def plot_kappa_simple(catalog_file,
remove_z_problem=False,
Npix=128,
kappa_filter=4,
kappa_cutoff=0):
"""
kappa_filter is in pixels
"""
gamma_plot, Ngal, RArange_g, DECrange_g = get_gamma_vector(
catalog_file, dtheta=2.0, remove_z_problem=remove_z_problem)
# get a square grid for the kappa measurement
NRA = NDEC = Npix
RAmin = RArange_g[0]
RAmax = RArange_g[-1]
DECmin = DECrange_g[0]
DECmax = DECrange_g[-1]
dtheta = (RAmax - RAmin) * 1. / NRA * 60
# DEC range is smaller than RA range: make half the
# zeros on the bottom
DECmin -= 0.5 * (DECmin + NDEC * dtheta / 60. - DECmax)
DECmax = DECmin + NDEC * dtheta / 60.
# get the shear realization
gamma, Ngal, RArange, DECrange = get_gamma_vector(
catalog_file,
dtheta,
RAmin,
DECmin,
NRA,
NDEC + 1,
remove_z_problem=remove_z_problem)
kappa = gamma_to_kappa(gamma.T, dtheta)
if kappa_filter:
kappa = filters.gaussian_filter(kappa.real, kappa_filter) \
+ 1j * filters.gaussian_filter(kappa.imag, kappa_filter)
if kappa_cutoff is not None:
kappa[np.where(kappa < kappa_cutoff)] = kappa_cutoff
pylab.figure(figsize=(10, 8))
pylab.imshow(kappa.real.T,
origin='lower',
cmap=BkBuW(1.0),
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.title('COSMOS convergence map: Kaiser-Squires')
pylab.colorbar().set_label(r'$\kappa\ \mathrm{(E-mode)}$')
#conjugate gamma: we're flipping the x-axis
whiskerplot(gamma_plot.conj(), RArange_g, DECrange_g, color='w')
pylab.ylim(DECmin, 2.9)
def plot_kappa_simple(catalog_file, remove_z_problem=False,
Npix=128, kappa_filter=4,
kappa_cutoff=0):
"""
kappa_filter is in pixels
"""
gamma_plot, Ngal, RArange_g, DECrange_g = get_gamma_vector(
catalog_file, dtheta=2.0, remove_z_problem=remove_z_problem)
# get a square grid for the kappa measurement
NRA = NDEC = Npix
RAmin = RArange_g[0]
RAmax = RArange_g[-1]
DECmin = DECrange_g[0]
DECmax = DECrange_g[-1]
dtheta = (RAmax-RAmin) * 1./NRA * 60
# DEC range is smaller than RA range: make half the
# zeros on the bottom
DECmin -= 0.5 * (DECmin + NDEC * dtheta/60. - DECmax)
DECmax = DECmin + NDEC * dtheta/60.
# get the shear realization
gamma, Ngal, RArange, DECrange = get_gamma_vector(
catalog_file, dtheta, RAmin, DECmin, NRA, NDEC+1,
remove_z_problem=remove_z_problem)
kappa = gamma_to_kappa(gamma.T, dtheta)
if kappa_filter:
kappa = filters.gaussian_filter(kappa.real, kappa_filter) \
+ 1j * filters.gaussian_filter(kappa.imag, kappa_filter)
if kappa_cutoff is not None:
kappa[np.where(kappa < kappa_cutoff)] = kappa_cutoff
pylab.figure(figsize=(10,8))
pylab.imshow(kappa.real.T,
origin='lower',
cmap=BkBuW(1.0),
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.title('COSMOS convergence map: Kaiser-Squires')
pylab.colorbar().set_label(r'$\kappa\ \mathrm{(E-mode)}$')
#conjugate gamma: we're flipping the x-axis
whiskerplot(gamma_plot.conj(), RArange_g, DECrange_g, color='w')
pylab.ylim(DECmin, 2.9)
def plot_mask(catalog_file,
dtheta,
RAmin=None,
DECmin=None,
NRA=None,
NDEC=None,
remove_z_problem=True,
N_bootstraps=0):
gamma, Ngal, RArange, DECrange = get_gamma_vector(
catalog_file,
dtheta,
RAmin,
DECmin,
NRA,
NDEC,
N_bootstraps=N_bootstraps,
remove_z_problem=remove_z_problem)
print RArange[0], RArange[-1]
print DECrange[0], DECrange[-1]
print gamma.shape
print Ngal.shape
pylab.imshow(Ngal.T, origin='lower', interpolation='nearest')
pylab.colorbar()
def plot_shear(catalog_file, dtheta):
gamma, Ngal, RArange, DECrange = get_gamma_vector(
catalog_file, dtheta, remove_z_problem=False)
pylab.imshow(Ngal.T, origin='lower',
cmap=BkBuW(0.8),
extent=(RArange[0], RArange[-1], DECrange[0], DECrange[-1]))
pylab.xlim(pylab.xlim()[::-1])
whiskerplot(gamma, RArange, DECrange, color='w')
def plot_shear(catalog_file, dtheta):
gamma, Ngal, RArange, DECrange = get_gamma_vector(catalog_file,
dtheta,
remove_z_problem=False)
pylab.imshow(Ngal.T,
origin='lower',
cmap=BkBuW(0.8),
extent=(RArange[0], RArange[-1], DECrange[0], DECrange[-1]))
pylab.xlim(pylab.xlim()[::-1])
whiskerplot(gamma, RArange, DECrange, color='w')
def plot_mask(catalog_file, dtheta,
RAmin = None, DECmin = None,
NRA = None, NDEC = None,
remove_z_problem = True,
N_bootstraps=0):
gamma, Ngal, RArange, DECrange = get_gamma_vector(
catalog_file, dtheta, RAmin, DECmin, NRA, NDEC,
N_bootstraps=N_bootstraps, remove_z_problem=remove_z_problem)
print RArange[0], RArange[-1]
print DECrange[0], DECrange[-1]
print gamma.shape
print Ngal.shape
pylab.imshow(Ngal.T,
origin='lower',
interpolation='nearest')
pylab.colorbar()
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_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 plot_kappa_SN(catalog_file, N_realizations=1000):
# compute a 64 x 64 grid which encompasses all the data
RAmin = 149.4317396
RAmax = 150.798406267
DECmin = 1.570097085
DECmax = 2.90343041833
NRA = 64
NDEC = 64
dtheta = (RAmax - RAmin) * 1. / NRA * 60
DECmin -= 0.5 * (DECmin + NDEC * dtheta / 60. - DECmax)
# get the shear realization
gamma, Ngal, d2gamma, RArange, DECrange = get_gamma_vector(
catalog_file,
dtheta,
RAmin,
DECmin,
NRA,
NDEC,
remove_z_problem=True,
N_bootstraps=N_realizations)
kappa = np.zeros(gamma.shape, dtype=complex)
kappa_2 = np.zeros(gamma.shape, dtype=float)
i_zero = np.where(d2gamma <= 0)
d2gamma[i_zero] = 1
dgamma = np.sqrt(d2gamma)
print "computing kappa %i times" % N_realizations
for i in range(N_realizations):
if (i + 1) % 100 == 0:
print " >", i + 1
phase = np.exp(2j * np.pi * np.random.random(gamma.shape))
noise = np.random.normal(0, dgamma)
noise[i_zero] = 0
k = gamma_to_kappa(gamma + phase * noise, dtheta)
kappa += k
kappa_2 += abs(k)**2
kappa /= N_realizations
d2kappa = kappa_2 / N_realizations - abs(kappa)**2
pylab.figure()
pylab.imshow(d2kappa.T,
origin='lower',
interpolation='nearest',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.colorbar()
pylab.figure()
pylab.imshow(Ngal.T,
origin='lower',
interpolation='nearest',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
# compute convergence signal-to-noise
i_zero = np.where(d2kappa == 0)
d2kappa[i_zero] = 1
kappa_SN = kappa / np.sqrt(d2kappa)
kappa_SN[i_zero] = np.nan
pylab.figure()
pylab.imshow(kappa_SN[4:-4, 4:-4].real.T,
origin='lower',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.colorbar()
pylab.figure()
pylab.imshow(kappa_SN[4:-4, 4:-4].imag.T,
origin='lower',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.colorbar()
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 plot_kappa_SN(catalog_file,
N_realizations=1000):
# compute a 64 x 64 grid which encompasses all the data
RAmin = 149.4317396
RAmax = 150.798406267
DECmin = 1.570097085
DECmax = 2.90343041833
NRA = 64
NDEC = 64
dtheta = (RAmax-RAmin) * 1./NRA * 60
DECmin -= 0.5 * (DECmin + NDEC * dtheta/60. - DECmax)
# get the shear realization
gamma, Ngal, d2gamma, RArange, DECrange = get_gamma_vector(
catalog_file, dtheta, RAmin, DECmin, NRA, NDEC,
remove_z_problem=True,
N_bootstraps=N_realizations)
kappa = np.zeros(gamma.shape, dtype=complex)
kappa_2 = np.zeros(gamma.shape, dtype=float)
i_zero = np.where(d2gamma <= 0)
d2gamma[i_zero] = 1
dgamma = np.sqrt(d2gamma)
print "computing kappa %i times" % N_realizations
for i in range(N_realizations):
if (i+1)%100 == 0:
print " >", i+1
phase = np.exp(2j * np.pi * np.random.random(gamma.shape))
noise = np.random.normal(0, dgamma)
noise[i_zero] = 0
k = gamma_to_kappa(gamma + phase * noise, dtheta)
kappa += k
kappa_2 += abs(k) ** 2
kappa /= N_realizations
d2kappa = kappa_2 / N_realizations - abs(kappa) ** 2
pylab.figure()
pylab.imshow(d2kappa.T, origin='lower', interpolation='nearest',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.colorbar()
pylab.figure()
pylab.imshow(Ngal.T, origin='lower', interpolation='nearest',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
# compute convergence signal-to-noise
i_zero = np.where(d2kappa == 0)
d2kappa[i_zero] = 1
kappa_SN = kappa / np.sqrt(d2kappa)
kappa_SN[i_zero] = np.nan
pylab.figure()
pylab.imshow(kappa_SN[4:-4,4:-4].real.T,
origin='lower',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.colorbar()
pylab.figure()
pylab.imshow(kappa_SN[4:-4,4:-4].imag.T,
origin='lower',
extent=(RAmin, RAmax, DECmin, DECmax))
pylab.xlim(pylab.xlim()[::-1])
pylab.colorbar()
