map_to_pix(s):
real_part = np.concatenate((np.zeros(2), s[:(config.L_MAX_SCALARS-1)] , np.zeros(1),
s[(config.L_MAX_SCALARS-1):(config.dimension_sph-3)]))
imag_part = np.concatenate((np.zeros(config.L_MAX_SCALARS+2), s[(config.dimension_sph-3):]))
return real_part + 1j*imag_part
def extend_cls(cls):
extended_cls = [cl for l in range(config.L_MAX_SCALARS+1) for cl in cls[l:]]
extended_cls_real = (extended_cls[:(config.L_MAX_SCALARS+1)] + extended_cls[(config.L_MAX_SCALARS+2):])[2:]
extended_cls_imag = extended_cls[(config.L_MAX_SCALARS+2):]
extended_cls = extended_cls_real + extended_cls_imag
return np.array(extended_cls)
def compute_log_likelihood2(s_pix, d):
return -(1/2)*np.sum(((d-s_pix)**2)/config.noise_covar)
def compute_CN_ratio2(s_pix, s_pix_prop, d):
return compute_log_likelihood2(s_pix_prop, d) - compute_log_likelihood2(s_pix, d)
def crankNicolson2(cls_, d):
#s = hp.synalm(cls_, lmax=config.L_MAX_SCALARS)
h, s = gradientDescent.gradient_ascent(d, cls_)
s_pix = hp.sphtfunc.alm2map(s, nside=config.NSIDE)
s = flatten_map(s)
accepted = 0
history = []
for i in range(config.N_CN):
history.append(s)
s_prop = np.sqrt(1 - config.beta_CN**2)*s +config.beta_CN*flatten_map(hp.synalm(cls_, lmax=config.L_MAX_SCALARS))
s_prop_pix = hp.alm2map(unflat_map_to_pix(s_prop), nside=config.NSIDE)
r = compute_CN_ratio2(s_pix, s_prop_pix, d)
if np.log(np.random.uniform()) < r:
s = s_prop
s_pix = s_prop_pix
accepted += 1
print(accepted/config.N_CN)
return history, s
#### Good one
def compute_log_likelihood_good(s_pix, d):
return -(1/2)*np.sum(((d-s_pix)**2)/config.noise_covar)
#def compute_log_likelihood_good(s, s_pix, d):
# return (-1/2)*(np.dot(d.T, (1/config.noise_covar)*d)
# - np.dot(s.T, utils.flatten_map(hp.map2alm((1/config.noise_covar)*d, lmax=config.L_MAX_SCALARS)))
# - np.dot(d.T, (1/config.noise_covar)*s_pix)
# + np.dot(s.T, utils.flatten_map(hp.map2alm((1/config.noise_covar)*s_pix, lmax=config.L_MAX_SCALARS))))
def compute_CN_ratio_good(s_pix, s_pix_prop, d):
return compute_log_likelihood_good(s_pix_prop, d) - compute_log_likelihood_good(s_pix, d)
#def compute_CN_ratio_good(s, s_prop, s_pix, s_pix_prop, d):
# return compute_log_likelihood_good(s_prop, s_pix_prop, d) - compute_log_likelihood_good(s, s_pix, d)
def crankNicolson_good(cls_, d):
s = hp.synalm(cls_, lmax=config.L_MAX_SCALARS)
s = utils.flatten_map(s)
#h, s = gradientDescent.gradient_ascent_good(d, cls_)
s_pix = hp.sphtfunc.alm2map(utils.unflat_map_to_pix(s), nside=config.NSIDE)
#s = utils.flatten_map(s)
accepted = 0
history = []
for i in range(config.N_CN):
if i == 40000:
config.beta_CN /= 9.5
history.append(s)
s_prop = np.sqrt(1 - config.beta_CN**2)*s +config.beta_CN*utils.flatten_map(hp.synalm(cls_, lmax=config.L_MAX_SCALARS))
### Ajouté le dénom !!!
s_prop_pix = hp.alm2map(utils.unflat_map_to_pix(s_prop), nside=config.NSIDE)*(1/config.NSIDE)
r = compute_CN_ratio_good(s_pix, s_prop_pix, d)
if np.log(np.random.uniform()) < r:
s = s_prop
s_pix = s_prop_pix
accepted += 1
print(accepted/config.N_CN)
return history, s