def __init__(self, alpha, beta, K):
"""
Note alpha/beta = mean, alpha/beta^2 = variance
@param alpha:
shape parameter
@param beta:
inverse scale parameter
@param K:
number of bins
"""
if alpha <= 0:
raise Exception("alpha = %f <= 0" % alpha)
if beta <= 0:
raise Exception("beta = %f <= 0" % beta)
if K < 1:
raise Exception("Num bins = %d < 1" % K)
# find upper boundaries of each bin
max_prob = gammainc(alpha, self.MAX_RATE)
bin_prob = max_prob / K
targets = np.arange(bin_prob, max_prob+bin_prob/2, bin_prob)
#XXX: not sure why we don't divide targets / beta
bin_ubounds = gammaincinv(alpha, targets) / beta
bin_lbounds = np.zeros(K)
bin_lbounds[1:] = bin_ubounds[:-1]
tmp = gammainc(alpha+1, bin_ubounds * beta) - gammainc(alpha+1, bin_lbounds * beta)
bin_rates = tmp * alpha / beta * K
# Rate of middle of each bin
self.bin_rates = bin_rates
# Probability mass of each bin
self.bin_probs = np.zeros(K) + bin_prob
def ppf(self, x):
"""
Computes the percent point function of the distribution at the point(s)
x. It is defined as the inverse of the CDF. y = ppf(x) can be
interpreted as the argument y for which the value of the cdf(x) is equal
to y. Essentially that means the random varable y is the place on the
distribution the CDF evaluates to x.
Parameters
----------
x: array, dtype=float, shape=(m x n), bounds=(0,1)
The value(s) at which the user would like the ppf evaluated.
If an array is passed in, the ppf is evaluated at every point
in the array and an array of the same size is returned.
Returns
-------
ppf: array, dtype=float, shape=(m x n)
The ppf at each point in x.
"""
if (x <= 0).any() or (x >= 1).any():
raise ValueError(
"all values in x must be between 0 and 1, \
exclusive"
)
ppf = 1.0 / gammaincinv(self.alpha, 1 - x)
return ppf
def truncated_gamma(shape=None, alpha=1., beta=1., x_min=None, x_max=None):
"""
Generate random variates from a lower-and upper-bounded gamma distribution.
@param shape: shape of the random sample
@param alpha: shape parameter (alpha > 0.)
@param beta: scale parameter (beta >= 0.)
@param x_min: lower bound of variate
@param x_max: upper bound of variate
@return: random variates of lower-bounded gamma distribution
"""
from scipy.special import gammainc, gammaincinv
from numpy.random import gamma
from numpy import inf
if x_min is None and x_max is None:
return gamma(alpha, 1 / beta, shape)
elif x_min is None:
x_min = 0.
elif x_max is None:
x_max = inf
x_min = max(0., x_min)
x_max = min(1e300, x_max)
a = gammainc(alpha, beta * x_min)
b = gammainc(alpha, beta * x_max)
return probability_transform(shape,
lambda x, alpha=alpha: gammaincinv(alpha, x),
a, b) / beta
def ep_rvs(mu=0, alpha=1, beta=1, size=1):
u = uniform.rvs(loc=0, scale=1, size=size)
z = 2 * np.abs(u - 1. / 2)
z = gammaincinv(1. / beta, z)
y = mu + np.sign(u - 1. / 2) * alpha * z**(1. / beta)
return y
def _testCompareToExplicitDerivative(self, dtype):
"""Compare to the explicit reparameterization derivative.
Verifies that the computed derivative satisfies
dsample / dalpha = d igammainv(alpha, u) / dalpha,
where u = igamma(alpha, sample).
Args:
dtype: TensorFlow dtype to perform the computations in.
"""
delta = 1e-3
np_dtype = dtype.as_numpy_dtype
try:
from scipy import misc # pylint: disable=g-import-not-at-top
from scipy import special # pylint: disable=g-import-not-at-top
alpha_val = np.logspace(-2, 3, dtype=np_dtype)
alpha = constant_op.constant(alpha_val)
sample = random_ops.random_gamma([], alpha, np_dtype(1.0), dtype=dtype)
actual = gradients_impl.gradients(sample, alpha)[0]
(sample_val, actual_val) = self.evaluate((sample, actual))
u = special.gammainc(alpha_val, sample_val)
expected_val = misc.derivative(
lambda alpha_prime: special.gammaincinv(alpha_prime, u),
alpha_val, dx=delta * alpha_val)
self.assertAllClose(actual_val, expected_val, rtol=1e-3, atol=1e-3)
except ImportError as e:
tf_logging.warn("Cannot use special functions in a test: %s" % str(e))
def inverse_gamma_cdf(p,k,theta,offset):
"""
Inverse gamma cumulative distribution function.
"""
x = gammaincinv(k,p)
x = (x * theta) + offset
return x
def bn_exact(n):
"""
Computes :math:`b_n` exactly for the current sersic index, using
incomplete gamma functions.
"""
from scipy.special import gammaincinv
n = float(n) #sometimes 0d array gets passed in
return gammaincinv(2*n,0.5)
def test_ufig_gal_intrinsic():
try:
from scipy.special import gammaincinv
except ImportError:
pytest.skip("Scipy is not available")
n = np.uint32(1.88 * np.float64(np.int64(1) << 32) / 10.)
sersicLTable = np.uint32(n >> np.uint32(32 - 9))
sersicBTable = np.float32(n - (sersicLTable << np.uint32(32 - 9))) / np.float32(1 << (32 - 9))
# gamma lookup has 1<<9, 512 elements, and a more precise fitt on 0-1/(1<<3) with 1<<11, 2048 elements
radiusTable = np.empty(((1 << 9) + 1, (1 << (11 + 1)) + 1, ), dtype=np.float32)
radiusTable[0][0:(1 << 11)] = (np.power(gammaincinv(2e-15, np.float64(range(0, 1 << 11)) / np.float64(1 << 11)), 1e-15) / 1e-15).astype(np.float32)
radiusTable[0][(1 << 11):(1 << (11 + 1))] = (np.power(gammaincinv(2e-15, 1. - 1. / np.float64(1 << 3) + np.float64(range(0, 1 << 11)) / np.float64(1 << (11 + 3))), 1e-15) / 1e-15).astype(np.float32)
radiusTable[0][1 << 11] = (np.power(gammaincinv(2e-15, (1. - 1e-15) / np.float64(1 << 11)), 1e-15) / 1e-15).astype(np.float32)
radiusTable[0][1 << (11 + 1)] = (np.power(gammaincinv(2e-15, 1. - 1. / np.float64(1 << 3) + (1. - 1e-15) / np.float64(1 << (11 + 3))), 1e-15) / 1e-15).astype(np.float32)
# TODO: make only one gamma interpolation instead of two
for i in range(1, (1 << 9) + 1):
n = 10. * np.float64(i << (32 - 9)) / (np.int64(1) << 32)
k = gammaincinv(2. * n, 0.5)
radiusTable[i][0:(1 << 11)] = (np.power(gammaincinv(2. * n, np.float64(range(0, 1 << 11)) / np.float64(1 << 11)), n) / np.power(k, n)).astype(np.float32)
radiusTable[i][(1 << 11):(1 << (11 + 1))] = (np.power(gammaincinv(2. * n, 1. - 1. / np.float64(1 << 3) + np.float64(range(0, 1 << 11)) / np.float64(1 << (11 + 3))), n) / np.power(k, n)).astype(np.float32)
radiusTable[i][1 << 11] = (np.power(gammaincinv(2. * n, (1. - 1e-15) / np.float64(1 << 11)), n) / np.power(k, n)).astype(np.float32)
radiusTable[i][1 << (11 + 1)] = (np.power(gammaincinv(2. * n, 1. - 1. / np.float64(1 << 3) + (1. - 1e-15) / np.float64(1 << (11 + 3))), n) / np.power(k, n)).astype(np.float32)
def fkt_intrinsic(rng, sersicLTable, sersicBTable, radiusTable):
drMaski = rng >> (32 - 3) == (1 << 3) - 1
drKi = rng >> np.uint32(drMaski * 3)
drLi = (drKi >> (32 - 11)) + np.uint32(drMaski * (1 << 11))
drBi = np.float64(drKi & ((1 << (32 - 11)) - 1)) / np.float64(1 << (32 - 11))
drAi = 1. - drBi
nLi = sersicLTable
nBi = sersicBTable
nAi = 1 - nBi
return drAi * (nAi * radiusTable[nLi, drLi] + nBi * radiusTable[nLi, drLi + 1]) \
+ drBi * (nAi * radiusTable[nLi + 1, drLi] + nBi * radiusTable[nLi + 1, drLi + 1])
rngBuffer = np.random.randint(0, 1<<32, size=(1000,)).astype(np.uint32)
hope.config.optimize = True
hintrinsic = hope.jit(fkt_intrinsic)
for rng in rngBuffer:
dr = fkt_intrinsic(rng, sersicLTable, sersicBTable, radiusTable)
hdr = hintrinsic(rng, sersicLTable, sersicBTable, radiusTable)
assert check(dr, hdr)
hope.config.optimize = False
def q_lambda2(y, z, n_k, extremes):
gam_a = n_k; gam_b = sum(z*y)
u = np.random.uniform(0, 1, len(n_k))
F_min, F_max = sp.gammainc(gam_a, gam_b*np.array(extremes))
lambda_const = F_max-F_min
lambda2 = sp.gammaincinv(gam_a, F_min+u*lambda_const)/gam_b
idx = np.where(gam_a == 0)
if len(idx[0]): # if any values with gam_a==0
F_min, F_max = np.log(extremes)
normC = F_max-F_min
lambda2[idx] = np.exp(u[idx]*normC+F_min)
return lambda2
def ppf(self,u):
'''
Evaluates the percent point function (i.e. the inverse c.d.f.)
of the current distribution.
:param u: Points at which the p.p.f. will be computed.
:type u: numpy.array
:returns: Data object with the resulting points in the domain of this distribution.
:rtype: natter.DataModule.Data
'''
q = 1/self.param['p']
s = self.param['s']
return Data(sign(u-.5) * s**q *gammaincinv(q,abs(2*u-1))**q,'Function values of the p.p.f of %s' % (self.name,))
def ppf(self,u):
'''
Evaluates the percent point function (i.e. the inverse c.d.f.)
of the current distribution.
:param u: Points at which the p.p.f. will be computed.
:type u: numpy.array
:returns: Data object with the resulting points in the domain of this distribution.
:rtype: natter.DataModule.Data
'''
q = 1/self.param['p']
s = self.param['s']
v = array([self.param['a'],self.param['b']])
v = .5 + 0.5*sign(v)*gammainc(1/self.param['p'],abs(v)**self.param['p'] / self.param['s'])
dv = v[1]-v[0]
return Data(sign(dv*u+v[0]-.5) * s**q *gammaincinv(q,abs(2*(dv*u+v[0])-1))**q,'Percentiles of %s' % (self.name,))
def __init__(self, params, calc_params=False):
"""
Initialize and calculate a bunch of useful quantities.
"""
self.params = params
self.I_e = params['I_e']
self.r_e = params['r_e']
self.n = params['n']
self.X0 = params['X0']
self.Y0 = params['Y0']
self.PA = params['PA']
self.ell = params['ell']
self.q = 1 - self.ell
self.theta = self.PA+90
self.b_n = gammaincinv(2.*self.n, 0.5)
if calc_params:
self.calc_params()
def _make_galaxy(pset, bbox_num_reff=10, band='i'):
"""
Make synthetic Sersic galaxy.
Parameters
----------
pset : dict, astropy.table.Row
Sersic parameters. Uses imfit's convention:
mu_0, r_e, n, X0, Y0, ell, and PA (except for mu_0)
bbox_num_reff : int, optional
Number of r_eff to extend the bounding box.
band : string, optional
Photometric band (need for central surface brightness).
Returns
-------
galaxy : ndarray
Image with synthetic galaxy.
"""
# convert mu_0 to I_e and r_e to pixels
mu_0 = pset['mu_0_' + band.lower()]
b_n = gammaincinv(2.*pset['n'], 0.5)
mu_e = mu_0 + 2.5*b_n/np.log(10)
I_e = (pixscale**2)*10**((zpt-mu_e)/2.5)
r_e = pset['r_e'] / pixscale
# calculate image shape
side = 2*int(bbox_num_reff*r_e) + 1
img_shape = (side, side)
params = dict(X0=img_shape[1]//2,
Y0=img_shape[0]//2,
I_e=I_e,
r_e=r_e,
n=pset['n'],
ell=pset['ell'],
PA=pset['PA'])
# generate image with synth
model = Sersic(params)
galaxy = model.array(img_shape)
return galaxy
def fastfood_params(n, d):
d0 = d
# n0 = n
l = int(np.ceil(np.log2(d)))
d = 2**l
k = int(np.ceil(n / d))
n = d * k
print('d0 =', d0, ', d =', d)
print('n0 =', n, ', n =', n)
B = []
G = []
PI = []
S = []
for ii in xrange(k):
B_ii = rng.choice([-1, 1], size=d)
G_ii = rng.normal(size=d)
PI_ii = rng.permutation(d)
print('PI_ii=', PI_ii)
B.append(B_ii)
G.append(G_ii)
PI.append(PI_ii)
p1 = rng.uniform(size=d)
p2 = d / 2
# print('p1 =',p1,'; p2 =',p2)
T = gammaincinv(p2, p1)
# print('T1 =',T)
T = (T * 2) ** (1 / 2)
# print('T2 =',T)
s_i = T * norm(G, 'fro')**(-1)
# print('s_i =', s_i)
S_ii = s_i
S.append(S_ii)
S1 = np.zeros(n)
for ii in xrange(k):
S1[ii * d:(ii + 1) * d] = S[ii]
# print('Shape of B:',len(B),', B[0]:',B[0].shape)
return FFPara(B, G, PI, S1)
def _ppf(self, q, a, c):
val1 = special.gammaincinv(a,q)
val2 = special.gammaincinv(a,1.0-q)
ic = 1.0/c
cond = c+0*val1
return np.where(cond > 0,val1**ic,val2**ic)
def _ppf(self, q, c):
return np.log(special.gammaincinv(c,q))
def _ppf(self, q, a):
return special.gammaincinv(a, q)
def random(self): c=self.randomObj.random() return gammaincinv(self.a,c)
def get_tmax(self, p, cutoff=None):
if cutoff is None:
cutoff = self.cutoff
return gammaincinv(p[1], cutoff) * p[2]
def _ppf(self, q, nu):
return numpy.sqrt(1.0 / nu * special.gammaincinv(nu, q))
def q_lambda(y, extremes):
gam_a = len(y); gam_b = sum(y)
u = np.random.uniform()
F_min, F_max = sp.gammainc(gam_a, gam_b*np.array(extremes))
lambda_const = F_max-F_min
return sp.gammaincinv(gam_a, F_min+u*lambda_const)/gam_b
def _ppf(self, q, a, c):
val = numpy.where(c > 0, q, 1 - q)
return special.gammaincinv(a, val)**(1. / c)
def find_galaxy_list(skymap_path, log=None):
# settings:
config = ConfigParser(inline_comment_prefixes=';')
config.read('config.ini')
cat_file = config.get('CATALOG', 'PATH') + config.get(
'CATALOG', 'NAME') + '.npy' # galaxy catalog file
# parameters:
credzone = config.getfloat(
'GALAXIES',
'CREDZONE') # Localization probability to consider credible
relaxed_credzone = config.getfloat('GALAXIES', 'RELAXED_CREDZONE')
nsigmas_in_d = config.getfloat(
'GALAXIES', 'NSIGMAS_IN_D') # Sigmas to consider in distance
relaxed_nsigmas_in_d = config.getfloat('GALAXIES', 'RELAXED_NSIGMAS_IN_D')
completeness = config.getfloat('GALAXIES', 'COMPLETENESS')
min_galaxies = config.getfloat(
'GALAXIES', 'MINGALAXIES') # minimal number of galaxies to output
max_galaxies = config.getint(
'GALAXIES', 'MAXGALAXIES') # maximal number of galaxies to use
# magnitude of event in r-band. values are value from Barnes... +-1.5 mag
minmag = config.getfloat('GALAXIES',
'MINMAG') # Estimated brightest KN abs mag
maxmag = config.getfloat('GALAXIES',
'MAXMAG') # Estimated faintest KN abs mag
sensitivity = config.getfloat(
'GALAXIES', 'SENSITIVITY') # Estimated faintest app mag we can see
min_dist_factor = config.getfloat(
'GALAXIES', 'MINDISTFACTOR'
) # reflecting a small chance that the theory is completely wrong and we can still see something
minL = mag.f_nu_from_magAB(minmag)
maxL = mag.f_nu_from_magAB(maxmag)
# Schechter function parameters:
alpha = config.getfloat('GALAXIES', 'ALPHA')
MB_star = config.getfloat(
'GALAXIES', 'MB_STAR'
) # random slide from https://www.astro.umd.edu/~richard/ASTRO620/LumFunction-pp.pdf but not really...?
if log is None:
log = logging.getLogger(__name__)
# Read the HEALPix sky map:
try:
prob, dist_mu, dist_sigma, dist_norm = hp.read_map(skymap_path,
field=None,
verbose=False)
except Exception as e:
log.error('Failed to read sky map!')
send_mail(subject="[GW@Wise] Failed to read LVC sky map",
text='''FITS file: {}
Exception: {}'''.format(skymap_path, e),
log=log)
# Load the galaxy catalog (glade_id, RA, DEC, distance, Bmag):
galaxy_cat = np.load(cat_file)
galaxy_cat = Table(galaxy_cat, names=('ID', 'RA', 'Dec', 'Dist', 'Bmag'))
galaxy_cat = galaxy_cat[np.where(
galaxy_cat['Dist'] > 0)] # remove entries with a negative distance
galaxy_cat = galaxy_cat[np.where(
~np.isnan(galaxy_cat['Bmag']))] # remove entries with no Bmag
# Skymap parameters:
npix = len(prob)
nside = hp.npix2nside(npix)
# Convert galaxy WCS (RA, DEC) to spherical coordinates (theta, phi):
theta = 0.5 * np.pi - np.deg2rad(galaxy_cat['Dec'])
phi = np.deg2rad(galaxy_cat['RA'])
d = np.array(galaxy_cat['Dist'])
# Convert galaxy coordinates to skymap pixels:
galaxy_pix = hp.ang2pix(nside, theta, phi)
# Most probable sky location
theta_maxprob, phi_maxprob = hp.pix2ang(nside, np.argmax(prob))
ra_maxprob = np.rad2deg(phi_maxprob)
dec_maxprob = np.rad2deg(0.5 * np.pi - theta_maxprob)
# Convert to coordinates
ra_maxprob = Angle(ra_maxprob * u.deg)
dec_maxprob = Angle(dec_maxprob * u.deg)
# Find given percent probability zone (default is 99%):
prob_cutoff = 1
prob_sum = 0
npix_credzone = 0
prob_sorted = np.sort(prob, kind="stable")
while prob_sum < credzone:
prob_sum = prob_sum + prob_sorted[-1]
prob_cutoff = prob_sorted[-1]
prob_sorted = prob_sorted[:-1]
npix_credzone = npix_credzone + 1
# area = npix_credzone * hp.nside2pixarea(nside, degrees=True)
####################################################
# calculate probability for galaxies by the localization map:
p = prob[galaxy_pix]
p_dist = dist_norm[galaxy_pix] * norm(dist_mu[galaxy_pix],
dist_sigma[galaxy_pix]).pdf(d)
# cutoffs - 99% of probability by angles and 3sigma by distance:
within_dist_idx = np.where(
np.abs(d - dist_mu[galaxy_pix]) < nsigmas_in_d *
dist_sigma[galaxy_pix])
within_credzone_idx = np.where(p >= prob_cutoff)
within_idx = np.intersect1d(within_credzone_idx, within_dist_idx)
do_mass_cutoff = True
# Relax credzone limits if no galaxies are found:
if within_idx.size == 0:
while prob_sum < relaxed_credzone:
if prob_sorted.size == 0:
break
prob_sum = prob_sum + prob_sorted[-1]
prob_cutoff = prob_sorted[-1]
prob_sorted = prob_sorted[:-1]
npix_credzone = npix_credzone + 1
within_dist_idx = np.where(
np.abs(d - dist_mu[galaxy_pix]) < relaxed_nsigmas_in_d *
dist_sigma[galaxy_pix])
within_credzone_idx = np.where(p >= prob_cutoff)
within_idx = np.intersect1d(within_credzone_idx, within_dist_idx)
do_mass_cutoff = False
p = p[within_idx]
p = (p * (p_dist[within_idx])) # d**2?
galaxy_cat = galaxy_cat[within_idx]
if len(galaxy_cat) == 0:
log.warning("No galaxies in field!")
log.warning("99.995% of probability is ",
npix_credzone * hp.nside2pixarea(nside, degrees=True),
"deg^2")
log.warning("Peaking at (deg) RA = {}, Dec = {}".format(
ra_maxprob.to_string(unit=u.hourangle,
sep=':',
precision=2,
pad=True),
dec_maxprob.to_string(sep=':',
precision=2,
alwayssign=True,
pad=True)))
return
# Normalize luminosity to account for mass:
luminosity = mag.L_nu_from_magAB(galaxy_cat['Bmag'] -
5 * np.log10(galaxy_cat['Dist'] *
(10**5)))
luminosity_norm = luminosity / np.sum(luminosity)
normalization = np.sum(p * luminosity_norm)
score = p * luminosity_norm / normalization
# Take 50% of mass:
# The area under the Schechter function between L=inf and the brightest galaxy in the field:
missing_piece = gammaincc(
alpha + 2,
10**(-(min(galaxy_cat['Bmag'] - 5 * np.log10(galaxy_cat['Dist'] *
(10**5))) - MB_star) /
2.5))
# there are no galaxies brighter than this in the field, so don't count that part of the Schechter function
while do_mass_cutoff:
MB_max = MB_star + 2.5 * np.log10(
gammaincinv(alpha + 2, completeness + missing_piece))
if (min(galaxy_cat['Bmag'] - 5 * np.log10(galaxy_cat['Dist'] *
(10**5))) - MB_star) > 0:
MB_max = 100 # if the brightest galaxy in the field is fainter than the cutoff brightness - don't cut by brightness
brightest = np.where(
galaxy_cat['Bmag'] - 5 * np.log10(galaxy_cat['Dist'] *
(10**5)) < MB_max)
# print MB_max
if len(brightest[0]) < min_galaxies:
# Not enough galaxies, allowing fainter galaxies
if completeness >= 0.9: # Tried hard enough, just take all of them
completeness = 1 # Just to be consistent
do_mass_cutoff = False
else:
completeness = (completeness + (1. - completeness) / 2)
else: # got enough galaxies
galaxy_cat = galaxy_cat[brightest]
p = p[brightest]
luminosity_norm = luminosity_norm[brightest]
score = score[brightest]
do_mass_cutoff = False
# Account for the distance
absolute_sensitivity = sensitivity - 5 * np.log10(galaxy_cat['Dist'] *
(10**5))
absolute_sensitivity_lum = mag.f_nu_from_magAB(absolute_sensitivity)
distance_factor = np.zeros(len(galaxy_cat))
distance_factor[:] = ((maxL - absolute_sensitivity_lum) / (maxL - minL))
distance_factor[min_dist_factor > (maxL - absolute_sensitivity_lum) /
(maxL - minL)] = min_dist_factor
distance_factor[absolute_sensitivity_lum < minL] = 1
distance_factor[absolute_sensitivity > maxL] = min_dist_factor
# Sort galaxies by probability
ranking_idx = np.argsort(p * luminosity_norm * distance_factor,
kind="stable")[::-1]
# # Count galaxies that constitute 50% of the probability (~0.5*0.98)
# sum = 0
# galaxies50per = 0
# sum_seen = 0
# while sum < 0.5:
# if galaxies50per >= len(ranking_idx):
# break
# sum = sum + (p[ranking_idx[galaxies50per]] * luminosity_norm[ranking_idx[galaxies50per]]) / float(normalization)
# sum_seen = sum_seen + (p[ranking_idx[galaxies50per]] * luminosity_norm[ranking_idx[galaxies50per]] * distance_factor[ranking_idx[galaxies50per]]) / float(normalization)
# galaxies50per = galaxies50per + 1
#
# # Event statistics:
# # Ngalaxies_50percent = the number of galaxies consisting 50% of probability (including luminosity but not distance factor)
# # actual_percentage = usually around 50
# # seen_percentage = if we include the distance factor - how much do the same galaxies worth
# # 99percent_area = area of map in [deg^2] consisting 99% (using only the map from LIGO)
# stats = {"Ngalaxies_50percent": galaxies50per, "actual_percentage": sum*100, "seen_percentage": sum_seen, "99percent_area": area}
# Limit the maximal number of galaxies to use:
if len(ranking_idx) > max_galaxies:
n = max_galaxies
else:
n = len(ranking_idx)
# Create sorted galaxy list (glade_id, RA, DEC, distance(Mpc), Bmag, score, distance factor (between 0-1))
# The score is normalized so that all the galaxies in the field sum to 1 (before applying luminosity cutoff)
galaxylist = np.ndarray((n, 7))
for i in range(ranking_idx.shape[0])[:n]:
ind = ranking_idx[i]
galaxylist[i, :] = [
galaxy_cat[ind]['ID'], galaxy_cat[ind]['RA'],
galaxy_cat[ind]['Dec'], galaxy_cat[ind]['Dist'],
galaxy_cat[ind]['Bmag'], score[ind], distance_factor[ind]
]
# Update galaxy table in SQL database:
lvc_galaxy_dict = {
'voeventid': '(SELECT MAX(id) from voevent_lvc)',
'score': score[ind],
'gladeid': galaxy_cat[ind]['ID']
}
mysql_update.insert_values('lvc_galaxies', lvc_galaxy_dict)
return galaxylist, ra_maxprob, dec_maxprob
print(mean2)
median2 = 5.3481
print(median2)
variance2 = k * tetha * tetha
print(variance2)
m = symbols('m')
x = symbols('x')
fx = integrate(((x ** (k-1)) * exp(-x/tetha)/((tetha ** k) * gamma(k))), (x, m, oo))
#print(fx, "\n")
quartile2_1 = ss.gammaincinv(k, 0.25) * tetha
quartile2_2 = ss.gammaincinv(k, 0.5) * tetha
quartile2_3 = ss.gammaincinv(k, 0.75) * tetha
print(quartile2_1, quartile2_2, quartile2_3)
iqr2 = quartile2_3 - quartile2_1
print(iqr2, "\n")
def delta(a, b):
return a - b
print(delta(mean1, mean2), delta(median1, median2), delta(variance1, variance2), delta(iqr1, iqr2), "\n")
i1 = mean1 - sqrt(variance1/len(rozpodil)) * np.percentile(rozpodil, 3)
i2 = mean1 + sqrt(variance1/len(rozpodil)) * np.percentile(rozpodil, 3)
print(i1, i2, "\n")
def _upper(self, a, c):
cond = c > 0
val = numpy.where(cond, 1 - 1e-15, 1e-15)
return special.gammaincinv(a, val)**(1. / c)
def SourceProfile(xsource,ysource,source,lens):
"""
Creates the source-plane profile of the given Source.
Inputs:
xsource,ysource:
Source-plane coordinates, in arcsec, on which to
calculate the luminosity profile of the source
Source:
Any supported source-plane object, e.g. a GaussSource
object. The object will contain all the necessary
parameters to create the profile.
Lens:
Any supported Lens object, e.g. an SIELens. We only need
this because, in the case of single lenses, the source
position is defined as offset from the lens centroid. If
there is more than one lens, or if the source is unlensed,
the source position is defined **relative to the field
center, aka (0,0) coordinates**.
Returns:
I:
The luminosity profile of the given Source. Has same
shape as xsource and ysource. Note: returned image has
units of flux / arcsec^2 (or whatever the x,y units are),
so to properly normalize, must multiply by pixel area. This
isn't done here since the lensing means the pixels likely
aren't on a uniform grid.
"""
lens = list(np.array([lens]).flatten())
# First case: a circular Gaussian source.
if source.__class__.__name__=='GaussSource':
sigma = source.width['value']
amp = source.flux['value']/(2.*np.pi*sigma**2.)
if source.lensed:# and len(lens)==1:
xs = source.xoff['value'] + lens[0].x['value']
ys = source.yoff['value'] + lens[0].y['value']
else:
xs = source.xoff['value']
ys = source.yoff['value']
return amp * np.exp(-0.5 * (np.sqrt((xsource-xs)**2.+(ysource-ys)**2.)/sigma)**2.)
elif source.__class__.__name__=='SersicSource':
if source.lensed:# and len(lens)==1:
xs = source.xoff['value'] + lens[0].x['value']
ys = source.yoff['value'] + lens[0].y['value']
else:
xs = source.xoff['value']
ys = source.yoff['value']
PA, ar = source.PA['value']*deg2rad, source.axisratio['value']
majax, index = source.majax['value'], source.index['value']
dX = (xsource-xs)*np.cos(PA) + (ysource-ys)*np.sin(PA)
dY = (-(xsource-xs)*np.sin(PA) + (ysource-ys)*np.cos(PA))/ar
R = np.sqrt(dX**2. + dY**2.)
# Calculate b_n, to make reff enclose half the light; this approx from Ciotti&Bertin99
# This approximation good to 1 in 10^4 for n > 0.36; for smaller n it gets worse rapidly!!
#bn = 2*index - 1./3. + 4./(405*index) + 46./(25515*index**2) + 131./(1148175*index**3) - 2194697./(30690717750*index**4)
# Note, now just calculating directly because everyone's scipy
# should be sufficiently modern.
bn = gammaincinv(2. * index, 0.5)
# Backing out from the integral to R=inf of a general sersic profile
Ieff = source.flux['value'] * bn**(2*index) / (2*np.pi*majax**2 * ar * np.exp(bn) * index * gamma(2*index))
return Ieff * np.exp(-bn*((R/majax)**(1./index)-1.))
elif source.__class__.__name__=='PointSource':
if source.lensed:# and len(lens)==1:
#xs = source.xoff['value'] + lens[0].x['value']
#ys = source.yoff['value'] + lens[0].y['value']
return ValueError("Lensed point sources not working yet... try a"\
"gaussian with small width instead...")
else:
xs = source.xoff['value']
ys = source.yoff['value']
yloc = np.abs(xsource[0,:] - xs).argmin()
xloc = np.abs(ysource[:,0] - ys).argmin()
m = np.zeros(xsource.shape)
m[xloc,yloc] += source.flux['value']/(xsource[0,1]-xsource[0,0])**2.
return m
else: raise ValueError("So far only GaussSource, SersicSource, and "\
"PointSource objects supported...")
def _fit_eeg_distribution(X,
min_clean_fraction=None,
max_dropout_fraction=None,
quantile_range=None,
step_sizes=None,
beta_range=None):
""" Estimate the mean and standard deviation of clean EEG from contaminated data
This function estimates the mean and standard deviation of clean EEG from a sample of amplitude
values (that have preferably been computed over short windows) that may include a large fraction
of contaminated samples. The clean EEG is assumed to represent a generalized Gaussian component in
a mixture with near-arbitrary artifact components. By default, at least 25% (min_clean_fraction) of
the data must be clean EEG, and the rest can be contaminated. No more than 10%
(max_dropout_fraction) of the data is allowed to come from contamination that cause lower-than-EEG
amplitudes (e.g., sensor unplugged). There are no restrictions on artifacts causing
larger-than-EEG amplitudes, i.e., virtually anything is handled (with the exception of a very
unlikely type of distribution that combines with the clean EEG samples into a larger symmetric
generalized Gaussian peak and thereby "fools" the estimator). The default parameters should be
fine for a wide range of settings but may be adapted to accommodate special circumstances.
The method works by fitting a truncated generalized Gaussian whose parameters are constrained by
min_clean_fraction, max_dropout_fraction, quantile_range, and beta_range. The alpha and beta parameters
of the gen. Gaussian are also returned. The fit is performed by a grid search that always finds a
close-to-optimal solution if the above assumptions are fulfilled.
Parameters
----------
X : ndarray, shape (n_samples,)
vector of amplitude values of EEG, possible containing artifacts
(coming from single samples or windowed averages)
min_clean_fraction : float (default: 0.25)
Minimum fraction of values in X that needs to be clean
max_dropout_fraction : float (default: 0.1)
Maximum fraction of values in X that can be subject to
signal dropouts (e.g., sensor unplugged)
quantile_range : ndarray, shape (2,) (default: [0.022 0.6])
Quantile range [lower,upper] of the truncated generalized Gaussian distribution
that shall be fit to the EEG contents
step_sizes : ndarray, shape (2,) (default: [0.01 0.01])
Step size of the grid search; the first value is the stepping of the lower bound
(which essentially steps over any dropout samples), and the second value
is the stepping over possible scales (i.e., clean-data quantiles)
beta_range : ndarray, shape (n_points,) (default: np.arange(1.70, 3.51, 0.15))
Range that the clean EEG distribution's shape parameter beta may take
Returns
-------
Mu : float
estimated mean of the clean EEG distribution
Sigma : float
estimated standard deviation of the clean EEG distribution
Alpha : float
estimated scale parameter of the generalized Gaussian clean EEG distribution (optional)
Beta : float
estimated shape parameter of the generalized Gaussian clean EEG distribution (optional)
"""
# sanity checks
if len(X.shape) > 1:
raise ValueError('X needs to be a 1D ndarray.')
# default parameters
if min_clean_fraction is None:
min_clean_fraction = 0.25
if max_dropout_fraction is None:
max_dropout_fraction = 0.1
if quantile_range is None:
quantile_range = np.array([0.022, 0.6])
if step_sizes is None:
step_sizes = np.array([0.01, 0.01])
if beta_range is None:
beta_range = np.arange(1.7, 3.51, 0.15)
# check valid parameters
n = len(X)
quantile_range = np.array(quantile_range)
step_sizes = np.array(step_sizes)
beta_range = np.array(beta_range)
if not len(quantile_range) == 2:
raise ValueError('quantile_range needs to be a 2-elements vector.')
if any(quantile_range > 1) | any(quantile_range < 0):
raise ValueError('Unreasonable quantile_range.')
if any(step_sizes < 0.0001) | any(step_sizes > 0.1):
raise ValueError('Unreasonable step sizes.')
if any(step_sizes * n < 1):
raise ValueError(
f"Step sizes compared to actual number of samples available, step_sizes * n should be "
f"greater than 1 (current value={step_sizes * n}. More training data required."
)
if any(beta_range >= 7) | any(beta_range <= 1):
raise ValueError('Unreasonable shape range.')
# sort data for quantiles
X = np.sort(X)
# compute z bounds for the truncated standard generalized Gaussian pdf and pdf rescaler for each beta
zbounds = []
rescale = []
for k, b in enumerate(beta_range):
zbounds.append(
np.sign(quantile_range - 0.5) * gammaincinv(
(1 / b),
np.sign(quantile_range - 0.5) *
(2 * quantile_range - 1))**(1 / b))
rescale.append(b / (2 * gamma(1 / b)))
# determine the quantile-dependent limits for the grid search and convert everything in samples
# we can generally skip the tail below the lower quantile
lower_min = int(round(min(quantile_range) * n))
# maximum width in samples is the fit interval if all data is clean
max_width = int(round(n * np.diff(quantile_range)[0]))
# minimum width in samples of the fit interval, as fraction of data
min_width = int(round(min_clean_fraction * n *
np.diff(quantile_range)[0])) #
max_dropout_fraction_n = int(round(max_dropout_fraction * n))
step_sizes_n = np.round(step_sizes * n).astype(int)
assert any(
step_sizes_n >= 1) # should be catched earlier but double-checking
# get matrix of shifted data ranges
indx = np.arange(lower_min, lower_min + max_dropout_fraction_n + 0.5,
step_sizes_n[0]).astype(int) # epochs start
assert indx.dtype == "int"
range_ind = np.arange(0, max_width) # interval indices
Xs = np.zeros(
(max_width, len(indx))) # preload entire quantile interval matrix
for k, i in enumerate(indx):
Xs[:, k] = X[i + range_ind] # build each quantile interval
X1 = Xs[0, :]
Xs = Xs - X1 # substract baseline value for each interval (starting at 0)
# gridsearch to find optimal fitting coefficient based on given parameters
opt_val = float("inf")
opt_lu = float("inf")
opt_bounds = float("inf")
opt_beta = float("inf")
gridsearch_val = np.arange(max_width - 1, min_width,
-step_sizes_n[0]).astype(int)
for m in gridsearch_val: # gridsearch for different quantile interval
# scale and bin the data in the intervals
nbins = int(round(3 * np.log2(1 + m / 2))) + 1 # scale interval
H = Xs[range(m), :] * nbins / Xs[m - 1, :] # scale data bins
binscounts = np.zeros((nbins, H.shape[1])) # init bincounts
for k in range(H.shape[1]):
binscounts[:, k], _ = np.histogram(H[:, k], nbins)
logq = np.log(binscounts + 0.01) # return log(bincounts) in intervals
# for each shape value...
for k, beta in enumerate(beta_range):
bounds = zbounds[k]
# evaluate truncated generalized Gaussian pdf at bin centers
x = bounds[0] + np.linspace(0.5, (nbins - 0.5),
num=nbins) / nbins * np.diff(bounds)[0]
p = np.exp(-np.abs(x)**beta) * rescale[k]
p = p / np.sum(p)
# calc KL divergences for the specific interval
kl = np.sum(p *
(np.log(p) - np.transpose(logq)), axis=1) + np.log(m)
# update optimal parameters
idx = np.argmin(kl)
if kl[idx] < opt_val:
opt_val = kl[idx]
opt_beta = beta
opt_bounds = bounds
opt_lu = [X1[idx], X1[idx] + Xs[m, idx]]
# recover distribution parameters at optimum
alpha = (opt_lu[1] - opt_lu[0]) / np.diff(opt_bounds)[0]
mu = opt_lu[0] - opt_bounds[0] * alpha
beta = opt_beta
# calculate the distribution's standard deviation from alpha and beta
sig = np.sqrt((alpha**2) * gamma(3 / beta) / gamma(1 / beta))
return mu, sig, alpha, beta
def expected_grad(s, c, r):
u = sp_special.gammainc(c, s * r)
delta = 1e-4
return sp_misc.derivative(
lambda x: sp_special.gammaincinv(x, u), c, dx=delta * c) / r
def _ppf(self, q, a, b):
return b/gammaincinv(a,1-q)
def sernorm(n): return gammaincinv(2.*n, 0.5)
d0, n0 = d, n
l = T.ceil(T.log2(d)) # TODO cast to int
d = 2**l
k = T.ceil(n/d) # TODO cast to int
n = d*k
# generate parameter 'matrices'
B = rng.choice([-1, 1], size=(k, d))
G = rng.normal(size=(k, d), dtype=np.float64)
PI = np.array([rng.permutation(d) for _ in xrange(k)]).T
S = np.empty((k*d, 1), dtype=np.float64)
# generate scaling matrix, S
for i in xrange(k):
for j in xrange(d):
p1 = rng.uniform(size=d)
p2 = d/2
Tmp = gammaincinv(p2, p1)
Tmp = T.sqrt(2*Tmp)
s_ij = Tmp * norm(G, 'fro')**(-1)
S[i+j] = s_ij
fastfood_params = function([n, d], [B, G, PI, S])
# {{{ Fastfood for kernel }}}
# params
X = T.dmatrix('X') # COLUMNS are input patterns (d0 dims, m samples)
B = T.dmatrix('B')
G = T.dmatrix('G')
PI = T.dmatrix('PI')
S = T.dmatrix('S')
para = [B, G, PI, S]
sgm = T.dscalar('sgm')
def kappa(index):
"""
Sersic profile exponential scaling factor, called either kappa or b_n
Ciotti & Bertin 1999, A&A, 352, 447 Eqn 5, exact formula!
"""
return gammaincinv(2 * index, 0.5)
def sigmaz(t, y, err, nseg, diagplot=False):
"""Compute sigma_z from lists of measurement times and values.
Input:
------
t: array of floats
The measurement times (days).
y: array of floats
The measurement values (seconds).
err: array of floats (1D)
Error bars of the measurements (seconds).
nseg : array of ints
In each iteration, the total time span of the measurements will be split into Nseg segments. This array contains all the values of Nseg we want to use.
diagplot: bool
Make a diagnostic plot of the polynomial fit to the full set of measurements.
Output:
-------
sz_corr : array of floats
Values of bias-corrected sigma-z for different segment length tau.
szerr_lower : array of floats
Lower error bars for the sigma-z values.
szerr_upper : array of floats
Upper error bars for the sigma-z values.
tz : array of floats
The values of the segment lengths, tau (days), for which sigma-z was calculated.
nsegments : array of ints
How many segments of each recorded length passed all criteria for being used when calculating tau and sigma-z statistics.
"""
# The length of the output arrays depends on how many segments meet our criteria of more than 6 points, and longer than T/sqrt(2)
sz = []
tz = []
ngood = [] # How many good segments went into each tz,sz point
toas = t
toaerr = err
toares = y
# Total span of the TOAs
durationday = (toas[-1] - toas[0]) # days
durationsec = durationday * 86400.0 # seconds
#The amount of wiggle room for the TOAs to fall on the other side of the segment range and still be included. It's really only supposed to account for roundoff error. We have no reason to expect TOAs to fall on the border except for the first and last TOAs of the whole batch, so I don't believe we're in danger of double counting any TOAs.
wiggle = 1e-5
# Polynomial order to fit (a cubic may fail to produce a good fit for a long TOA span for pulsars with a lot of red noise; it fails for the NANOGrav data set on B1937+21).
polyorder = 3
for iseg in nseg:
# For each duration of length durationday/iseg compute sz.
dur_oneseg = durationday / iseg # how long is one segment
ngoodsegs = 0 # Reset the counter for good segments
C3sqr = 0 # This will accumulate values of C3sqr
C3un_sum = 0 # This will accumulate the sum of 1/C3_sigma^2 to normalize the C3^2 weights at the end
n_sing_matrix = 0 # how many segments make polyfit fail with a singular matrix error
n_few_points = 0 # how many segments have too few points
n_short_dataspan = 0 # in how many segments the points are clustered within too small a portion of the selected time span
n_C3_neg_var = 0 # for how many segments the C3 coefficient has a negative variance in the covariance matrix
for jseg in range(
0, iseg): # Now loop through each segment of this length
# for iseq > 1 there are multiple segments we need to analyze
segrange = (toas[0] + dur_oneseg * jseg,
toas[0] + dur_oneseg * (jseg + 1))
centertime = (segrange[1] + segrange[0]
) / 2.0 # Midpoint of observation interval
# Fit the polynomial using only the toas in the interval
desind = np.where((toas > (segrange[0] - wiggle))
& (toas < (segrange[1] + wiggle)))
if (
np.size(desind)
) > polyorder + 3: # if cov. matrix needed for error estimates on fitted params
#if (np.size(desind))>polyorder: # if cov. matrix not needed
dataspan = np.max(toas[desind]) - np.min(toas[desind])
else:
n_few_points = n_few_points + 1
continue
# Matsakis recommends segment be longer than dur_oneseg/sqrt(2)
if (dataspan <=
(dur_oneseg / np.sqrt(2))): #xAL added this criterion
n_short_dataspan = n_short_dataspan + 1
continue
else:
res = toares[desind]
toaerrs = toaerr[desind]
try:
#NOTE: polyfit needs 1/sigma, not 1/sigma^2 weights. Times and residuals need to be in the same units, here are in seconds
p, pcov = np.polyfit((toas[desind] - centertime) * 86400.0,
res.astype(np.float),
polyorder,
cov=True,
full=False,
w=np.abs(1. / toaerrs))
#p = np.polyfit((toas[desind]-centertime)*86400.0,
# res.astype(np.float),polyorder, cov=False, full=False, w = np.abs(1./toaerrs) )
except:
#print('Polyfit failed!')
#traceback.print_exc()
n_sing_matrix = n_sing_matrix + 1
continue
# Get C3 coefficient uncertainty from the covariance matrix
C3variance = np.diag(pcov)[-4]
if C3variance < 0:
n_C3_neg_var = n_C3_neg_var + 1
#print('C3variance = %e' % C3variance)
continue
C3un = np.sqrt(C3variance)
C3un_sum = C3un_sum + 1.0 / C3un**2 # for normalizing weights at the end
C3sqr = C3sqr + p[-4]**2 / C3un**2
#C3sqr=C3sqr+p[0]**2 # Accumulate to eventually find avg C3^2
ngoodsegs += 1 # the number of good segments (with at least 6 TOAs in them)
# Plot data and fit for case where the full set of resids is treated as one segment
if (iseg == 1 and diagplot):
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
toas_secs = (toas[desind] - centertime) * 86400.0
ax.plot(toas[desind], res.astype(np.float) * 1.e6, 'ko')
ax.errorbar(toas[desind],
res.astype(np.float) * 1.e6,
yerr=toaerr[desind] * 1.e6,
fmt='none',
color='k',
capsize=2.0)
ax.plot(toas[desind], np.polyval(p, toas_secs) * 1.e6, 'r')
ax.set_xlabel('MJD')
ax.set_ylabel('Res (us)')
plt.title('Order-%d polynomial fit to full TOA set' %
polyorder)
#plt.savefig("sigmaz-diagnostic.png", dpi=300, format='png', bbox_inches='tight')
print(
"Divided data into %d segments of length %.1f days. Number of good segments: %d"
% (iseg, dur_oneseg, ngoodsegs))
if n_few_points > 0:
print('--->Segments with too few TOAs: %d' % n_few_points)
if n_short_dataspan > 0:
print('--->Segments with too short TOA span: %d' %
n_short_dataspan)
if n_sing_matrix > 0:
print('--->Segments causing singular matrix error in polyfit: %d' %
n_sing_matrix)
if n_C3_neg_var > 0:
print('--->Segments with C3 variance <0: %d' % n_C3_neg_var)
if ngoodsegs != 0:
#C3sqr=C3sqr/ngoodsegs # unweighted average
C3sqr = C3sqr / C3un_sum # average weighted by the uncertainties in fitted C3 values
sz.append((dur_oneseg * 86400)**2 * np.sqrt(C3sqr) /
(2.0 * np.sqrt(5.0))) # sigma_z formula
tz.append(dur_oneseg) #days
ngood.append(ngoodsegs)
# Sigma-z bias correction and error bars
nsegments = np.array(ngood)
x16 = np.divide(gammaincinv(0.5 * nsegments, 0.16), 0.5 * nsegments)
x50 = np.divide(gammaincinv(0.5 * nsegments, 0.50), 0.5 * nsegments)
x84 = np.divide(gammaincinv(0.5 * nsegments, 0.84), 0.5 * nsegments)
sz_corr = np.divide(sz, np.sqrt(x50))
szerr_upper = np.multiply(sz_corr, np.sqrt(np.divide(x50, x16)) - 1.0)
szerr_lower = np.multiply(sz_corr, 1.0 - np.sqrt(np.divide(x50, x84)))
return sz_corr, szerr_lower, szerr_upper, tz, nsegments
def __init__(self, data, params, data_handler, variables, weights=None):
# store mandatory parameters in class
self._dt = params['time_step' ] # time-step of the data
self._nt = params['n_snapshots' ] # number of time-frames
self._xdim = params['n_space_dims'] # number of spatial dimensions
self._nv = params['n_variables' ] # number of variables
self._n_DFT = int(params['n_DFT' ]) # number of DFT (per block)
# store optional parameters in class
self._overlap = params.get('overlap', 0) # percentage overlap
self._mean_type = params.get('mean_type', 'longtime') # type of mean
self._normalize_weights = params.get('normalize_weights', False) # normalize weights if required
self._normalize_data = params.get('normalize_data', False) # normalize data by variance if required
self._n_modes_save = params.get('n_modes_save', 1e10) # default is all (large number)
self._conf_level = params.get('conf_level', 0.95) # what confidence level to use fo eigs
self._reuse_blocks = params.get('reuse_blocks', False) # reuse blocks if present
self._savefft = params.get('savefft', False) # save fft block if required
self._save_dir = params.get('savedir', os.path.join(CWD, 'results')) # where to save data
# type of data management
# - data_handler: read type online
# - not data_handler: data is entirely pre-loaded
self._data_handler = data_handler
self._variables = variables
if data_handler:
self._data = data
X = data_handler(self._data, t_0=0, t_end=1, variables=variables)
if self._nv == 1 and (X.ndim != self._xdim + 2):
X = X[...,np.newaxis]
else:
def data_handler(data, t_0, t_end, variables):
if t_0 > t_end:
raise ValueError('`t_0` cannot be greater than `t_end`.')
elif t_0 >= self._nt:
raise ValueError('`t_0` cannot be greater or equal to time dimension.')
elif t_0 == t_end:
ti = np.arange(t_0, t_0+1)
d = data[[t_0],...,:]
else:
ti = np.arange(t_0, t_end)
d = data[ti,...,:]
return d
self._data_handler = data_handler
self._data = np.array(data)
X = self._data_handler(self._data, t_0=0, t_end=0, variables=self._variables)
if self._nv == 1 and (self._data.ndim != self._xdim + 2):
X = X[...,np.newaxis]
self._data = self._data[...,np.newaxis]
# get data dimensions and store in class
self._nx = X[0,...,0].size
self._dim = X.ndim
self._shape = X.shape
self._xdim = X[0,...,0].ndim
self._xshape = X[0,...,0].shape
# check weights
if isinstance(weights, dict):
self._weights = weights['weights']
self._weights_name = weights['weights_name']
if np.size(self._weights) != int(self.nx * self.nv):
raise ValueError(
'parameter ``weights`` must have the '
'same size as flattened data spatial '
'dimensions, that is: ', int(self.nx * self.nv))
else:
self._weights = np.ones(self._xshape+(self._nv,))
self._weights_name = 'uniform'
warnings.warn(
'Parameter `weights` not equal to an `numpy.ndarray`.'
'Using default uniform weighting')
# normalize weigths if required
if self._normalize_weights:
self._weights = utils_weights.apply_normalization(
data=self._data,
weights=self._weights,
n_variables=self._nv,
method='variance')
# flatten weights to number of spatial point
try:
self._weights = np.reshape(
self._weights, [int(self._nx*self._nv), 1])
except:
raise ValurError(
'parameter ``weights`` must be cast into '
'1d array with dimension equal to flattened '
'spatial dimension of data.')
# Determine whether data is real-valued or complex-valued-valued
# to decide on one- or two-sided spectrum from data
self._isrealx = np.isreal(X[0]).all()
# get default spectral estimation parameters and options
# define default spectral estimation parameters
if isinstance(self._n_DFT, int):
self._window = SPOD_base._hamming_window(self._n_DFT)
self._window_name = 'hamming'
else:
self._n_DFT = int(2**(np.floor(np.log2(self.nt / 10))))
self._window = SPOD_base._hamming_window(self._n_DFT)
self._window_name = 'hamming'
warnings.warn(
'Parameter `n_DFT` not equal to an integer.'
'Using default `n_DFT` = ', self._n_DFT)
# define block overlap
self._n_overlap = int(np.ceil(self._n_DFT * self._overlap / 100))
if self._n_overlap > self._n_DFT - 1:
raise ValueError('Overlap is too large.')
# define number of blocks
self._n_blocks = \
int(np.floor((self.nt - self._n_overlap) \
/ (self._n_DFT - self._n_overlap)))
# set number of modes to save
if self._n_modes_save > self._n_blocks:
self._n_modes_save = self._n_blocks
# test feasibility
if (self._n_DFT < 4) or (self._n_blocks < 2):
raise ValueError(
'Spectral estimation parameters not meaningful.')
# apply mean
self.select_mean()
# get frequency axis
self.get_freq_axis()
# determine correction for FFT window gain
self._winWeight = 1 / np.mean(self._window)
self._window = self._window.reshape(self._window.shape[0], 1)
# get default for confidence interval
self._xi2_upper = 2 * sc.gammaincinv(self._n_blocks, 1 - self._conf_level)
self._xi2_lower = 2 * sc.gammaincinv(self._n_blocks, self._conf_level)
self._eigs_c = np.zeros([self._n_freq,self._n_blocks,2], dtype='complex_')
# create folder to save results
self._save_dir_blocks = os.path.join(self._save_dir, \
'nfft'+str(self._n_DFT)+'_novlp'+str(self._n_overlap) \
+'_nblks'+str(self._n_blocks))
if not os.path.exists(self._save_dir_blocks):
os.makedirs(self._save_dir_blocks)
# compute approx problem size (assuming double)
self._pb_size = self._nt * self._nx * self._nv * 8 * BYTE_TO_GB
# print parameters to the screen
self.print_parameters()
import scipy as sy
import matplotlib.pyplot as plt
from scipy.special import gamma
from scipy.special import gammaincinv
def chi2(x,dx):
return (1 / (2*gamma(dx/2)) * (x/2)**(dx/2-1) * sy.exp(-x/2))
rand=sy.random.random(size=10000)
dev=120
lista1,lista2=[],[]
for i in rand:
lista1.append(2*gammaincinv(dev/2,i))
#plt.figure("1")
x=sy.linspace(min(lista1),max(lista1),100)
for i in range(len(x)):
lista2.append(10000*(chi2(x[i],dev)))
plt.hist(lista1, 140, facecolor='green', alpha=0.5)
plt.plot(x,lista2,'-r')
plt.xlabel("X")
plt.ylabel("$\phi_{\mu,\sigma^2}(X)$")
plt.show()
def _ppf(self, q, a, c):
val1 = special.gammaincinv(a,q)
val2 = special.gammaincinv(a,1.0-q)
ic = 1.0/c
cond = c+0*val1
return np.where(cond > 0,val1**ic,val2**ic)
def income_cumulative_prob_inverse(gender, race, age): (inc_med, inc_mean) = income_table.get_income(gender, race, age) k = (.2*(inc_med/inc_mean) + .8)/(3-3*(inc_med/inc_mean)) theta = inc_mean/k func = lambda prob: gammaincinv(k, prob)*theta return func
def _ppf(self, q, df):
return np.sqrt(2*special.gammaincinv(df*0.5,q))
def sernorm(n): return gammaincinv(2.*n, 0.5)
def find_galaxy_list(map_path, airmass_threshold = airmass_thresholdp, completeness = completenessp, credzone = 0.99):
#loading the map:
prob, distmu, distsigma, distnorm = hp.read_map(map_path, field=[0, 1, 2, 3], verbose=False)
#loading the galaxy catalog. this one contains only RA, DEC, distance, Bmag
galax = np.load("glade_RA_DEC.npy")
#map parameters:
npix = len(prob)
nside = hp.npix2nside(npix)
#galaxy parameters(RA, DEC to theta, phi):
galax = (galax[np.where(galax[:,2]>0),:])[0] #no distance<0
theta = 0.5 * np.pi - np.pi*(galax[:,1])/180
phi = np.deg2rad(galax[:,0])
d = np.array(galax[:,2])
#converting galaxy coordinates to map pixels:
ipix = hp.ang2pix(nside, theta, phi)
#finding given percent probability zone(default is 99%):
####################################################
probcutoff = 1
probsum = 0
sortedprob = np.sort(prob)
while probsum<credzone:
probsum = probsum+sortedprob[-1]
probcutoff = sortedprob[-1]
sortedprob = sortedprob[:-1]
####################################################
#calculating probability for galaxies by the localization map:
p = prob[ipix]
distp = (norm(distmu[ipix], distsigma[ipix]).pdf(d) * distnorm[ipix])# * d**2)#/(norm(distmu[ipix], distsigma[ipix]).pdf(distmu[ipix]) * distnorm[ipix] * distmu[ipix]**2)
#cuttoffs- 99% of probability by angles and 3sigma by distance:
inddistance = np.where(np.abs(d-distmu[ipix])<nsigmas_in_d*distsigma[ipix])
indcredzone = np.where(p>=probcutoff)
galax = galax[np.intersect1d(indcredzone,inddistance)]
ipix = ipix[np.intersect1d(indcredzone,inddistance)]
p = p[np.intersect1d(indcredzone,inddistance)]
p = (p*(distp[np.intersect1d(indcredzone,inddistance)]))##d**2?
# normalized luminosity to account for mass:
luminosity = mag.L_nu_from_magAB(galax[:, 3] - 5 * np.log10(galax[:, 2] * (10 ** 5)))
luminosityNorm = luminosity / np.sum(luminosity)
normalization = np.sum(p * luminosityNorm)
#taking 50% of mass (missingpiece is the area under the schecter function between l=inf and the brightest galaxy in the field.
#if the brightest galaxy in the field is fainter than the schecter function cutoff- no cutoff is made.
#while the number of galaxies in the field is smaller than minGalaxies- we allow for fainter galaxies, until we take all of them.
missingpiece = gammaincc(alpha + 2, 10 ** (-(min(galax[:,3]-5*np.log10(galax[:,2]*(10**5))) - MB_star) / 2.5)) ##no galaxies brighter than this in the field- so don't count that part of the Schechter function
doMassCuttoff = True
while doMassCuttoff:
MB_max = MB_star + 2.5 * np.log10(gammaincinv(alpha + 2, completeness+missingpiece))
if (min(galax[:,3]-5*np.log10(galax[:,2]*(10**5))) - MB_star)>0: #if the brightest galaxy in the field is fainter then cutoff brightness- don't cut by brightness
MB_max = 100
brightest = np.where(galax[:,3]-5*np.log10(galax[:,2]*(10**5))<MB_max)
# print MB_max
if len(brightest[0])<minGalaxies:
if completeness>=0.9: #tried hard enough. just take all of them
completeness = 1 # just to be consistent.
doMassCuttoff = False
else:
completeness = (completeness + (1. - completeness) / 2)
else: #got enough galaxies
galax = galax[brightest]
p = p[brightest]
luminosityNorm = luminosityNorm[brightest]
doMassCuttoff = False
#including observation constraints. (uses code in observational_const.py)
indices = get_observables(galax, airmass_threshold)
haleakalaObservable = indices['indHal']
sidingSpringObservable = indices['indSS']
#sorting glaxies by probability
ii = np.argsort(p*luminosityNorm)[::-1]
####counting galaxies that constitute 50% of the probability(~0.5*0.98)
sum = 0
galaxies50per = 0
observable50per = 0 #how many of the galaxies in the top 50% of probability are observable.
enough = True
while sum<0.5:
if galaxies50per>= len(ii):
enough = False
break
sum = sum + (p[ii[galaxies50per]]*luminosityNorm[ii[galaxies50per]])/float(normalization)
if ii[galaxies50per] in haleakalaObservable or ii[galaxies50per] in sidingSpringObservable:
observable50per = observable50per + 1
galaxies50per = galaxies50per+1
####
#creating sorted galaxy list, containing info on #ngalaxtoshow. each entry is (RA, DEC, distance(Mpc), Bmag, score)
#score is normalized so that all the galaxies in the field sum to 1 (before luminosity cutoff)
galaxylist = np.ndarray((ngalaxtoshow, 5))
###uncomment to include only observable galaxies.
# i=0
# n=0
# while i<ngalaxtoshow and n<galax.shape[0]:
# ind = ii[n]
# if ind in haleakalaObservable or ind in sidingSpringObservable:
# galaxylist[i,:] = [galax[ind, 0], galax[ind, 1], galax[ind,2], galax[ind,3], (p*luminosityNorm/normalization)[ind]]
# i = i+1
# n = n+1
for i in range(ngalaxtoshow):
ind = ii[i]
galaxylist[i, :] = [galax[ind, 0], galax[ind, 1], galax[ind, 2], galax[ind, 3],
(p * luminosityNorm / normalization)[ind]]
return galaxylist#[:i,:]#uncomment to include only observable galaxies.
##########################################################################################################
#to call function with commandline:
# print find_galaxy_list(sys.argv[1])
def _ppf(self, q, nu):
return np.sqrt(1.0/nu*special.gammaincinv(nu,q))
def synthetic_sersics(mu_range=[23, 28], r_eff_range=[3, 15],
n_range=[0.3, 1.5], ell_range=[0., 0.65],
theta_range=[0, 180], nsynths=100, random_state=None,
master_band='g', mu_type="central",
g_i=0.6, g_r=0.4, **kwargs):
"""
Generate catalog of Sersic galaxies.
Notes
-----
full sample:
median g-i = 0.64
median g-r = 0.43
reds:
median g-i = 0.82
median g-r = 0.56
blues:
median g-i = 0.47
median g-r = 0.32
"""
size = int(nsynths)
rng = check_random_state(random_state)
r_eff = rng.uniform(*r_eff_range, size=size)
sersic_n = rng.uniform(*n_range, size=size)
ell = rng.uniform(*ell_range, size=size)
theta = rng.uniform(*theta_range, size=size)
b_a = 1 - ell
b_n = gammaincinv(2.*sersic_n, 0.5)
f_n = gamma(2*sersic_n)*sersic_n*np.exp(b_n)/b_n**(2*sersic_n)
mu = rng.uniform(*mu_range, size=size)
if mu_type=='central':
mu_0 = mu
mu_e = mu_0 + 2.5*b_n/np.log(10)
mu_e_ave = mu_e - 2.5*np.log10(f_n)
elif mu_type=='average':
mu_e_ave = mu
mu_e = mu_e_ave + 2.5*np.log10(f_n)
mu_0 = mu_e - 2.5*b_n/np.log(10)
else:
raise Exception(mu_type+' is not a valid mu type')
r_circ = r_eff*np.sqrt(b_a)
A_eff = np.pi*r_circ**2
m_tot = mu_e_ave - 2.5*np.log10(2*A_eff)
cat = {'m_' + master_band: m_tot,
'mu_0_' + master_band: mu_0,
'mu_e_ave_' + master_band: mu_e_ave}
if master_band == 'g':
# write i band
cat['m_i'] = m_tot - g_i
cat['mu_0_i'] = mu_0 - g_i
cat['mu_e_ave_i'] = mu_e_ave - g_i
# write r band
cat['m_r'] = m_tot - g_r
cat['mu_0_r'] = mu_0 - g_r
cat['mu_e_ave_r'] = mu_e_ave - g_r
elif master_band == 'i':
# write g band
cat['m_g'] = m_tot + g_i
cat['mu_0_g'] = mu_0 + g_i
cat['mu_e_ave_g'] = mu_e_ave + g_i
# write r band
cat['m_r'] = m_tot + g_i - g_r
cat['mu_0_r'] = mu_0 + g_i - g_r
cat['mu_e_ave_r'] = mu_e_ave + g_i - g_r
else:
raise Exception('master_band must be g or i')
cat = Table(cat)
cat['theta'] = theta
cat['PA'] = theta - 90
cat['r_e'] = r_eff
cat['ell'] = 1 - b_a
cat['n'] = sersic_n
cat['g-i'] = g_i
cat['g-r'] = g_r
return cat
def _ppf(self, q, df):
return np.sqrt(2*special.gammaincinv(df*0.5,q))
def _ppf(self, q, a):
return special.gammaincinv(a, q)
def get_tmax(self, p, cutoff=None):
if cutoff is None:
cutoff = self.cutoff
return gammaincinv(p[1], cutoff) * p[2]
transnoise=numpy.kron(accelnoise**2*numpy.array([(timestep**2/4.0,timestep/2.0),
(timestep/2.0,1.0)]),numpy.eye(numdim))
# Create the measurement gain and noise.
measgain=numpy.kron(numpy.array([1.0,0.0]),numpy.eye(numdim))
measnoise=numpy.kron(numpy.array([obsnoise**2]),numpy.eye(numdim))
# Define the clutter density.
area=imwidth*imheight
clutterdens=lambda x:1.0/float(area)
# Instantiate the filter.
filt=gmphd.filt(initweight,initmean,initcovar,transgain,transnoise,measgain,measnoise,
clutterdens,birthrate,clutterrate,survprob,detecprob)
scale=special.gammaincinv(numdim,0.99)
# Create a figure and a pair of axes.
fig,axes=pyplot.subplots()
axes.invert_yaxis()
for frame in range(min(names.keys()),max(names.keys())):
try:
# Perform a prediction-update step.
filt.pred()
if frame in detections:
obs=numpy.array(detections[frame],dtype=float).transpose()
obs[:2,:]+=obs[2:,:]/2.0
filt.update(obs[:numdim,:],numpy.spacing(1.0))
filt.prune(truncthres=truncthres,
def _ppf(self, q, a, b, s):
"""
"""
return gammaincinv(s, q*gammainc(s, b) + gammainc(s, a))
def _ppf(self, q, c):
return np.log(special.gammaincinv(c,q))
def _ppf(self, q, zm, a, b):
k = (a + 1) / b
t = sc.gammainccinv(k, 0.5)
return zm * (sc.gammaincinv(k, q) / t)**(1 / b)
def get_catalog(params, map_struct):
if not os.path.isdir(params["catalogDir"]):
os.makedirs(params["catalogDir"])
catalogFile = os.path.join(params["catalogDir"],
"%s.hdf5" % params["galaxy_catalog"])
"""AB Magnitude zero point."""
MAB0 = -2.5 * np.log10(3631.e-23)
pc_cm = 3.08568025e18
const = 4. * np.pi * (10. * pc_cm)**2.
if params["galaxy_catalog"] == "2MRS":
if not os.path.isfile(catalogFile):
import astropy.constants as c
cat, = Vizier.get_catalogs('J/ApJS/199/26/table3')
ra, dec = cat["RAJ2000"], cat["DEJ2000"]
cz = cat["cz"]
magk = cat["Ktmag"]
z = (u.Quantity(cat['cz']) / c.c).to(u.dimensionless_unscaled)
completeness = 0.5
alpha = -1.0
MK_star = -23.55
MK_max = MK_star + 2.5 * np.log10(gammaincinv(alpha + 2,
completeness))
MK = magk - cosmo.distmod(z)
idx = (z > 0) & (MK < MK_max)
ra, dec = ra[idx], dec[idx]
z = z[idx]
magk = magk[idx]
distmpc = cosmo.luminosity_distance(z).to('Mpc').value
with h5py.File(catalogFile, 'w') as f:
f.create_dataset('ra', data=ra)
f.create_dataset('dec', data=dec)
f.create_dataset('z', data=z)
f.create_dataset('magk', data=magk)
f.create_dataset('distmpc', data=distmpc)
else:
with h5py.File(catalogFile, 'r') as f:
ra, dec = f['ra'][:], f['dec'][:]
z = f['z'][:]
magk = f['magk'][:]
distmpc = f['distmpc'][:]
r = distmpc * 1.0
mag = magk * 1.0
elif params["galaxy_catalog"] == "GLADE":
if not os.path.isfile(catalogFile):
cat, = Vizier.get_catalogs('VII/281/glade2')
ra, dec = cat["RAJ2000"], cat["DEJ2000"]
distmpc, z = cat["Dist"], cat["z"]
magb, magk = cat["Bmag"], cat["Kmag"]
# Keep track of galaxy identifier
GWGC, PGC, HyperLEDA = cat["GWGC"], cat["PGC"], cat["HyperLEDA"]
_2MASS, SDSS = cat["_2MASS"], cat["SDSS-DR12"]
idx = np.where(distmpc >= 0)[0]
ra, dec = ra[idx], dec[idx]
distmpc, z = distmpc[idx], z[idx]
magb, magk = magb[idx], magk[idx]
GWGC, PGC, HyperLEDA = GWGC[idx], PGC[idx], HyperLEDA[idx]
_2MASS, SDSS = _2MASS[idx], SDSS[idx]
with h5py.File(catalogFile, 'w') as f:
f.create_dataset('ra', data=ra)
f.create_dataset('dec', data=dec)
f.create_dataset('distmpc', data=distmpc)
f.create_dataset('magb', data=magb)
f.create_dataset('magk', data=magk)
f.create_dataset('z', data=z)
# Add galaxy identifier
f.create_dataset('GWGC', data=GWGC)
f.create_dataset('PGC', data=PGC)
f.create_dataset('HyperLEDA', data=HyperLEDA)
f.create_dataset('2MASS', data=_2MASS)
f.create_dataset('SDSS', data=SDSS)
else:
with h5py.File(catalogFile, 'r') as f:
ra, dec = f['ra'][:], f['dec'][:]
distmpc, z = f['distmpc'][:], f['z'][:]
magb, magk = f['magb'][:], f['magk'][:]
GWGC, PGC, _2MASS = f['GWGC'][:], f['PGC'][:], f['2MASS'][:]
HyperLEDA, SDSS = f['HyperLEDA'][:], f['SDSS'][:]
# Convert bytestring to unicode
GWGC = GWGC.astype('U')
PGC = PGC.astype('U')
HyperLEDA = HyperLEDA.astype('U')
_2MASS = _2MASS.astype('U')
SDSS = SDSS.astype('U')
# Keep only galaxies with finite B mag when using it in the grade
if params["galaxy_grade"] == "S":
idx = np.where(~np.isnan(magb))[0]
ra, dec, distmpc = ra[idx], dec[idx], distmpc[idx]
magb, magk = magb[idx], magk[idx]
GWGC, PGC, HyperLEDA = GWGC[idx], PGC[idx], HyperLEDA[idx]
_2MASS, SDSS = _2MASS[idx], SDSS[idx]
r = distmpc * 1.0
mag = magb * 1.0
elif params["galaxy_catalog"] == "CLU":
if not os.path.isfile(catalogFile):
raise ValueError("Please add %s." % catalogFile)
with h5py.File(catalogFile, 'r') as f:
name = f['name'][:]
ra, dec = f['ra'][:], f['dec'][:]
sfr_fuv, mstar = f['sfr_fuv'][:], f['mstar'][:]
distmpc, magb = f['distmpc'][:], f['magb'][:]
a, b2a, pa = f['a'][:], f['b2a'][:], f['pa'][:]
btc = f['btc'][:]
idx = np.where(distmpc >= 0)[0]
ra, dec = ra[idx], dec[idx]
sfr_fuv, mstar = sfr_fuv[idx], mstar[idx]
distmpc, magb = distmpc[idx], magb[idx]
a, b2a, pa = a[idx], b2a[idx], pa[idx]
btc = btc[idx]
idx = np.where(~np.isnan(magb))[0]
ra, dec = ra[idx], dec[idx]
sfr_fuv, mstar = sfr_fuv[idx], mstar[idx]
distmpc, magb = distmpc[idx], magb[idx]
a, b2a, pa = a[idx], b2a[idx], pa[idx]
btc = btc[idx]
z = -1*np.ones(distmpc.shape)
r = distmpc * 1.0
mag = magb * 1.0
L_nu = const * 10.**((mag + MAB0)/(-2.5))
L_nu = np.log10(L_nu)
L_nu = L_nu**params["catalog_n"]
Slum = L_nu / np.sum(L_nu)
mlim, M_KNmin, M_KNmax = 22, -17, -12
L_KNmin = const * 10.**((M_KNmin + MAB0)/(-2.5))
L_KNmax = const * 10.**((M_KNmax + MAB0)/(-2.5))
Llim = 4. * np.pi * (r * 1e6 * pc_cm)**2. * 10.**((mlim + MAB0)/(-2.5))
Sdet = (L_KNmax-Llim)/(L_KNmax-L_KNmin)
Sdet[Sdet < 0.01] = 0.01
Sdet[Sdet > 1.0] = 1.0
n, cl = params["powerlaw_n"], params["powerlaw_cl"]
dist_exp = params["powerlaw_dist_exp"]
prob_scaled = copy.deepcopy(map_struct["prob"])
prob_sorted = np.sort(prob_scaled)[::-1]
prob_indexes = np.argsort(prob_scaled)[::-1]
prob_cumsum = np.cumsum(prob_sorted)
index = np.argmin(np.abs(prob_cumsum - cl)) + 1
prob_scaled[prob_indexes[index:]] = 0.0
prob_scaled = prob_scaled**n
theta = 0.5 * np.pi - dec * 2 * np.pi / 360.0
phi = ra * 2 * np.pi / 360.0
ipix = hp.ang2pix(map_struct["nside"], ra, dec, lonlat=True)
if "distnorm" in map_struct:
if map_struct["distnorm"] is not None:
#creat an mask to cut at 3 sigma in distance
mask = np.zeros(len(r))
condition_indexer = np.where( (r < (map_struct["distmu"][ipix] + (3*map_struct["distsigma"][ipix]))) & (r > (map_struct["distmu"][ipix] - (3*map_struct["distsigma"][ipix])) ))
mask[condition_indexer] = 1
Sloc = prob_scaled[ipix] * (map_struct["distnorm"][ipix] *
norm(map_struct["distmu"][ipix],
map_struct["distsigma"][ipix]).pdf(r))**params["powerlaw_dist_exp"] / map_struct["pixarea"]
#multiplie the Sloc by 1 or 0 according to the 3 sigma condistion
Sloc = Sloc*mask
else:
Sloc = copy.copy(prob_scaled[ipix])
else:
Sloc = copy.copy(prob_scaled[ipix])
# Set nan values to zero
Sloc[np.isnan(Sloc)] = 0
S = Sloc*Slum*Sdet
prob = np.zeros(map_struct["prob"].shape)
if params["galaxy_grade"] == "Sloc":
prob[ipix] = prob[ipix] + Sloc
grade = Sloc
elif params["galaxy_grade"] == "S":
prob[ipix] = prob[ipix] + S
grade = S
prob = prob / np.sum(prob)
map_struct['prob_catalog'] = prob
if params["doUseCatalog"]:
map_struct['prob'] = prob
idx = np.where(~np.isnan(grade))[0]
grade = grade[idx]
ra, dec, Sloc, S = ra[idx], dec[idx], Sloc[idx], S[idx]
distmpc, z = distmpc[idx], z[idx]
if params["galaxy_catalog"] == "GLADE":
GWGC, PGC, HyperLEDA = GWGC[idx], PGC[idx], HyperLEDA[idx]
_2MASS, SDSS = _2MASS[idx], SDSS[idx]
"""
Sthresh = np.max(grade)*0.01
idx = np.where(grade >= Sthresh)[0]
grade = grade[idx]
ra, dec, Sloc, S = ra[idx], dec[idx], Sloc[idx], S[idx]
distmpc, z = distmpc[idx], z[idx]
if params["galaxy_catalog"] == "GLADE":
GWGC, PGC, HyperLEDA = GWGC[idx], PGC[idx], HyperLEDA[idx]
_2MASS, SDSS = _2MASS[idx], SDSS[idx]
"""
idx = np.argsort(grade)[::-1]
grade = grade[idx]
ra, dec, Sloc, S = ra[idx], dec[idx], Sloc[idx], S[idx]
distmpc, z = distmpc[idx], z[idx]
if params["galaxy_catalog"] == "GLADE":
GWGC, PGC, HyperLEDA = GWGC[idx], PGC[idx], HyperLEDA[idx]
_2MASS, SDSS = _2MASS[idx], SDSS[idx]
if len(ra) > 1000:
print('Cutting catalog to top 1000 galaxies...')
idx = np.arange(1000).astype(int)
ra, dec, Sloc, S = ra[idx], dec[idx], Sloc[idx], S[idx]
distmpc, z = distmpc[idx], z[idx]
if params["galaxy_catalog"] == "GLADE":
GWGC, PGC, HyperLEDA = GWGC[idx], PGC[idx], HyperLEDA[idx]
_2MASS, SDSS = _2MASS[idx], SDSS[idx]
catalog_struct = {}
catalog_struct["ra"] = ra
catalog_struct["dec"] = dec
catalog_struct["Sloc"] = Sloc
catalog_struct["S"] = S
if params["writeCatalog"]:
catalogfile = os.path.join(params["outputDir"], 'catalog.csv')
fid = open(catalogfile, 'w')
cnt = 1
if params["galaxy_catalog"] == "GLADE":
fid.write("id, RAJ2000, DEJ2000, Sloc, S, Dist, z, GWGC, PGC, HyperLEDA, 2MASS, SDSS\n")
for a, b, c, d, e, f, g, h, i, j, k in zip(ra, dec, Sloc, S, distmpc, z, GWGC, PGC, HyperLEDA, _2MASS, SDSS):
fid.write("%d, %.5f, %.5f, %.5e, %.5e, %.4f, %.4f, %s, %s, %s, %s, %s\n" % (cnt, a, b, c, d, e, f, g, h, i, j, k))
cnt = cnt + 1
else:
fid.write("id, RAJ2000, DEJ2000, Sloc, S, Dist, z\n")
for a, b, c, d in zip(ra, dec, Sloc, S, distmpc, z):
fid.write("%d, %.5f, %.5f, %.5e, %.5e, %.4f, %.4f\n" % (cnt, a, b, c, d, e, f))
cnt = cnt + 1
fid.close()
return map_struct, catalog_struct