def SNR_fun(l, rank):
n_l = sum(num_ell_array[0: rank]) + l
ell = l_min + n_l * delta_l
# put the whole array cij for an given ell into the upper triangle part of the matrix
cijl_array = Cijl_sets[l*N_dset_ext: (l+1)*N_dset_ext]
#print(cijl_array, cijl_array.shape)
cijl_m[iu1] = np.array(cijl_array)
#print(cijl_m, cijl_m.shape)
cijl_m_select = np.array(cijl_m[0:red_bin, 0:red_bin]) # select the first red_bin bins of Cij, match the case with T-F
cijl_true = np.array(cijl_m_select[iu2]) # convert upper triangle matrix to an array
cijl_sn = np.array(cijl_true)
cijl_sn[sn_id] = cijl_true[sn_id] + pseudo_sn # add shape noise terms in Cii(l) terms
Cov_cij_cpq = cal_cov_matrix(red_bin, iu2, cijl_sn) # calculate the covariance matrix of Cij(l), Cpq(l')
Cov_cij_cpq = Cov_cij_cpq.T + np.triu(Cov_cij_cpq, k=1) # It's symmetric. From up triangular matrix, construct the whole matrix for inversion.
#inv_Cov_cij_cpq = linalg.inv(Cov_cij_cpq, overwrite_a=True)
inv_Cov_cij_cpq = linalg.inv(Cov_cij_cpq)
inv_Cov_cij_cpq = inv_Cov_cij_cpq * ((2.0*ell+1.0)*delta_l*f_sky) # Take account of the number of modes (the denominator)
SN_square_per_ell = reduce(np.dot, [cijl_true, inv_Cov_cij_cpq, cijl_true])
SN_per_ell = SN_square_per_ell**0.5
if rank == size-1:
print('ell from rank', rank, 'is', ell, '\n')
#print(np.allclose(np.dot(Cov_cij_cpq, inv_Cov_cij_cpq), np.eye(N_dset)))
return ell, SN_per_ell
def cal_C_G(l, rank):
n_l = default_num_l_in_rank * rank + l
ell = l_min + n_l * delta_l
#offset_cijl = n_l * N_dset * data_type_size
#offset_Gm = n_l * N_dset * num_kout * data_type_size
# put the whole array cij at ell into the upper triangle part of the matrix
cijl_array = Cijl_sets[l * N_dset_ext:(l + 1) * N_dset_ext]
#print(cijl_array, cijl_array.shape)
cijl_m[iu1] = np.array(cijl_array)
#print(cijl_m, cijl_m.shape)
cijl_m_select = np.array(
cijl_m[0:red_bin, 0:red_bin]
) # select the first red_bin bins of Cij, match the case with T-F
cijl_true = np.array(
cijl_m_select[iu2]) # convert upper triangle matrix to an array
cijl_sn = np.array(cijl_true)
cijl_sn[sn_id] = cijl_true[
sn_id] + pseudo_sn # add shape noise terms in Cii(l) terms
Cov_cij_cpq = cal_cov_matrix(
red_bin, iu2,
cijl_sn) # calculate the covariance matrix of Cij(l), Cpq(l')
# if rank == 0:
# rank_matrix = np.linalg.matrix_rank(Cov_cij_cpq)
# print('ell, rank of Cov:', ell, rank_matrix)
Cov_cij_cpq = Cov_cij_cpq / (
(2.0 * ell + 1.0) * delta_l * f_sky
) # account the number of modes for each l with the interval delta_l
w_ccij, v_ccij = linalg.eigh(
Cov_cij_cpq, lower=False, overwrite_a=True
) # Get eigenvalue and eigenvectors from Scipy routine
w_inv = 1.0 / w_ccij
if not np.all(w_inv > 0.0):
print('w_inv from ell ', ell, ' is negative.'
) # show below which ell, the inverse of Cov_cij_cpq fails
# If uncomment the below, overwrite_a should be set False in the linalg.eigh()
# sqrt_w_inv = np.diag(w_inv**0.5)
# v_inv = np.transpose(v_ccij)
# Cov_cij_sym = np.triu(Cov_cij_cpq, k=1) + Cov_cij_cpq.T
# print reduce(np.dot, [np.diag(sqrt_w_inv**2.0), v_inv, Cov_cij_sym, v_inv.T])
Cov_inv_half = np.transpose(
w_inv**0.5 * v_ccij
) # Simplify the expression of dot(sqrt_w_inv, v_inv), 05/09/2016
G_l_array = Gm_sets[l * N_dset_ext * num_kout:(l + 1) * N_dset_ext *
num_kout]
Gm_l_ext = np.reshape(
G_l_array, (N_dset_ext, num_kout), 'C'
) # In Python, the default storage of a matrix follows C language format.
#print(Gm_l_ext)
Gm_l = np.array(Gm_l_ext[Gmrow_sel_ind, :])
Gm_l = np.dot(Cov_inv_half, Gm_l)
cijl_true = np.dot(Cov_inv_half, cijl_true)
return cijl_true, Gm_l
def cal_C_G(l, rank):
n_l = default_num_l_in_rank * rank + l
ell = l_min + n_l * delta_l
cijl_true = Cijl_sets[l * N_dset:(l + 1) * N_dset]
# if rank == 0:
# print(cijl_true)
cijl_sn = np.array(
cijl_true
) # Distinguish the observed C^ijl) (denoted by cijl_sn) from the true C^ij(l)
cijl_sn[sn_id] = cijl_true[
sn_id] + pseudo_sn # Add shape noise on C^ii terms to get cijl_sn
# if rank == 0:
# print('cijl_sn:', cijl_sn)
Cov_cij_cpq = cal_cov_matrix(
num_rbin, iu1, cijl_sn
) # Get an upper-triangle matrix for Cov(C^ij, C^pq) from Fortran subroutine wrapped.
if rank == 0:
rank_matrix = np.linalg.matrix_rank(Cov_cij_cpq)
print('ell, rank of Cov:', ell, rank_matrix)
# ofile = ofprefix + "Cov_cij_cpq_ell_{}_{}rbins_{}kbins_snf{}_rank{}.npz".format(ell, num_rbin, num_kin, snf, rank)
# np.savez_compressed(ofile, Cov_cij_cpq = Cov_cij_cpq)
Cov_cij_cpq = Cov_cij_cpq / (
(2.0 * ell + 1.0) * delta_l * f_sky
) # Take account of the number of modes (the denominator)
# if rank == 0:
# print('Cov_cij_cpq:', Cov_cij_cpq)
w_ccij, v_ccij = linalg.eigh(
Cov_cij_cpq, lower=False, overwrite_a=True
) # Get eigenvalue and eigenvectors from Scipy routine
w_inv = 1. / w_ccij
# if rank == 0:
# print('w_ccij', w_ccij, 'v_ccij:', v_ccij)
#--If uncomment the below, overwrite_a should be set False in the linalg.eigh()
# sqrt_w_inv = np.diag(w_inv**0.5)
# v_inv = np.transpose(v_ccij)
# Cov_cij_sym = np.triu(Cov_cij_cpq, k=1) + Cov_cij_cpq.T # Once Cov_cij_cpq set to be overwriten, the criterion couldn't be used anymore
# print(reduce(np.dot, [np.diag(w_inv), v_inv, Cov_cij_sym, v_inv.T]))
Cov_inv_half = np.transpose(
w_inv**0.5 * v_ccij
) # Simplify the expression of dot(sqrt_w_inv, v_inv), 05/09/2016
# if rank == 0:
# print('Cov_inv_half:', Cov_inv_half)
G_l_array = Gm_sets[l * N_dset * num_kout:(l + 1) * N_dset * num_kout]
Gm_l = np.reshape(
G_l_array, (N_dset, num_kout), 'C'
) # In Python, the default storage of a matrix follows C language format.
#print Gm_l[0,:]
Gm_l = np.dot(Cov_inv_half, Gm_l)
cijl_true = np.dot(Cov_inv_half, cijl_true)
# if rank == 0:
# print('ell from rank', rank, 'is', ell, '\n')
return cijl_true, Gm_l
def SNR_fun(l, rank):
n_l = default_num_l_in_rank * rank + l
ell = l_min + n_l * delta_l
cijl_true = Cijl_sets[l*N_dset: (l+1)*N_dset]
# if rank == 0:
# print(cijl_true)
cijl_sn = np.array(cijl_true) # Distinguish the observed C^ijl) (denoted by cijl_sn) from the true C^ij(l)
cijl_sn[sn_id] = cijl_true[sn_id] + pseudo_sn # Add shape noise on C^ii terms to get cijl_sn
# if rank == 0:
# print('cijl_sn:', cijl_sn)
Cov_cij_cpq = cal_cov_matrix(num_rbin, iu1, cijl_sn) # Get an upper-triangle matrix for Cov(C^ij, C^pq) from Fortran subroutine wrapped.
Cov_cij_cpq = Cov_cij_cpq.T + np.triu(Cov_cij_cpq, k=1) # It's symmetric. Construct the whole matrix for inversion.
inv_Cov_cij_cpq = linalg.inv(Cov_cij_cpq, )
inv_Cov_cij_cpq = inv_Cov_cij_cpq * ((2.0*ell+1.0)*delta_l*f_sky) # Take account of the number of modes (the denominator)
SN_square_per_ell = reduce(np.dot, [cijl_true, inv_Cov_cij_cpq, cijl_true])
SN_per_ell = SN_square_per_ell**0.5
if rank == size-1:
print('ell from rank', rank, 'is', ell, '\n')
return ell, SN_per_ell