def invC(mock, ell=0, rebin=None):
''' ***TESTED***
Test inverting the covariance matrix. This is
inspired by the fact that the original binning of
Nseries P(k) is not invertible...
'''
pkay = Data.Pk()
n_mock = pkay._n_mock(mock)
for i in range(1, n_mock+1):
pkay.Read(mock, i, NorS='ngc')
k, pk = pkay.k, pkay.pk
if i == 1:
pks = np.zeros((len(k), n_mock))
pks[:, i-1] = pk
C_pk = np.cov(pks.T) # covariance matrix
invC_pk = np.linalg.inv(C_pk)
fig = plt.figure(figsize=(10,5))
sub = fig.add_subplot(1,2,1)
im = sub.imshow(C_pk, interpolation='None')
fig.colorbar(im, ax=sub)
sub = fig.add_subplot(1,2,2)
im = sub.imshow(invC_pk, interpolation='None')
fig.colorbar(im, ax=sub)
plt.show()
return None
def lnPost(zbin=1):
''' *** TESTED ***
Likelihood and posterior functions can reproduce the chi-squared from
Florian's MCMC chain.
Test that the ln(Posterior) reproduces the chi-squared values of
Florian's MCMC chains
'''
# read in Florian's chains
chain_file = ''.join([
UT.dat_dir(), 'Beutler/public_full_shape/',
'Beutler_et_al_full_shape_analysis_z',
str(zbin), '_chain',
str(0), '.dat'
])
sample = np.loadtxt(chain_file, skiprows=1)
chi2s = sample[:, -1]
sample = sample[:, 1:-1]
# read in BOSS P(k) NGC + SGC
pkay = Dat.Pk()
k0, p0k_ngc = pkay.Observation(0, zbin, 'ngc')
k2, p2k_ngc = pkay.Observation(2, zbin, 'ngc')
k4, p4k_ngc = pkay.Observation(4, zbin, 'ngc')
k0, p0k_sgc = pkay.Observation(0, zbin, 'sgc')
k2, p2k_sgc = pkay.Observation(2, zbin, 'sgc')
k4, p4k_sgc = pkay.Observation(4, zbin, 'sgc')
k_list = [k0, k2, k4]
pk_ngc_list = [p0k_ngc, p2k_ngc, p4k_ngc]
pk_sgc_list = [p0k_sgc, p2k_sgc, p4k_sgc]
# read in Covariance matrix
# currently for testing purposes,
# implemented to read in Florian's covariance matrix
_, _, C_pk_ngc = Dat.beutlerCov(zbin, NorS='ngc', ell='all')
_, _, C_pk_sgc = Dat.beutlerCov(zbin, NorS='sgc', ell='all')
# calculate precision matrices (including the hartlap factor)
n_mocks_ngc = 2045
n_mocks_sgc = 2048
f_hartlap_ngc = (float(n_mocks_ngc) - float(
len(np.concatenate(pk_ngc_list))) - 2.) / (float(n_mocks_ngc) - 1.)
f_hartlap_sgc = (float(n_mocks_sgc) - float(
len(np.concatenate(pk_sgc_list))) - 2.) / (float(n_mocks_sgc) - 1.)
Cinv_ngc = np.linalg.inv(C_pk_ngc)
Cinv_sgc = np.linalg.inv(C_pk_sgc)
Cinv_ngc *= f_hartlap_ngc
Cinv_sgc *= f_hartlap_sgc
lnpost_args = (k_list, pk_ngc_list, pk_sgc_list, Cinv_ngc, Cinv_sgc)
for i in range(10):
print('Like', -2. * Inf.lnLike(sample[i, :], *lnpost_args))
print('Post', -2. * Inf.lnPost(sample[i, :], *lnpost_args))
print('chi2', chi2s[i])
return None
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 X_pk(mock, ell=0, krange=None, NorS='ngc', sys='fc', k_arr=False):
''' Construct data matrix X from P(k) measures of mock catalogs.
X_i = P(k)_i
X has N_mock x N_k dimensions.
'''
pkay = Data.Pk() # read in P(k) data
n_mock = pkay._n_mock(mock)
for i in range(1, n_mock + 1):
pkay.Read(mock, i, ell=ell, NorS=NorS, sys=sys)
pkay.krange(krange)
k, pk = pkay.k, pkay.pk
if i == 1:
pks = np.zeros((n_mock, len(k)))
pks[i - 1, :] = pk
if k_arr:
return pks, k
return pks
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
def mcmc(tag=None,
zbin=1,
nwalkers=48,
Nchains=4,
minlength=600,
likelihood='pseudo'):
'''
Parameters
----------
Nchains : int
Number of independent chains to run for the gelman rubin convergence test
'''
if tag is None:
raise ValueError("specify a tag, otherwise it's confusing")
temperature = 2.e-3 # temperature
# read in BOSS P(k) NGC
pkay = Dat.Pk()
k0, p0k_ngc = pkay.Observation(0, zbin, 'ngc')
k2, p2k_ngc = pkay.Observation(2, zbin, 'ngc')
k4, p4k_ngc = pkay.Observation(4, zbin, 'ngc')
pk_ngc_list = [p0k_ngc, p2k_ngc, p4k_ngc]
k_list = [k0, k2, k4]
# read in BOSS P(k) SGC
k0, p0k_sgc = pkay.Observation(0, zbin, 'sgc')
k2, p2k_sgc = pkay.Observation(2, zbin, 'sgc')
k4, p4k_sgc = pkay.Observation(4, zbin, 'sgc')
pk_sgc_list = [p0k_sgc, p2k_sgc, p4k_sgc]
if likelihood == 'psuedo': # standard pseudo Gaussian likelihood
# read in Covariance matrix
# currently for testing purposes,
# implemented to read in Florian's covariance matrix
_, _, C_pk_ngc = Dat.beutlerCov(zbin, NorS='ngc', ell='all')
_, _, C_pk_sgc = Dat.beutlerCov(zbin, NorS='sgc', ell='all')
# calculate precision matrices (including the hartlap factor)
Cinv_ngc = np.linalg.inv(C_pk_ngc)
Cinv_sgc = np.linalg.inv(C_pk_sgc)
# hartlap factor
n_mocks_ngc = 2045
n_mocks_sgc = 2048
f_hartlap_ngc = (float(n_mocks_ngc) - float(
len(np.concatenate(pk_ngc_list))) - 2.) / (float(n_mocks_ngc) - 1.)
f_hartlap_sgc = (float(n_mocks_sgc) - float(
len(np.concatenate(pk_sgc_list))) - 2.) / (float(n_mocks_sgc) - 1.)
Cinv_ngc *= f_hartlap_ngc
Cinv_sgc *= f_hartlap_sgc
# ln Posterior function
lnPost = lnPost_pseudo
# args for ln Posterior function
# data ks, BOSS NGC P_l(k), BOSS SGC P_l(k), NGC precision matrix, SGC precision matrix
lnpost_args = (k_list, pk_ngc_list, pk_sgc_list, Cinv_ngc, Cinv_sgc)
elif likelihood in ['pca', 'ica']:
# read in patchy mock P(k)s for ngc and sgc
pk_ngc_list, pk_sgc_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.z' + str(kwargs['zbin']),
krange=[0.01, kmax],
ell=ell,
NorS='ngc',
sys='fc'))
pk_sgc_list.append(
NG.X_pk('patchy.z' + str(kwargs['zbin']),
krange=[0.01, kmax],
ell=ell,
NorS='sgc',
sys='fc'))
pk_ngc_mock = np.concatenate(pk_ngc_list, axis=1)
pk_sgc_mock = np.concatenate(pk_sgc_list, axis=1)
else:
raise NotImplementedError
if zbin == 1: # 0.2 < z < 0.5
# maximum likelihood value
start = np.array([
1.008, 1.001, 0.478, 1.339, 1.337, 1.16, 0.32, -1580., -930., 6.1,
6.8
])
ndim = len(start)
# initialize MPI pool
try:
pool = MPIPool()
if not pool.is_master():
pool.wait()
sys.exit(0)
except ValueError:
pool = None
print("initializing ", Nchains, " independent emcee chains")
pos, samplers = [], []
for ichain in range(Nchains):
pos.append([
start + temperature * start *
(2. * np.random.random_sample(ndim) - 1.) for i in range(nwalkers)
])
samplers.append(
emcee.EnsembleSampler(nwalkers,
ndim,
lnPost,
args=lnpost_args,
pool=pool))
# Start MCMC
print("Running MCMC...")
withinchainvar = np.zeros((Nchains, ndim))
meanchain = np.zeros((Nchains, ndim))
scalereduction = np.repeat(2., ndim)
# bunch of numbers for the mcmc run
itercounter = 0
chainstep = minlength
loop = 1
epsilon = 0.02 #0.02
ichaincheck = 100
rstate = np.random.get_state()
while loop:
itercounter += chainstep
print("chain length =", itercounter)
for jj in range(Nchains):
for result in samplers[jj].sample(pos[jj],
iterations=chainstep,
rstate0=rstate,
storechain=True):
pos[jj] = result[0]
chainchi2 = -2. * result[1]
rstate = result[2]
# append chain outputs to chain file
chain_file = ''.join([
UT.dat_dir(), 'mcmc/', tag, '.chain',
str(jj), '.zbin',
str(zbin), '.dat'
])
f = open(chain_file, 'a')
for k in range(pos[jj].shape[0]):
output_str = '\t'.join(
pos[jj][k].astype('str')) + '\t' + str(
chainchi2[k]) + '\n'
f.write(output_str)
f.close()
# we do the convergence test on the second half of the current chain (itercounter/2)
chainsamples = samplers[jj].chain[:, itercounter / 2:, :].reshape(
(-1, ndim))
withinchainvar[jj] = np.var(chainsamples, axis=0)
meanchain[jj] = np.mean(chainsamples, axis=0)
scalereduction = gelman_rubin_convergence(withinchainvar, meanchain,
itercounter / 2, Nchains,
ndim)
print("scalereduction = ", scalereduction)
loop = 0
for jj in range(ndim):
if np.abs(1 - scalereduction[jj]) > epsilon:
loopcriteria = 1
chainstep = ichaincheck
if pool is not None:
pool.close()
return None
def W_importance(tag,
chain,
ica_algorithm=None,
density_method='kde',
n_comp_max=20,
info_crit='bic',
njobs=1,
**kwargs):
''' Given a dictionary with the MCMC chain, evaluate the likelihood ratio
'''
if 'RSD' in tag: # Florian's RSD analysis
if 'zbin' not in kwargs.keys():
raise ValueError('specify zbin in kwargs')
# read in BOSS P(k) (data D)
k_list, pk_ngc_data, pk_sgc_data = [], [], []
pkay = Dat.Pk()
for ell in [0, 2, 4]:
k, plk_ngc = pkay.Observation(ell, kwargs['zbin'], 'ngc')
_, plk_sgc = pkay.Observation(ell, kwargs['zbin'], 'sgc')
k_list.append(k)
pk_ngc_data.append(plk_ngc)
pk_sgc_data.append(plk_sgc)
pk_ngc_data = np.concatenate(pk_ngc_data)
pk_sgc_data = np.concatenate(pk_sgc_data)
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)
# calculate D - m(theta) for all the mcmc chain
delta_ngc = chain['pk_ngc'] - pk_ngc_data
delta_sgc = chain['pk_sgc'] - pk_sgc_data
# import PATCHY mocks
pk_ngc_list, pk_sgc_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.z' + str(kwargs['zbin']),
krange=[0.01, kmax],
ell=ell,
NorS='ngc',
sys='fc'))
pk_sgc_list.append(
NG.X_pk('patchy.z' + str(kwargs['zbin']),
krange=[0.01, kmax],
ell=ell,
NorS='sgc',
sys='fc'))
pk_ngc_mock = np.concatenate(pk_ngc_list, axis=1)
pk_sgc_mock = np.concatenate(pk_sgc_list, axis=1)
if tag == 'RSD_pXiICA_gauss': # P_ICA(D - m(theta)) / P_PCA,Gauss(D - m(theta))
lnP_ica_ngc = NG.lnL_pXi_ICA(delta_ngc,
pk_ngc_mock,
ica_algorithm=ica_algorithm,
density_method=density_method,
n_comp_max=n_comp_max,
info_crit=info_crit,
njobs=njobs)
lnP_ica_sgc = NG.lnL_pXi_ICA(delta_sgc,
pk_sgc_mock,
ica_algorithm=ica_algorithm,
density_method=density_method,
n_comp_max=n_comp_max,
info_crit=info_crit,
njobs=njobs)
lnP_gauss_ngc = NG.lnL_pca_gauss(delta_ngc, pk_ngc_mock)
lnP_gauss_sgc = NG.lnL_pca_gauss(delta_sgc, pk_sgc_mock)
lnP_num = lnP_ica_ngc + lnP_ica_sgc
lnP_den = lnP_gauss_ngc + lnP_gauss_sgc
elif tag == 'RSD_ica_chi2':
# this should be consistent with above!
lnP_ica_ngc = NG.lnL_pXi_ICA(delta_ngc,
pk_ngc_mock,
ica_algorithm=ica_algorithm,
density_method=density_method,
n_comp_max=n_comp_max,
info_crit=info_crit,
njobs=njobs)
lnP_ica_sgc = NG.lnL_pXi_ICA(delta_sgc,
pk_sgc_mock,
ica_algorithm=ica_algorithm,
density_method=density_method,
n_comp_max=n_comp_max,
info_crit=info_crit,
njobs=njobs)
lnP_num = lnP_ica_ngc + lnP_ica_sgc
lnP_den = -0.5 * chain['chi2']
elif 'gmf' in tag: # GMF
geemf = Dat.Gmf() # read in SDSS GMF (data D)
nbins, gmf_data = geemf.Observation()
# calculate D - m(theta) for all the mcmc chain
dgmf = gmf_data - chain['gmf']
# read mock gmfs (all mocks from 100 differnet HOD parameter points)
gmf_mock = NG.X_gmf_all(
) #gmf_mock = NG.X_gmf('manodeep.run'+str(kwargs['run']))#
# old likelihood derived from chi-squared of MCMC chain
lnP_den = -0.5 * chain['chi2'] # -0.5 chi-squared from MCMC chain
if tag == 'gmf_all_chi2':
# importance weight determined by the ratio of
# the chi^2 from the chain and the chi^2 calculated
# using the covariance matrix from the entire catalog
# we note that Sinha et al.(2017) does not include the
# hartlap factor
Cgmf = np.cov(gmf_mock.T) # covariance matrix
Cinv = np.linalg.inv(Cgmf) # precision matrix
lnP_num = np.empty(dgmf.shape[0])
for i in range(dgmf.shape[0]): # updated chi-square
lnP_num[i] = -0.5 * np.dot(dgmf[i, :],
np.dot(Cinv, dgmf[i, :].T))
if tag == 'gmf_pXiICA_chi2':
# updated likelihood is calculated using
# ln( PI_i p( delta_X_ICA_i | X_ICA_i^(gmm/kde)) )
lnP_num = NG.lnL_pXi_ICA(dgmf,
gmf_mock,
ica_algorithm=ica_algorithm,
density_method=density_method,
n_comp_max=n_comp_max,
info_crit=info_crit,
njobs=njobs)
elif tag == 'gmf_pX_chi2':
# updated likelihood is calculated using
# ln( p( delta_X | X^(gmm/kde) ) )
lnP_num = NG.lnL_pX(dgmf,
gmf_mock,
density_method=density_method,
n_comp_max=n_comp_max,
info_crit=info_crit,
njobs=njobs)
elif tag == 'gmf_lowN_chi2':
# importance weight determined by the ratio of
# the chi^2 from the chain and the chi^2 calculated
# using the covariance matrix from the entire catalog
# and *excluding the highest N bin*
Cgmf = np.cov(gmf_mock.T) # covariance matrix
Cinv = np.linalg.inv(Cgmf) # precision matrix
Nlim = Cinv.shape[0] - 1
lnP_num = np.empty(dgmf.shape[0])
for i in range(dgmf.shape[0]): # updated chi-square
lnP_num[i] = -0.5 * np.dot(
dgmf[i, :Nlim], np.dot(Cinv[:Nlim, :Nlim],
dgmf[i, :Nlim].T))
else:
raise NotImplementedError
else:
raise ValueError
ws = np.exp(lnP_num - lnP_den)
return [lnP_den, lnP_num, ws]