def test_subtract_noise(self):
Q = n.diag(n.arange(1,9))
N = n.identity(8)
a = n.arange(2,17,2)
n_vec = uf.rand_from_covar(N)
Qa = uf.vdot(Q,a)
y = Qa+n_vec
a,ahat,err = qgea.test_recover_alms(y,Q,N,a,num_remov=-4)
_,nhat,err = qgea.test_recover_alms(n_vec,Q,N,a,num_remov=-4)
ahat_better = ahat - nhat
W = qgea.window_fn_matrix(Q,N,num_remov=-4)
self.assertTrue(n.allclose(n.dot(W,a),ahat_better))
def construct_gs_hist(del_bl=8.,num_bl=10,beam_sig=0.09,fq=0.1):
save_tag = 'grid_del_bl_{0:.2f}_num_bl_{1}_beam_sig_{2:.2f}_fq_{3:.3f}'.format(del_bl,num_bl,beam_sig,fq)
save_tag_mc = 'grid_del_bl_{0:.2f}_num_bl_{1}_beam_sig_{2:.2f}_fq_{3}'.format(del_bl,num_bl,beam_sig,fq)
ys = load_mc_data('{0}/monte_carlo/{1}'.format(data_loc,save_tag_mc))
print 'ys ',ys.shape
alms_fg = qgea.generate_sky_model_alms(gsm_fits_file,lmax=3)
alms_fg = alms_fg[:,2]
baselines,Q,lms = load_Q_file(gh='grid',del_bl=del_bl,num_bl=num_bl,beam_sig=beam_sig,fq=fq,lmax=3)
N = total_noise_covar(0.1,baselines.shape[0],'{0}/gsm_matrices/gsm_{1}.npz'.format(data_loc,save_tag))
MQN = return_MQdagNinv(Q,N,num_remov=None)
print MQN
ahat00s = n.array([])
for ii in xrange(ys.shape[1]):
#_,ahat,_ = qgea.test_recover_alms(ys[:,ii],Q,N,alms_fg,num_remov=None)
ahat = uf.vdot(MQN,ys[:,ii])
ahat00s = n.append(n.real(ahat[0]),ahat00s)
#print ahat00s
print ahat00s.shape
_,bins,_ = p.hist(ahat00s,bins=36,normed=True)
# plot best fit line
mu,sigma = norm.fit(ahat00s)
print "mu, sigma = ",mu,', ',sigma
y_fit = mpl.mlab.normpdf(bins,mu,sigma)
p.plot(bins, y_fit, 'r--', linewidth=2)
p.xlabel('ahat_00')
p.ylabel('Probability')
p.title(save_tag)
p.annotate('mu = {0:.2f}\nsigma = {1:.2f}'.format(mu,sigma), xy=(0.05, 0.5), xycoords='axes fraction')
p.savefig('./figures/monte_carlo/{0}.pdf'.format(save_tag))
p.clf()
def test_sum(self):
N = n.identity(8)
Q = n.identity(8)
Q[0,3] = 1; Q[3,0] = 1
a = n.arange(8); a[0] = 10
y = uf.vdot(Q,a)
a,ahat,err = qgea.test_recover_alms(y,Q,N,a,num_remov=1)
W = qgea.window_fn_matrix(Q,N,num_remov=1)
Wa = uf.vdot(W,a)
print 'Wa ',Wa
print 'ahat ',ahat
print Wa[0]/Wa[1]
print a[0]/a[1]
self.assertAlmostEqual(ahat[0],(a[0]+a[3])/2.)
self.assertAlmostEqual(ahat[3],(a[0]+a[3])/2.)
self.assertTrue(n.allclose(Wa,ahat))
def test_recover_gs_ratio(self):
print "GS Ratio"
Q = n.diag(n.arange(1,9))
N = n.identity(8)*50
#N[0,0]=1
a = n.array([16,4,0,0,0,0,0,0])#n.arange(16,1,-2)
print 'a ',a
n_vec = uf.rand_from_covar(N)
Qa = uf.vdot(Q,a)
y = Qa+n_vec
self.assertTrue(y.shape==(8,))
a,ahat,err = qgea.test_recover_alms(y,Q,N,a,num_remov=0)
W = qgea.window_fn_matrix(Q,N,num_remov=0)
Wa = uf.vdot(W,a)
print 'Wa ',Wa
print 'ahat ',ahat
print Wa[0]/Wa[1]
print a[0]/a[1]
self.assertTrue(n.abs(Wa[0]/Wa[1]-a[0]/a[1])<0.1)
def test_recover_diag(self):
Q = n.diag(n.arange(1,9)[::-1])
N = n.identity(8)
a = n.arange(2,17,2)
#a = a[::-1]
y = n.dot(Q,a)#+uf.rand_from_covar(N)
a,ahat,err = qgea.test_recover_alms(y,Q,N,a,num_remov=3)
print "diag"
print a
print ahat
self.assertTrue(n.allclose(a[:-3],ahat[:-3]))
self.assertTrue(n.allclose(0,ahat[-3:]))
def test_recover_wind(self):
print "Window"
num=100
Q = n.diag(n.arange(1,9))
N = n.identity(8)
a = n.arange(2,17,2)
a1 = n.arange(2,17,2)
ahat_avg = 0
for ii in range(num):
n_vec = uf.rand_from_covar(N)
Qa = uf.vdot(Q,a)
y = Qa+n_vec
self.assertTrue(y.shape==(8,))
a,ahat,err = qgea.test_recover_alms(y,Q,N,a,num_remov=-4)
ahat_avg += ahat
self.assertTrue(n.all(y==n.dot(Q,a1)+n_vec))
ahat_avg = ahat_avg/num
W = qgea.window_fn_matrix(Q,N,num_remov=-4)
print uf.vdot(W,a)
print ahat_avg
self.assertTrue(n.all(n.abs(n.dot(W,a)-ahat_avg)<0.1))
def test_recover_gs(self):
print "GS"
num=500
Q = n.diag(n.arange(1,9))
N = n.identity(8)*50
N[0,0]=1
a = n.array([16,0,0,0,0,0,0,0])#n.arange(16,1,-2)
print 'a ',a
ahat_avg = 0
for ii in range(num):
n_vec = uf.rand_from_covar(N)
Qa = uf.vdot(Q,a)
y = Qa+n_vec
self.assertTrue(y.shape==(8,))
a,ahat,err = qgea.test_recover_alms(y,Q,N,a,num_remov=0)
ahat_avg += ahat
ahat_avg = ahat_avg/num
W = qgea.window_fn_matrix(Q,N,num_remov=0)
print uf.vdot(W,a)
print ahat_avg
self.assertTrue(n.abs(uf.vdot(W,a)[0]-ahat_avg[0])<0.1)
def construct_gs_hist(del_bl=8., num_bl=10, beam_sig=0.09, fq=0.1):
save_tag = 'grid_del_bl_{0:.2f}_num_bl_{1}_beam_sig_{2:.2f}_fq_{3:.3f}'.format(
del_bl, num_bl, beam_sig, fq)
save_tag_mc = 'grid_del_bl_{0:.2f}_num_bl_{1}_beam_sig_{2:.2f}_fq_{3}'.format(
del_bl, num_bl, beam_sig, fq)
ys = load_mc_data('{0}/monte_carlo/{1}'.format(data_loc, save_tag_mc))
print 'ys ', ys.shape
alms_fg = qgea.generate_sky_model_alms(gsm_fits_file, lmax=3)
alms_fg = alms_fg[:, 2]
baselines, Q, lms = load_Q_file(gh='grid',
del_bl=del_bl,
num_bl=num_bl,
beam_sig=beam_sig,
fq=fq,
lmax=3)
N = total_noise_covar(
0.1, baselines.shape[0],
'{0}/gsm_matrices/gsm_{1}.npz'.format(data_loc, save_tag))
MQN = return_MQdagNinv(Q, N, num_remov=None)
print MQN
ahat00s = n.array([])
for ii in xrange(ys.shape[1]):
#_,ahat,_ = qgea.test_recover_alms(ys[:,ii],Q,N,alms_fg,num_remov=None)
ahat = uf.vdot(MQN, ys[:, ii])
ahat00s = n.append(n.real(ahat[0]), ahat00s)
#print ahat00s
print ahat00s.shape
_, bins, _ = p.hist(ahat00s, bins=36, normed=True)
# plot best fit line
mu, sigma = norm.fit(ahat00s)
print "mu, sigma = ", mu, ', ', sigma
y_fit = mpl.mlab.normpdf(bins, mu, sigma)
p.plot(bins, y_fit, 'r--', linewidth=2)
p.xlabel('ahat_00')
p.ylabel('Probability')
p.title(save_tag)
p.annotate('mu = {0:.2f}\nsigma = {1:.2f}'.format(mu, sigma),
xy=(0.05, 0.5),
xycoords='axes fraction')
p.savefig('./figures/monte_carlo/{0}.pdf'.format(save_tag))
p.clf()