def lnLike_pca(theta, k_list, pk_ngc_list, pk_sgc_list, pk_ngc_mock,
pk_sgc_mock):
''' wrapper for nongauss.lnL_pca . lnL_pca decomposes P_data - P_model into
PCA componenets, then measures the likelihood by calculating the probability
of each of the components p(x_pca,i), which is estimated using a nonparametric
density estimation method (e.g. KDE) from the mock catalogs
parameters
----------
theta : array
cosmological parameters : alpha_perp, alpha_para, fsig8 and
nuisance parameters : b1NGCsig8, b1SGCsig8, b2NGCsig8, b2SGCsig8,
NNGC, NSGC, sigmavNGC, sigmavSGC
k_list : list
list of k values for the mono, quadru, and hexadecaopoles -- [k0, k2, k4]
pk_ngc_list : list
pk_sgc_list : list
mocks_ngc : np.ndarray (N_mock x N_k)
Array of the mock catalog P(k)s for NGC
mocks_sgc : np.ndarray (N_mock x N_k)
Array of the mock catalog P(k)s for SGC
'''
if 0.8 < theta[0] < 1.4 and 0.8 < theta[1] < 1.4:
binrange1, binrange2, binrange3 = len(k_list[0]), len(k_list[1]), len(
k_list[2])
maxbin1 = len(k_list[0]) + 1
k = np.concatenate(k_list)
pk_ngc = np.concatenate(pk_ngc_list)
pk_sgc = np.concatenate(pk_sgc_list)
modelX = Mod.taruya_model(100, binrange1, binrange2, binrange3,
maxbin1, k, theta[0], theta[1], theta[2],
theta[3], theta[4], theta[5], theta[6],
theta[7], theta[8], theta[9], theta[10])
model_ngc = modelX[0]
model_sgc = modelX[1]
diff_ngc = model_ngc - pk_ngc
diff_sgc = model_sgc - pk_sgc
lnP_pca_ngc = NG.lnL_pca(delta_ngc, pk_ngc_mock)
lnP_pca_sgc = NG.lnL_pca(delta_sgc, pk_sgc_mock)
return lnP_pca_ngc + ln_pca_sgc #-0.5*(chi2_ngc + chi2_sgc)
else:
return -0.5 * (10000.)
def importance_weight():
'''
'''
# read in BOSS P(k) (read in data D)
pkay = Dat.Pk()
k_list, pk_ngc_data = [], []
for ell in [0, 2, 4]:
k, plk_ngc = pkay.Observation(ell, 1, 'ngc')
k_list.append(k)
pk_ngc_data.append(plk_ngc)
binrange1, binrange2, binrange3 = len(k_list[0]), len(k_list[1]), len(
k_list[2])
maxbin1 = len(k_list[0]) + 1
k = np.concatenate(k_list)
chain = Inf.mcmc_chains('beutler_z1')
# calculate D - m(theta) for all the mcmc chain
delta_ngc = []
for i in range(10): #len(chain['chi2'])):
model_i = Mod.taruya_model(
100, binrange1, binrange2, binrange3, maxbin1, k,
chain['alpha_perp'][i], chain['alpha_para'][i], chain['fsig8'][i],
chain['b1sig8_NGC'][i], chain['b1sig8_SGC'][i],
chain['b2sig8_NGC'][i], chain['b2sig8_SGC'][i], chain['N_NGC'][i],
chain['N_SGC'][i], chain['sigmav_NGC'][i], chain['sigmav_SGC'][i])
delta_ngc.append(model_i[0] - np.concatenate(pk_ngc_data))
# import PATCHY mocks
pk_ngc_list = []
for ell in [0, 2, 4]:
if ell == 4: kmax = 0.1
else: kmax = 0.15
pk_ngc_list.append(
NG.X_pk('patchy.ngc.z1', krange=[0.01, kmax], ell=ell, sys='fc'))
pk_ngc_mock = np.concatenate(pk_ngc_list, axis=1)
lnP_ica_ngc = NG.lnL_ica(np.array(delta_ngc), pk_ngc_mock)
lnP_pca_ngc = NG.lnL_pca(np.array(delta_ngc), pk_ngc_mock)
lnw_ngc = lnP_ica_ngc - lnP_pca_ngc
print(np.exp(lnw_ngc))
return None
def lnLike_pseudo(theta, k_list, pk_ngc_list, pk_sgc_list, Cinv_ngc, Cinv_sgc):
''' log of the pseudo Gaussian likelihood function. This is identical to
Florian's implementation.
parameters
----------
theta : array
cosmological parameters : alpha_perp, alpha_para, fsig8 and
nuisance parameters : b1NGCsig8, b1SGCsig8, b2NGCsig8, b2SGCsig8,
NNGC, NSGC, sigmavNGC, sigmavSGC
k_list : list
list of k values for the mono, quadru, and hexadecaopoles -- [k0, k2, k4]
pk_ngc_list : list
'''
if 0.8 < theta[0] < 1.4 and 0.8 < theta[1] < 1.4:
binrange1, binrange2, binrange3 = len(k_list[0]), len(k_list[1]), len(
k_list[2])
maxbin1 = len(k_list[0]) + 1
k = np.concatenate(k_list)
pk_ngc = np.concatenate(pk_ngc_list)
pk_sgc = np.concatenate(pk_sgc_list)
modelX = Mod.taruya_model(100, binrange1, binrange2, binrange3,
maxbin1, k, theta[0], theta[1], theta[2],
theta[3], theta[4], theta[5], theta[6],
theta[7], theta[8], theta[9], theta[10])
model_ngc = modelX[0]
model_sgc = modelX[1]
diff_ngc = model_ngc - pk_ngc
diff_sgc = model_sgc - pk_sgc
chi2_ngc = np.dot(diff_ngc, np.dot(Cinv_ngc, diff_ngc))
chi2_sgc = np.dot(diff_sgc, np.dot(Cinv_sgc, diff_sgc))
return -0.5 * (chi2_ngc + chi2_sgc)
else:
return -0.5 * (10000.)
def Pk_model_mcmc(tag, **kwargs):
''' Evalulate the P(k) model for the `tag` MCMC chain
'''
if tag == 'beutler_z1':
# read in BOSS P(k) (read in data D)
pkay = Dat.Pk()
k_list, pk_ngc_data = [], []
for ell in [0, 2, 4]:
k, plk_ngc = pkay.Observation(ell, 1, 'ngc')
k_list.append(k)
pk_ngc_data.append(plk_ngc)
binrange1, binrange2, binrange3 = len(k_list[0]), len(k_list[1]), len(
k_list[2])
maxbin1 = len(k_list[0]) + 1
k = np.concatenate(k_list)
if 'ichain' in kwargs.keys():
nchains = [kwargs['ichain']]
else:
nchains = range(4)
# read in Florian's RSD MCMC chains
for ichain in nchains:
chain_file = ''.join([
UT.dat_dir(), 'Beutler/public_full_shape/',
'Beutler_et_al_full_shape_analysis_z1_chain',
str(ichain), '.dat'
])
sample = np.loadtxt(chain_file, skiprows=1)
chain = sample[:, 1:]
fname_ngc = ''.join([
UT.dat_dir(), 'Beutler/public_full_shape/',
'Beutler_et_al_full_shape_analysis_z1_chain',
str(ichain), '.model.ngc.dat'
])
fname_sgc = ''.join([
UT.dat_dir(), 'Beutler/public_full_shape/',
'Beutler_et_al_full_shape_analysis_z1_chain',
str(ichain), '.model.sgc.dat'
])
if not os.path.isfile(fname_ngc):
f_ngc = open(fname_ngc, 'w')
f_sgc = open(fname_sgc, 'w')
mocks = range(sample.shape[0])
else:
ns_ngc = np.loadtxt(fname_ngc, unpack=True, usecols=[0])
ns_sgc = np.loadtxt(fname_sgc, unpack=True, usecols=[0])
f_ngc = open(fname_ngc, 'a')
f_sgc = open(fname_sgc, 'a')
if ns_ngc.max() != ns_sgc.max():
raise ValueError
mocks = range(int(ns_ngc.max()) + 1, sample.shape[0])
for i in mocks:
model_i = Mod.taruya_model(100, binrange1, binrange2,
binrange3, maxbin1, k, chain[i, 0],
chain[i, 1], chain[i, 2],
chain[i, 3], chain[i, 4],
chain[i, 5], chain[i, 6], chain[i,
7],
chain[i, 8], chain[i, 9], chain[i,
10])
f_ngc.write('\t'.join(
[str(i)] +
[str(model_i[0][ii]) for ii in range(len(model_i[0]))]))
f_sgc.write('\t'.join(
[str(i)] +
[str(model_i[1][ii]) for ii in range(len(model_i[1]))]))
f_ngc.write('\n')
f_sgc.write('\n')
else:
raise ValueError
return None
def model():
kbins = 60
binsize = 120 / kbins
minbin1 = 2
minbin2 = 2
minbin3 = 2
maxbin1 = 30
maxbin2 = 30
maxbin3 = 20
binrange1 = int(0.5 * (maxbin1 - minbin1))
binrange2 = int(0.5 * (maxbin2 - minbin2))
binrange3 = int(0.5 * (maxbin3 - minbin3))
totbinrange = binrange1 + binrange2 + binrange3
pkay = Dat.Pk()
k0, p0k = pkay.Observation(0, 1, 'ngc')
k2, p2k = pkay.Observation(2, 1, 'ngc')
k4, p4k = pkay.Observation(4, 1, 'ngc')
k = np.concatenate([k0, k2, k4])
# alpha_perp, alpha_para, fsig8, b1NGCsig8, b1SGCsig8, b2NGCsig8, b2SGCsig8, NNGC, NSGC, sigmavNGC, sigmavSGC
#value_array = [1.008, 1.001, 0.478, 1.339, 1.337, 1.16, 1.16, -1580., -1580., 6.1, 6.1]
value_array = [
1.008, 1.001, 0.478, 1.339, 1.337, 1.16, 0.32, -1580., -930., 6.1, 6.8
]
#value_array = [1.00830111426, 1.0007368972, 0.478098423689, 1.33908539185, 1.33663505549, 1.15627984704, 0.31657562682, -1580.01689181, -928.488535962, 6.14815801563, 6.79551199595] #z1 max likelihood
t_start = time.time()
modelX = Mod.taruya_model(100, binrange1, binrange2, binrange3,
maxbin1 / binsize, k, value_array[0],
value_array[1], value_array[2], value_array[3],
value_array[4], value_array[5], value_array[6],
value_array[7], value_array[8], value_array[9],
value_array[10])
print(time.time() - t_start, ' seconds')
model_ngc = modelX[0]
model_sgc = modelX[1]
# read in pre-window convlution
k_nw, p0k_ngc_nw, p2k_ngc_nw, p4k_ngc_nw, p0k_sgc_nw, p2k_sgc_nw, p4k_sgc_nw = np.loadtxt(
''.join([UT.dat_dir(), 'boss/test.nowindow.dat']), unpack=True)
# now plot
pretty_colors = prettycolors()
fig = plt.figure(figsize=(11, 5))
sub = fig.add_subplot(121)
sub.scatter(k0, k0 * p0k, c=pretty_colors[1], lw=0)
sub.plot(k0, k0 * model_ngc[:binrange1], c=pretty_colors[1])
sub.plot(k_nw, k_nw * p0k_ngc_nw, c=pretty_colors[1], lw=1, ls='--')
sub.scatter(k2, k2 * p2k, c=pretty_colors[3], lw=0)
sub.plot(k_nw, k_nw * p2k_ngc_nw, c=pretty_colors[3], lw=1, ls='--')
sub.plot(k2,
k2 * model_ngc[binrange1:binrange1 + binrange2],
c=pretty_colors[3])
sub.scatter(k4, k4 * p4k, c=pretty_colors[5], lw=0)
sub.plot(k_nw, k_nw * p4k_ngc_nw, c=pretty_colors[5], lw=1, ls='--')
sub.plot(k4,
k4 * model_ngc[binrange1 + binrange2:totbinrange],
c=pretty_colors[5])
sub.text(0.9,
0.05,
'NGC',
ha='right',
va='bottom',
transform=sub.transAxes,
fontsize=20)
sub.set_xlim([0.01, 0.15])
sub.set_ylim([-750, 2250])
sub.set_xlabel('$k$', fontsize=25)
sub.set_ylabel('$k \, P_{\ell}(k)$', fontsize=25)
k0, p0k = pkay.Observation(0, 1, 'sgc')
k2, p2k = pkay.Observation(2, 1, 'sgc')
k4, p4k = pkay.Observation(4, 1, 'sgc')
k = np.concatenate([k0, k2, k4])
sub = fig.add_subplot(122)
sub.scatter(k0, k0 * p0k, c=pretty_colors[1], lw=0)
sub.plot(k0, k0 * model_sgc[:binrange1], c=pretty_colors[1])
sub.plot(k_nw, k_nw * p0k_sgc_nw, c=pretty_colors[1], lw=1, ls='--')
sub.scatter(k2, k2 * p2k, c=pretty_colors[3], lw=0)
sub.plot(k2,
k2 * model_sgc[binrange1:binrange1 + binrange2],
c=pretty_colors[3])
sub.plot(k_nw, k_nw * p2k_sgc_nw, c=pretty_colors[3], lw=1, ls='--')
sub.scatter(k4, k4 * p4k, c=pretty_colors[5], lw=0)
sub.plot(k4,
k4 * model_sgc[binrange1 + binrange2:totbinrange],
c=pretty_colors[5])
sub.plot(k_nw, k_nw * p4k_sgc_nw, c=pretty_colors[5], lw=1, ls='--')
sub.text(0.9,
0.05,
'SGC',
ha='right',
va='bottom',
transform=sub.transAxes,
fontsize=20)
sub.set_xlim([0.01, 0.15])
sub.set_ylim([-750, 2250])
sub.set_xlabel('$k$', fontsize=25)
fig.savefig(''.join([UT.fig_dir(), 'tests/test.model.plk.png']),
bbox_inches='tight')
return None