def lnL_sys(mock, ell=0, rebin=None, sys='fc'):
''' Compare the pseudo gaussian L with no systematics, ICA L estimation with
no systematics, and ICA L estimation with fiber collisions.
'''
# Likelihood without systematics
Pk_nosys = NG.dataX(mock, ell=ell, rebin=rebin, sys=None)
gauss = NG.lnL_pca_gauss(Pk_nosys, Pk_nosys)
ica_nosys = NG.lnL_ica(Pk_nosys, Pk_nosys)
# Likelihood with specified systematics
Pk_sys = NG.dataX(mock, ell=ell, rebin=rebin, sys=sys)
ica_sys = NG.lnL_ica(Pk_sys, Pk_sys)
prettyplot()
fig = plt.figure()
sub = fig.add_subplot(111)
nbin = 32
sub.hist(gauss, bins=nbin, range=[-2.2*Pk_nosys.shape[0], -0.8*Pk_nosys.shape[0]],
normed=True, alpha=0.75, label='Gaussian $\mathcal{L^\mathtt{pseudo}}$; no sys.')
sub.hist(ica_nosys, bins=nbin, range=[-2.2*Pk_nosys.shape[0], -0.8*Pk_nosys.shape[0]],
normed=True, alpha=0.75, label='ICA; no sys.')
sub.hist(ica_sys, bins=nbin, range=[-2.2*Pk_nosys.shape[0], -0.8*Pk_nosys.shape[0]],
normed=True, alpha=0.75, label='ICA; w/ sys.')
sub.set_xlabel('log $\mathcal{L}$', fontsize=25)
sub.set_xlim([-2.2*Pk_nosys.shape[0], -0.5*Pk_nosys.shape[0]])
sub.legend(loc='upper left', prop={'size': 20})
if rebin is None: # save fig
f = ''.join([UT.fig_dir(), 'tests/test.lnL_sys.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.lnL_sys.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def ica(mock, ell=0, rebin=None):
''' *** TESTED ***
Test that the ICA works!
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin)
X, _ = NG.meansub(Pk)
X_w, W = NG.whiten(X) # whitened data
X_ica, W = NG.Ica(X_w)
# compare covariance?
C_X = np.cov(X.T)
C_Xica = np.cov(X_ica.T)
prettyplot()
fig = plt.figure(figsize=(20, 8))
sub = fig.add_subplot(121)
im = sub.imshow(np.log10(C_X), interpolation='none')
sub.set_title('log(Cov.) of Data')
fig.colorbar(im, ax=sub)
sub = fig.add_subplot(122)
im = sub.imshow(C_Xica, interpolation='none')
fig.colorbar(im, ax=sub)
sub.set_title('Cov. of ICA transformed Data')
# save fig
if rebin is None:
f = ''.join([UT.fig_dir(), 'tests/test.ICAcov.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.ICAcov.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def lnL_pca_kde(mock, ell=0, rebin=None, krange=None):
''' ***TESTED: expectedly, more discrepant for low number of
mock catalogs. For Nseries monopole with 1000 mocks, no
significant discrepancy in the likelihood distribution
***
Test whether or not the Gaussian KDE approximation of pdfs
is sufficiently accurate by comparing the likelihood estimated
from NG.lnL_pca vs NG.lnL_pca_gauss. If they are highly
discrepant, then KDE estimate of the pdfs are not very accurate.
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
pca_gauss = NG.lnL_pca_gauss(Pk, Pk)
pca_kde = NG.lnL_pca(Pk, Pk)
prettyplot()
fig = plt.figure()
sub = fig.add_subplot(111)
nbin = 32
sub.hist(pca_gauss, bins=nbin, range=[-2.2*Pk.shape[1], -0.5*Pk.shape[1]],
normed=True, alpha=0.75, label='Gaussian $\mathcal{L^\mathtt{pseudo}}$')
sub.hist(pca_kde, bins=nbin, range=[-2.2*Pk.shape[1], -0.8*Pk.shape[1]],
normed=True, alpha=0.75, label='$\mathcal{L^\mathtt{pseudo}}$ KDE estimate')
sub.set_xlabel('log $\mathcal{L}$', fontsize=25)
sub.set_xlim([-2.2*Pk.shape[1], -0.5*Pk.shape[1]])
sub.legend(loc='upper left', prop={'size': 20})
if rebin is None: # save fig
f = ''.join([UT.fig_dir(), 'tests/test.lnL_kde_test.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.lnL_kde_test.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def lnL(mock, ell=0, rebin=None, krange=None):
''' Test the ICA likelihood estimation and pseudo gaussian likelihood
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
ica = NG.lnL_ica(Pk, Pk)
gauss = NG.lnL_pca_gauss(Pk, Pk)
prettyplot()
fig = plt.figure()
sub = fig.add_subplot(111)
nbin = 32
sub.hist(gauss, bins=nbin, range=[-2.2*Pk.shape[1], -0.8*Pk.shape[1]],
normed=True, alpha=0.75, label='Gaussian $\mathcal{L^\mathtt{pseudo}}$')
sub.hist(ica, bins=nbin, range=[-2.2*Pk.shape[1], -0.8*Pk.shape[1]],
normed=True, alpha=0.75, label='ICA')
sub.set_xlabel('log $\mathcal{L}$', fontsize=25)
sub.set_xlim([-2.2*Pk.shape[1], -0.5*Pk.shape[1]])
sub.legend(loc='upper left', prop={'size': 20})
str_rebin = ''
if rebin is not None:
str_rebin = '.rebin'+str(rebin)
str_krange = ''
if krange is not None:
str_krange = '.kmin'+str(krange[0])+'.kmax'+str(krange[1])
f = ''.join([UT.fig_dir(), 'tests/test.lnL.', mock, '.ell', str(ell),
str_rebin, str_krange, '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def whiten(mock, ell=0, rebin=None, krange=None, method='choletsky'):
''' ***TESTED: Choletsky decomposition fails for full binned Nseries
P(k) because the precision matrix estimate is not positive definite***
test the data whitening.
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
X, _ = NG.meansub(Pk)
X_w, W = NG.whiten(X, method=method) # whitened data
prettyplot()
fig = plt.figure(figsize=(15,7))
sub = fig.add_subplot(121)
for i in range(X.shape[1]):
sub.plot(range(X_w.shape[0]), X_w[:,i])
sub.set_xlim([0, X.shape[0]])
sub.set_xlabel('$\mathtt{k}$ bins', fontsize=25)
sub.set_ylim([-7., 7.])
sub.set_ylabel('$\mathtt{W^{T} (P^i_'+str(ell)+'- \overline{P_'+str(ell)+'})}$', fontsize=25)
C_Xw = np.cov(X_w.T)
sub = fig.add_subplot(122)
im = sub.imshow(C_Xw, interpolation='none')
fig.colorbar(im, ax=sub)
if rebin is None:
f = ''.join([UT.fig_dir(), 'tests/test.whiten.', method, '.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.whiten.', method, '.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def whiten_recon(mock, ell=0, rebin=None, krange=None, method='choletsky'):
''' ***TESTED: The whitening matrices reconstruct the P(k)s***
Test whether P(k) can be reconstructed using the whitening matrix
'''
Pk, k = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange, k_arr=True)
X, mu_X = NG.meansub(Pk)
X_w, W = NG.whiten(X, method=method) # whitened data
prettyplot()
fig = plt.figure(figsize=(15,7))
sub = fig.add_subplot(121)
for i in range(X.shape[0]):
sub.plot(k, Pk[i,:])
if krange is None:
sub.set_xlim([1e-3, 0.5])
else:
sub.set_xlim(krange)
sub.set_xscale('log')
sub.set_xlabel('$\mathtt{k}$', fontsize=25)
sub.set_yscale('log')
sub.set_ylim([2e3, 2.5e5])
np.random.seed(7)
sub = fig.add_subplot(122)
for i in range(X.shape[0]):
X_noise = np.random.normal(size=X_w.shape[1])
X_rec = np.linalg.solve(W.T, X_noise.T)
sub.plot(k, X_rec.T + mu_X)
if krange is None:
sub.set_xlim([1e-3, 0.5])
else:
sub.set_xlim(krange)
sub.set_xscale('log')
sub.set_xlabel('$\mathtt{k}$', fontsize=25)
sub.set_yscale('log')
sub.set_ylim([2e3, 2.5e5])
if rebin is None:
f = ''.join([UT.fig_dir(), 'tests/test.whiten_recon.', method, '.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.whiten_recon.', method, '.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def p_Xw_i_MISE(mock, ell=0, rebin=None, krange=None, method='choletsky', b=0.1):
''' Examine the pdf of X_w^i components that deviate significantly from
N(0,1) based on MISE
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
X, _ = NG.meansub(Pk)
X_w, W = NG.whiten(X, method=method) # whitened data
# calculate the chi-squared values of each p(X_w^i)
x = np.arange(-5., 5.1, 0.1)
mise = np.zeros(X_w.shape[1])
for i_bin in range(X_w.shape[1]):
mise[i_bin] = NG.MISE(X_w[:,i_bin], b=b)
# plot the most discrepant components.
prettyplot()
fig = plt.figure()
sub = fig.add_subplot(111)
i_sort = np.argsort(mise)
print 'outlier bins = ', i_sort[-5:]
print 'mise = ', mise[i_sort[-5:]]
nbin = int(10./b)
for i_bin in i_sort[-10:]:
hb_Xi, Xi_edges = np.histogram(X_w[:,i_bin], bins=nbin, range=[-5., 5.], normed=True)
p_X_w_arr = UT.bar_plot(Xi_edges, hb_Xi)
sub.plot(p_X_w_arr[0], p_X_w_arr[1])
sub.plot(x, UT.gauss(x, 1., 0.), c='k', lw=3, label='$\mathcal{N}(0,1)$')
sub.set_xlim([-2.5, 2.5])
sub.set_xlabel('$\mathtt{X^{i}_{W}}$', fontsize=25)
sub.set_ylim([0., 0.6])
sub.set_ylabel('$\mathtt{P(X^{i}_{W})}$', fontsize=25)
sub.legend(loc='upper right')
str_rebin = ''
if rebin is not None:
str_rebin = '.rebin'+str(rebin)
f = ''.join([UT.fig_dir(), 'tests/test.p_Xw_i_outlier.', method, '.', mock, '.ell', str(ell),
str_rebin, '.b', str(b), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def p_Xw_i_outlier(mock, ell=0, rebin=None, krange=None, method='choletsky'):
''' Examine the pdf of X_w^i components that deviate significantly from
N(0,1)
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
X, _ = NG.meansub(Pk)
X_w, W = NG.whiten(X, method=method) # whitened data
# calculate the chi-squared values of each p(X_w^i)
x = np.arange(-5., 5.1, 0.1)
chi2 = np.zeros(X_w.shape[1])
for i_bin in range(X_w.shape[1]):
kern = gkde(X_w[:,i_bin]) # gaussian KDE kernel using "rule of thumb" scott's rule.
chi2[i_bin] = np.sum((UT.gauss(x, 1., 0.) - kern.evaluate(x))**2)/np.float(len(x))
# plot the most discrepant components.
prettyplot()
fig = plt.figure()
sub = fig.add_subplot(111)
i_sort = np.argsort(chi2)
print 'outlier bins = ', i_sort[-5:]
for i_bin in i_sort[-10:]:
kern = gkde(X_w[:,i_bin]) # gaussian KDE kernel using "rule of thumb" scott's rule.
sub.plot(x, kern.evaluate(x))
sub.plot(x, UT.gauss(x, 1., 0.), c='k', lw=3, label='$\mathcal{N}(0,1)$')
sub.set_xlim([-2.5, 2.5])
sub.set_xlabel('$\mathtt{X^{i}_{W}}$', fontsize=25)
sub.set_ylim([0., 0.6])
sub.set_ylabel('$\mathtt{P(X^{i}_{W})}$', fontsize=25)
sub.legend(loc='upper right')
if rebin is None:
f = ''.join([UT.fig_dir(), 'tests/test.p_Xw_i_outlier.', method, '.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.p_Xw_i_outlier.', method, '.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def dataX(mock, ell=0, rebin=None, krange=None):
''' ***TESTED***
Test the data X calculation
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
X, _ = NG.meansub(Pk)
prettyplot()
fig = plt.figure()
sub = fig.add_subplot(111)
for i in range(X.shape[0]):
sub.plot(range(X.shape[1]), X[i,:])
sub.set_xlim([0, X.shape[1]])
sub.set_xlabel('$\mathtt{k}$ bins', fontsize=25)
sub.set_ylim([-1e5, 1e5])
sub.set_ylabel('$\mathtt{P^i_'+str(ell)+'(k) - \overline{P_'+str(ell)+'(k)}}$', fontsize=25)
if rebin is not None:
f = ''.join([UT.fig_dir(), 'tests/test.dataX.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.dataX.', mock, '.ell', str(ell), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def p_Xw_i(mock, ell=0, rebin=None, krange=None, ica=False, pca=False):
''' Test the probability distribution function of each X_w^i
component -- p(X_w^i). First compare the histograms of p(X_w^i)
with N(0,1). Then compare the gaussian KDE of p(X_w^i).
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
X, _ = NG.meansub(Pk)
str_w = 'W'
if ica and pca:
raise ValueError
if ica: # ICA components
# ICA components do not need to be Gaussian.
# in fact the whole point of the ICA transform
# is to capture the non-Gaussianity...
X_white, _ = NG.whiten(X) # whitened data
X_w, _ = NG.Ica(X_white)
str_w = 'ICA'
if pca: # PCA components
X_w, _ = NG.whiten(X, method='pca') # whitened data
str_w = 'PCA'
if not ica and not pca: # just whitened
X_w, W = NG.whiten(X) # whitened data
# p(X_w^i) histograms
fig = plt.figure(figsize=(15,7))
sub = fig.add_subplot(121)
for i_bin in range(X_w.shape[1]):
p_X_w, edges = np.histogram(X_w[:,i_bin], normed=True)
p_X_w_arr = UT.bar_plot(edges, p_X_w)
sub.plot(p_X_w_arr[0], p_X_w_arr[1])
x = np.arange(-5., 5.1, 0.1)
sub.plot(x, UT.gauss(x, 1., 0.), c='k', lw=3, label='$\mathcal{N}(0,1)$')
sub.set_xlim([-2.5, 2.5])
sub.set_xlabel('$\mathtt{X_{'+str_w+'}}$', fontsize=25)
sub.set_ylim([0., 0.6])
sub.set_ylabel('$\mathtt{P(X_{'+str_w+'})}$', fontsize=25)
sub.legend(loc='upper right')
# p(X_w^i) gaussian KDE fits
pdfs = NG.p_Xw_i(X_w, range(X_w.shape[1]), x=x)
sub = fig.add_subplot(122)
for i_bin in range(X_w.shape[1]):
sub.plot(x, pdfs[i_bin])
sub.plot(x, UT.gauss(x, 1., 0.), c='k', lw=3, label='$\mathcal{N}(0,1)$')
sub.set_xlim([-2.5, 2.5])
sub.set_xlabel('$\mathtt{X_{W}}$', fontsize=25)
sub.set_ylim([0., 0.6])
sub.set_ylabel('$\mathtt{P(X_{W})}$', fontsize=25)
sub.legend(loc='upper right')
str_ica, str_pca = '', ''
if ica:
str_ica = '.ICA'
if pca:
str_pca = '.PCA'
if rebin is None:
f = ''.join([UT.fig_dir(), 'tests/test.p_Xw_i', str_pca, str_ica, '.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.p_Xw_i', str_pca, str_ica, '.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None
def p_Xwi_Xwj_outlier(mock, ell=0, rebin=None, krange=None, ica=False, pca=False):
''' Compare the joint pdfs of whitened X components (i.e. X_w^i, X_w^j)
p(X_w^i, X_w^j) to p(X_w^i) p(X_w^j) in order to test the independence
argument.
'''
Pk = NG.dataX(mock, ell=ell, rebin=rebin, krange=krange)
X, _ = NG.meansub(Pk)
if ica and pca:
raise ValueError
if ica: # ICA components
X_white, _ = NG.whiten(X) # whitened data
X_w, _ = NG.Ica(X_white)
if pca: # PCA components
X_w, _ = NG.whiten(X, method='pca') # whitened data
if not ica and not pca: # just whitened
X_w, _ = NG.whiten(X, method='choletsky') # whitened data
x, y = np.linspace(-5., 5., 50), np.linspace(-5., 5., 50)
xx, yy = np.meshgrid(x,y)
pos = np.vstack([xx.ravel(), yy.ravel()])
ij_i, ij_j = np.meshgrid(range(X_w.shape[1]), range(X_w.shape[1]))
ij = np.vstack([ij_i.ravel(), ij_j.ravel()])
# joint pdfs of X_w^i and X_w^j estimated from mocks
# i.e. p(X_w^i, X_w^j)
pdfs_2d = NG.p_Xwi_Xwj(X_w, ij, x=x, y=y)
# p(X_w^i) * p(X_w^j) estimated from mocks
pXwi = NG.p_Xw_i(X_w, range(X_w.shape[1]), x=x)
pXwj = pXwi
# calculate L2 norm difference betwen joint pdf and 2d gaussian
chi2 = np.zeros(len(pdfs_2d))
for i in range(len(pdfs_2d)):
if not isinstance(pdfs_2d[i], float):
pXwipXwj = np.dot(pXwi[ij[0,i]][:,None], pXwj[ij[1,i]][None,:]).T.flatten()
chi2[i] = np.sum((pXwipXwj - pdfs_2d[i])**2)
# ij values with the highest chi-squared
ii_out = np.argsort(chi2)[-10:]
inc = np.where(ij[0,ii_out] > ij[1,ii_out])
prettyplot()
fig = plt.figure(figsize=(len(inc[0])*10, 8))
for ii, i_sort_i in enumerate(ii_out[inc]):
sub = fig.add_subplot(1, len(inc[0]), ii+1)
# plot p(X_w^i) * p(X_w^j)
pXwipXwj = np.dot(pXwi[ij[0,i_sort_i]][:,None], pXwj[ij[1,i_sort_i]][None,:]).T
sub.contourf(xx, yy, pXwipXwj, cmap='gray_r', levels=[0.05, 0.1, 0.15, 0.2])
# p(X_w^i, X_w^j)
Z = np.reshape(pdfs_2d[i_sort_i], xx.shape)
cs = sub.contour(xx, yy, Z, colors='k', linestyles='dashed', levels=[0.05, 0.1, 0.15, 0.2])
cs.collections[0].set_label('$\mathtt{p(X_w^i, X_w^j)}$')
sub.set_xlim([-3., 3.])
sub.set_xlabel('$\mathtt{X_w^{i='+str(ij[0,i_sort_i])+'}}$', fontsize=25)
sub.set_ylim([-3., 3.])
sub.set_ylabel('$\mathtt{X_w^{j='+str(ij[1,i_sort_i])+'}}$', fontsize=25)
if ii == 0:
sub.legend(loc='upper right', prop={'size':25})
else:
sub.set_yticklabels([])
str_ica, str_pca = '', ''
if ica:
str_ica = '.ICA'
if pca:
str_pca = '.PCA'
if rebin is None:
f = ''.join([UT.fig_dir(), 'tests/test.p_Xwi_Xwj_outlier', str_ica, str_pca, '.', mock, '.ell', str(ell), '.png'])
else:
f = ''.join([UT.fig_dir(), 'tests/test.p_Xwi_Xwj_outlier', str_ica, str_pca, '.', mock, '.ell', str(ell), '.rebin', str(rebin), '.png'])
fig.savefig(f, bbox_inches='tight')
return None