In [41]:
%matplotlib inline
# We use CAMB generated scalar C_l values, set at N_side=2, N_side=4, N_side=8.
# That is total pixels Npix=48, Npix=192, Npix=768
# This amounts to lmax=96, lmax=384, lmax=1536
In [42]:
import math
import matplotlib.pyplot as plt
import numpy as np
import healpy as hp
import pyfits as pf
import astropy as ap
import os
In [43]:
cd ~/downloads
/Users/evanbiederstedt/Downloads
In [44]:
file1 = "camb_cls_nside2.fits"
file2 = "camb_cls_nside4.fits"
file3 = "camb_cls_nside8.fits"
In [45]:
ff1 = pf.open(file1) # open a FITS file
ff2 = pf.open(file2)
ff3 = pf.open(file3) #type()=pyfits.hdu.hdulist.HDUList
In [46]:
###Recall there are four columns: temp, E pol, B pol, grad-temp cross terms
##first two values are zero, i.e. monopole, dipole
cls1 = ff1[1].data # actually second HDU, first is empty
cls2 = ff2[1].data
cls3 = ff3[1].data
In [47]:
#XXX.field() references columns by 0-index
##field(0) is temperature values
cltemp1 = cls1.field(0) #all Cl scalar temp values put into ndarray
cltemp2 = cls2.field(0)
cltemp3 = cls3.field(0) #type()=numpy.ndarray
#len(cltemp1) = 97
#len(cltemp2) = 385
#len(cltemp3) = 1537
In [48]:
##define ell values
#array from 0 to lmax, the size of map
ll_1 = np.arange(97)
ll_2 = np.arange(385)
ll_3 = np.arange(1537)
In [49]:
##P_0 is the monopole, P_1 is the dipole
##remove 0, 1
ll_nodipoles1 = np.delete(ll_1, [0,1]) #numpy.ndarray, [2,3,..,95,96], len()=95
ll_nodipoles2 = np.delete(ll_2, [0,1])
ll_nodipoles3 = np.delete(ll_3, [0,1])
In [50]:
# First calculate the covariance matrix by the definition, i.e.
#
# C_ij = < \delta T_i \delta T_j > = 1/4pi \sum^{N_pix} p =
# ( T_i(p) - mean(T_i) ) * ( T_j(p) - mean(T_j) )
#
#
# Larson, Weiland, Hinshaw, Bennett,
# http://arxiv.org/pdf/1409.7718.pdf
#
In [51]:
temp1 = "camb_nside2.fits" #CAMB simulated maps associated with scalar C_l values above
temp2 = "camb_nside4.fits"
temp3 = "camb_nside8.fits"
In [52]:
tempmap1 = hp.mrdfits("camb_nside2.fits") #type() = list
tempmap2 = hp.mrdfits("camb_nside4.fits")
tempmap3 = hp.mrdfits("camb_nside8.fits")
In [53]:
tempdata1 = tempmap1[0] #len()=48, type()=numpy.ndarray
tempdata2 = tempmap2[0] #len()=192
tempdata3 = tempmap3[0] #len()=768
In [54]:
# First calculate the mean
#
# numpy.mean
#
# numpy.mean(a, axis=None, dtype=None, out=None, keepdims=False)
# Compute the arithmetic mean along the specified axis.
# Use either mean1 = np.mean(tempdata1) or mean1 = np.average(tempdata1)
In [55]:
mean1 = np.average(tempdata1) #print mean1 = -3.92499e-07
mean2 = np.average(tempdata2) #print mean2 = -1.006e-07
mean3 = np.average(tempdata3) #print mean3 = -1.76321e-08
In [56]:
Tpi1 = (tempdata1 - mean1) #type()=numpy.ndarray
Tpi2 = (tempdata2 - mean2)
Tpi3 = (tempdata3 - mean3)
In [57]:
Tp1 = np.matrix(Tpi1) #Tp1.shape = (1, 48)
Tp2 = np.matrix(Tpi2) #Tp2.shape = (1, 192)
Tp3 = np.matrix(Tpi3) #Tp3.shape = (1, 768)
In [58]:
transpose1 = Tp1.T #shape = (48, 1)
transpose2 = Tp2.T #shape = (192, 1)
transpose3 = Tp3.T #shape = (768, 1)
In [59]:
cov1 = (1/(4*math.pi)) * ( transpose1 * Tp1 ) #covariance matrix 1, shape (48, 48)
cov2 = (1/(4*math.pi)) * ( transpose2 * Tp2 ) #covariance matrix 2, shape (192, 192)
cov3 = (1/(4*math.pi)) * ( transpose3 * Tp3 ) #covariance matrix 3, shape (768, 768)
In [60]:
###Begin calculating S_ij piece by piece, in order to do the summation correctly.
#
# S_ij = sum(2ell+1) C_l P_l(dotproductmatrix)
In [61]:
ell_1 = np.arange(48)
ell_2 = np.arange(192)
ell_3 = np.arange(768)
In [62]:
vecval_1 = hp.pix2vec(2, ell_1) #Nside = 2, type()=tuple
vecval_2 = hp.pix2vec(4, ell_2) #Nside = 4
vecval_3 = hp.pix2vec(8, ell_3) #Nside = 8
###will give three arrays
##arrays of all x values, all y values, all z values
##RING scheme default
#len()=3
#type()=tuple
In [63]:
vecvalx1 = vecval_1[0] #shape (48,)
vecvaly1 = vecval_1[1]
vecvalz1 = vecval_1[2]
vecvalx2 = vecval_2[0] #shape (192,)
vecvaly2 = vecval_2[1]
vecvalz2 = vecval_2[2]
vecvalx3 = vecval_3[0] #shape (768,)
vecvaly3 = vecval_3[1]
vecvalz3 = vecval_3[2]
In [64]:
###First arrange arrays vertically
##numpy.vstack = Stack arrays in sequence vertically (row wise), input sequence of arrays
totalvecval_1 = np.vstack((vecvalx1, vecvaly1, vecvalz1)) #type()=numpy.ndarray
totalvecval_2 = np.vstack((vecvalx2, vecvaly2, vecvalz2))
totalvecval_3 = np.vstack((vecvalx3, vecvaly3, vecvalz3))
#type(totalvecval) = numpy.ndarray
In [65]:
trans1 = totalvecval_1.T
trans2 = totalvecval_2.T
trans3 = totalvecval_3.T
In [66]:
dotproductmatrix1 = trans1.dot(totalvecval_1)
dotproductmatrix2 = trans2.dot(totalvecval_2)
dotproductmatrix3 = trans3.dot(totalvecval_3)
In [67]:
###We set C_l scalar TT values to lmax=2Npix
###Fix this by simply deleting high C_l values
#print np.arange(48,96)
#len(cltemp1) = 97
###our indices to remove, arr1, arr2, arr3
arr1 = np.arange(48,97,1) #numpy.ndarray such that [48,49,...95,96]
arr2 = np.arange(192,384)
arr3 = np.arange(768,1536)
In [68]:
#We screwed up above. Write lmax = Npix. Remove excess C_l values.
#[x for i,x in enumerate(a) if i not in ind2remove]
#enumerate() is a build-in python function
#clscalar1 = np.delete(cltemp1, [48:96])
#clscalar2 = np.delete(cltemp2, [192:384])
#clscalar3 = np.delete(cltemp3, [768:1536])
newcls1 = [ x for i,x in enumerate(cltemp1) if i not in arr1]
newcls2 = [ x for i,x in enumerate(cltemp2) if i not in arr2]
newcls3 = [ x for i,x in enumerate(cltemp3) if i not in arr3]
In [69]:
from scipy.special import eval_legendre
In [70]:
###Begin calculating S_ij piece by piece, in order to do the summation correctly.
#
# S_ij = sum(2ell+1) C_l P_l(dotproductmatrix)
summatrix1 = sum( [eval_legendre(i, dotproductmatrix1) for i in ell_1])
summatrix2 = sum( [eval_legendre(i, dotproductmatrix2) for i in ell_2])
#summatrix3 = sum( [eval_legendre(i, dotproductmatrix3) for i in ell_3])
In [71]:
#matrix_total =
#(1/(4*math.pi)) * sum((2 * ll + 1) * cltemp ) * eval_legendre(ll, matrix_dotprod)
#
# Begin with adding theoretical scalar C_l values
#
add_clvalues1 = sum([ i * summatrix1 for i in newcls1 ])
add_clvalues2 = sum([ i * summatrix2 for i in newcls2 ])
#add_clvalues3 = sum([ i * summatrix3 for i in newcls3 ])
In [72]:
#matrix_total =
#(1/(4*math.pi)) * np.sum((2*ll + 1) * cltemp ) * eval_legendre(ll, matrix_dotprod)
wholematrix1 = sum([((2 * i) + 1) * add_clvalues1 for i in newcls1 ])
wholematrix2 = sum([((2 * i) + 1) * add_clvalues2 for i in newcls2 ])
#wholematrix3 = sum([((2 * i) + 1) * add_clvalues3 for i in newcls3 ])
In [73]:
covmatrix1 = (1/(4 * math.pi)) * wholematrix1 #covariance matrix for Nside=2
covmatrix2 = (1/(4 * math.pi)) * wholematrix2 #covariance matrix for Nside=4
#covmatrix3 = (1/(4 * math.pi)) * wholematrix3 #covariance matrix for Nside=8
In [74]:
np.set_printoptions(threshold='nan')
##Use this to print all values, disables corner printing
In [75]:
#Compare with what we calculated above
#covmatrix1.shape = (48, 48), covmatrix1.size = 2304
#covmatrix2.shape = (192, 192), covmatrix2.size = 36864
#covmatrix3.shape = (768, 768), covmatrix3.size = 589824
In [76]:
###Comparison 1:
###Temp-temp covariance matrix, cov1
###Dot product-generated covariance matrix, covmatrix 1
#
print cov1
print "******"
print covmatrix1
[[ 3.30189505e-11 8.56748058e-12 3.55139808e-11 1.62672208e-11
-2.52406081e-11 -2.91426362e-11 -3.58311351e-11 -8.13029555e-11
-1.01029635e-11 8.30859171e-12 2.57290595e-11 -6.97434902e-11
-3.42698185e-11 -6.45329111e-11 3.12494826e-12 -9.99308856e-12
-3.24604628e-11 -2.98758778e-11 -4.71070242e-12 -3.77236182e-11
3.42193647e-11 7.61850190e-11 5.11156705e-11 4.29608564e-11
4.32321622e-11 9.33798430e-13 3.14013210e-12 2.36365969e-11
9.03160644e-11 5.16764995e-11 5.55128139e-11 -2.15380183e-11
7.72696588e-11 -1.92658058e-11 -2.77058118e-12 -6.50507419e-12
-1.98232002e-11 -3.75798085e-11 -5.87285049e-11 -1.25663020e-11
3.03526849e-11 2.38366825e-11 2.04826728e-11 1.84621249e-11
-7.29026203e-11 -3.19545050e-11 -3.56716767e-12 -2.17311929e-11]
[ 8.56748058e-12 2.22301805e-12 9.21487033e-12 4.22088209e-12
-6.54922150e-12 -7.56168703e-12 -9.29716222e-12 -2.10958086e-11
-2.62143222e-12 2.15584360e-12 6.67596053e-12 -1.80964561e-11
-8.89204514e-12 -1.67444586e-11 8.10835343e-13 -2.59292263e-12
-8.42256876e-12 -7.75194218e-12 -1.22229351e-12 -9.78820894e-12
8.87895351e-12 1.97678497e-11 1.32630654e-11 1.11471230e-11
1.12175193e-11 2.42294179e-13 8.14775144e-13 6.13302549e-12
2.34344550e-11 1.34085846e-11 1.44040000e-11 -5.58850459e-12
2.00492824e-11 -4.99892970e-12 -7.18887150e-13 -1.68788213e-12
-5.14355769e-12 -9.75089374e-12 -1.52383798e-11 -3.26059864e-12
7.87566024e-12 6.18494253e-12 5.31467209e-12 4.79039740e-12
-1.89161612e-11 -8.29128695e-12 -9.25578684e-13 -5.63862759e-12]
[ 3.55139808e-11 9.21487033e-12 3.81975473e-11 1.74964301e-11
-2.71478785e-11 -3.13447595e-11 -3.85386662e-11 -8.74464973e-11
-1.08663794e-11 8.93641829e-12 2.76732399e-11 -7.50135589e-11
-3.68593687e-11 -6.94092492e-11 3.36108043e-12 -1.07482019e-11
-3.49132911e-11 -3.21334046e-11 -5.06666005e-12 -4.05741505e-11
3.68051005e-11 8.19418318e-11 5.49781538e-11 4.62071338e-11
4.64989408e-11 1.00435960e-12 3.37741169e-12 2.54226617e-11
9.71406689e-11 5.55813637e-11 5.97075635e-11 -2.31655082e-11
8.31084239e-11 -2.07215987e-11 -2.97993623e-12 -6.99662063e-12
-2.13211111e-11 -4.04194740e-11 -6.31662400e-11 -1.35158566e-11
3.26462425e-11 2.56378682e-11 2.20304168e-11 1.98571902e-11
-7.84114073e-11 -3.43691026e-11 -3.83671554e-12 -2.33732801e-11]
[ 1.62672208e-11 4.22088209e-12 1.74964301e-11 8.01426064e-12
-1.24351173e-11 -1.43575031e-11 -1.76526804e-11 -4.00549692e-11
-4.97735770e-12 4.09333688e-12 1.26757605e-11 -3.43600491e-11
-1.68834776e-11 -3.17929880e-11 1.53954680e-12 -4.92322642e-12
-1.59920741e-11 -1.47187435e-11 -2.32078946e-12 -1.85850368e-11
1.68586195e-11 3.75335535e-11 2.51828081e-11 2.11652308e-11
2.12988936e-11 4.60048081e-13 1.54702746e-12 1.16448798e-11
4.44953946e-11 2.54591078e-11 2.73491192e-11 -1.06109886e-11
3.80679132e-11 -9.49155264e-12 -1.36496334e-12 -3.20481028e-12
-9.76616040e-12 -1.85141866e-11 -2.89333712e-11 -6.19095410e-12
1.49536495e-11 1.17434549e-11 1.00910574e-11 9.09560892e-12
-3.59164358e-11 -1.57428070e-11 -1.75741204e-12 -1.07061579e-11]
[ -2.52406081e-11 -6.54922150e-12 -2.71478785e-11 -1.24351173e-11
1.92946251e-11 2.22774443e-11 2.73903207e-11 6.21502472e-11
7.72298699e-12 -6.35131922e-12 -1.96680112e-11 5.33138712e-11
2.61968065e-11 4.93307565e-11 -2.38879756e-12 7.63899549e-12
2.48136849e-11 2.28379552e-11 3.60099254e-12 2.88369871e-11
-2.61582379e-11 -5.82379573e-11 -3.90742451e-11 -3.28404772e-11
-3.30478715e-11 -7.13821592e-13 -2.40040465e-12 -1.80684738e-11
-6.90401194e-11 -3.95029618e-11 -4.24355481e-11 1.64642628e-11
-5.90670793e-11 1.47273199e-11 2.11790969e-12 4.97266030e-12
1.51534071e-11 2.87270548e-11 4.48937104e-11 9.60603162e-12
-2.32024402e-11 -1.82214254e-11 -1.56575261e-11 -1.41129637e-11
5.57288001e-11 2.44269162e-11 2.72684248e-12 1.66119300e-11]
[ -2.91426362e-11 -7.56168703e-12 -3.13447595e-11 -1.43575031e-11
2.22774443e-11 2.57213887e-11 3.16246793e-11 7.17582611e-11
8.91690923e-12 -7.33319068e-12 -2.27085552e-11 6.15558369e-11
3.02466576e-11 5.69569624e-11 -2.75808978e-12 8.81993324e-12
2.86497121e-11 2.63685498e-11 4.15768154e-12 3.32949939e-11
-3.02021254e-11 -6.72411579e-11 -4.51148606e-11 -3.79173935e-11
-3.81568495e-11 -8.24173587e-13 -2.77149118e-12 -2.08617374e-11
-7.97132613e-11 -4.56098521e-11 -4.89957955e-11 1.90095282e-11
-6.81984562e-11 1.70040648e-11 2.44532419e-12 5.74140037e-12
1.74960226e-11 3.31680633e-11 5.18339723e-11 1.10910602e-11
-2.67893814e-11 -2.10383355e-11 -1.80780751e-11 -1.62947337e-11
6.43440966e-11 2.82031534e-11 3.14839408e-12 1.91800236e-11]
[ -3.58311351e-11 -9.29716222e-12 -3.85386662e-11 -1.76526804e-11
2.73903207e-11 3.16246793e-11 3.88828287e-11 8.82274295e-11
1.09634206e-11 -9.01622426e-12 -2.79203734e-11 7.56834632e-11
3.71885384e-11 7.00290996e-11 -3.39109636e-12 1.08441873e-11
3.52250804e-11 3.24203679e-11 5.11190731e-12 4.09364952e-11
-3.71337843e-11 -8.26736068e-11 -5.54691299e-11 -4.66197798e-11
-4.69141931e-11 -1.01332893e-12 -3.40757340e-12 -2.56496959e-11
-9.80081741e-11 -5.60777246e-11 -6.02407747e-11 2.33723856e-11
-8.38506152e-11 2.09066495e-11 3.00654825e-12 7.05910307e-12
2.15115181e-11 4.07804360e-11 6.37303379e-11 1.36365586e-11
-3.29377867e-11 -2.58668239e-11 -2.22271562e-11 -2.00345216e-11
7.91116506e-11 3.46760328e-11 3.87097883e-12 2.35820106e-11]
[ -8.13029555e-11 -2.10958086e-11 -8.74464973e-11 -4.00549692e-11
6.21502472e-11 7.17582611e-11 8.82274295e-11 2.00193229e-10
2.48766466e-11 -2.04583437e-11 -6.33529695e-11 1.71730233e-10
8.43829782e-11 1.58900141e-10 -7.69459722e-12 2.46060985e-11
7.99277809e-11 7.35637251e-11 1.15992179e-11 9.28873132e-11
-8.42587422e-11 -1.87591288e-10 -1.25862721e-10 -1.05783022e-10
-1.06451062e-10 -2.29930291e-12 -7.73198475e-12 -5.82006697e-11
-2.22386309e-10 -1.27243665e-10 -1.36689868e-10 5.30333197e-11
-1.90261983e-10 4.74384192e-11 6.82203468e-12 1.60175208e-11
4.88108993e-11 9.25332026e-11 1.44607894e-10 3.09421543e-11
-7.47377783e-11 -5.86933465e-11 -5.04347270e-11 -4.54595090e-11
1.79508987e-10 7.86819576e-11 8.78347889e-12 5.35089717e-11]
[ -1.01029635e-11 -2.62143222e-12 -1.08663794e-11 -4.97735770e-12
7.72298699e-12 8.91690923e-12 1.09634206e-11 2.48766466e-11
3.09125095e-12 -2.54221874e-12 -7.87244103e-12 2.13397417e-11
1.04856968e-11 1.97454356e-11 -9.56155079e-13 3.05763204e-12
9.93207934e-12 9.14126203e-12 1.44135560e-12 1.15424726e-11
-1.04702590e-11 -2.33106872e-11 -1.56401016e-11 -1.31449343e-11
-1.32279468e-11 -2.85718673e-13 -9.60800912e-13 -7.23219979e-12
-2.76344283e-11 -1.58117013e-11 -1.69855159e-11 6.59008832e-12
-2.36425582e-11 5.89484888e-12 8.47727706e-13 1.99038794e-12
6.06539729e-12 1.14984694e-11 1.79694360e-11 3.84497007e-12
-9.28715341e-12 -7.29342105e-12 -6.26717919e-12 -5.64894286e-12
2.23063564e-11 9.77726915e-12 1.09146297e-12 6.64919473e-12]
[ 8.30859171e-12 2.15584360e-12 8.93641829e-12 4.09333688e-12
-6.35131922e-12 -7.33319068e-12 -9.01622426e-12 -2.04583437e-11
-2.54221874e-12 2.09069911e-12 6.47422888e-12 -1.75496238e-11
-8.62334845e-12 -1.62384798e-11 7.86333821e-13 -2.51457055e-12
-8.16805868e-12 -7.51769654e-12 -1.18535877e-12 -9.49243171e-12
8.61065219e-12 1.91705128e-11 1.28622868e-11 1.08102824e-11
1.08785517e-11 2.34972623e-13 7.90154559e-13 5.94770020e-12
2.27263200e-11 1.30034096e-11 1.39687444e-11 -5.41963315e-12
1.94434398e-11 -4.84787378e-12 -6.97164127e-13 -1.63687826e-12
-4.98813127e-12 -9.45624406e-12 -1.47779117e-11 -3.16207102e-12
7.63767634e-12 5.99804794e-12 5.15407506e-12 4.64564296e-12
-1.83445592e-11 -8.04074372e-12 -8.97609889e-13 -5.46824152e-12]
[ 2.57290595e-11 6.67596053e-12 2.76732399e-11 1.26757605e-11
-1.96680112e-11 -2.27085552e-11 -2.79203734e-11 -6.33529695e-11
-7.87244103e-12 6.47422888e-12 2.00486242e-11 -5.43455945e-11
-2.67037626e-11 -5.02854000e-11 2.43502521e-12 -7.78682392e-12
-2.52938735e-11 -2.32799110e-11 -3.67067816e-12 -2.93950376e-11
2.66644474e-11 5.93649692e-11 3.98304043e-11 3.34760006e-11
3.36874081e-11 7.27635332e-13 2.44685676e-12 1.84181316e-11
7.03761732e-11 4.02674170e-11 4.32567540e-11 -1.67828771e-11
6.02101398e-11 -1.50123197e-11 -2.15889508e-12 -5.06889030e-12
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******
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2.05587215e-08 2.05587215e-08 1.18396172e-08 9.55504891e-09
8.23206500e-09 8.23206500e-09 9.55504891e-09 1.18396172e-08
5.95467303e-07 2.50177412e-08 1.28996930e-08 9.13972109e-09
7.37259283e-09 9.13972109e-09 1.28996930e-08 2.50177412e-08
2.46863074e-08 1.14616076e-08 1.20402232e-08 1.46601940e-08]
[ 7.63727784e-09 6.45008451e-09 7.40943039e-09 7.08451638e-09
9.53300645e-09 9.46191466e-09 9.53300645e-09 7.85156169e-09
6.74706524e-09 3.30550755e-23 6.74706524e-09 7.85156169e-09
8.87258676e-09 1.15615133e-08 1.15615133e-08 8.87258676e-09
6.33541349e-09 6.14577294e-09 6.14577294e-09 6.33541349e-09
1.15775390e-08 1.81831891e-08 1.15775390e-08 8.05410908e-09
7.68758948e-09 7.52968202e-09 7.68758948e-09 8.05410908e-09
1.18396172e-08 2.05587215e-08 2.05587215e-08 1.18396172e-08
9.55504891e-09 8.23206500e-09 8.23206500e-09 9.55504891e-09
2.50177412e-08 5.95467303e-07 2.50177412e-08 1.28996930e-08
9.13972109e-09 7.37259283e-09 9.13972109e-09 1.28996930e-08
2.46863074e-08 1.46601940e-08 1.20402232e-08 1.14616076e-08]
[ 6.45008451e-09 7.63727784e-09 7.08451638e-09 7.40943039e-09
7.85156169e-09 9.53300645e-09 9.46191466e-09 9.53300645e-09
7.85156169e-09 6.74706524e-09 1.79048326e-23 6.74706524e-09
6.33541349e-09 8.87258676e-09 1.15615133e-08 1.15615133e-08
8.87258676e-09 6.33541349e-09 6.14577294e-09 6.14577294e-09
8.05410908e-09 1.15775390e-08 1.81831891e-08 1.15775390e-08
8.05410908e-09 7.68758948e-09 7.52968202e-09 7.68758948e-09
9.55504891e-09 1.18396172e-08 2.05587215e-08 2.05587215e-08
1.18396172e-08 9.55504891e-09 8.23206500e-09 8.23206500e-09
1.28996930e-08 2.50177412e-08 5.95467303e-07 2.50177412e-08
1.28996930e-08 9.13972109e-09 7.37259283e-09 9.13972109e-09
1.46601940e-08 2.46863074e-08 1.14616076e-08 1.20402232e-08]
[ 7.08451638e-09 7.63727784e-09 6.45008451e-09 7.40943039e-09
6.74706524e-09 7.85156169e-09 9.53300645e-09 9.46191466e-09
9.53300645e-09 7.85156169e-09 6.74706524e-09 3.30550755e-23
6.14577294e-09 6.33541349e-09 8.87258676e-09 1.15615133e-08
1.15615133e-08 8.87258676e-09 6.33541349e-09 6.14577294e-09
7.68758948e-09 8.05410908e-09 1.15775390e-08 1.81831891e-08
1.15775390e-08 8.05410908e-09 7.68758948e-09 7.52968202e-09
8.23206500e-09 9.55504891e-09 1.18396172e-08 2.05587215e-08
2.05587215e-08 1.18396172e-08 9.55504891e-09 8.23206500e-09
9.13972109e-09 1.28996930e-08 2.50177412e-08 5.95467303e-07
2.50177412e-08 1.28996930e-08 9.13972109e-09 7.37259283e-09
1.14616076e-08 2.46863074e-08 1.46601940e-08 1.20402232e-08]
[ 7.40943039e-09 6.45008451e-09 7.63727784e-09 7.08451638e-09
1.79048326e-23 6.74706524e-09 7.85156169e-09 9.53300645e-09
9.46191466e-09 9.53300645e-09 7.85156169e-09 6.74706524e-09
6.14577294e-09 6.14577294e-09 6.33541349e-09 8.87258676e-09
1.15615133e-08 1.15615133e-08 8.87258676e-09 6.33541349e-09
7.52968202e-09 7.68758948e-09 8.05410908e-09 1.15775390e-08
1.81831891e-08 1.15775390e-08 8.05410908e-09 7.68758948e-09
8.23206500e-09 8.23206500e-09 9.55504891e-09 1.18396172e-08
2.05587215e-08 2.05587215e-08 1.18396172e-08 9.55504891e-09
7.37259283e-09 9.13972109e-09 1.28996930e-08 2.50177412e-08
5.95467303e-07 2.50177412e-08 1.28996930e-08 9.13972109e-09
1.20402232e-08 1.46601940e-08 2.46863074e-08 1.14616076e-08]
[ 7.40943039e-09 7.08451638e-09 7.63727784e-09 6.45008451e-09
6.74706524e-09 3.30550755e-23 6.74706524e-09 7.85156169e-09
9.53300645e-09 9.46191466e-09 9.53300645e-09 7.85156169e-09
6.33541349e-09 6.14577294e-09 6.14577294e-09 6.33541349e-09
8.87258676e-09 1.15615133e-08 1.15615133e-08 8.87258676e-09
7.68758948e-09 7.52968202e-09 7.68758948e-09 8.05410908e-09
1.15775390e-08 1.81831891e-08 1.15775390e-08 8.05410908e-09
9.55504891e-09 8.23206500e-09 8.23206500e-09 9.55504891e-09
1.18396172e-08 2.05587215e-08 2.05587215e-08 1.18396172e-08
9.13972109e-09 7.37259283e-09 9.13972109e-09 1.28996930e-08
2.50177412e-08 5.95467303e-07 2.50177412e-08 1.28996930e-08
1.20402232e-08 1.14616076e-08 2.46863074e-08 1.46601940e-08]
[ 7.08451638e-09 7.40943039e-09 6.45008451e-09 7.63727784e-09
7.85156169e-09 6.74706524e-09 1.79048326e-23 6.74706524e-09
7.85156169e-09 9.53300645e-09 9.46191466e-09 9.53300645e-09
8.87258676e-09 6.33541349e-09 6.14577294e-09 6.14577294e-09
6.33541349e-09 8.87258676e-09 1.15615133e-08 1.15615133e-08
8.05410908e-09 7.68758948e-09 7.52968202e-09 7.68758948e-09
8.05410908e-09 1.15775390e-08 1.81831891e-08 1.15775390e-08
1.18396172e-08 9.55504891e-09 8.23206500e-09 8.23206500e-09
9.55504891e-09 1.18396172e-08 2.05587215e-08 2.05587215e-08
1.28996930e-08 9.13972109e-09 7.37259283e-09 9.13972109e-09
1.28996930e-08 2.50177412e-08 5.95467303e-07 2.50177412e-08
1.14616076e-08 1.20402232e-08 1.46601940e-08 2.46863074e-08]
[ 6.45008451e-09 7.40943039e-09 7.08451638e-09 7.63727784e-09
9.53300645e-09 7.85156169e-09 6.74706524e-09 3.30550755e-23
6.74706524e-09 7.85156169e-09 9.53300645e-09 9.46191466e-09
1.15615133e-08 8.87258676e-09 6.33541349e-09 6.14577294e-09
6.14577294e-09 6.33541349e-09 8.87258676e-09 1.15615133e-08
1.15775390e-08 8.05410908e-09 7.68758948e-09 7.52968202e-09
7.68758948e-09 8.05410908e-09 1.15775390e-08 1.81831891e-08
2.05587215e-08 1.18396172e-08 9.55504891e-09 8.23206500e-09
8.23206500e-09 9.55504891e-09 1.18396172e-08 2.05587215e-08
2.50177412e-08 1.28996930e-08 9.13972109e-09 7.37259283e-09
9.13972109e-09 1.28996930e-08 2.50177412e-08 5.95467303e-07
1.46601940e-08 1.20402232e-08 1.14616076e-08 2.46863074e-08]
[ 6.26307287e-09 6.47911433e-09 3.30550755e-23 6.47911433e-09
7.63727784e-09 7.63727784e-09 6.45008451e-09 7.08451638e-09
7.40943039e-09 7.40943039e-09 7.08451638e-09 6.45008451e-09
9.48331660e-09 1.00238658e-08 9.48331660e-09 8.58301683e-09
6.84765413e-09 6.17345314e-09 6.84765413e-09 8.58301683e-09
1.09169429e-08 1.09169429e-08 8.47909136e-09 8.44687856e-09
6.60441888e-09 6.60441888e-09 8.44687856e-09 8.47909136e-09
1.50849416e-08 1.71419797e-08 1.50849416e-08 1.05146146e-08
8.47977491e-09 8.95172122e-09 8.47977491e-09 1.05146146e-08
2.46863074e-08 2.46863074e-08 1.46601940e-08 1.14616076e-08
1.20402232e-08 1.20402232e-08 1.14616076e-08 1.46601940e-08
5.95467303e-07 2.53785780e-08 1.72425190e-08 2.53785780e-08]
[ 6.47911433e-09 6.26307287e-09 6.47911433e-09 3.30550755e-23
7.08451638e-09 6.45008451e-09 7.63727784e-09 7.63727784e-09
6.45008451e-09 7.08451638e-09 7.40943039e-09 7.40943039e-09
6.84765413e-09 8.58301683e-09 9.48331660e-09 1.00238658e-08
9.48331660e-09 8.58301683e-09 6.84765413e-09 6.17345314e-09
8.44687856e-09 8.47909136e-09 1.09169429e-08 1.09169429e-08
8.47909136e-09 8.44687856e-09 6.60441888e-09 6.60441888e-09
8.47977491e-09 1.05146146e-08 1.50849416e-08 1.71419797e-08
1.50849416e-08 1.05146146e-08 8.47977491e-09 8.95172122e-09
1.14616076e-08 1.46601940e-08 2.46863074e-08 2.46863074e-08
1.46601940e-08 1.14616076e-08 1.20402232e-08 1.20402232e-08
2.53785780e-08 5.95467303e-07 2.53785780e-08 1.72425190e-08]
[ 3.30550755e-23 6.47911433e-09 6.26307287e-09 6.47911433e-09
7.40943039e-09 7.40943039e-09 7.08451638e-09 6.45008451e-09
7.63727784e-09 7.63727784e-09 6.45008451e-09 7.08451638e-09
6.84765413e-09 6.17345314e-09 6.84765413e-09 8.58301683e-09
9.48331660e-09 1.00238658e-08 9.48331660e-09 8.58301683e-09
6.60441888e-09 6.60441888e-09 8.44687856e-09 8.47909136e-09
1.09169429e-08 1.09169429e-08 8.47909136e-09 8.44687856e-09
8.47977491e-09 8.95172122e-09 8.47977491e-09 1.05146146e-08
1.50849416e-08 1.71419797e-08 1.50849416e-08 1.05146146e-08
1.20402232e-08 1.20402232e-08 1.14616076e-08 1.46601940e-08
2.46863074e-08 2.46863074e-08 1.46601940e-08 1.14616076e-08
1.72425190e-08 2.53785780e-08 5.95467303e-07 2.53785780e-08]
[ 6.47911433e-09 3.30550755e-23 6.47911433e-09 6.26307287e-09
6.45008451e-09 7.08451638e-09 7.40943039e-09 7.40943039e-09
7.08451638e-09 6.45008451e-09 7.63727784e-09 7.63727784e-09
9.48331660e-09 8.58301683e-09 6.84765413e-09 6.17345314e-09
6.84765413e-09 8.58301683e-09 9.48331660e-09 1.00238658e-08
8.47909136e-09 8.44687856e-09 6.60441888e-09 6.60441888e-09
8.44687856e-09 8.47909136e-09 1.09169429e-08 1.09169429e-08
1.50849416e-08 1.05146146e-08 8.47977491e-09 8.95172122e-09
8.47977491e-09 1.05146146e-08 1.50849416e-08 1.71419797e-08
1.46601940e-08 1.14616076e-08 1.20402232e-08 1.20402232e-08
1.14616076e-08 1.46601940e-08 2.46863074e-08 2.46863074e-08
2.53785780e-08 1.72425190e-08 2.53785780e-08 5.95467303e-07]]
In [77]:
###Comparison 2:
###Temp-temp covariance matrix, cov2
###Dot product-generated covariance matrix, covmatrix 2
#
print cov2
print "******"
print covmatrix2
[[ 3.06734880e-11 -3.68033468e-11 -7.20815513e-11 -6.87150446e-11
4.16210522e-11 5.65911412e-11 6.67000859e-12 -1.37274190e-12
3.84595013e-11 -5.02538948e-11 -7.66563419e-11 -1.09821549e-11
-4.67771763e-13 5.29009026e-11 1.15913177e-10 7.78302658e-12
9.25378133e-12 -5.20251634e-11 -2.40923505e-11 1.14978255e-11
-4.31004960e-11 -1.88477793e-11 1.43941391e-11 7.32276023e-11
-3.98664550e-11 1.39156070e-11 1.97255316e-10 1.27717735e-10
1.89372007e-12 7.02365336e-11 5.14846822e-12 -4.14835639e-11
-1.25016976e-10 -1.07467574e-11 6.83640527e-11 1.25485262e-11
-1.98470477e-11 3.21903919e-13 8.43527364e-11 2.96532787e-11
3.13063897e-11 -2.37542333e-11 1.05386451e-10 9.41256621e-11
3.96818017e-11 6.17310943e-11 -1.16301653e-11 -1.16034100e-11
-3.37429729e-11 -2.89800635e-11 9.21121590e-11 1.11261733e-11
1.82260593e-11 -2.39091660e-11 -4.86807983e-13 5.89225850e-11
5.12457906e-11 -4.78882977e-12 6.27825238e-11 3.47328587e-11
2.54258710e-11 -2.07288631e-11 -7.53005421e-11 -4.27815748e-11
4.23633053e-11 9.61243470e-12 -2.85634876e-12 -2.19390797e-11
-2.38221911e-11 -1.38572748e-10 -2.42962528e-11 6.01459102e-11
3.90057660e-11 -3.32197539e-11 1.64511872e-11 5.92293892e-11
6.99526735e-11 -9.33436433e-11 -9.28428738e-11 -4.31140001e-11
-5.51548767e-13 5.93512177e-11 3.31173313e-11 6.03886661e-11
-5.53128454e-11 -1.34442064e-10 -1.02508367e-10 -2.42954179e-11
-6.80958392e-11 -2.35301323e-11 3.15703625e-11 6.10155136e-11
-3.01525573e-11 -8.81515821e-11 -1.29866324e-10 -5.85506544e-11
4.94704624e-11 6.70373550e-11 7.52060266e-11 -5.41889157e-12
-4.11353815e-11 -1.24404163e-10 -4.12762757e-11 -5.77519200e-11
-9.39826962e-11 -6.80344147e-11 -4.16814032e-11 2.71819590e-11
2.67724979e-11 -9.35353534e-12 -1.12917448e-10 -9.90177440e-11
-5.29505635e-11 4.77325013e-11 8.47360021e-11 1.23699800e-11
6.26702458e-12 -6.78302584e-11 -3.09409947e-11 -7.60920706e-12
-3.51621629e-11 -7.79901428e-11 -2.07474937e-11 2.54977824e-11
3.49937061e-11 -2.55488612e-11 -1.07715112e-10 -5.60973424e-11
-3.51313800e-11 3.80365052e-11 1.15807919e-10 -3.46394343e-11
-4.14220599e-11 -7.33112907e-11 7.17779320e-11 -2.85505782e-11
4.04657157e-11 -9.05111031e-11 -9.78725676e-11 -7.14416524e-12
-1.58132187e-11 4.31747973e-11 -2.14550743e-11 -3.91078883e-11
-6.71289638e-11 2.61638436e-11 1.07956852e-10 3.62643024e-11
-2.80723906e-11 -1.54309227e-11 3.06942439e-12 7.80152603e-11
-2.57150187e-11 -8.76731913e-11 -3.62346172e-11 -3.98263845e-11
1.72850491e-11 8.06329540e-11 -3.48553608e-11 -3.76057698e-11
-9.09789715e-12 6.54850632e-11 9.05359203e-11 4.83387592e-11
7.26064179e-11 6.77195531e-11 3.46761344e-11 5.56896130e-11
-6.98631718e-11 -5.95709720e-11 -5.13745898e-11 3.86542661e-11
5.75876708e-11 -4.79916767e-12 -3.32728272e-11 2.64487418e-11
6.37249884e-11 3.98071819e-11 3.48455563e-11 1.44146327e-11
-5.54136866e-11 -2.75511187e-12 6.98443889e-11 6.86910270e-11
-3.08230481e-12 -1.63636822e-11 -4.50305665e-12 2.63780849e-11
1.46653576e-11 1.13176513e-10 2.51706646e-11 6.09150876e-11]
[ -3.68033468e-11 4.41582116e-11 8.64864910e-11 8.24472131e-11
-4.99386974e-11 -6.79004427e-11 -8.00295807e-12 1.64707371e-12
-4.61453338e-11 6.02967480e-11 9.19755277e-11 1.31768536e-11
5.61252358e-13 -6.34727395e-11 -1.39077528e-10 -9.33840451e-12
-1.11030779e-11 6.24219903e-11 2.89070212e-11 -1.37955775e-11
5.17137959e-11 2.26143622e-11 -1.72706968e-11 -8.78615774e-11
4.78334574e-11 -1.66965338e-11 -2.36675269e-10 -1.53241139e-10
-2.27216535e-12 -8.42727631e-11 -6.17735006e-12 4.97737327e-11
1.50000648e-10 1.28944148e-11 -8.20260812e-11 -1.50562511e-11
2.38133275e-11 -3.86233950e-13 -1.01209985e-10 -3.55792573e-11
-3.75627307e-11 2.85013348e-11 -1.26447113e-10 -1.12935940e-10
-4.76119008e-11 -7.40675780e-11 1.39543645e-11 1.39222619e-11
4.04862435e-11 3.47715046e-11 -1.10520061e-10 -1.33496527e-11
-2.18683963e-11 2.86872272e-11 5.84092785e-13 -7.06978068e-11
-6.14868630e-11 5.74584045e-12 -7.53291317e-11 -4.16739510e-11
-3.05070368e-11 2.48713656e-11 9.03487711e-11 5.13311399e-11
-5.08292837e-11 -1.15334058e-11 3.42716804e-12 2.63234345e-11
2.85828741e-11 1.66265440e-10 2.91516721e-11 -7.21656018e-11
-4.68007666e-11 3.98584639e-11 -1.97388294e-11 -7.10659251e-11
-8.39321787e-11 1.11997641e-10 1.11396799e-10 5.17299991e-11
6.61771552e-13 -7.12121025e-11 -3.97355752e-11 -7.24568744e-11
6.63666909e-11 1.61309270e-10 1.22993870e-10 2.91506694e-11
8.17042620e-11 2.82324454e-11 -3.78794521e-11 -7.32089916e-11
3.61783147e-11 1.05767994e-10 1.55819102e-10 7.02515485e-11
-5.93567528e-11 -8.04342489e-11 -9.02353755e-11 6.50181522e-12
4.93559712e-11 1.49265375e-10 4.95250221e-11 6.92931943e-11
1.12764411e-10 8.16305615e-11 5.00111081e-11 -3.26140637e-11
-3.21227740e-11 1.12227661e-11 1.35483130e-10 1.18805680e-10
6.35323219e-11 -5.72714707e-11 -1.01669832e-10 -1.48420253e-11
-7.51944087e-12 8.13856058e-11 3.71243133e-11 9.12984847e-12
4.21890507e-11 9.35758768e-11 2.48937200e-11 -3.05933182e-11
-4.19869308e-11 3.06546035e-11 1.29241150e-10 6.73079672e-11
4.21521121e-11 -4.56378100e-11 -1.38951242e-10 4.15618585e-11
4.96999394e-11 8.79619857e-11 -8.61222027e-11 3.42561907e-11
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******
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3.94314461e-08 3.99946626e-08 3.99946626e-08 3.94314461e-08
4.14669025e-08 3.68622943e-08 3.83708810e-08 3.78504778e-08
4.05754669e-08 3.70493070e-08 3.74036199e-08 3.70493070e-08
4.05754669e-08 4.20292288e-08 3.97403615e-08 4.39934014e-08
4.70019438e-08 4.72043802e-08 4.74618351e-08 4.72043802e-08
4.70019438e-08 4.39934014e-08 3.97403615e-08 4.20292288e-08
3.92308890e-08 3.92691667e-08 3.92691667e-08 3.92308890e-08
4.44480616e-08 4.37106648e-08 4.76645107e-08 5.33587592e-08
5.51962393e-08 5.69507956e-08 5.69507956e-08 5.51962393e-08
5.33587592e-08 4.76645107e-08 4.37106648e-08 4.44480616e-08
4.85849499e-08 4.37669119e-08 4.77666593e-08 4.37669119e-08
4.85849499e-08 4.90182823e-08 5.64655217e-08 5.38880279e-08
5.76294408e-08 6.81526881e-08 6.25839730e-08 6.81526881e-08
5.76294408e-08 5.38880279e-08 5.64655217e-08 4.90182823e-08
5.35005004e-08 5.06858888e-08 5.06858888e-08 5.35005004e-08
6.02106619e-08 6.56372050e-08 6.54435800e-08 7.21800046e-08
7.72403699e-08 8.61892595e-08 8.61892595e-08 7.72403699e-08
7.21800046e-08 6.54435800e-08 6.56372050e-08 6.02106619e-08
6.92992180e-08 7.03640263e-08 6.92992180e-08 7.14800879e-08
7.78505680e-08 9.72672231e-08 1.09023176e-07 1.20360846e-07
1.09023176e-07 9.72672231e-08 7.78505680e-08 7.14800879e-08
9.56212835e-08 9.56212835e-08 9.69763384e-08 1.43182855e-07
2.37781616e-07 2.37781616e-07 1.43182855e-07 9.69763384e-08
1.41104368e-07 1.68921948e-07 1.03184904e-05 1.68921948e-07]
[ 2.83959077e-08 -9.90451593e-22 2.83959077e-08 2.91777431e-08
2.65409507e-08 2.99454291e-08 2.39964909e-08 2.39964909e-08
2.99454291e-08 2.65409507e-08 2.94914624e-08 2.94914624e-08
3.05958882e-08 2.81849984e-08 3.00223489e-08 2.69788453e-08
2.89959486e-08 2.69788453e-08 3.00223489e-08 2.81849984e-08
3.05958882e-08 3.11641923e-08 2.81032576e-08 3.11641923e-08
3.18269694e-08 3.05749281e-08 2.75194106e-08 3.07107961e-08
3.01451616e-08 3.04000858e-08 3.04000858e-08 3.01451616e-08
3.07107961e-08 2.75194106e-08 3.05749281e-08 3.18269694e-08
2.90947740e-08 3.13209224e-08 3.13209224e-08 2.90947740e-08
3.43693224e-08 3.36860647e-08 3.10321216e-08 2.95620167e-08
3.07884390e-08 2.86265386e-08 3.08208362e-08 2.86265386e-08
3.07884390e-08 2.95620167e-08 3.10321216e-08 3.36860647e-08
3.43693224e-08 3.36865386e-08 3.17570703e-08 3.36865386e-08
3.27535290e-08 3.17761869e-08 3.44827043e-08 3.11440810e-08
3.25931693e-08 3.22247753e-08 3.22247753e-08 3.25931693e-08
3.11440810e-08 3.44827043e-08 3.17761869e-08 3.27535290e-08
3.52826910e-08 3.70656908e-08 3.70656908e-08 3.52826910e-08
3.71185789e-08 3.61447193e-08 3.38755089e-08 3.60984519e-08
3.49355183e-08 3.07846883e-08 3.44830285e-08 3.07846883e-08
3.49355183e-08 3.60984519e-08 3.38755089e-08 3.61447193e-08
3.71185789e-08 4.05622144e-08 3.64964952e-08 4.05622144e-08
4.14669025e-08 3.68622943e-08 3.83708810e-08 3.78504778e-08
3.58877202e-08 3.47227920e-08 3.47227920e-08 3.58877202e-08
3.78504778e-08 3.83708810e-08 3.68622943e-08 4.14669025e-08
3.94314461e-08 3.99946626e-08 3.99946626e-08 3.94314461e-08
4.70019438e-08 4.39934014e-08 3.97403615e-08 4.20292288e-08
4.05754669e-08 3.70493070e-08 3.74036199e-08 3.70493070e-08
4.05754669e-08 4.20292288e-08 3.97403615e-08 4.39934014e-08
4.70019438e-08 4.72043802e-08 4.74618351e-08 4.72043802e-08
5.33587592e-08 4.76645107e-08 4.37106648e-08 4.44480616e-08
3.92308890e-08 3.92691667e-08 3.92691667e-08 3.92308890e-08
4.44480616e-08 4.37106648e-08 4.76645107e-08 5.33587592e-08
5.51962393e-08 5.69507956e-08 5.69507956e-08 5.51962393e-08
5.76294408e-08 5.38880279e-08 5.64655217e-08 4.90182823e-08
4.85849499e-08 4.37669119e-08 4.77666593e-08 4.37669119e-08
4.85849499e-08 4.90182823e-08 5.64655217e-08 5.38880279e-08
5.76294408e-08 6.81526881e-08 6.25839730e-08 6.81526881e-08
7.21800046e-08 6.54435800e-08 6.56372050e-08 6.02106619e-08
5.35005004e-08 5.06858888e-08 5.06858888e-08 5.35005004e-08
6.02106619e-08 6.56372050e-08 6.54435800e-08 7.21800046e-08
7.72403699e-08 8.61892595e-08 8.61892595e-08 7.72403699e-08
9.72672231e-08 7.78505680e-08 7.14800879e-08 6.92992180e-08
7.03640263e-08 6.92992180e-08 7.14800879e-08 7.78505680e-08
9.72672231e-08 1.09023176e-07 1.20360846e-07 1.09023176e-07
1.43182855e-07 9.69763384e-08 9.56212835e-08 9.56212835e-08
9.69763384e-08 1.43182855e-07 2.37781616e-07 2.37781616e-07
1.68921948e-07 1.41104368e-07 1.68921948e-07 1.03184904e-05]]
In [78]:
###Comparison 3:
###Temp-temp covariance matrix, cov3
###Dot product-generated covariance matrix, covmatrix 3
#
#print cov3
#print "******"
#print covmatrix3
In [ ]:
Content source: evanbiederstedt/CMBintheLikeHoodz
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