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corrcal_cramer_rao_bound.py
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import sys
import numpy
import os
import time
import multiprocessing
from scipy.constants import c
from scipy import sparse
from functools import partial
import matplotlib
matplotlib.use("Agg")
from matplotlib import pyplot
from matplotlib import colors
from src.plottools import colorbar
from src.util import hexagonal_array
from src.util import redundant_baseline_finder
from src.radiotelescope import beam_width
from src.radiotelescope import AntennaPositions
from src.radiotelescope import BaselineTable
from src.radiotelescope import RadioTelescope
from src.covariance import sky_covariance
from src.covariance import beam_covariance
from src.covariance import position_covariance
from src.covariance import thermal_variance
from src.skymodel import sky_moment_returner
from cramer_rao_bound import restructure_covariance_matrix
def main(nu =150e6, position_precision = 1e-2, broken_tile_fraction=0.3, sky_model_depth = 1e-2, verbose = False):
var_dense = []
var_sparse = []
parallisation_flag = False
vectorisation_flag = True
for i in range(2,3):
print("")
print(f"Array size {i}")
antenna_positions = hexagonal_array(i)
antenna_table = AntennaPositions(load=False)
antenna_table.antenna_ids = numpy.arange(0, antenna_positions.shape[0], 1)
antenna_table.x_coordinates = antenna_positions[:, 0]
antenna_table.y_coordinates = antenna_positions[:, 1]
antenna_table.z_coordinates = antenna_positions[:, 2]
baseline_table = BaselineTable(position_table=antenna_table)
if verbose:
print("")
print("Finding redundant baselines")
skymodel_baselines = redundant_baseline_finder(baseline_table, group_minimum=3)
sky_signal = numpy.sqrt(sky_moment_returner(n_order=2))
modelled_signal = numpy.sqrt(sky_moment_returner(n_order=2, s_low=sky_model_depth))
thermal_noise = thermal_variance()
uv_scales = numpy.array([0, 0])
sky_block_covariance = sky_covariance(nu, u=uv_scales, v=uv_scales, mode='baseline', S_high=sky_model_depth)
beam_block_covariance = beam_covariance(nu, u=uv_scales, v=uv_scales, broken_tile_fraction=broken_tile_fraction,
mode='baseline')
position_block_covariance = position_covariance(nu, u=uv_scales, v=uv_scales, position_precision=position_precision,
mode='baseline')
non_redundant_block = sky_block_covariance #+ beam_block_covariance
# sky_noise = sky_covariance(nu, u=skymodel_baselines.u(nu), v=skymodel_baselines.v(nu), mode='baseline', S_high=sky_model_depth)
# beam_error = beam_covariance(nu, u=skymodel_baselines.u(nu), v=skymodel_baselines.v(nu),
# broken_tile_fraction=broken_tile_fraction, mode='baseline')
# position_error = position_covariance(nu, u=skymodel_baselines.u(nu), v=skymodel_baselines.v(nu),
# position_precision=position_precision, mode='baseline')
# ideal_covariance = sky_noise #+ position_error + beam_error
# sky_model_covariance = sky_noise/sky_noise[0,0]*modelled_signal
# covariance_matrix = restructure_covariance_matrix(ideal_covariance, diagonal= non_redundant_block[0, 0],
# off_diagonal=non_redundant_block[0, 1])
# data = numpy.zeros(skymodel_baselines.number_of_baselines) + sky_signal
# noise_covariance = numpy.diag(numpy.zeros(skymodel_baselines.number_of_baselines) + thermal_variance())
# FIM_loop = compute_fim_sparse(antenna_table, skymodel_baselines, non_redundant_block, sky_signal, modelled_signal, thermal_noise,
# parallelised=parallisation_flag, vectorised = False)
FIM_vec = compute_fim_sparse(antenna_table, skymodel_baselines, non_redundant_block, sky_signal,
modelled_signal, thermal_noise, parallelised=parallisation_flag,
vectorised = vectorisation_flag)
# fig, axes = pyplot.subplots(1, 3, figsize = (15, 5))
# axes[0].imshow(FIM_loop)
# axes[1].imshow(FIM_vec)
# axes[2].imshow(FIM_loop - FIM_vec)
# pyplot.show()
# norm = colors.Normalize()
# fig,axes = pyplot.subplots(1, 3, figsize = (15, 5))
# axes[1].imshow(FIM_sparse, norm = norm)
# axes[0].imshow(FIM_dense, norm = norm)
# plot_diff = axes[2].imshow(FIM_dense - FIM_sparse, norm = norm)
#
# colorbar(plot_diff)
# pyplot.show()
# var_dense.append(numpy.median(numpy.diag(numpy.linalg.pinv(FIM_loop))))
var_sparse.append(numpy.median(numpy.diag(numpy.linalg.pinv(FIM_vec))))
numpy.savetxt("corrcal_CLRB_vectorised.txt",numpy.array(var_sparse))
pyplot.semilogy(var_dense)
pyplot.savefig("test.pdf")
return
def compute_fim_sparse(antenna_table, baseline_table, covariance_block, total_signal, sky_model, thermal_noise,
parallelised = False, vectorised = False):
n_antennas = len(antenna_table.antenna_ids)
group_indices = numpy.unique(baseline_table.group_indices)
n_groups = len(group_indices)
FIM = numpy.zeros((n_antennas, n_antennas))
if parallelised:
k = numpy.arange(0, n_groups)
pool = multiprocessing.Pool(processes = 4)
FIM_blocks = pool.map(partial(single_group_fim, covariance_block[0,0], covariance_block[0, 1], total_signal, sky_model,
thermal_noise, antenna_table, baseline_table, group_indices, vectorised), k)
FIM = numpy.sum(numpy.array(FIM_blocks), axis=0)
else:
for k in range(n_groups):
print(f"group {k}")
FIM +=single_group_fim(covariance_block[0,0], covariance_block[0, 1], total_signal, sky_model,
thermal_noise, antenna_table, baseline_table, group_indices, vectorised, k)
return FIM
def compute_fim_dense(antenna_table, baseline_table, R, S, N, D, verbose = False):
C = R + S
H = numpy.diag(numpy.zeros(baseline_table.number_of_baselines) + 1)
HCH = H.T @ C @ H
N_HCH = N + HCH
inv_N_HCH = numpy.linalg.pinv(N_HCH)
n_antennas = len(antenna_table.antenna_ids)
FIM = numpy.zeros((n_antennas, n_antennas))
for i in range(n_antennas):
di_H = numpy.diag(compute_gain_derivative(baseline_table, antenna_index=antenna_table.antenna_ids[i]))
di_HCH = di_H.T @ C @ H
for j in range(i, n_antennas):
dj_H = numpy.diag(compute_gain_derivative(baseline_table, antenna_index=antenna_table.antenna_ids[j]))
dj_HCH = dj_H.T @ C @ H
di_dj_H = numpy.diag(compute_gain_double_derivative(baseline_table, antenna_table.antenna_ids[i],
antenna_table.antenna_ids[j]))
FIM_element = 4*D.T @ inv_N_HCH @ dj_HCH @ inv_N_HCH @ di_HCH @ inv_N_HCH @ D +\
D.T @ inv_N_HCH @ (di_dj_H.T @ C @ H + di_dj_H.T @ C @ dj_H) @ inv_N_HCH @ D + \
4*D.T @ inv_N_HCH @ di_HCH @ inv_N_HCH @ dj_HCH @ inv_N_HCH @ D
FIM[i, j] = FIM_element
FIM[j, i] = FIM_element
return FIM
def single_group_fim(diagonal, offdiagonal, total_signal, sky_model, thermal_noise, antenna_table, baseline_table,
group_indices, vectorised = False, index=0):
baseline_indices = numpy.where(baseline_table.group_indices == group_indices[index])[0]
block_size = len(baseline_indices)
print(f"\t with size {block_size}")
R = numpy.zeros((block_size, block_size))
R += offdiagonal
R -= numpy.diag(numpy.zeros(block_size) + offdiagonal)
R += numpy.diag(numpy.zeros(block_size) + diagonal)
S = numpy.zeros((block_size, block_size)) + sky_model
N = numpy.diag(numpy.zeros(block_size) + thermal_noise)
D = numpy.zeros(block_size) + total_signal
group_table = baseline_table.sub_table(baseline_indices)
if vectorised:
FIM_block = compute_fim_vectorised(antenna_table, group_table, R, S, N, D)
else:
FIM_block = compute_fim_dense(antenna_table, group_table, R, S, N, D)
return FIM_block
def compute_fim_vectorised(antenna_table, baseline_table, covariance_block, model_block, noise_block, total_signal,
verbose = False):
n_antennas = len(antenna_table.antenna_ids)
# stacked_di_H = numpy.zeros((baseline_table.number_of_baselines, n_antennas*baseline_table.number_of_baselines))
# stacked_C = stacked_di_H.copy()
# stacked_N = stacked_di_H.copy()
D = numpy.zeros((n_antennas*baseline_table.number_of_baselines, n_antennas))
di_H = numpy.zeros((n_antennas*baseline_table.number_of_baselines, baseline_table.number_of_baselines))
C = covariance_block
N = noise_block
H_block = numpy.diag(numpy.zeros(baseline_table.number_of_baselines) + 1)
H = di_H.copy()
for i in range(n_antennas):
start = i*baseline_table.number_of_baselines
end = (i + 1)*baseline_table.number_of_baselines
di_H[start:end, :] = numpy.diag(compute_gain_derivative(baseline_table,
antenna_index=antenna_table.antenna_ids[i]))
H[start:end, :] = H_block
D[start:end, i] = total_signal
# C[start:end, start:end] = covariance_block + model_block
# N[start:end, start:end] = noise_block
# inv_N_HCH[start:end, start:end] = invert_block
inv_N_HCH = H @ numpy.linalg.pinv(noise_block + covariance_block + model_block) @ H.T
# di_H = numpy.tile(stacked_di_H, (n_antennas, 1))
# N = numpy.tile(stacked_N, (n_antennas, 1))
# C = numpy.tile(stacked_C, (n_antennas, 1))
# HCH = C
# N_HCH = N + HCH
# print("Hier")
# inv_N_HCH = numpy.linalg.pinv(N_HCH)
# print("Daar")
dj_H = di_H.T
di_dj_H = di_H @ dj_H
t0 = time.clock()
di_HCH = numpy.dot(di_H, C)
# if noise_block.shape[0] >= 80:
# pyplot.imshow(C)
# pyplot.savefig("blaaaaaaaaaaaah.pdf")
t1 = time.clock()
dj_HCH = dj_H.T @ C
t2 = time.clock()
print(f"\t time {t1-t0}")
print(f"\t time {t2-t1}")
print(D.T.shape)
print(inv_N_HCH.shape)
print(dj_HCH.shape)
print(inv_N_HCH.shape)
print(di_HCH.shape)
print(inv_N_HCH.shape)
print(D.shape)
print(di_dj_H.shape)
FIM = 4*D.T @ inv_N_HCH @ dj_HCH @ inv_N_HCH @ di_HCH @ inv_N_HCH @ D +\
D.T @ inv_N_HCH @ (di_dj_H.T @ C @ H + di_dj_H.T @ C @ dj_H) @ inv_N_HCH @ D + \
4*D.T @ inv_N_HCH @ di_HCH @ inv_N_HCH @ dj_HCH @ inv_N_HCH @ D
return FIM
def compute_gain_derivative(baseline_table, antenna_index):
gains = numpy.zeros(baseline_table.number_of_baselines)
indices = numpy.where(((baseline_table.antenna_id1 == antenna_index) |
(baseline_table.antenna_id2 == antenna_index)))[0]
gains[indices] = 1
return gains
def compute_gain_double_derivative(baseline_table, antenna_index1, antenna_index2):
gains = numpy.zeros(baseline_table.number_of_baselines)
indices_antenna1 = numpy.where((baseline_table.antenna_id1 == antenna_index1) |
(baseline_table.antenna_id2 == antenna_index1))[0]
indices_antenna2 = numpy.where((baseline_table.antenna_id1 == antenna_index2) |
(baseline_table.antenna_id2 == antenna_index2))[0]
overlapping_indices = numpy.intersect1d(indices_antenna1, indices_antenna2)
gains[overlapping_indices] = 1
return gains
if __name__ == "__main__":
main()