def calc_b_iso(Tlm, Elm, Blm, ls, ms, hs, lmax=100):
result = np.zeros((lmax + 1, lmax + 1))
for i in np.arange(len(ls)):
l1 = ls[i]
m1 = ms[i]
for j in np.arange(len(ls)):
l2 = ls[j]
m2 = ms[j]
for k in np.arange(len(ms)):
l3 = ls[j]
m3 = ms[k]
factor = 2.
if l1 == l2:
factor = 1.
w3jfactor = wig.wig3jj(
[2 * l1, 2 * l2, 2 * l2, 2 * m1, 2 * m2,
2 * m3]) #get_w3j(l1,l2,l2,m1,m2,m2)
result[
l1,
l2] += w3jfactor #Tlm[i] * Elm[j] * Blm[j] * factor * w3jfactor
#if hs[l1,l2,l2] == 0.:
# result[l1,l2] = 0.
#else:
# result[l1,l2] /= hs[l1,l2,l2]
return result
def calc_b_iso(Tlm, Elm, Blm,
ls, ms, hs, lmax=100):
result = np.zeros((lmax+1,lmax+1))
for i in np.arange(len(ls)):
l1 = ls[i]
m1 = ms[i]
for j in np.arange(len(ls)):
l2 = ls[j]
m2 = ms[j]
for k in np.arange(len(ms)):
l3 = ls[j]
m3 = ms[k]
factor = 2.
if l1==l2:
factor = 1.
w3jfactor = wig.wig3jj([2*l1, 2*l2, 2*l2, 2*m1, 2*m2, 2*m3])#get_w3j(l1,l2,l2,m1,m2,m2)
result[l1,l2] += w3jfactor#Tlm[i] * Elm[j] * Blm[j] * factor * w3jfactor
#if hs[l1,l2,l2] == 0.:
# result[l1,l2] = 0.
#else:
# result[l1,l2] /= hs[l1,l2,l2]
return result
def w3j_factor(L, l, lp):
"""This computes the wigner-3j symbol for m's all zeros
"""
#w3j = N(wigner_3j(L, l, lp, 0, 0, 0))
#w3j = w3j_000(L, l, lp)
w3j = val3j = wig.wig3jj([2*L, 2*l, 2*lp, 0, 0, 0])
res = w3j**2 * (2.*l + 1.) * (2.*lp + 1.) / (4.*np.pi)
return res
for i in xrange(0, Nbin):
for j in xrange(0, i + 1):
for k in xrange(0, j + 1):
i3 = index[i]
i2 = index[j]
i1 = index[k]
Bis = 0.0
# we applied selection condition tirangle inequality and#parity condition
if abs(i2 - i1) <= i3 <= i2 + i1 and (i3 + i2 + i1) % 2 == 0:
# Intiation of array for wigner 3j coefficient evaluation
b = [2 * i1, 2 * i2, 2 * i3, 2 * 0, 2 * 0, 2 * 0]
wigner = wig.wig3jj(b)
alpha = np.sqrt(
(2 * i1 + 1) * (2 * i2 + 1) *
(2 * i3 + 1)) * (wigner / np.sqrt(np.pi * 4.0))
# Bispectrum Estimation
for ipix in xrange(0, npix):
Bis += Esti_Map[i, ipix] * Esti_Map[
j, ipix] * Esti_Map[k, ipix] #*Binary_Mask[ipix]
# All sky correction
Bis /= (4.0 * np.pi * npix) #np.sum(Binary_Mask))
# Counting triplets in given bin
tripCount = count_triplet(i1, i3)
Bis /= (1.0 * tripCount)
import sys
failure = int(sys.argv[1])
print('WIGXJPF python error handling test (%d)' % failure)
sys.stdout.flush()
# Initialize
if (failure != 1):
wig.wig_table_init(2 * 100 if failure != 2 else 2 * 1,
9 if failure != 3 else -1)
if (failure != 4):
wig.wig_temp_init(2 * 100 if failure != 5 else 1)
# Note that arguments are in two_j = 2*j.
val3j = wig.wig3jj(2* 10 , 2* 15 , 2* 10 ,\
2*(-3), 2* 12 , 2*(-9))
if failure == 6:
val3j = wig.wig3jj(2* 1000 , 2* 1500 , 2* 1000 ,\
2*(-300), 2* 1200 , 2*(-900))
print('3J(10 15 10; -3 12 -9): %.12g' % val3j)
sys.stdout.flush()
val6j = wig.wig6jj(2* 10 , 2* 15 , 2* 10 ,\
2* 7, 2* 7 , 2* 9)
if failure == 7:
val6j = wig.wig6jj(2* 1000 , 2* 1500 , 2* 1000 ,\
2* 700, 2* 700 , 2* 900)
print('6J{10 15 10; 7 7 9}: %.12g' % val6j)
sys.stdout.flush()
val9j = wig.wig9jj( 1, 2, 3,\
#
# You should have received a copy of the GNU Lesser General Public
# License along with WIGXJPF. If not, see
# <http://www.gnu.org/licenses/>.
#
import pywigxjpf as wig
print('WIGXJPF python test program')
# Initialize
wig.wig_table_init(2 * 100, 9)
wig.wig_temp_init(2 * 100)
# Note that arguments are in two_j = 2*j.
val3j = wig.wig3jj(2* 10 , 2* 15 , 2* 10 ,\
2*(-3), 2* 12 , 2*(-9))
print('3J(10 15 10; -3 12 -9): %.12g' % val3j)
val6j = wig.wig6jj(2* 10 , 2* 15 , 2* 10 ,\
2* 7, 2* 7 , 2* 9)
print('6J{10 15 10; 7 7 9}: %.12g' % val6j)
val9j = wig.wig9jj( 1, 2, 3,\
4, 6, 8, \
3, 6, 9 )
print('9J{0.5 1 1.5; 2 3 4; 1.5 3 4.5}: %.12g' % val9j)
print('Using the (numpy) array interface')
val3j = wig.wig3jj_array([2* 10 , 2* 15 , 2* 10 ,\
2*(-3), 2* 12 , 2*(-9)])
def clebsch_gordan(two_j1, two_j2, two_j3, two_m1, two_m2, two_m3):
from math import sqrt
threej = pywigxjpf.wig3jj((two_j1, two_j2, two_j3,
two_m1, two_m2, -two_m3))
phase = -1 if (two_m3+two_j1-two_j2) % 4 == 2 else 1
return phase * sqrt(float(two_j3+1)) * threej
return ret
n = 0
for lidx, ell in enumerate(xrange(2, lmax + 1)):
print ell
for lpidx, ellp in enumerate(xrange(2, lmax + 1)):
n += 1
for ellpp in xrange(np.abs(ell - ellp), ell + ellp + 1):
if ellpp < 2:
continue
val = np.sqrt(2 * ellpp + 1) * i_ell(ellpp)
# print val
val *= wig.wig3jj(
[2 * ell, 2 * ellp, 2 * ellpp, 2 * -m, 2 * (m + 2), 2 * -2])
# print val
val *= wig.wig3jj(
[2 * ell, 2 * ellp, 2 * ellpp, 2 * 2, 2 * 0, 2 * -2])
# print val
trans[lidx, lpidx] += val
trans[lidx, lpidx] *= np.sqrt(2 * ellp + 1)
trans[lidx, :] *= np.sqrt((2 * ell + 1) / 4. / np.pi)
trans *= 2 * np.pi
trans *= (-1)**m
# Free memory space
wig.wig_temp_free()
wig.wig_table_free()
def get_w3j(l1, l2, l3, m1, m2, m3):
return wig.wig3jj([2 * l1, 2 * l2, 2 * l3, 2 * m1, 2 * m2, 2 * m3])
def get_w3j(l1,l2,l3,m1,m2,m3):
return wig.wig3jj([2*l1, 2*l2, 2*l3, 2*m1, 2*m2, 2*m3])
def bispec_estimator(nside_f_est, loop, limit):
"""
:param nside_f_est:
:param loop:
:param limit:
:return:
"""
npix = hp.nside2npix(nside_f_est)
print npix
binary_mask = masking_map(Haslam_512, nside_f_est, npix, limit)
ap_map = apodiz(binary_mask)
haslam = Haslam_512 * ap_map
lmax = 250
nbin = 249
index = np.linspace(2, 250, nbin) #logrithmic bins
for k in xrange(len(index)):
index[k] = int(index[k])
print index
# creating filtered map
est_map = np.zeros((nbin, npix), dtype=np.float64)
fwhm = 56. / 3600. # For Haslam FWHM is 56 arc min
beam_l = hp.sphtfunc.gauss_beam(m.radians(fwhm), lmax=lmax, pol=False)
for i in xrange(0, nbin):
window_func = np.zeros(lmax, float)
ini = int(index[i])
if ini < 250:
window_func[ini] = 1.0
alms = hp.sphtfunc.map2alm(haslam, lmax=lmax, iter=3)
alm_obs = hp.sphtfunc.almxfl(alms,
window_func,
mmax=None,
inplace=True)
beam = 1. / beam_l
alm_obs = hp.sphtfunc.almxfl(alm_obs,
beam,
mmax=None,
inplace=True)
alm_true = alm_obs
est_map[i, :] = hp.sphtfunc.alm2map(alm_true, nside_f_est)
bin_cl = hp.sphtfunc.anafast(haslam, lmax=lmax, iter=3)
s1 = '/home/sandeep/final_Bispectrum/DimensionlessQ_Bispec/Temp_Fluctuation'
s2 = '/Rework_16April2017/DimensionLess_Bin_Bispectrum_%d_%d.txt' % (
nside_f_est, loop)
file_name = s1 + s2
with open(file_name, 'w') as f:
f.write("Bis\tangAvg_Bis\tVarB\tCl1\tCl2\tCl3\ti3\ti2\ti1\n")
for i in xrange(0, nbin):
for j in xrange(0, i + 1):
for k in xrange(0, j + 1):
i3 = index[i]
i2 = index[j]
i1 = index[k]
if abs(i2 -
i1) <= i3 <= i2 + i1 and (i3 + i2 + i1) % 2 == 0:
b = [2 * i1, 2 * i2, 2 * i3, 2 * 0, 2 * 0, 2 * 0]
wigner = wig.wig3jj(b)
alpha = np.sqrt(((2 * i1 + 1) * (2 * i2 + 1) *
(2 * i3 + 1)) / (4. * np.pi)) * wigner
m1 = est_map[i, :]
m2 = est_map[j, :]
m3 = est_map[k, :]
bis = summation(m1, m2, m3, ap_map, npix)
ang_avg_bis = bis / alpha
var_bis = g(
i1, i2,
i3) * alpha**2 * bin_cl[i] * bin_cl[j] * bin_cl[k]
f.write(
"%0.6e\t%0.6e\t%0.6e\t%0.6e\t%0.6e\t%0.6e\t%d\t%d\t%d\n"
% (bis, ang_avg_bis, var_bis, bin_cl[i], bin_cl[j],
bin_cl[k], i3, i2, i1))