print "\t \tSignal Correlation"

hdu_i=fits.open(i_file)

hdu_j=fits.open(j_file)

alpha_radio=hp.read_map(alpha_file,hdu='maps/phi',verbose=False)

delta_alpha_radio=hp.read_map(alpha_file,hdu='uncertainty/phi',verbose=False)

iqu_band_i=np.array([hdu_i['freq-map'].data.field(i) for i in xrange(3)])

iqu_band_j=np.array([hdu_j['freq-map'].data.field(i) for i in xrange(3)])

sigma_q_i=np.sqrt(hdu_i['freq-map'].data.field('QQ_cov '))

sigma_u_i=np.sqrt(hdu_i['freq-map'].data.field('UU_cov '))

sigma_q_j=np.sqrt(hdu_j['freq-map'].data.field('QQ_cov '))

sigma_u_j=np.sqrt(hdu_j['freq-map'].data.field('UU_cov '))

nside_i=hdu_i['freq-map'].header['nside']

nside_j=hdu_j['freq-map'].header['nside']

order_i=hdu_i['freq-map'].header['ordering']

order_j=hdu_j['freq-map'].header['ordering']

hdu_i.close()

hdu_j.close()

ind_i=np.argwhere( wl == wl_i)[0][0]

ind_j=np.argwhere( wl == wl_j)[0][0]

npix_i=hp.nside2npix(nside_i)

npix_j=hp.nside2npix(nside_j)

#ipdb.set_trace()

if npix_i != iqu_band_i[1].shape[0]:

print 'NSIDE parameter not equal to size of map for file I'

print 'setting npix to larger parameter'

npix_i=iqu_band_i[1].shape[0]

if npix_j != iqu_band_j[1].shape[0]:

print 'NSIDE parameter not equal to size of map for file J'

print 'setting npix to larger parameter'

npix_j=iqu_band_j[1].shape[0]

sigma_i=np.array([sigma_q_i*np.random.normal(0,1,npix_i),sigma_u_i*np.random.normal(0,1,npix_i)])

sigma_j=np.array([sigma_q_j*np.random.normal(0,1,npix_j),sigma_u_j*np.random.normal(0,1,npix_j)])

# sigma_i=[noise_const_pol[ind_i]*np.random.normal(0,1,npix_i),noise_const_pol[ind_i]*np.random.normal(0,1,npix_i)]

# sigma_j=[noise_const_pol[ind_j]*np.random.normal(0,1,npix_j),noise_const_pol[ind_j]*np.random.normal(0,1,npix_j)]

# iqu_band_i[1]+=sigma_i[0]

# iqu_band_i[2]+=sigma_i[1]

# iqu_band_j[1]+=sigma_j[0]

# iqu_band_j[2]+=sigma_j[1]

sigma_i=hp.reorder(sigma_i,n2r=1)

sigma_j=hp.reorder(sigma_j,n2r=1)

sigma_q_i=hp.smoothing(sigma_i[0],fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_i])**2)*np.pi/(180.*60.),verbose=False)

sigma_u_i=hp.smoothing(sigma_i[1],fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_i])**2)*np.pi/(180.*60.),verbose=False)

sigma_q_j=hp.smoothing(sigma_j[0],fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_j])**2)*np.pi/(180.*60.),verbose=False)

sigma_u_j=hp.smoothing(sigma_j[1],fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_j])**2)*np.pi/(180.*60.),verbose=False)

sigma_q_i=hp.ud_grade(sigma_q_i,nside_out=nside_out,order_in='ring',order_out='ring')

sigma_u_i=hp.ud_grade(sigma_u_i,nside_out=nside_out,order_in='ring',order_out='ring')

sigma_q_j=hp.ud_grade(sigma_q_j,nside_out=nside_out,order_in='ring',order_out='ring')

sigma_u_j=hp.ud_grade(sigma_u_j,nside_out=nside_out,order_in='ring',order_out='ring')

iqu_band_i=hp.reorder(iqu_band_i,n2r=1)

iqu_band_j=hp.reorder(iqu_band_j,n2r=1)

iqu_band_i=hp.smoothing(iqu_band_i,pol=1,fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_i])**2)*np.pi/(180.*60.),verbose=False)

iqu_band_j=hp.smoothing(iqu_band_j,pol=1,fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_j])**2)*np.pi/(180.*60.),verbose=False)

#alpha_radio=hp.smoothing(alpha_radio,fwhm=np.pi/180.,lmax=383)

iqu_band_i=hp.ud_grade(iqu_band_i,nside_out=nside_out,order_in='ring',order_out='ring')

iqu_band_j=hp.ud_grade(iqu_band_j,nside_out=nside_out,order_in='ring',order_out='ring')

const=2.*(wl_i**2-wl_j**2)

Delta_Q=(iqu_band_i[1]-iqu_band_j[1])/const

Delta_U=(iqu_band_i[2]-iqu_band_j[2])/const

alpha_u=alpha_radio*iqu_band_j[2]

alpha_q=-alpha_radio*iqu_band_j[1]

DQm=hp.ma(Delta_Q)

DUm=hp.ma(Delta_U)

aQm=hp.ma(alpha_q)

aUm=hp.ma(alpha_u)

#ipdb.set_trace()

Bl_factor=np.repeat(1.,3*nside_out)

#ipdb.set_trace()

if beam:

Bl_factor=hp.gauss_beam(smoothing_scale*np.pi/(180.*60.),3*nside_out-1)

pix_area=hp.nside2pixarea(nside_out)

#ipdb.set_trace()

mask_bool=np.repeat(False,npix_out)

if gal_cut > 0:

pix=np.arange(hp.nside2npix(nside_out))

x,y,z=hp.pix2vec(nside_out,pix,nest=0)

mask_bool= np.abs(z)<= np.sin(gal_cut*np.pi/180.)

elif gal_cut < 0:

pix=np.arange(hp.nside2npix(nside_out))

x,y,z=hp.pix2vec(nside_out,pix,nest=0)

mask_bool= np.abs(z)>= np.sin(np.abs(gal_cut)*np.pi/180.)

#mask_bool1[np.where(np.sqrt(iqu_band_j[1]**2+iqu_band_j[2]**2)<.2e-6)]=True

DQm.mask=mask_bool

DUm.mask=mask_bool

aQm.mask=mask_bool

aUm.mask=mask_bool

#ipdb.set_trace()

cross1=hp.anafast(DQm,map2=aUm)/Bl_factor**2

cross2=hp.anafast(DUm,map2=aQm)/Bl_factor**2

print "\t \tNoise Correlation"

hdu_i=fits.open(i_file)

hdu_j=fits.open(j_file)

alpha_radio=hp.read_map(alpha_file,hdu='maps/phi',verbose=False)

delta_alpha_radio=hp.read_map(alpha_file,hdu='uncertainty/phi',verbose=False)

iqu_band_i=np.array([hdu_i['freq-map'].data.field(i) for i in xrange(3)])

iqu_band_j=np.array([hdu_j['freq-map'].data.field(i) for i in xrange(3)])

sigma_q_i=np.sqrt(hdu_i['freq-map'].data.field('QQ_cov '))

sigma_u_i=np.sqrt(hdu_i['freq-map'].data.field('UU_cov '))

sigma_q_j=np.sqrt(hdu_j['freq-map'].data.field('QQ_cov '))

sigma_u_j=np.sqrt(hdu_j['freq-map'].data.field('UU_cov '))

nside_i=hdu_i['freq-map'].header['nside']

nside_j=hdu_j['freq-map'].header['nside']

order_i=hdu_i['freq-map'].header['ordering']

order_j=hdu_j['freq-map'].header['ordering']

hdu_i.close()

hdu_j.close()

ind_i=np.argwhere( wl == wl_i)[0][0]

ind_j=np.argwhere( wl == wl_j)[0][0]

npix_i=hp.nside2npix(nside_i)

npix_j=hp.nside2npix(nside_j)

#ipdb.set_trace()

if npix_i != iqu_band_i[1].shape[0]:

print 'NSIDE parameter not equal to size of map for file I'

print 'setting npix to larger parameter'

npix_i=iqu_band_i[1].shape[0]

if npix_j != iqu_band_j[1].shape[0]:

print 'NSIDE parameter not equal to size of map for file J'

print 'setting npix to larger parameter'

npix_j=iqu_band_j[1].shape[0]

sigma_i=np.array([sigma_q_i*np.random.normal(0,1,npix_i),sigma_u_i*np.random.normal(0,1,npix_i)])

sigma_j=np.array([sigma_q_j*np.random.normal(0,1,npix_j),sigma_u_j*np.random.normal(0,1,npix_j)])

# sigma_i=[noise_const_pol[ind_i]*np.random.normal(0,1,npix_i),noise_const_pol[ind_i]*np.random.normal(0,1,npix_i)]

# sigma_j=[noise_const_pol[ind_j]*np.random.normal(0,1,npix_j),noise_const_pol[ind_j]*np.random.normal(0,1,npix_j)]

sigma_i=hp.reorder(sigma_i,n2r=1)

sigma_j=hp.reorder(sigma_j,n2r=1)

tmp_i=np.copy(iqu_band_i)

tmp_j=np.copy(iqu_band_j)

iqu_band_i[1]=np.copy(sigma_i[0])

iqu_band_i[2]=np.copy(sigma_i[1])

iqu_band_j[1]=np.copy(sigma_j[0])

iqu_band_j[2]=np.copy(sigma_j[1])

iqu_band_i=hp.smoothing(iqu_band_i,pol=1,fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_i])**2)*np.pi/(180.*60.),verbose=False)

iqu_band_j=hp.smoothing(iqu_band_j,pol=1,fwhm=np.sqrt((smoothing_scale)**2-(beam_fwhm[ind_j])**2)*np.pi/(180.*60.),verbose=False)

#alpha_radio=hp.smoothing(alpha_radio,fwhm=np.pi/180.,lmax=383)

iqu_band_i=hp.ud_grade(iqu_band_i,nside_out=nside_out,order_out='ring')

iqu_band_j=hp.ud_grade(iqu_band_j,nside_out=nside_out,order_out='ring')

tmp_i=hp.reorder(tmp_i,n2r=1)

tmp_j=hp.reorder(tmp_j,n2r=1)

tmp_i=hp.smoothing(tmp_i,pol=1,fwhm=np.sqrt( (smoothing_scale)**2-(beam_fwhm[ind_i])**2)/(np.pi*180.*60))

tmp_j=hp.smoothing(tmp_j,pol=1,fwhm=np.sqrt( (smoothing_scale)**2-(beam_fwhm[ind_j])**2)/(np.pi*180.*60))

tmp_i=hp.ud_grade(tmp_i,128)

tmp_j=hp.ud_grade(tmp_j,128)

const=2.*(wl_i**2-wl_j**2)

Delta_Q=(iqu_band_i[1]-iqu_band_j[1])/const

Delta_U=(iqu_band_i[2]-iqu_band_j[2])/const

alpha_u=alpha_radio*iqu_band_j[2]

alpha_q=-alpha_radio*iqu_band_j[1]

DQm=hp.ma(Delta_Q)

DUm=hp.ma(Delta_U)

aQm=hp.ma(alpha_q)

aUm=hp.ma(alpha_u)

sqi=hp.ma(iqu_band_i[1])

sui=hp.ma(iqu_band_i[2])

sqj=hp.ma(iqu_band_j[1])

suj=hp.ma(iqu_band_j[2])

salpha=hp.ma(delta_alpha_radio)

alpham=hp.ma(alpha_radio)

um=hp.ma(tmp_j[2])

qm=hp.ma(tmp_j[1])

Bl_factor=np.repeat(1.,3*nside_out)

#ipdb.set_trace()

if beam:

Bl_factor=hp.gauss_beam(smoothing_scale*np.pi/(180.*60.),3*nside_out-1)

pix_area=hp.nside2pixarea(nside_out)

#ipdb.set_trace()

mask_bool=np.repeat(False,npix_out)

if gal_cut > 0:

pix=np.arange(hp.nside2npix(nside_out))

x,y,z=hp.pix2vec(nside_out,pix,nest=0)

mask_bool= np.abs(z) <= np.sin(gal_cut*np.pi/180.)

elif gal_cut > 0:

pix=np.arange(hp.nside2npix(nside_out))

x,y,z=hp.pix2vec(nside_out,pix,nest=0)

mask_bool= np.abs(z) >= np.sin(np.abs(gal_cut)*np.pi/180.)

#mask_bool1[np.where(np.sqrt(iqu_band_j[1]**2+iqu_band_j[2]**2)<.2e-6)]=True

DQm.mask=mask_bool

DUm.mask=mask_bool

aQm.mask=mask_bool

aUm.mask=mask_bool

sqi.mask=mask_bool

sui.mask=mask_bool

sqj.mask=mask_bool

suj.mask=mask_bool

salpha.mask=mask_bool

alpham.mask=mask_bool

um.mask=mask_bool

qm.mask=mask_bool

#ipdb.set_trace()

cross1=hp.anafast(DQm,map2=aUm)/Bl_factor**2

cross2=hp.anafast(DUm,map2=aQm)/Bl_factor**2

#cross1=np.mean(cross1_array,axis=0) ##Average over all Cross Spectra

#cross2=np.mean(cross2_array,axis=0) ##Average over all Cross Spectra

##calculate theoretical variance for correlations

N_dq=( (sqi-sqj)**2 ).sum()*(pix_area/const)**2/(4.*np.pi)

N_du=( (sui-suj)**2 ).sum()*(pix_area/const)**2/(4.*np.pi)

N_au=( (salpha*um+alpham*suj+salpha*suj)**2 ).sum()*pix_area**2/(4.*np.pi)

N_aq=( (salpha*qm+alpham*sqj+salpha*sqj)**2 ).sum()*pix_area**2/(4.*np.pi)

#ipdb.set_trace()

bins=[1,5,10,20,25,50]

gal_cut=[-20,-10,-05,00,05,10,20]

bls=hp.gauss_beam(smoothing_scale*np.pi/(180.*60.),3*nside_out-1)**2

l=np.arange(3*nside_out)

ll=l*(l+1)/(2*np.pi)

for cut in gal_cut:

data=np.load('FR_planck_cut_{0:2>02d}.npz'.format(cut))

theory_in=data['theory']

cross1_array_in=data['c1']

cross2_array_in=data['c2']

noise1_array_in=data['n1']

noise2_array_in=data['n2']

Ndq_array_in=data['ndq']

Ndu_array_in=data['ndu']

Naq_array_in=data['naq']

Nau_array_in=data['nau']

#print( str(np.shape(cross1_array_in)) + ' line 596')

if cut >= 0:

fsky= 1. - np.sin(cut*np.pi/180.)

else:

fsky= np.abs(np.sin(cut*np.pi/180.))

L=np.sqrt(fsky*4*np.pi)

dl_eff=2*np.pi/L

#print( str(np.shape(cross1_array_in)) + ' line 604')

#ipdb.set_trace()

cross1_array_in=np.array(cross1_array_in)/fsky

cross2_array_in=np.array(cross2_array_in)/fsky

noise1_array_in=np.array(noise1_array_in)/fsky

noise2_array_in=np.array(noise2_array_in)/fsky

Nau_array_in=np.array(Nau_array_in)/fsky

Naq_array_in=np.array(Naq_array_in)/fsky

Ndu_array_in=np.array(Ndu_array_in)/fsky

Ndq_array_in=np.array(Ndq_array_in)/fsky

#ipdb.set_trace()

for b in bins:

#N_dq=np.mean(Ndq_array_in)

#N_au=np.mean(Nau_array_in)

#Transpose arrays to match dimensions for operations

#cross1_array_in=cross1_array_in.T

#cross2_array_in=cross2_array_in.T

#noise1_array_in=noise1_array_in.T

#noise2_array_in=noise2_array_in.T

#ipdb.set_trace()

delta1=np.sqrt( np.divide(2.*abs( (cross1_array_in - noise1_array_in).T**2 + (cross1_array_in - noise1_array_in). T * (Ndq_array_in+Nau_array_in)/2. + Ndq_array_in*Nau_array_in/2.).T,((2.*l+1.)*np.sqrt(b**2+dl_eff**2)*fsky)))

#N_du=np.mean(Ndu_array_in)

#N_aq=np.mean(Naq_array_in)

delta2=np.sqrt( np.divide(2.*abs( (cross2_array_in - noise2_array_in).T**2 + (cross2_array_in - noise2_array_in).T * (Ndu_array_in+Naq_array_in)/2. + Ndu_array_in*Naq_array_in/2.).T,((2.*l+1.)*np.sqrt(b**2+dl_eff**2)*fsky)))

#Transpose arrays back to match for plotting

#cross1_array=cross1_array_in.T

#cross2_array=cross2_array_in.T

#noise1_array=noise1_array_in.T

#noise2_array=noise2_array_in.T

#ipdb.set_trace()

cosmic=np.sqrt(2./((2.*l+1)*np.sqrt(b**2+dl_eff**2)*fsky)*theory_in**2)

delta_array=np.sqrt(delta1**2+delta2**2)

cross_array = np.add(np.subtract(cross1_array_in,noise1_array_in),np.subtract(cross2_array_in,noise2_array_in))

cross=np.average(cross_array,weights=1./delta_array**2,axis=0)

dcross=np.average(delta_array,weights=1./delta_array**2,axis=0)

plot_l=[]

if( b != 1):

tmp_c1=bin_llcl.bin_llcl(ll*cross/bls,b)

cross=tmp_c1['llcl']

tmp_dc1=bin_llcl.bin_llcl(ll*dcross/bls,b)

dcross= tmp_dc1['llcl']

plot_l=tmp_c1['l_out']

tmp_t1=bin_llcl.bin_llcl(ll*theory_in/bls,b)

theory=tmp_t1['llcl']

tmp_c1=bin_llcl.bin_llcl(ll*cosmic/bls,b)

cosmic=tmp_c1['llcl']

else:

plot_l=l

theory=np.multiply(ll/bls,theory_in)

#cross1_array=np.multiply(ll/bls,cross1_array_in)

#noise1_array=np.multiply(ll/bls,noise1_array_in)

#cross2_array=np.multiply(ll/bls,cross2_array_in)

#noise2_array=np.multiply(ll/bls,noise2_array_in)

cross*=ll/bls

cosmic*=ll/bls

dcross*=ll/bls

#cosmic2*=ll/bls

#delta1*=ll/bls

#delta2*=ll/bls

#ipdb.set_trace()

bad=np.where(plot_l < dl_eff)

#noise1=np.mean(noise1_array,axis=0)

#noise2=np.mean(noise2_array,axis=0)

#theory_array = np.add(theory1_array,theory2_array)

#theory=np.mean(theory_array,axis=0)

#dtheory=np.std(theory_array,axis=0,ddof=1)

#cross_array = np.add(np.subtract(cross1_array,noise1_array),np.subtract(cross2_array,noise2_array))

#delta_array=np.sqrt(delta1**2+delta2**2)

##cross_array=np.add(cross1_array,cross2_array)

#ipdb.set_trace()

#cross=np.average(cross_array,weights=1./delta_array**2,axis=0)

#cosmic=np.sqrt(cosmic1**2+cosmic2**2)

#theory1=np.mean(theory1_array,axis=0)

#dtheory1=np.std(theory1_array,axis=0,ddof=1)

#cross1=np.mean(cross1_array,axis=0)

#dcross1=np.std(np.subtract(cross1_array,noise1),axis=0,ddof=1)

#dcross=np.average(delta_array,weights=1./delta_array**2,axis=0)

#ipdb.set_trace()

plot_binned.plotBinned((cross)*1e12,dcross*1e12,plot_l,b,'Cross_FR_cut_{0:0>2d}'.format(cut), title='Faraday Rotation Correlator',theory=theory*1e12,dtheory=cosmic*1e12)

#theory2=np.mean(theory2_array,axis=0)

#dtheory2=np.std(theory2_array,axis=0,ddof=1)

#cross2=np.mean(cross2_array,axis=0)

##delta2=np.mean(delta2_array,axis=0)

#dcross2=np.std(np.subtract(cross2_array,noise2),axis=0,ddof=1)

##ipdb.set_trace()

#plot_binned.plotBinned((cross2-noise2)*1e12,dcross2*1e12,plot_l,b,'Cross_43x95_FR_UxaQ', title='Cross 43x95 FR UxaQ',theory=theory2*1e12,dtheory=dtheory2*1e12,delta=delta2*1e12,cosmic=cosmic2*1e12)

#ipdb.set_trace()

if b == 25 :

a_scales=np.linspace(-10,10,1001)

chi_array=[]

for a in a_scales:

chi_array.append(np.sum( (cross - a*theory)**2/(dcross)**2))

ind = np.argmin(chi_array)

#likelihood=np.exp(np.multiply(-1./2.,chi_array))/np.sqrt(2*np.pi)

likelihood=np.exp(np.multiply(-1./2.,chi_array))/np.sum(np.exp(np.multiply(-1./2.,chi_array))*.05)

Sig=np.sum(cross/(dcross**2))/np.sum(1./dcross**2)

#Noise=np.std(np.sum(cross_array/dcross**2,axis=1)/np.sum(1./dcross**2)) \

Noise=np.sqrt(1./np.sum(1./dcross**2))

Sig1=np.sum(cross*(theory/dcross)**2)/np.sum((theory/dcross)**2)

Noise1=np.sum(dcross*(theory/dcross)**2)/np.sum((theory/dcross)**2)

SNR=Sig/Noise

SNR1=Sig1/Noise1

#Sig2=np.sum(cross/(dcross**2))/np.sum(1./dcross**2)

#Noise2=np.sqrt(1./np.sum(1./dcross**2))

#Sig3=np.sum(cross*(theory/dcross)**2)/np.sum((theory/dcross)**2)

#Noise3=np.sqrt(np.sum(theory**2)/np.sum(theory**2/dcross**2))

#SNR2=Sig2/Noise2

#SNR3=Sig3/Noise3

#ipdb.set_trace()

fig,ax1=plt.subplots(1,1)

ax1.plot(a_scales,likelihood,'k.')

ax1.set_title('Faraday Rotation Correlator')

ax1.set_xlabel('Likelihood scalar')

ax1.set_ylabel('Likelihood of Correlation')

fig.savefig('FR_Correlation_Likelihood.png',format='png')

fig.savefig('FR_Correlation_Likelihood.eps',format='eps')

#ipdb.set_trace()

f=open('Maximum_likelihood.txt','w')

f.write('Maximum Likelihood: {0:2.5f}% for scale factor {1:.2f} \n'.format(float(likelihood[ind]*100),float(a_scales[ind])))

f.write('Probability of scale factor =1: {0:2.5f}% \n \n'.format(float(likelihood[np.where(a_scales ==1)])*100))

f.write('Detection Levels using Standard Deviation \n')

f.write('Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n'.format(SNR,Sig, Noise))

f.write('Weighted Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n \n'.format(SNR1,Sig1,Noise))

#f.write('Detection using Theoretical Noise \n')

#f.write('Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n'.format(SNR2,Sig2, Noise2))

#f.write('Weighted Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n'.format(SNR3,Sig3,Noise3))

f.close()

#if b == 1 :

# xbar= np.matrix(ll[1:]*(cross-np.mean(cross))[1:]).T

# vector=np.matrix(ll[1:]*cross[1:]).T

# mu=np.matrix(ll[1:]*theory[1:]).T

# fact=len(xbar)-1

# cov=(np.dot(xbar,xbar.T)/fact).squeeze()

# ipdb.set_trace()

# likelihood=np.exp(-np.dot(np.dot((vector-mu).T,lin.inv(cov)),(vector-mu))/2. )/(np.sqrt(2*np.pi*lin.det(cov)))

# print('Likelihood of fit is #{0:.5f}'.format(likelihood[0,0]))

# f=open('FR_likelihood.txt','w')

# f.write('Likelihood of fit is #{0:.5f}'.format(likelihood[0,0]))

# f.close()

subprocess.call('mv Maximum_likelihood_cut_{:2>02d}.txt' .format(cut), shell=True)

subprocess.call('mv *01*.png bin_01/', shell=True)

subprocess.call('mv *05*.png bin_05/', shell=True)

subprocess.call('mv *10*.png bin_10/', shell=True)

subprocess.call('mv *20*.png bin_20/', shell=True)

subprocess.call('mv *25*.png bin_25/', shell=True)

subprocess.call('mv *50*.png bin_50/', shell=True)

f=open('cl_theory_FR_QxaU.json','r')

theory1_array=json.load(f)

f.close()

f=open('cl_theory_FR_UxaQ.json','r')

theory2_array=json.load(f)

f.close()

bins=[1,5,10,20,50]

f=open('cl_array_FR_QxaU.json','r')

cross1_array=json.load(f)

f.close()

f=open('cl_array_FR_UxaQ.json','r')

cross2_array=json.load(f)

f.close()

f=open('cl_noise_FR_QxaU.json','r')

noise1_array=json.load(f)

f.close()

f=open('cl_noise_FR_UxaQ.json','r')

noise2_array=json.load(f)

f.close()

f=open('cl_Nau_FR_QxaU.json','r')

Nau_array=json.load(f)

f.close()

f=open('cl_Ndq_FR_QxaU.json','r')

Ndq_array=json.load(f)

f.close()

f=open('cl_Naq_FR_UxaQ.json','r')

Naq_array=json.load(f)

f.close()

f=open('cl_Ndu_FR_UxaQ.json','r')

Ndu_array=json.load(f)

f.close()

f=open('cl_delta_FR_UxaQ.json','r')

delta2_array=json.load(f)

f.close()

f=open('mixing_matrix.json','r')

mll=json.load(f)

f.close()

mll=np.matrix(mll)

kll=mll.getI()

kll=kll.tolist()

theory1=np.array([np.sum(np.mean(theory1_array,axis=0)[j]*kll[i][j] for j in xrange(len(kll[i]))) for i in xrange(len(mll))])

dtheory1=np.std(theory1_array,axis=0,ddof=1)

cross1=np.array([np.sum(np.mean(cross1_array,axis=0)[j]*kll[i][j] for j in xrange(len(kll[i]))) for i in xrange(len(mll))])

N_dq=np.array([np.sum(np.mean(Ndq_array)*m[j] for j in xrange(len(m))) for m in kll])

N_au=np.array([np.sum(np.mean(Nau_array)*m[j] for j in xrange(len(m))) for m in kll])

noise1=np.array([np.sum(np.mean(noise1_array,axis=0)[j]*kll[i][j] for j in xrange(len(kll[i]))) for i in xrange(len(mll))])

l=np.arange(len(cross1))

dcross1=np.std(np.subtract(cross1_array,noise1),axis=0,ddof=1)

delta1=np.sqrt(2.*((cross1-noise1)**2+abs(cross1-noise1)/2.*(N_dq+N_au)+N_dq*N_au/2.)/(2.*l+1.))

plot_binned.plotBinned((cross1-noise1)*1e12,dcross1*1e12,plot_l,b,'Cross_43x95_FR_QxaU', title='Cross 43x95 FR QxaU',theory=theory1*1e12,dtheory=dtheory1*1e12,delta=delta1*1e12)

theory2=np.array([np.sum(np.mean(theory2_array,axis=0)[j]*kll[i][j] for j in xrange(len(kll[i]))) for i in xrange(len(mll))])

dtheory2=np.std(theory2_array,axis=0,ddof=1)

cross2=np.array([np.sum(np.mean(cross2_array,axis=0)[j]*kll[i][j] for j in xrange(len(kll[i]))) for i in xrange(len(mll))])

#delta2=np.mean(delta2_array,axis=0)

N_du=np.array([np.sum(np.mean(Ndu_array)*m[i] for i in xrange(len(m))) for m in kll])

N_aq=np.array([np.sum(np.mean(Naq_array)*m[i] for i in xrange(len(m))) for m in kll])

noise2=np.array([np.sum(np.mean(noise2_array,axis=0)[j]*kll[i][j] for j in xrange(len(kll[i]))) for i in xrange(len(mll))])

dcross2=np.std(np.subtract(cross2_array,noise2),axis=0,ddof=1)

delta2=np.sqrt(2.*((cross2-noise2)**2+abs(cross2-noise2)/2.*(N_du+N_aq)+N_du*N_aq/2.)/(2.*l+1.))

#ipdb.set_trace()

plot_binned.plotBinned((cross2-noise2)*1e12,dcross2*1e12,plot_l,b,'Cross_43x95_FR_UxaQ', title='Cross 43x95 FR UxaQ',theory=theory2*1e12,dtheory=dtheory2*1e12,delta=delta2*1e12)

subprocess.call('mv *01*.png mll/bin_01/', shell=True)

subprocess.call('mv *05*.png mll/bin_05/', shell=True)

subprocess.call('mv *10*.png mll/bin_10/', shell=True)

subprocess.call('mv *20*.png mll/bin_20/', shell=True)

subprocess.call('mv *50*.png mll/bin_50/', shell=True)

##Parameters for Binning, Number of Runs

## Beam correction

use_beam=0

N_runs=10

bins=[1,5,10,20,25,50]

gal_cut=[-20,-10,-05,00,05,10,20]

bls=hp.gauss_beam(smoothing_scale*np.pi/(180.*60.),3*nside_out-1)**2

l=np.arange(3*nside_out)

ll=l*(l+1)/(2*np.pi)

#map_prefix='/home/matt/Planck/data/faraday/simul_maps/'

#file_prefix=map_prefix+'planck_simulated_'

alpha_file='/data/wmap/faraday_MW_realdata.fits'

#wl=np.array([299792458./(band*1e9) for band in bands])

#theory1_array_in=[]

#theory2_array_in=[]

dsets=glob.glob('/data/Planck/LFI*1024*R2.00*.fits')

dsets.sort()

#simulate_fields.main()

for cut in gal_cut:

cross1_array_in=[]

cross2_array_in=[]

dcross1_array_in=[]

dcross2_array_in=[]

Ndq_array_in=[]

Ndu_array_in=[]

Nau_array_in=[]

Naq_array_in=[]

noise1_array_in=[]

noise2_array_in=[]

print('Galactic cut: {:2d}'.format(cut))

for i in xrange(len(bands)-1):

for j in xrange(i+1,len(bands)):

print(' Bands: {0:0>3.0f} x {1:0>3.0f}'.format(bands[i],bands[j]))

tmp_cross1_array=[]

tmp_cross2_array=[]

tmp_noise1_array=[]

tmp_noise2_array=[]

##arrays used to average over noise realizations

tmp_Ndq_array=[]

tmp_Ndu_array=[]

tmp_Nau_array=[]

tmp_Naq_array=[]

tmp_c1,tmp_c2=correlate_signal(dsets[i],dsets[j],wl[i],wl[j],alpha_file,'{0:0>3.0f}x{1:0>3.0f}'.format(bands[i],bands[j]),beam=use_beam,gal_cut=cut)

cross1_array_in.append(tmp_c1)

cross2_array_in.append(tmp_c2)

for n in xrange(N_runs):

print('\tNoise Correlation #{:0>3d}'.format(n+1))

tmp_n1,tmp_n2,tmp_dq,tmp_du,tmp_au,tmp_aq=correlate_noise(dsets[i],dsets[j],wl[i],wl[j],alpha_file,'{0:0>3.0f}x{1:0>3.0f}'.format(bands[i],bands[j]),beam=use_beam,gal_cut=cut)

tmp_noise1_array.append(tmp_n1)

tmp_noise2_array.append(tmp_n2)

tmp_Ndq_array.append(tmp_dq)

tmp_Ndu_array.append(tmp_du)

tmp_Naq_array.append(tmp_aq)

tmp_Nau_array.append(tmp_au)

noise1_array_in.append(np.mean(tmp_noise1_array,axis=0))

noise2_array_in.append(np.mean(tmp_noise2_array,axis=0))

Ndq_array_in.append(np.mean(tmp_Ndq_array))

Ndu_array_in.append(np.mean(tmp_Ndu_array))

Nau_array_in.append(np.mean(tmp_Nau_array))

Naq_array_in.append(np.mean(tmp_Naq_array))

#print( str(np.shape(cross1_array_in) ) + ' line 587')

#read in theory_cls

theory_in=hp.read_cl('/home/matt/Planck/data/faraday/correlation/fr_theory_cl.fits')

#print( str(np.shape(cross1_array_in)) + ' line 592' )

#out_dic={'theory':theory_in,'c1':cross1_array_in,'c2':cross2_array_in,'n1':noise1_array_in,'n2':noise2_array_in,'ndq':Ndq_array_in,'nau':Nau_array_in,'ndu':Ndu_array_in,'naq':Naq_array_in}

np.savez('FR_planck_cut_{0:2>02d}.npz'.format(cut),theory=theory_in,c1=cross1_array_in,c2=cross2_array_in,n1=noise1_array_in,n2=noise2_array_in,ndq=Ndq_array_in,nau=Nau_array_in,ndu=Ndu_array_in,naq=Naq_array_in)

#print( str(np.shape(cross1_array_in)) + ' line 596')

if cut >= 0:

fsky= 1. - np.sin(cut*np.pi/180.)

else:

fsky= np.abs(np.sin(cut*np.pi/180.))

L=np.sqrt(fsky*4*np.pi)

dl_eff=2*np.pi/L

#print( str(np.shape(cross1_array_in)) + ' line 604')

#ipdb.set_trace()

cross1_array_in=np.array(cross1_array_in)/fsky

cross2_array_in=np.array(cross2_array_in)/fsky

noise1_array_in=np.array(noise1_array_in)/fsky

noise2_array_in=np.array(noise2_array_in)/fsky

Nau_array_in=np.array(Nau_array_in)/fsky

Naq_array_in=np.array(Naq_array_in)/fsky

Ndu_array_in=np.array(Ndu_array_in)/fsky

Ndq_array_in=np.array(Ndq_array_in)/fsky

#ipdb.set_trace()

for b in bins:

#N_dq=np.mean(Ndq_array_in)

#N_au=np.mean(Nau_array_in)

#Transpose arrays to match dimensions for operations

#cross1_array_in=cross1_array_in.T

#cross2_array_in=cross2_array_in.T

#noise1_array_in=noise1_array_in.T

#noise2_array_in=noise2_array_in.T

#ipdb.set_trace()

delta1=np.sqrt( np.divide(2.*abs( (cross1_array_in - noise1_array_in).T**2 + (cross1_array_in - noise1_array_in). T * (Ndq_array_in+Nau_array_in)/2. + Ndq_array_in*Nau_array_in/2.).T,((2.*l+1.)*np.sqrt(b**2+dl_eff**2)*fsky)))

#N_du=np.mean(Ndu_array_in)

#N_aq=np.mean(Naq_array_in)

delta2=np.sqrt( np.divide(2.*abs( (cross2_array_in - noise2_array_in).T**2 + (cross2_array_in - noise2_array_in).T * (Ndu_array_in+Naq_array_in)/2. + Ndu_array_in*Naq_array_in/2.).T,((2.*l+1.)*np.sqrt(b**2+dl_eff**2)*fsky)))

#Transpose arrays back to match for plotting

#cross1_array=cross1_array_in.T

#cross2_array=cross2_array_in.T

#noise1_array=noise1_array_in.T

#noise2_array=noise2_array_in.T

#ipdb.set_trace()

cosmic=np.sqrt(2./((2.*l+1)*np.sqrt(b**2+dl_eff**2)*fsky)*theory_in**2)

delta_array=np.sqrt(delta1**2+delta2**2)

cross_array = np.add(np.subtract(cross1_array_in,noise1_array_in),np.subtract(cross2_array_in,noise2_array_in))

cross=np.average(cross_array,weights=1./delta_array**2,axis=0)

dcross=np.average(delta_array,weights=1./delta_array**2,axis=0)

plot_l=[]

if( b != 1):

tmp_c1=bin_llcl.bin_llcl(ll*cross/bls,b)

cross=tmp_c1['llcl']

tmp_dc1=bin_llcl.bin_llcl(ll*dcross/bls,b)

dcross= tmp_dc1['llcl']

plot_l=tmp_c1['l_out']

tmp_t1=bin_llcl.bin_llcl(ll*theory_in/bls,b)

theory=tmp_t1['llcl']

tmp_c1=bin_llcl.bin_llcl(ll*cosmic/bls,b)

cosmic=tmp_c1['llcl']

else:

plot_l=l

theory=np.multiply(ll/bls,theory_in)

#cross1_array=np.multiply(ll/bls,cross1_array_in)

#noise1_array=np.multiply(ll/bls,noise1_array_in)

#cross2_array=np.multiply(ll/bls,cross2_array_in)

#noise2_array=np.multiply(ll/bls,noise2_array_in)

cross*=ll/bls

cosmic*=ll/bls

dcross*=ll/bls

#cosmic2*=ll/bls

#delta1*=ll/bls

#delta2*=ll/bls

#ipdb.set_trace()

bad=np.where(plot_l < dl_eff)

#noise1=np.mean(noise1_array,axis=0)

#noise2=np.mean(noise2_array,axis=0)

#theory_array = np.add(theory1_array,theory2_array)

#theory=np.mean(theory_array,axis=0)

#dtheory=np.std(theory_array,axis=0,ddof=1)

#cross_array = np.add(np.subtract(cross1_array,noise1_array),np.subtract(cross2_array,noise2_array))

#delta_array=np.sqrt(delta1**2+delta2**2)

##cross_array=np.add(cross1_array,cross2_array)

#ipdb.set_trace()

#cross=np.average(cross_array,weights=1./delta_array**2,axis=0)

#cosmic=np.sqrt(cosmic1**2+cosmic2**2)

#theory1=np.mean(theory1_array,axis=0)

#dtheory1=np.std(theory1_array,axis=0,ddof=1)

#cross1=np.mean(cross1_array,axis=0)

#dcross1=np.std(np.subtract(cross1_array,noise1),axis=0,ddof=1)

#dcross=np.average(delta_array,weights=1./delta_array**2,axis=0)

#ipdb.set_trace()

plot_binned.plotBinned((cross)*1e12,dcross*1e12,plot_l,b,'Cross_FR_cut_{0:0>2d}'.format(cut), title='Faraday Rotation Correlator',theory=theory*1e12,dtheory=cosmic*1e12)

#theory2=np.mean(theory2_array,axis=0)

#dtheory2=np.std(theory2_array,axis=0,ddof=1)

#cross2=np.mean(cross2_array,axis=0)

##delta2=np.mean(delta2_array,axis=0)

#dcross2=np.std(np.subtract(cross2_array,noise2),axis=0,ddof=1)

##ipdb.set_trace()

#plot_binned.plotBinned((cross2-noise2)*1e12,dcross2*1e12,plot_l,b,'Cross_43x95_FR_UxaQ', title='Cross 43x95 FR UxaQ',theory=theory2*1e12,dtheory=dtheory2*1e12,delta=delta2*1e12,cosmic=cosmic2*1e12)

#ipdb.set_trace()

if b == 25 :

a_scales=np.linspace(-10,10,1001)

chi_array=[]

for a in a_scales:

chi_array.append(np.sum( (cross - a*theory)**2/(dcross)**2))

ind = np.argmin(chi_array)

#likelihood=np.exp(np.multiply(-1./2.,chi_array))/np.sqrt(2*np.pi)

likelihood=np.exp(np.multiply(-1./2.,chi_array))/np.sum(np.exp(np.multiply(-1./2.,chi_array))*.05)

Sig=np.sum(cross/(dcross**2))/np.sum(1./dcross**2)

#Noise=np.std(np.sum(cross_array/dcross**2,axis=1)/np.sum(1./dcross**2)) \

Noise=np.sqrt(1./np.sum(1./dcross**2))

Sig1=np.sum(cross*(theory/dcross)**2)/np.sum((theory/dcross)**2)

Noise1=np.sum(dcross*(theory/dcross)**2)/np.sum((theory/dcross)**2)

SNR=Sig/Noise

SNR1=Sig1/Noise1

#Sig2=np.sum(cross/(dcross**2))/np.sum(1./dcross**2)

#Noise2=np.sqrt(1./np.sum(1./dcross**2))

#Sig3=np.sum(cross*(theory/dcross)**2)/np.sum((theory/dcross)**2)

#Noise3=np.sqrt(np.sum(theory**2)/np.sum(theory**2/dcross**2))

#SNR2=Sig2/Noise2

#SNR3=Sig3/Noise3

#ipdb.set_trace()

fig,ax1=plt.subplots(1,1)

ax1.plot(a_scales,likelihood,'k.')

ax1.set_title('Faraday Rotation Correlator')

ax1.set_xlabel('Likelihood scalar')

ax1.set_ylabel('Likelihood of Correlation')

fig.savefig('FR_Correlation_Likelihood.png',format='png')

fig.savefig('FR_Correlation_Likelihood.eps',format='eps')

#ipdb.set_trace()

f=open('Maximum_likelihood_{0:0>2d}.txt'.format(cut),'w')

f.write('Maximum Likelihood: {0:2.5f}% for scale factor {1:.2f} \n'.format(float(likelihood[ind]*100),float(a_scales[ind])))

f.write('Probability of scale factor =1: {0:2.5f}% \n \n'.format(float(likelihood[np.where(a_scales ==1)])*100))

f.write('Detection Levels using Standard Deviation \n')

f.write('Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n'.format(SNR,Sig, Noise))

f.write('Weighted Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n \n'.format(SNR1,Sig1,Noise))

#f.write('Detection using Theoretical Noise \n')

#f.write('Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n'.format(SNR2,Sig2, Noise2))

#f.write('Weighted Detection Level: {0:.4f} sigma, Signal= {1:.4e}, Noise= {2:.4e} \n'.format(SNR3,Sig3,Noise3))

f.close()

#if b == 1 :

# xbar= np.matrix(ll[1:]*(cross-np.mean(cross))[1:]).T

# vector=np.matrix(ll[1:]*cross[1:]).T

# mu=np.matrix(ll[1:]*theory[1:]).T

# fact=len(xbar)-1

# cov=(np.dot(xbar,xbar.T)/fact).squeeze()

# ipdb.set_trace()

# likelihood=np.exp(-np.dot(np.dot((vector-mu).T,lin.inv(cov)),(vector-mu))/2. )/(np.sqrt(2*np.pi*lin.det(cov)))

# print('Likelihood of fit is #{0:.5f}'.format(likelihood[0,0]))

# f=open('FR_likelihood.txt','w')

# f.write('Likelihood of fit is #{0:.5f}'.format(likelihood[0,0]))

# f.close()

subprocess.call('mv Maximum_likelihood_cut_{:2>02d}.txt' .format(cut), shell=True)

subprocess.call('mv *01.png bin_01/', shell=True)

subprocess.call('mv *05.png bin_05/', shell=True)

subprocess.call('mv *10.png bin_10/', shell=True)

subprocess.call('mv *20.png bin_20/', shell=True)

subprocess.call('mv *25.png bin_25/', shell=True)

subprocess.call('mv *50.png bin_50/', shell=True)