def calc_C_matrices(Npix = 32, #pixels
field_width = 120., #arcmin
z0 = 0.5,
nz_a = 2,
nz_b = 1.5,
zlim = (0,3),
ngal_arcmin=20,
compute=True,
filename='C_calc.npz'):
dpix = field_width/Npix
n_z = lambda z: z**nz_a * numpy.exp(-(z/z0)**nz_b)
ngal = ngal_arcmin*dpix**2
if compute:
Om_range = (0.1,0.3,0.5)
s8_range = (0.6,0.8,1.0)
C = numpy.zeros((3,3,Npix**2,Npix**2))
for i,Om in enumerate(Om_range):
for j,s8 in enumerate(s8_range):
xi = xi_plus(n_z,
zlim,
Nz=20,
Or=0,
Om=Om,
sigma8=s8)
C[i,j] = compute_correlation_matrix(xi,
Npix = Npix,
dpix = dpix,
ngal = ngal,
sigma = sigma,
whiten=True)
evals,evecs = compute_KL(C[1,1])
numpy.savez(filename,
C=C,
Om_range=Om_range,
s8_range=s8_range,
evals=evals,
evecs=evecs)
else:
X = numpy.load(filename)
C = X['C']
Om_range = X['Om_range']
s8_range = X['s8_range']
evals = X['evals']
evecs = X['evecs']
return C,Om_range,s8_range,evals,evecs
def shear_correlation_matrix(sigma, RArange, DECrange, Ngal,
n_z = zdist,
whiten = True,
cosmo=None, **kwargs):
"""
Compute the correlation matrix based on the COSMOS geometry
Parameters
----------
sigma : float
intrinsic ellipticity in each pixel
RArange : float array, size = NRA + 1
RA bin edges
DECrange : float array, size = NDEC + 1
DEC bin edges
Ngal : integer array, shape = (NRA, NDEC)
number of galaxies in each bin. This can be determined using
the routine `shear_mask_vector`
z0, nz_a, nz_b : float
specify the galaxy redshift distribution:
n(z) ~ z^a * exp[-(z/z0)^b]
cosmo : cosmology object
if unspecified, a Cosmology object will be initialized from kwargs
Returns
-------
C : the theoretical covariance matrix of the COSMOS data
"""
xi = xi_plus(n_z, Nz=20, cosmo=cosmo, **kwargs)
dpix1 = 60. * (RArange[1] - RArange[0])
dpix2 = 60. * (DECrange[1] - DECrange[0])
Npix1 = len(RArange) - 1
Npix2 = len(DECrange) - 1
#compute correlation, no shot noise
if (Npix1 == Npix2) and (dpix1 == dpix2):
C = compute_correlation_matrix(xi, Npix=Npix1, dpix=dpix1,
ngal=1, sigma=0, whiten=False)
else:
C = compute_correlation_matrix_nonsquare(xi, Npix1=Npix1, dpix1=dpix1,
Npix2=Npix2, dpix2=dpix2,
ngal=1, sigma=0,
whiten=False)
Ngal = Ngal.reshape(Npix1 * Npix2)
i_zero = np.where(Ngal==0)[0]
Ngal[i_zero] = 1
noise_squared_diag = sigma**2 / Ngal.reshape(Npix1*Npix2)
Ngal[i_zero] = 0
#add shot noise
C.flat[::Npix1 * Npix2 + 1] += noise_squared_diag
#zero-out correlation matrix where there is no data
C[i_zero] = 0
C[:,i_zero] = 0
if whiten:
noise_inv = noise_squared_diag**-0.5
C *= noise_inv[:,None]
C *= noise_inv
return C