/
cramer_rao_bound.py
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/
cramer_rao_bound.py
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import sys
import numpy
import os
import argparse
from scipy.constants import c
from src.util import hexagonal_array
from src.util import redundant_baseline_finder
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 matplotlib import pyplot
def cramer_rao_bound_comparison(maximum_factor=20, nu=150e6, verbose=True, compute_data=False, compute_telescopes=True,
load_data=False, save_output=True, make_plot=False, show_plot=True):
"""
Parameters
----------
maximum_factor : int
Size factor of the hexagonal array - how many hexagonal layers
nu : float
Frequency for calculation in MHz
verbose : bool
True of False if you want stderr output
compute_data : bool
Flag to compute data for this settings
compute_telescopes
load_data : bool
Flag to load previously computed data
save_output : bool
Flag to save computed data
make_plot : bool
Flag to plot and save plot of computed or loaded data
show_plot : bool
Flag to show plot interactively
Returns
-------
"""
position_precision = 1e-2
broken_tile_fraction = 0.3
sky_model_limit = 1e-1
output_path = "/data/rjoseph/Hybrid_Calibration/theoretical_calculations/sky_limit_100mJy_Thesis/"
if not os.path.exists(output_path + "/"):
print("Creating Project folder at output destination!")
os.makedirs(output_path)
if compute_data:
size_factor = numpy.arange(2, maximum_factor, 1)
redundant_data, sky_data = cramer_rao_bound_calculator(size_factor, position_precision, broken_tile_fraction,
sky_model_depth = sky_model_limit, nu=nu,
verbose=verbose)
if save_output:
input_parameters = numpy.array([[position_precision], [broken_tile_fraction], [sky_model_limit]])
header_string = "Position_Precision[m] Broken_Tile[Fraction] Sky_Model_Depth[Jy]"
numpy.savetxt(output_path + "input_parameters.txt", input_parameters.T, header = header_string)
numpy.savetxt(output_path + "redundant_crlb.txt", redundant_data)
numpy.savetxt(output_path + "skymodel_crlb.txt", sky_data)
if compute_telescopes:
# print("Redundant Calibration Errors")
# print("MWA Hexes")
# mwa_hexes_redundant = telescope_bounds("data/MWA_Hexes_Coordinates.txt", bound_type="redundant",
# position_precision=position_precision,
# broken_tile_fraction=broken_tile_fraction,
# sky_model_depth=sky_model_limit)
#
# print("HERA 128")
# hera_128_redundant = telescope_bounds("data/HERA_128.txt", bound_type="redundant",
# position_precision=position_precision,
# broken_tile_fraction=broken_tile_fraction,
# sky_model_depth=sky_model_limit)
#
#
# print("HERA 350")
# hera_350_redundant = telescope_bounds("data/HERA_350.txt", bound_type="redundant",
# position_precision=position_precision,
# broken_tile_fraction=broken_tile_fraction,
# sky_model_depth=sky_model_limit)
#
#
# print("")
# print("Sky Model")
# print("MWA Hexes")
# mwa_hexes_sky = telescope_bounds("data/MWA_Hexes_Coordinates.txt", bound_type="sky",
# position_precision=position_precision,
# broken_tile_fraction=broken_tile_fraction,
# sky_model_depth=sky_model_limit)
# print("MWA Compact")
# mwa_compact_sky = telescope_bounds("data/MWA_Compact_Coordinates.txt", bound_type="sky",
# position_precision=position_precision,
# broken_tile_fraction=broken_tile_fraction,
# sky_model_depth=sky_model_limit)
# print("HERA 350")
# hera_350_sky = telescope_bounds("data/HERA_350.txt", bound_type="sky",
# position_precision=position_precision,
# broken_tile_fraction=broken_tile_fraction,
# sky_model_depth=sky_model_limit)
print('SKA')
ska_low_sky = telescope_bounds("data/SKA_Low_v5_ENU_fullcore.txt", bound_type="sky",
position_precision=position_precision,
broken_tile_fraction=broken_tile_fraction,
sky_model_depth=sky_model_limit, lambda_treshold=10)
if save_output:
# numpy.savetxt(output_path + "hera_350_redundant.txt", hera_350_redundant)
# numpy.savetxt(output_path + "hera_128_redundant.txt", hera_128_redundant)
# numpy.savetxt(output_path + "mwa_hexes_redundant.txt", mwa_hexes_redundant)
# numpy.savetxt(output_path + "hera_350_skymodel.txt", hera_350_sky)
numpy.savetxt(output_path + "ska_low_skymodel.txt", ska_low_sky)
# numpy.savetxt(output_path + "mwa_hexes_skymodel.txt", mwa_hexes_sky)
# numpy.savetxt(output_path + "mwa_compact_skymodel.txt", mwa_compact_sky)
return
def cramer_rao_bound_calculator(size_factor, position_precision=1e-2, broken_tile_fraction=0.3,
sky_model_depth = 1.0, nu=150e6, verbose=True):
"""
Parameters
----------
maximum_factor : int
Maximum size factor of the hexagonal array - how many hexagonal layers do you want to go up
to
position_precision : float
Set the position precision of the antennas in meters
broken_tile_fraction : float
Set the fraction of broken tiles to down weight the covariances
nu : float
Set the frequency of the observations
verbose : bool
Flag to set if outputs to STDERR are desired
Returns
-------
"""
# Initialise empty Arrays for relative calibration results
redundancy_metric = numpy.zeros(len(size_factor))
relative_gain_variance = numpy.zeros_like(redundancy_metric)
relative_gain_spread = numpy.zeros_like(redundancy_metric)
# Initialise empty arrays for absolute calibration results
absolute_gain_variance = numpy.zeros_like(redundancy_metric)
# Initialise empty array for thermal noise results
thermal_redundant_variance = numpy.zeros_like(redundancy_metric)
# Initialise empty array for sky calibrated results
sky_gain_variance = numpy.zeros_like(redundancy_metric)
thermal_sky_variance = numpy.zeros_like(redundancy_metric)
for i in range(len(size_factor)):
antenna_positions = hexagonal_array(size_factor[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(f"Hexagonal array with size {size_factor[i]}")
print("Finding redundant baselines")
redundant_baselines = redundant_baseline_finder(baseline_table)
skymodel_baselines = redundant_baseline_finder(baseline_table, group_minimum=1)
if verbose:
print("Populating matrices")
redundant_crlb = relative_calibration_crlb(redundant_baselines, nu=nu, position_precision=position_precision,
broken_tile_fraction=broken_tile_fraction)
absolute_crlb = absolute_calibration_crlb(skymodel_baselines, nu=150e6, position_precision=position_precision,
sky_model_depth=sky_model_depth, broken_tile_fraction=broken_tile_fraction)
sky_crlb = sky_calibration_crlb(skymodel_baselines, position_precision=position_precision,
sky_model_depth=sky_model_depth, broken_tile_fraction=broken_tile_fraction)
# Save data into arrays
redundancy_metric[i] = antenna_table.number_antennas()
relative_gain_variance[i] = numpy.median(numpy.diag(redundant_crlb))
relative_gain_spread[i] = numpy.std(numpy.diag(redundant_crlb))
absolute_gain_variance[i] = absolute_crlb
thermal_redundant_variance[i] = numpy.median(numpy.diag(thermal_redundant_crlb(redundant_baselines)))
sky_gain_variance[i] = numpy.median(numpy.diag(sky_crlb))
thermal_sky_variance[i] = numpy.median(numpy.diag(thermal_sky_crlb(skymodel_baselines,
sky_model_depth=sky_model_depth)))
redundant_data = numpy.stack((redundancy_metric, relative_gain_variance, absolute_gain_variance,
thermal_redundant_variance))
sky_data = numpy.stack((redundancy_metric, sky_gain_variance, thermal_sky_variance))
return redundant_data, sky_data
def thermal_redundant_crlb(redundant_baselines, nu=150e6, SEFD=20e3, B=40e3, t=120):
"""
Parameters
----------
redundant_baselines : object
a radiotelescope object containing the baseline table for the redundant baselines
nu : float
The frequency at which you want to compute the gains
SEFD : float
System Equivalent Flux Density of the array in Jy
B : float
Frequency Bandwidth in MHZ
t : float
Integration time for the calibration observation
Returns
-------
"""
sky_block_covariance = sky_covariance(u=numpy.array([0,0]), v=numpy.array([0,0]), nu=nu, mode='baseline')
redundant_sky = numpy.sqrt(sky_block_covariance[0,0])
jacobian_gain_matrix, red_tiles, red_groups = redundant_matrix_populator(redundant_baselines)
jacobian_gain_matrix[:, :len(red_tiles)] *= redundant_sky
thermal_noise = thermal_variance()
redundant_fisher_information = numpy.dot(jacobian_gain_matrix.T, jacobian_gain_matrix) / thermal_noise
redundant_crlb = 2 * numpy.real(numpy.linalg.pinv(redundant_fisher_information))
return redundant_crlb[:len(red_tiles), :len(red_tiles)]
def absolute_calibration_crlb(redundant_baselines, position_precision=1e-2, broken_tile_fraction = 1, sky_model_depth=1.0, nu=150e6,
verbose=True):
"""
Parameters
----------
sky_model_depth
redundant_baselines : object
a radiotelescope object containing the baseline table for the redundant baselines
position_precision :
nu
Returns
-------
"""
if verbose:
print("Computing Absolute Calibration CRLB")
model_covariance = sky_covariance(u=numpy.array([0,0]), v=numpy.array([0,0]), nu=nu, mode='baseline',
S_low=sky_model_depth)
sky_based_model = numpy.sqrt(model_covariance[0,0])
jacobian_vector = numpy.zeros(redundant_baselines.number_of_baselines) + sky_based_model
# Compute perturbations within a redundant block, off diagonals
uv_scales = numpy.array([0, position_precision / c * nu])
sky_block_covariance = sky_covariance(nu=nu, u=uv_scales, v=uv_scales, S_high=sky_model_depth,
mode='baseline')
beam_block_covariance = beam_covariance(nu=nu, u=uv_scales, v=uv_scales, broken_tile_fraction=broken_tile_fraction,
mode='baseline', calibration_type='sky', model_limit=sky_model_depth)
non_redundant_block = sky_block_covariance + numpy.diag(numpy.zeros(len(uv_scales)) + beam_block_covariance[0, 0])
# + thermal_variance() )
if redundant_baselines.number_of_baselines < 3000:
ideal_covariance = sky_covariance(nu=nu, u=redundant_baselines.u_coordinates,
v=redundant_baselines.v_coordinates, S_high=sky_model_depth,
mode='baseline')
# ideal_covariance += numpy.diag(numpy.zeros(redundant_baselines.number_of_baselines) + thermal_variance() +
# beam_block_covariance[0, 0])
absolute_crlb = small_matrix(jacobian_vector, non_redundant_block, ideal_covariance)
elif redundant_baselines.number_of_baselines > 3000:
absolute_crlb = large_matrix(redundant_baselines, jacobian_vector, non_redundant_block)
return absolute_crlb
def relative_calibration_crlb(redundant_baselines, nu=150e6, position_precision=1e-2, broken_tile_fraction=1.0,
verbose =True):
"""
Parameters
----------
redundant_baselines
nu
position_precision
broken_tile_fraction
Returns
-------
"""
if verbose:
print("Computing Relative Calibration CRLB")
# Compute the signal
sky_block_covariance = sky_covariance(u=numpy.array([0,0]), v=numpy.array([0,0]), nu=nu, mode='baseline')
redundant_sky = numpy.sqrt(sky_block_covariance[0,0])
# Compute the Jacobian matrix that determines which measurements contribute to the Fisher Information
jacobian_gain_matrix, red_tiles, red_groups = redundant_matrix_populator(redundant_baselines)
jacobian_gain_matrix[:, :len(red_tiles)] *= redundant_sky
jacobian_gain_matrix = jacobian_gain_matrix[:, 1:]
# Compute a 2x2 covariance block
uv_scales = numpy.array([0, position_precision/c*nu*150])
beam_block_covariance = beam_covariance(nu=nu, u=uv_scales, v=uv_scales, broken_tile_fraction=broken_tile_fraction,
mode='baseline', calibration_type='redundant')
position_block_covariance = position_covariance(nu=nu, u=uv_scales, v=uv_scales, position_precision=position_precision,
mode='baseline')
# non_redundant_block = sky_block_covariance + numpy.diag(numpy.zeros(len(uv_scales)) + beam_block_covariance[0,0]) + \
# numpy.diag(numpy.zeros(len(uv_scales)) + position_block_covariance[0, 0]) + \
# numpy.diag(numpy.zeros(len(uv_scales)) + thermal_variance())
non_redundant_block = numpy.diag(numpy.zeros(len(uv_scales)) + beam_block_covariance[0,0] +
position_block_covariance[0, 0])# + thermal_variance())
if redundant_baselines.number_of_baselines < 2000:
sky_noise = sky_covariance(nu=nu, u=redundant_baselines.u(nu), v=redundant_baselines.v(nu), mode='baseline')
ideal_covariance = numpy.diag(numpy.zeros(redundant_baselines.number_of_baselines) +
beam_block_covariance[0, 0] + position_block_covariance[0, 0] +
thermal_variance())
redundant_crlb = small_matrix(jacobian_gain_matrix, non_redundant_block, ideal_covariance,
covariance_jacobian=2*numpy.sqrt(sky_noise), antennas_indices=red_tiles,
redundant_groups=red_groups, redundant_baselines=redundant_baselines)
elif redundant_baselines.number_of_baselines > 2000:
redundant_crlb = large_matrix(redundant_baselines, jacobian_gain_matrix, non_redundant_block,
covariance_jacobian=2*numpy.sqrt(sky_block_covariance[0,0]), redundant_groups=red_groups,
antennas_indices=red_tiles)
return redundant_crlb[:len(red_tiles)-1, :len(red_tiles)-1]
def thermal_sky_crlb(redundant_baselines, sky_model_depth = 1, nu=150e6, SEFD=20e3, B=40e3, t=120):
"""
Parameters
----------
redundant_baselines : array_like
a radiotelescope object containing the baseline table for the redundant baselines
nu : float
The frequency at which you want to compute the gain variance in MHz
SEFD : float
The system equivalent flux density of the array in Jy
B : float
Calibration bandwidth in MHz
t : float
Observation integration time
Returns
-------
"""
model_covariance = sky_covariance(u=numpy.array([0,0]), v=numpy.array([0,0]), nu=nu, mode='baseline',
S_low=sky_model_depth)
sky_based_model = numpy.sqrt(model_covariance[0,0])
antenna_baseline_matrix, red_tiles, red_groups = redundant_matrix_populator(redundant_baselines)
jacobian_gain_matrix = antenna_baseline_matrix[:, :len(red_tiles)] * sky_based_model
thermal_noise = thermal_variance()
redundant_fisher_information = numpy.dot(jacobian_gain_matrix.T, jacobian_gain_matrix) / thermal_noise
redundant_crlb = 2 * numpy.real(numpy.linalg.pinv(redundant_fisher_information))
return redundant_crlb[:len(red_tiles), :len(red_tiles)]
def sky_calibration_crlb(redundant_baselines, nu=150e6, position_precision=1e-2, broken_tile_fraction=1,
sky_model_depth=1, verbose=True):
"""
Parameters
----------
redundant_baselines : object
a radiotelescope object containing the baseline table for the redundant baselines
nu : float
Frequency of observations in MHz
position_precision : float
Array position precision in metres
broken_tile_fraction : float
Fraction of tiles that have broken dipole
Returns
-------
"""
if verbose:
print("Computing Sky Calibration CRLB")
model_covariance = sky_covariance(u=numpy.array([0,0]), v=numpy.array([0,0]), nu=nu, mode='baseline',
S_low=sky_model_depth)
sky_based_model = numpy.sqrt(model_covariance[0,0])
antenna_baseline_matrix, red_tiles = sky_model_matrix_populator(redundant_baselines)
uv_scales = numpy.array([0, position_precision / c * nu])
sky_block_covariance = sky_covariance(nu=nu, u=uv_scales, v=uv_scales, S_high=sky_model_depth, mode='baseline')
beam_block_covariance = beam_covariance(nu=nu, u=uv_scales, v=uv_scales, broken_tile_fraction=broken_tile_fraction,
mode='baseline', calibration_type='sky', model_limit=sky_model_depth)
non_redundant_covariance = sky_block_covariance + numpy.diag(numpy.zeros(len(uv_scales)) + beam_block_covariance[0, 0])
# + thermal_variance()
jacobian_matrix = antenna_baseline_matrix[:, :len(red_tiles)] * sky_based_model
# print(f"Model:\n {sky_based_model}")
# print(f"Sky Noise:\n {sky_block_covariance}")
# print(f"Beam Noise:\n {beam_block_covariance}\n")
#
if redundant_baselines.number_of_baselines < 5000:
ideal_covariance = sky_covariance(nu=nu, u = redundant_baselines.u(nu), v = redundant_baselines.v(nu),
S_high=sky_model_depth, mode = 'baseline')
# ideal_covariance += numpy.diag(numpy.zeros(redundant_baselines.number_of_baselines) + thermal_variance())
sky_crlb = small_matrix(jacobian_matrix, non_redundant_covariance, ideal_covariance)
elif redundant_baselines.number_of_baselines > 5000:
sky_crlb = large_matrix(redundant_baselines, jacobian_matrix, non_redundant_covariance)
return sky_crlb
def small_matrix(jacobian, non_redundant_covariance, ideal_covariance, covariance_jacobian = None,
antennas_indices = None, redundant_groups = None, redundant_baselines = None , constraints_matrix = None):
"""
Parameters
----------
redundant_baselines
jacobian
non_redundant_covariance
ideal_covariance
Returns
-------
"""
covariance_matrix = restructure_covariance_matrix(ideal_covariance, diagonal= non_redundant_covariance[0, 0],
off_diagonal=non_redundant_covariance[0, 1])
fisher_information = compute_fisher_information(covariance_matrix=covariance_matrix, jacobian=jacobian,
covariance_jacobian=covariance_jacobian,
antennas_indices=antennas_indices, redundant_groups=redundant_groups,
redundant_baselines=redundant_baselines)
# figure, axes = pyplot.subplots(1,2 , figsize = (10, 5))
# axes[0].imshow(covariance_matrix)
# axes[1].imshow(numpy.linalg.pinv(covariance_matrix))
# pyplot.show()
cramer_rao_lower_bound = compute_cramer_rao_lower_bound(fisher_information)
return fisher_information, cramer_rao_lower_bound
def large_matrix(redundant_baselines, jacobian_matrix, non_redundant_covariance, covariance_jacobian = None,
antennas_indices = None, redundant_groups = None):
"""
Parameters
----------
redundant_baselines
jacobian_matrix
non_redundant_covariance
Returns
-------
"""
groups = numpy.unique(redundant_baselines.group_indices)
fisher_information = 0
for group_index in range(len(groups)):
# Determine which baselines are part of the group
group_visibilities_indices = numpy.where(redundant_baselines.group_indices == groups[group_index])[0]
# Determine the size of the group
number_of_redundant_baselines = len(group_visibilities_indices)
if number_of_redundant_baselines == 1:
# Compute FIM for a single baseline
# jacobi_vector = jacobian_matrix[group_visibilities_indices, ...]
# covariance_vector = numpy.zeros((1, redundant_baselines.number_of_baselines))
# covariance_vector[0, group_visibilities_indices] = 1/non_redundant_covariance[0, 0]
matrix = numpy.dot(jacobian_matrix[group_visibilities_indices, ...].T,
jacobian_matrix[group_visibilities_indices, ...])/non_redundant_covariance[0, 0]
# fisher_information += numpy.dot(numpy.dot(jacobian_matrix.T, covariance_vector), jacobian_matrix)
fisher_information += matrix
# if isinstance(matrix, float):
# fisher_information += matrix
# elif matrix.shape[0] > 1:
# fisher_information += numpy.diag(numpy.diag(matrix))
elif number_of_redundant_baselines > 1:
group_start_index = numpy.min(group_visibilities_indices)
group_end_index = numpy.max(group_visibilities_indices)
# Create a perfectly redundant block
redundant_block = numpy.zeros((number_of_redundant_baselines, number_of_redundant_baselines)) + \
non_redundant_covariance[0, 0]
# Perturb the redundancy
redundant_block = restructure_covariance_matrix(redundant_block, diagonal=non_redundant_covariance[0, 0],
off_diagonal=non_redundant_covariance[0, 1])
jacobian_block = jacobian_matrix[group_start_index:group_end_index + 1, ...]
# Compute FIM for a group of baselines
fisher_information += compute_fisher_information(redundant_block, jacobian_block, covariance_jacobian,
antennas_indices, redundant_groups, redundant_baselines,
block_index=group_index)
cramer_rao_lower_bound = compute_cramer_rao_lower_bound(fisher_information)
return fisher_information, cramer_rao_lower_bound
def compute_fisher_information(covariance_matrix, jacobian, covariance_jacobian = None, antennas_indices = None,
redundant_groups = None, redundant_baselines = None, block_index = None,
verbose =False):
if verbose:
print(f"\tCovariance matrix condition number {numpy.linalg.cond(covariance_matrix)}")
fisher_information = numpy.dot(jacobian.T, numpy.linalg.solve(covariance_matrix, jacobian))
if covariance_jacobian is not None:
n_antennas = len(antennas_indices) - 1
if block_index is not None:
signal_covariance = numpy.zeros_like(covariance_matrix)
signal_covariance += covariance_jacobian
jacobi_covariance = numpy.linalg.solve(covariance_matrix, signal_covariance)
fisher_information[n_antennas + block_index, n_antennas + block_index] += numpy.trace(numpy.dot(jacobi_covariance,
jacobi_covariance))
else:
for i in range(len(redundant_groups)):
i_indices = numpy.where(redundant_baselines.group_indices == redundant_groups[i])[0]
covariance_derivative = covariance_jacobian.copy()
covariance_derivative[:i_indices.min(), :] = 0
covariance_derivative[i_indices.max() + 1:, :] = 0
covariance_derivative[:i_indices.min(), :] = 0
covariance_derivative[i_indices.max() + 1:, :] = 0
jacobi_covariance = numpy.linalg.solve(covariance_matrix, covariance_derivative)
fisher_information[n_antennas + i, n_antennas + i] += numpy.trace(numpy.dot(jacobi_covariance,
jacobi_covariance))
return fisher_information
def compute_cramer_rao_lower_bound(fisher_information, verbose =True):
if type(fisher_information) == numpy.ndarray:
cramer_rao_lower_bound = 2*numpy.real(numpy.linalg.pinv(fisher_information))
if verbose:
print(f"\tFIM condition number {numpy.linalg.cond(fisher_information)}")
else:
cramer_rao_lower_bound = 2 * numpy.real(1 / fisher_information)
return cramer_rao_lower_bound
def restructure_covariance_matrix(matrix, diagonal, off_diagonal):
"""
Takes a covariance matrix, and perturbs the off-diagonals in each block
Parameters
----------
matrix
diagonal
off_diagonal
Returns
-------
"""
new_matrix = matrix.copy()
new_matrix /= matrix[0, 0]
new_matrix -= numpy.diag(numpy.zeros(matrix.shape[0]) + 1)
new_matrix *= off_diagonal
new_matrix += numpy.diag(numpy.zeros(matrix.shape[0]) + diagonal)
return new_matrix
def redundant_matrix_populator(uv_positions):
"""
Parameters
----------
uv_positions
Returns
-------
"""
# so first we sort out the unique antennas
# and the unique redudant groups, this will allows us to populate the matrix adequately
antenna_indices = numpy.stack((uv_positions.antenna_id1, uv_positions.antenna_id2))
red_tiles = numpy.unique(antenna_indices)
# it's not really finding unique antennas, it just finds unique values
red_groups = numpy.unique(uv_positions.group_indices)
# print "There are", len(red_tiles), "redundant tiles"
# print ""
# print "Creating the equation matrix"
# create am empty matrix (#measurements)x(#tiles + #redundant groups)
amp_matrix = numpy.zeros((uv_positions.number_of_baselines, len(red_tiles) + len(red_groups)))
for i in range(uv_positions.number_of_baselines):
index1 = numpy.where(red_tiles == uv_positions.antenna_id1[i])
index2 = numpy.where(red_tiles == uv_positions.antenna_id2[i])
index_group = numpy.where(red_groups == uv_positions.group_indices[i])
amp_matrix[i, index1[0]] = 1
amp_matrix[i, index2[0]] = 1
amp_matrix[i, len(red_tiles) + index_group[0]] = 1
return amp_matrix, red_tiles, red_groups
def sky_model_matrix_populator(uv_positions):
"""
Parameters
----------
uv_positions
Returns
-------
"""
# so first we sort out the unique antennas
# and the unique redudant groups, this will allows us to populate the matrix adequately
antenna_indices = numpy.stack((uv_positions.antenna_id1, uv_positions.antenna_id2))
red_tiles = numpy.unique(antenna_indices)
# it's not really finding unique antennas, it just finds unique values
# create am empty matrix (#measurements)x(#tiles + #redundant groups)
amp_matrix = numpy.zeros((uv_positions.number_of_baselines, len(red_tiles)))
for i in range(uv_positions.number_of_baselines):
index1 = numpy.where(red_tiles == uv_positions.antenna_id1[i])
index2 = numpy.where(red_tiles == uv_positions.antenna_id2[i])
amp_matrix[i, index1[0]] = 1
amp_matrix[i, index2[0]] = 1
return amp_matrix, red_tiles
def telescope_bounds(position_path, bound_type="redundant", nu=150e6, position_precision=1e-2, broken_tile_fraction=0.3,
sky_model_depth = 1e-1, lambda_treshold = 1/6):
"""
Parameters
----------
position_path
bound_type
nu
position_precision
broken_tile_fraction
Returns
-------
"""
telescope = RadioTelescope(load=True, path=position_path)
number_antennas = telescope.antenna_positions.number_antennas()
if bound_type == "redundant":
redundant_table = redundant_baseline_finder(telescope.baseline_table)
sky_table = redundant_baseline_finder(telescope.baseline_table, group_minimum=1, threshold=lambda_treshold)
print("Relative Bounds")
redundant_crlb = relative_calibration_crlb(redundant_table, nu=nu, position_precision=position_precision,
broken_tile_fraction=broken_tile_fraction)
print("Absolute Bounds")
absolute_crlb = absolute_calibration_crlb(sky_table, nu=150e6, position_precision=position_precision,
broken_tile_fraction=broken_tile_fraction,
sky_model_depth=sky_model_depth)
crlb_data = numpy.array([number_antennas, numpy.median(numpy.diag(redundant_crlb)), absolute_crlb])
elif bound_type == "sky":
redundant_table = redundant_baseline_finder(telescope.baseline_table, group_minimum=1, threshold=1.5)
print(telescope.baseline_table.number_of_baselines)
groups = numpy.unique(redundant_table.group_indices)
print(len(groups)/telescope.baseline_table.number_of_baselines)
sky_crlb = sky_calibration_crlb(redundant_table, sky_model_depth=sky_model_depth,
broken_tile_fraction=broken_tile_fraction,
position_precision=position_precision)
crlb_data = numpy.array([number_antennas, numpy.median(numpy.diag(sky_crlb))])
return crlb_data
if __name__ == "__main__":
parser = argparse.ArgumentParser()
parser.add_argument("--ssh", action="store_true", dest="ssh_key", default=False)
params = parser.parse_args()
import matplotlib
if params.ssh_key:
matplotlib.use("Agg")
from matplotlib import pyplot
cramer_rao_bound_comparison()