def test_W_dB(self):
W_dB_analytic = W_dB(self.A, self.A_dB, self.mm.comp_of_dB)
W_params = W(self.A)
for i in range(len(self.params)):
diff_params = [p for p in self.params]
diff_params[i] = self.DX + diff_params[i]
diff_A = self.mm.eval(self.nu, *diff_params)
diff_W = W(diff_A)
W_dB_numerical = (diff_W - W_params) / self.DX
aac(W_dB_numerical, W_dB_analytic[i], rtol=1e-3)
def _get_sys_stat_residuals(self):
Cl_fgs = self._get_cls_fg()
i_cmb = self.A.components.index('CMB')
print('======= ESTIMATION OF STAT AND SYS RESIDUALS =======')
W_maxL = W(self.A_maxL, invN=self.invN)[i_cmb, :]
W_dB_maxL = W_dB(self.A_maxL,
self.A_dB_maxL,
self.A.comp_of_dB,
invN=self.invN)[:, i_cmb]
W_dBdB_maxL = W_dBdB(self.A_maxL,
self.A_dB_maxL,
self.A_dBdB_maxL,
self.A.comp_of_dB,
invN=self.invN)[:, :, i_cmb]
V_maxL = np.einsum('ij,ij...->...', self.res.Sigma, W_dBdB_maxL)
# Check dimentions
assert ((self.n_freqs, ) == W_maxL.shape == W_dB_maxL.shape[1:] ==
W_dBdB_maxL.shape[2:] == V_maxL.shape)
assert (len(self.res.params) == W_dB_maxL.shape[0] ==
W_dBdB_maxL.shape[0] == W_dBdB_maxL.shape[1])
# elementary quantities defined in Stompor, Errard, Poletti (2016)
Cl_xF = {}
Cl_xF['yy'] = _utmv(W_maxL, Cl_fgs.T, W_maxL) # (ell,)
Cl_xF['YY'] = _mmm(W_dB_maxL, Cl_fgs.T,
W_dB_maxL.T) # (ell, param, param)
Cl_xF['yz'] = _utmv(W_maxL, Cl_fgs.T, V_maxL) # (ell,)
Cl_xF['Yy'] = _mmv(W_dB_maxL, Cl_fgs.T, W_maxL) # (ell, param)
Cl_xF['Yz'] = _mmv(W_dB_maxL, Cl_fgs.T, V_maxL) # (ell, param)
# bias and statistical foregrounds residuals
#self.res.noise = Cl_noise
self.res.bias = Cl_xF['yy'] + 2 * Cl_xF['yz'] # S16, Eq 23
self.res.stat = np.einsum('ij, lij -> l', self.res.Sigma,
Cl_xF['YY']) # E11, Eq. 12
self.res.var = self.res.stat**2 + 2 * np.einsum(
'li, ij, lj -> l', # S16, Eq. 28
Cl_xF['Yy'],
self.res.Sigma,
Cl_xF['Yy'])
return self.res.bias, self.res.stat, self.res.var
def test_W_on_d_is_s(self):
aaae(self.s, _mv(W(self.A), self.d))
def W_displaced(i_step, j_step):
diff_params = [p for p in self.params]
diff_params[i] = i_step * self.DX + diff_params[i]
diff_params[j] = j_step * self.DX + diff_params[j]
diff_A = self.mm.eval(self.nu, *diff_params)
return W(diff_A, self.invN)