def TestInverseLensing():
f = lens.fid_displacement()
sim1,sim2 = lens.fid_two_HD_unlensed_cmb_sim()
N_max = 3
testmap = sim1
len_map = f.lens_map(testmap)
f_mat = f.M_mat
maps = [testmap,len_map,f.dx_in_grid_units(),f.dy_in_grid_units(),f_mat['kappa'],f_mat['omega'],len_map-testmap]
titles = ['input map','lensed map','$d_0(x)$ in grid units','$d_1(x)$ in grid units','$\kappa(x)$','$\omega(x)$','Len map - Unl map']
for i in xrange(N_max + 1) :
print "N_it",i
finv = f.inverse_displacement_NR(NR_iter = i)
maps.append(finv.lens_map(len_map) - testmap)
titles.append('residuals, NR it ' + str(i))
maps.append(np.log10(np.abs(finv.lens_map(len_map) - testmap)))
titles.append('$\log_{10}$ abs. residuals, NR it ' + str(i))
""" plot all the maps """
pp = PdfPages("TestInverseLensing.pdf")
for map,title in zip(maps,titles) :
pl.figure()
pl.imshow(map)
pl.title(title)
pl.colorbar()
pp.savefig()
pl.close()
pp.close()
def TestConjGradInversionHighRes():
"""
We first generate high displacements and then subsample
"""
Cl_len = lens.fiducial_Cl_len()
Cl_unl = lens.fiducial_Cl_unl()
res_low_arr= [8,9,10,11]
sN_uKamin,Beam_FWHM_amin = [35.,5.]
Nit = []
total_time = []
status = []
pp = PdfPages("TestHighResConjGRadInv.pdf")
def plot_save_map(map,title) :
pl.figure()
pl.imshow(map)
pl.title(title)
pl.colorbar()
pp.savefig()
pl.close()
def callback(v):
CovPhi.cg_it += 1
print "This is callback",CovPhi.cg_it
for res_low in res_low_arr :
res_high = res_low + 1
lside = 0.0005*2**res_low
f = lens.fid_displacement(params = [sN_uKamin,Beam_FWHM_amin,res_low,res_high,lside])
f_inv = f.inverse_displacement_NR(NR_iter = 2)
CovPhi = lens.LensedCovMatrix(sN_uKamin,Beam_FWHM_amin,Cl_unl,Cl_len,res_low,res_high,lside,f,f_inv,verbose = False)
dat1,dat2 = CovPhi.get_two_sims()
plot_save_map(dat1.map,"Input map, res_low = " + str(res_low))
CovPhi.cg_it = 0
t0= time.time()
output_map,stat = CovPhi.apply_cg_inverse_to_LD_map(dat1.map,callback = callback)
total_time.append( (time.time() -t0)/60.) # minutes
Nit.append(CovPhi.cg_it)
status.append(stat)
plot_save_map(np.log10(np.fft.fftshift(np.fft.fft2(dat1.map)).real**2), \
'Input map, $\log_{10}$ Spectrum') # Cov^-1 T has cov Cov^-1 and thus the inverse spectrum of the map modulo lensing
plot_save_map(-np.log10(np.fft.fftshift(np.fft.fft2(output_map.reshape((2**res_low,2**res_low))).real**2)), \
'Current solution vector, $\log_{10}$ Inverse Spectrum, Nit = ' + str(CovPhi.cg_it))
print Nit
print status
print total_time
np.savetxt('TestConjGradInversionHighRes_Nit.txt',Nit)
np.savetxt('TestConjGradInversionHighRes_Nit_status.txt',status)
np.savetxt('TestConjGradInversionHighRes_total_time_min.txt',status)
pp.close()
def TestCurvatureMatrices():
ell_grid = np.logspace(1.,np.log10(2000),100)
w = ell_grid**2*(ell_grid + 1)**2
def plot_noiselevels(tag):
pl.figure(tag)
pl.loglog()
pl.xlim(min(ell_grid),max(ell_grid))
pl.plot(ell_grid,1e7/Fpp*w/2./np.pi,label = '$\phi\phi$')
pl.plot(ell_grid,1e7/FOO*w/2./np.pi,label = '$\Omega\Omega$')
pl.legend(loc= 'lower left')
pl.xlabel('$\ell$')
pl.ylabel('$10^{7}[\ell(\ell + 1)]^2 N_\ell /2\pi$')
pl.setp(pl.gca().get_legend().get_frame(), visible=False)
pl.title('Noise levels ' + tag)
pl.close('all')
for tag,sN_uKamin,Beam_FWHM_amin in zip(['TT'],[35.],[5.]) :
Cl_len = lens.fiducial_Cl_len(tag)
Cl_len.extend_lmin(0,Cl_len.Cl[0])
print 'Beam',Beam_FWHM_amin
print 'noise',sN_uKamin
lib128 = lens.Fisher_lib(sN_uKamin,Beam_FWHM_amin,Cl_len)
Fpp,FOO,FpO = lib128.get_phiOmega_curvature_matrix(ell_grid)
pp = PdfPages('TestCurvatureMatrix.pdf')
plot_noiselevels(tag)
pp.savefig()
""" plot correlation """
pl.figure()
pl.plot(ell_grid,-FpO/np.sqrt(FOO*Fpp))
pl.title('corr. coeff. $F_{\phi\Omega}/\sqrt{F_{\phi\phi} F_{\Omega\Omega}}$')
pl.ylabel('corr. coeff. $F_{\phi\Omega}/\sqrt{F_{\phi\phi} F_{\Omega\Omega}}$')
pp.savefig()
pl.close()
f = lens.fid_displacement()
f_inv = f.inverse_displacement_NR(NR_iter = 2)
Beam_FWHM_amin,sN_uKamin,res_low,res_high,lside = lens.fid_params()
Cl_len = lens.fiducial_Cl_len()
Cl_unl = lens.fiducial_Cl_len()
Cl_unl.extend_lmin(0,Cl_unl.Cl[0])
CovPhi = lens.LensedCovMatrix(sN_uKamin,Beam_FWHM_amin,Cl_unl,Cl_len,res_low,res_high,lside,f,f_inv,verbose = False)
Fpp,FOO = CovPhi.get_curvature_kappaomega()
def plot_save_map(map,title) :
pl.figure()
pl.imshow(map)
pl.title(title)
pl.colorbar()
pp.savefig()
pl.close()
plot_save_map(np.fft.fftshift(1e-7*Fpp),'$10^{-7}$ Curvature (F) matrix $\kappa \kappa$')
plot_save_map(np.fft.fftshift(1e-7*FOO),'$10^{-7}$ Curvature (F) matrix $\omega \omega$')
pp.close()
def TestConjGradInversion():
f = lens.fid_displacement()
f_inv = f.inverse_displacement_NR(NR_iter = 2)
Beam_FWHM_amin,sN_uKamin,res_low,res_high,lside = lens.fid_params()
Cl_len = lens.fiducial_Cl_len()
Cl_unl = lens.fiducial_Cl_unl()
CovPhi = lens.LensedCovMatrix(sN_uKamin,Beam_FWHM_amin,Cl_unl,Cl_len,res_low,res_high,lside,f,f_inv,verbose = False)
dat1,dat2 = CovPhi.get_two_sims()
print "Starting conj. gradient inversion for u = CovInv T with conditioner :"
CovPhi.cg_it = 0
pp = PdfPages("TestConjGradInvFakeData.pdf")
def plot_save_map(map,title) :
pl.figure()
pl.imshow(map)
pl.title(title)
pl.colorbar()
pp.savefig()
pl.close()
def callback(v):
CovPhi.cg_it += 1
print 'This is callback ! it',CovPhi.cg_it
plot_save_map(v.reshape(LD_shape),'Current solution vector, Nit = ' + str(CovPhi.cg_it))
plot_save_map(-np.log10(np.fft.fftshift(np.fft.fft2(v.reshape(LD_shape)).real**2)), \
'Current solution vector, $\log_{10}$ Inverse Spectrum, Nit = ' + str(CovPhi.cg_it))
ly,lx = CovPhi.likelihood_gradient_dxdy(v.reshape(LD_shape))
plot_save_map(lx,'Likelihood gradient (wo det) - $d(x)$ direction'+ str(CovPhi.cg_it))
plot_save_map(ly,'Likelihood gradient (wo det) - $d(y)$ direction'+ str(CovPhi.cg_it))
lphi,lOmega = CovPhi.likelihood_gradient_phiOmega(v.reshape(LD_shape))
plot_save_map(lphi,'Likelihood gradient (wo det) - $\phi(x)$ direction (finite diffs.)'+ str(CovPhi.cg_it))
plot_save_map(lOmega,'Likelihood gradient (wo det) - $\Omega(x)$ direction (finite diffs.)'+ str(CovPhi.cg_it))
print -0.5*np.sum(dat1.map*v.reshape(LD_shape))/CovPhi.low_res_cub.npix() # likelihood term
plot_save_map(dat1.map,'Input sim. data map')
plot_save_map(np.log10(np.fft.fftshift(np.fft.fft2(dat1.map)).real**2), \
'Input map, $\log_{10}$ Spectrum') # Cov^-1 T has cov Cov^-1 and thus the inverse spectrum of the map modulo lensing
LD_shape = np.array( (2**res_low,2**res_low) )
output_map,status = CovPhi.apply_cg_inverse_to_LD_map(dat1.map,callback = callback)
print 'Status',status
pp.close()
def TestInterp():
f = lens.fid_displacement()
f_inv = f.inverse_displacement_NR(NR_iter = 2)
Beam_FWHM_amin,sN_uKamin,res_low,res_high,lside = lens.fid_params()
Cl_len = lens.fiducial_Cl_len()
Cl_unl = lens.fiducial_Cl_unl()
CovPhi = lens.LensedCovMatrix(sN_uKamin,Beam_FWHM_amin,Cl_unl,Cl_len,res_low,res_high,lside,f,f_inv,verbose = False)
dat1,dat2 = CovPhi.get_two_HD_unlensed_cmb_sims()
del dat2
""" Setting up splines """
s = CovPhi.high_res_cub.shape()
rmin = CovPhi.high_res_cub.rmin()
xcoord = np.arange(s[1])*rmin[1]
ycoord = np.arange(s[0])*rmin[0]
k = 3
lx = (np.outer(np.ones(s[0]),xcoord) + f.dx.map).flatten()
ly = (np.outer(ycoord,np.ones(s[1]),) + f.dy.map).flatten()
lxy = np.zeros((s[0],s[1],2))
lxy[:,:,0] = ly.reshape(s)
lxy[:,:,1] = lx.reshape(s)
maps = []
title = []
maps.append(dat1)
title.append("Input map")
print "RectBivariateSpline"
t0 =time.time()
maps.append(interpolate.RectBivariateSpline(ycoord,xcoord,dat1,kx = k,ky = k).ev(ly,lx).reshape(s))
t0 = utils.PrtAndRstTime(1,t0)
title.append("RectBivariateSpline")
print "Lin. interp"
t0 =time.time()
maps.append(interpolate.interpn((ycoord,xcoord), dat1,lxy, method='linear',bounds_error= False))
title.append("Lin. interp.")
t0 = utils.PrtAndRstTime(1,t0)
print "splinefd2. interp"
t0 =time.time()
maps.append(interpolate.interpn((ycoord,xcoord), dat1,lxy, method='splinef2d',bounds_error= False))
title.append("splinefd2. interp")
t0 = utils.PrtAndRstTime(1,t0)
maps.append(maps[1]-maps[0])
title.append('Len - Unl')
maps.append(maps[2]-maps[1])
title.append('Res. Lin - rectbiv.')
maps.append(maps[3]-maps[1])
title.append('Res. splinef2d - rectbiv.')
resmap = f_inv.lens_map(f.lens_map(dat1))- dat1
maps.append(np.log10(np.abs(resmap)))
title.append('delensed Lensed map - map $\log_{10}$ res.')
maps.append(resmap)
title.append('delensed Lensed map - map res.')
pp = PdfPages("TestInterp.pdf")
def plot_save_map(map,title) :
pl.figure()
pl.imshow(map)
pl.title(title)
pl.colorbar()
pp.savefig()
pl.close()
for map,title in zip(maps,title) :
plot_save_map(map,title)
pp.close()