def compute_all(
catalog_file,
dtheta,
n_z,
sigma=0.39,
RAmin=None,
DECmin=None,
NRA=None,
NDEC=None,
remove_z_problem=True,
N_bootstraps=1000,
cosmo=None,
**kwargs
):
"""
parse catalog data and compute eigenvalue decomposition
Parameters
----------
catalog_file : string or list of strings
location of the COSMOS catalog(s) to use
dtheta : float
size of (square) pixels in arcmin
sigma : float (default = 0.39)
intrinsic ellipticity of galaxies
cosmo : Cosmology object
the fiducial cosmology used for determination of KL vectors
if unspecified, it will be initialized from remaining kwargs
Other Parameters
----------------
n_z : `shear_KL_source.zdist.zdist` object
n_z(z) returns the galaxy distribution
If the following are unspecified, they will be determined from the data
RAmin/DECmin : float
minimum of RA/DEC bins (degrees).
NRA/NDEC : int
number of RA/DEC bins
Returns
-------
evals, evecs, a_fit, shape
"""
gamma, Ngal, noise, RArange, DECrange = get_gamma_vector(
catalog_file, dtheta, RAmin, DECmin, NRA, NDEC, N_bootstraps=N_bootstraps, remove_z_problem=False
)
if cosmo is None:
cosmo = Cosmology(**kwargs)
NRA, NDEC = gamma.shape
# use results of bootstrap resampling to compute
# the noise on observed shear
gamma = gamma.reshape(gamma.size)
Ngal = Ngal.reshape(Ngal.size)
noise = noise.reshape(noise.size)
i_sigma = np.where(Ngal > 5)
sigma_estimate = np.sqrt(np.mean(noise[i_sigma] * Ngal[i_sigma]))
print "average sigma: %.2g" % sigma_estimate
izero = np.where(Ngal <= 5)
noise[izero] = sigma_estimate ** 2
N_m_onehalf = noise ** -0.5
# noise = sigma^2 / Ngal
# correlation matrix takes a constant sigma and a variable
# ngal. So we'll encode the noise as an "effective Ngal"
# using the user-defined sigma.
Ngal_eff = sigma ** 2 / noise
Ngal_eff[np.where(Ngal == 0)] = 0
# construct fiducial correlation matrix
print ">> fiducial correlation matrix"
R_fid = shear_correlation_matrix(sigma, RArange, DECrange, Ngal_eff, n_z, whiten=True, cosmo=cosmo)
evals, evecs = np.linalg.eigh(R_fid)
isort = np.argsort(evals)[::-1]
evals = evals[isort]
evecs = evecs[:, isort]
a = np.dot(evecs.T, N_m_onehalf * gamma)
return (evals, evecs, a, RArange, DECrange, Ngal, noise, N_bootstraps, dtheta)
def compute_likelihoods(catalog_file,
out_file,
cosmo_dict,
nmodes,
dtheta,
n_z,
sigma=0.3,
RAmin = None, DECmin = None,
NRA = None, NDEC = None,
remove_z_problem=True,
fiducial_cosmology = None,
**kwargs):
"""
compute the likelihoods for a range of cosmologies
Parameters
----------
catalog_file : string or list of strings
location of the COSMOS catalog(s) to use
out_file : string
location to save likelihood output
Output will be a text file, with columns labeled
cosmo_dict : Dictionary
keys are arguments for cosmology object
values are the corresponding range
nmodes :
number of modes to use. This should be less than NRA*NDEC
alternatively, a list of integers can be supplied
dtheta : float
size of (square) pixels in arcmin
sigma : float (default = 0.3)
intrinsic ellipticity of galaxies
fiducial_cosmology : Cosmology object
the fiducial cosmology used for determination of KL vectors
if unspecified, it will be initialized from remaining kwargs
Other Parameters
----------------
n_z : `shear_KL_source.zdist.zdist` object
n_z(z) returns the galaxy distribution
If the following are unspecified, they will be determined from the data
RAmin/DECmin : float
minimum of RA/DEC bins (degrees).
NRA/NDEC : int
number of RA/DEC bins
"""
gamma, Ngal, noise, RArange, DECrange = get_gamma_vector(
catalog_file, dtheta, RAmin, DECmin, NRA, NDEC, N_bootstraps=10,
remove_z_problem=True)
if fiducial_cosmology is None:
fiducial_cosmology = Cosmology(**kwargs)
# use results of bootstrap resampling to compute
# the noise on observed shear
gamma = gamma.reshape(gamma.size)
Ngal = Ngal.reshape(Ngal.size)
noise = noise.reshape(noise.size)
i_sigma = np.where(Ngal > 1)
sigma_estimate = np.sqrt(np.mean(noise[i_sigma] * Ngal[i_sigma]))
print "average sigma: %.2g" % sigma_estimate
izero = np.where(Ngal <= 1)
noise[izero] = sigma_estimate ** 2
N_m_onehalf = noise ** -0.5
# noise = sigma^2 / Ngal
# correlation matrix takes a constant sigma and a variable
# ngal. So we'll encode the noise as an "effective Ngal"
# using the user-defined sigma.
Ngal_eff = sigma**2 / noise
Ngal_eff[np.where(Ngal == 0)] = 0
# construct fiducial correlation matrix
print ">> fiducial correlation matrix"
R_fid = shear_correlation_matrix(sigma, RArange, DECrange, Ngal_eff,
n_z,
whiten=True,
cosmo=fiducial_cosmology)
evals, evecs = np.linalg.eigh(R_fid)
isort = np.argsort(evals)[::-1]
evals = evals[isort]
evecs = evecs[:,isort]
#compute KL transform of data
a_data = np.dot(evecs.T, N_m_onehalf * gamma)
#iterate through all nmodes requested
if not hasattr(nmodes, '__iter__'):
nmodes = [nmodes]
cosmo_keys = cosmo_dict.keys()
cosmo_vals = [cosmo_dict[k] for k in cosmo_keys]
cosmo_kwargs = fiducial_cosmology.get_dict()
log2pi = np.log(2*np.pi)
OF = open(out_file, 'w')
OF.write('# fiducial cosmology: %s\n' % str(cosmo_kwargs))
OF.write('# ncut ')
OF.write(' '.join(cosmo_keys))
OF.write(' chi2 log|det(C)| log(Likelihood)\n')
for cosmo_tup in iter_product(*cosmo_vals):
cosmo_kwargs.update(dict(zip(cosmo_keys,cosmo_tup)))
#flat universe prior
cosmo_kwargs['Ol'] = 1. - cosmo_kwargs['Om']
print ">>", cosmo_keys, ['%.2g' % v for v in cosmo_tup]
R = shear_correlation_matrix(sigma, RArange, DECrange, Ngal_eff,
n_z,
whiten=True,
**cosmo_kwargs)
cosmo_args = (len(cosmo_keys) * " %.6g") % cosmo_tup
for ncut in nmodes:
evecs_n = evecs[:,:ncut]
a_n = a_data[:ncut]
C_n = np.dot(evecs_n.T, np.dot(R, evecs_n))
# compute chi2 = (a_n-<a_n>)^T C_n^-1 (a_n-<a_n>)
# model predicts <a> = 0 so this simplifies:
chi2_raw = np.dot(a_n.conj(), np.linalg.solve(C_n, a_n))
#chi2_raw is complex because a_n is complex. The imaginary
# part of chi2 should be zero (within machine precision), because
# C_n is Hermitian. We'll skip checking that this is the case.
chi2 = chi2_raw.real
s, logdetC = np.linalg.slogdet(C_n)
X0 = -0.5 * ncut * log2pi
X1 = -0.5 * logdetC
X2 = -0.5 * chi2
print chi2, logdetC, X0, X1, X2
OF.write("%i %s %.6g %.6g %.6g\n" % (ncut, cosmo_args, chi2,
logdetC, X0+X1+X2))
###
###
OF.close()
def compute_likelihoods(catalog_file,
out_file,
cosmo_dict,
nmodes,
dtheta,
n_z,
sigma=0.3,
RAmin=None,
DECmin=None,
NRA=None,
NDEC=None,
remove_z_problem=True,
fiducial_cosmology=None,
**kwargs):
"""
compute the likelihoods for a range of cosmologies
Parameters
----------
catalog_file : string or list of strings
location of the COSMOS catalog(s) to use
out_file : string
location to save likelihood output
Output will be a text file, with columns labeled
cosmo_dict : Dictionary
keys are arguments for cosmology object
values are the corresponding range
nmodes :
number of modes to use. This should be less than NRA*NDEC
alternatively, a list of integers can be supplied
dtheta : float
size of (square) pixels in arcmin
sigma : float (default = 0.3)
intrinsic ellipticity of galaxies
fiducial_cosmology : Cosmology object
the fiducial cosmology used for determination of KL vectors
if unspecified, it will be initialized from remaining kwargs
Other Parameters
----------------
n_z : `shear_KL_source.zdist.zdist` object
n_z(z) returns the galaxy distribution
If the following are unspecified, they will be determined from the data
RAmin/DECmin : float
minimum of RA/DEC bins (degrees).
NRA/NDEC : int
number of RA/DEC bins
"""
gamma, Ngal, noise, RArange, DECrange = get_gamma_vector(
catalog_file,
dtheta,
RAmin,
DECmin,
NRA,
NDEC,
N_bootstraps=10,
remove_z_problem=True)
if fiducial_cosmology is None:
fiducial_cosmology = Cosmology(**kwargs)
# use results of bootstrap resampling to compute
# the noise on observed shear
gamma = gamma.reshape(gamma.size)
Ngal = Ngal.reshape(Ngal.size)
noise = noise.reshape(noise.size)
i_sigma = np.where(Ngal > 1)
sigma_estimate = np.sqrt(np.mean(noise[i_sigma] * Ngal[i_sigma]))
print "average sigma: %.2g" % sigma_estimate
izero = np.where(Ngal <= 1)
noise[izero] = sigma_estimate**2
N_m_onehalf = noise**-0.5
# noise = sigma^2 / Ngal
# correlation matrix takes a constant sigma and a variable
# ngal. So we'll encode the noise as an "effective Ngal"
# using the user-defined sigma.
Ngal_eff = sigma**2 / noise
Ngal_eff[np.where(Ngal == 0)] = 0
# construct fiducial correlation matrix
print ">> fiducial correlation matrix"
R_fid = shear_correlation_matrix(sigma,
RArange,
DECrange,
Ngal_eff,
n_z,
whiten=True,
cosmo=fiducial_cosmology)
evals, evecs = np.linalg.eigh(R_fid)
isort = np.argsort(evals)[::-1]
evals = evals[isort]
evecs = evecs[:, isort]
#compute KL transform of data
a_data = np.dot(evecs.T, N_m_onehalf * gamma)
#iterate through all nmodes requested
if not hasattr(nmodes, '__iter__'):
nmodes = [nmodes]
cosmo_keys = cosmo_dict.keys()
cosmo_vals = [cosmo_dict[k] for k in cosmo_keys]
cosmo_kwargs = fiducial_cosmology.get_dict()
log2pi = np.log(2 * np.pi)
OF = open(out_file, 'w')
OF.write('# fiducial cosmology: %s\n' % str(cosmo_kwargs))
OF.write('# ncut ')
OF.write(' '.join(cosmo_keys))
OF.write(' chi2 log|det(C)| log(Likelihood)\n')
for cosmo_tup in iter_product(*cosmo_vals):
cosmo_kwargs.update(dict(zip(cosmo_keys, cosmo_tup)))
#flat universe prior
cosmo_kwargs['Ol'] = 1. - cosmo_kwargs['Om']
print ">>", cosmo_keys, ['%.2g' % v for v in cosmo_tup]
R = shear_correlation_matrix(sigma,
RArange,
DECrange,
Ngal_eff,
n_z,
whiten=True,
**cosmo_kwargs)
cosmo_args = (len(cosmo_keys) * " %.6g") % cosmo_tup
for ncut in nmodes:
evecs_n = evecs[:, :ncut]
a_n = a_data[:ncut]
C_n = np.dot(evecs_n.T, np.dot(R, evecs_n))
# compute chi2 = (a_n-<a_n>)^T C_n^-1 (a_n-<a_n>)
# model predicts <a> = 0 so this simplifies:
chi2_raw = np.dot(a_n.conj(), np.linalg.solve(C_n, a_n))
#chi2_raw is complex because a_n is complex. The imaginary
# part of chi2 should be zero (within machine precision), because
# C_n is Hermitian. We'll skip checking that this is the case.
chi2 = chi2_raw.real
s, logdetC = np.linalg.slogdet(C_n)
X0 = -0.5 * ncut * log2pi
X1 = -0.5 * logdetC
X2 = -0.5 * chi2
print chi2, logdetC, X0, X1, X2
OF.write("%i %s %.6g %.6g %.6g\n" %
(ncut, cosmo_args, chi2, logdetC, X0 + X1 + X2))
###
###
OF.close()
