Calibration¶
This module provides basic radio interferometry calibration utilities. Calibration is the process of estimating the \(2\times 2\) Jones matrices which describe transformations of the signal as it propagates from source to observer. Currently, all utilities assume a discretised form of the radio interferometer measurement equation (RIME) as described in Radio Interferometer Measurement Equation.
Calibration is usually divided into three phases viz.
 First generation calibration (1GC): using an external calibrator to infer the gains during the target observation. Sometimes also refered to as calibrator transfer
 Second generation calibration (2GC): using a partially incomplete sky model to perform direction independent calibration. Also known as direction independent selfcalibration.
 Third generation calibration (3GC): using a partially incomplete sky model to perform direction dependent calibration. Also known as direction dependent selfcalibration.
On top of these three phases, there are usually
three possible calibration scenarios. The first
is when both the Jones terms and the visibilities
are assumed to be diagonal. In this case the two
correlations can be calibrated separately and it
is refered to as diagdiag
calibration.
The second case is when the Jones matrices are
assumed to be diagonal but the visibility data
are full \(2\times 2\) matrices. This is
refered to as diag
calibration. The final
scenario is when both the full \(2\times 2\)
Jones matrices and the full \(2\times 2\)
visibilities are used for calibration. This is
simply refered to as calibration. The specific
scenario is determined from the shapes of the input
gains and the input data.
This module also provides a number of utilities which are useful for calibration.
Utils¶
Numpy¶
corrupt_vis (time_bin_indices, …) 
Corrupts model visibilities with arbitrary Jones terms. 
residual_vis (time_bin_indices, …) 
Computes residual visibilities given model visibilities and gains solutions. 
correct_vis (time_bin_indices, …) 
Apply inverse of direction independent gains to visibilities to generate corrected visibilities. 
compute_and_corrupt_vis (time_bin_indices, …) 
Corrupts time variable component model with arbitrary Jones terms. 

africanus.calibration.utils.
corrupt_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, model)[source]¶ Corrupts model visibilities with arbitrary Jones terms.
Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
antenna1 :
numpy.ndarray
First antenna indices of shape
(row,)
.antenna2 :
numpy.ndarray
Second antenna indices of shape
(row,)
jones :
numpy.ndarray
Gains of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.model :
numpy.ndarray
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.Returns: vis :
numpy.ndarray
visibilities of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.utils.
residual_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, vis, flag, model)[source]¶ Computes residual visibilities given model visibilities and gains solutions.
Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
antenna1 :
numpy.ndarray
First antenna indices of shape
(row,)
.antenna2 :
numpy.ndarray
Second antenna indices of shape
(row,)
jones :
numpy.ndarray
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.vis :
numpy.ndarray
Data values of shape
(row, chan, corr)
. or(row, chan, corr, corr)
.flag :
numpy.ndarray
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
model :
numpy.ndarray
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.Returns: residual :
numpy.ndarray
Residual visibilities of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.utils.
correct_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, vis, flag)[source]¶ Apply inverse of direction independent gains to visibilities to generate corrected visibilities. For a measurement model of the form
\[V_{pq} = G_{p} X_{pq} G_{q}^H + n_{pq}\]the corrected visibilities are defined as
\[C_{pq} = G_{p}^{1} V_{pq} G_{q}^{H}\]The corrected visibilities therefore have a nontrivial noise contribution. Note it is only possible to form corrected data from direction independent gains solutions so the
dir
axis on the jones terms should always be one.Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
.time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
.antenna1 :
numpy.ndarray
Antenna 1 index used to look up the antenna Jones for a particular baseline with shape
(row,)
.antenna2 :
numpy.ndarray
Antenna 2 index used to look up the antenna Jones for a particular baseline with shape
(row,)
.jones :
numpy.ndarray
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.vis :
numpy.ndarray
Data values of shape
(row, chan, corr)
or(row, chan, corr, corr)
.flag :
numpy.ndarray
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
.Returns
——
corrected_vis :
numpy.ndarray
True visibilities of shape
(row,chan,corr_1,corr_2)

africanus.calibration.utils.
compute_and_corrupt_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, model, uvw, freq, lm)[source]¶ Corrupts time variable component model with arbitrary Jones terms. Currrently only time variable point source models are supported.
Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
antenna1 :
numpy.ndarray
First antenna indices of shape
(row,)
.antenna2 :
numpy.ndarray
Second antenna indices of shape
(row,)
jones :
numpy.ndarray
Gains of shape
(utime, ant, chan, dir, corr)
or(utime, ant, chan, dir, corr, corr)
.model :
numpy.ndarray
Model image as a function of time with shape
(utime, chan, dir, corr)
or(utime, chan, dir, corr, corr)
.uvw :
numpy.ndarray
uvw coordinates of shape
(row, 3)
lm :
numpy.ndarray
Source lm coordinates as a function of time
(utime, dir, 2)
Returns: vis :
numpy.ndarray
visibilities of shape
(row, chan, corr)
or(row, chan, corr, corr)
.
Dask¶
corrupt_vis (time_bin_indices, …) 
Corrupts model visibilities with arbitrary Jones terms. 
residual_vis (time_bin_indices, …) 
Computes residual visibilities given model visibilities and gains solutions. 
correct_vis (time_bin_indices, …) 
Apply inverse of direction independent gains to visibilities to generate corrected visibilities. 
compute_and_corrupt_vis (time_bin_indices, …) 
Corrupts time variable component model with arbitrary Jones terms. 

africanus.calibration.utils.dask.
corrupt_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, model)[source]¶ Corrupts model visibilities with arbitrary Jones terms.
Parameters: time_bin_indices :
dask.array.Array
The start indices of the time bins of shape
(utime)
time_bin_counts :
dask.array.Array
The counts of unique time in each time bin of shape
(utime)
antenna1 :
dask.array.Array
First antenna indices of shape
(row,)
.antenna2 :
dask.array.Array
Second antenna indices of shape
(row,)
jones :
dask.array.Array
Gains of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.model :
dask.array.Array
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.Returns: vis :
dask.array.Array
visibilities of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.utils.dask.
residual_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, vis, flag, model)[source]¶ Computes residual visibilities given model visibilities and gains solutions.
Parameters: time_bin_indices :
dask.array.Array
The start indices of the time bins of shape
(utime)
time_bin_counts :
dask.array.Array
The counts of unique time in each time bin of shape
(utime)
antenna1 :
dask.array.Array
First antenna indices of shape
(row,)
.antenna2 :
dask.array.Array
Second antenna indices of shape
(row,)
jones :
dask.array.Array
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.vis :
dask.array.Array
Data values of shape
(row, chan, corr)
. or(row, chan, corr, corr)
.flag :
dask.array.Array
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
model :
dask.array.Array
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.Returns: residual :
dask.array.Array
Residual visibilities of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.utils.dask.
correct_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, vis, flag)[source]¶ Apply inverse of direction independent gains to visibilities to generate corrected visibilities. For a measurement model of the form
\[V_{pq} = G_{p} X_{pq} G_{q}^H + n_{pq}\]the corrected visibilities are defined as
\[C_{pq} = G_{p}^{1} V_{pq} G_{q}^{H}\]The corrected visibilities therefore have a nontrivial noise contribution. Note it is only possible to form corrected data from direction independent gains solutions so the
dir
axis on the jones terms should always be one.Parameters: time_bin_indices :
dask.array.Array
The start indices of the time bins of shape
(utime)
.time_bin_counts :
dask.array.Array
The counts of unique time in each time bin of shape
(utime)
.antenna1 :
dask.array.Array
Antenna 1 index used to look up the antenna Jones for a particular baseline with shape
(row,)
.antenna2 :
dask.array.Array
Antenna 2 index used to look up the antenna Jones for a particular baseline with shape
(row,)
.jones :
dask.array.Array
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.vis :
dask.array.Array
Data values of shape
(row, chan, corr)
or(row, chan, corr, corr)
.flag :
dask.array.Array
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
.Returns
——
corrected_vis :
dask.array.Array
True visibilities of shape
(row,chan,corr_1,corr_2)

africanus.calibration.utils.dask.
compute_and_corrupt_vis
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, model, uvw, freq, lm)[source]¶ Corrupts time variable component model with arbitrary Jones terms. Currrently only time variable point source models are supported.
Parameters: time_bin_indices :
dask.array.Array
The start indices of the time bins of shape
(utime)
time_bin_counts :
dask.array.Array
The counts of unique time in each time bin of shape
(utime)
antenna1 :
dask.array.Array
First antenna indices of shape
(row,)
.antenna2 :
dask.array.Array
Second antenna indices of shape
(row,)
jones :
dask.array.Array
Gains of shape
(utime, ant, chan, dir, corr)
or(utime, ant, chan, dir, corr, corr)
.model :
dask.array.Array
Model image as a function of time with shape
(utime, chan, dir, corr)
or(utime, chan, dir, corr, corr)
.uvw :
dask.array.Array
uvw coordinates of shape
(row, 3)
lm :
dask.array.Array
Source lm coordinates as a function of time
(utime, dir, 2)
Returns: vis :
dask.array.Array
visibilities of shape
(row, chan, corr)
or(row, chan, corr, corr)
.
Phase only¶
Numpy¶
compute_jhr (time_bin_indices, …) 
Computes the residual projected in to gain space. 
compute_jhj (time_bin_indices, …) 
Computes the diagonal of the Hessian required to perform phaseonly maximum likelihood calibration. 
compute_jhj_and_jhr (time_bin_indices, …) 
Computes the diagonal of the Hessian and the residual locally projected in to gain space. 
gauss_newton (time_bin_indices, …[, tol, …]) 
Performs phaseonly maximum likelihood calibration using a GaussNewton optimisation algorithm. 

africanus.calibration.phase_only.
compute_jhr
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, residual, model, flag)[source]¶ Computes the residual projected in to gain space.
Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
antenna1 :
numpy.ndarray
First antenna indices of shape
(row,)
.antenna2 :
numpy.ndarray
Second antenna indices of shape
(row,)
jones :
numpy.ndarray
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.residual :
numpy.ndarray
Residual values of shape
(row, chan, corr)
. or(row, chan, corr, corr)
.model :
numpy.ndarray
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.flag :
numpy.ndarray
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
Returns: jhr :
numpy.ndarray
The residual projected into gain space shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.phase_only.
compute_jhj
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, model, flag)[source]¶ Computes the diagonal of the Hessian required to perform phaseonly maximum likelihood calibration. Currently assumes scalar or diagonal inputs.
Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
antenna1 :
numpy.ndarray
First antenna indices of shape
(row,)
.antenna2 :
numpy.ndarray
Second antenna indices of shape
(row,)
jones :
numpy.ndarray
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.model :
numpy.ndarray
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.flag :
numpy.ndarray
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
Returns: jhj :
numpy.ndarray
The diagonal of the Hessian of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.phase_only.
compute_jhj_and_jhr
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, residual, model, flag)[source]¶ Computes the diagonal of the Hessian and the residual locally projected in to gain space.
Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
antenna1 :
numpy.ndarray
First antenna indices of shape
(row,)
.antenna2 :
numpy.ndarray
Second antenna indices of shape
(row,)
jones :
numpy.ndarray
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.residual :
numpy.ndarray
Residual values of shape
(row, chan, corr)
. or(row, chan, corr, corr)
.model :
numpy.ndarray
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.flag :
numpy.ndarray
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
Returns: jhj :
numpy.ndarray
The diagonal of the Hessian of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.jhr :
numpy.ndarray
Residuals projected into signal space of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.phase_only.
gauss_newton
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, vis, flag, model, weight, tol=0.0001, maxiter=100)[source]¶ Performs phaseonly maximum likelihood calibration using a GaussNewton optimisation algorithm. Currently only DIAG mode is supported.
Parameters: time_bin_indices :
numpy.ndarray
The start indices of the time bins of shape
(utime)
time_bin_counts :
numpy.ndarray
The counts of unique time in each time bin of shape
(utime)
antenna1 :
numpy.ndarray
First antenna indices of shape
(row,)
.antenna2 :
numpy.ndarray
Second antenna indices of shape
(row,)
.jones :
numpy.ndarray
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.vis :
numpy.ndarray
Data values of shape
(row, chan, corr)
or(row, chan, corr, corr)
.flag :
numpy.ndarray
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
.model :
numpy.ndarray
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.weight :
numpy.ndarray
Weight spectrum of shape
(row, chan, corr)
. If the channel axis is missing weights are duplicated for each channel.tol: float, optional
The tolerance of the solver. Defaults to 1e4.
maxiter: int, optional
The maximum number of iterations. Defaults to 100.
Returns: gains :
numpy.ndarray
Gain solutions of shape
(time, ant, chan, dir, corr)
or shape(time, ant, chan, dir, corr, corr)
jhj :
numpy.ndarray
The diagonal of the Hessian of shape
(time, ant, chan, dir, corr)
or shape(time, ant, chan, dir, corr, corr)
jhr :
numpy.ndarray
Residuals projected into gain space of shape
(time, ant, chan, dir, corr)
or shape(time, ant, chan, dir, corr, corr)
.k: int
Number of iterations (will equal maxiter if not converged)
Dask¶
compute_jhr (time_bin_indices, …) 
Computes the residual projected in to gain space. 
compute_jhj (time_bin_indices, …) 
Computes the diagonal of the Hessian required to perform phaseonly maximum likelihood calibration. 

africanus.calibration.phase_only.dask.
compute_jhr
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, residual, model, flag)[source]¶ Computes the residual projected in to gain space.
Parameters: time_bin_indices :
dask.array.Array
The start indices of the time bins of shape
(utime)
time_bin_counts :
dask.array.Array
The counts of unique time in each time bin of shape
(utime)
antenna1 :
dask.array.Array
First antenna indices of shape
(row,)
.antenna2 :
dask.array.Array
Second antenna indices of shape
(row,)
jones :
dask.array.Array
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.residual :
dask.array.Array
Residual values of shape
(row, chan, corr)
. or(row, chan, corr, corr)
.model :
dask.array.Array
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.flag :
dask.array.Array
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
Returns: jhr :
dask.array.Array
The residual projected into gain space shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.

africanus.calibration.phase_only.dask.
compute_jhj
(time_bin_indices, time_bin_counts, antenna1, antenna2, jones, model, flag)[source]¶ Computes the diagonal of the Hessian required to perform phaseonly maximum likelihood calibration. Currently assumes scalar or diagonal inputs.
Parameters: time_bin_indices :
dask.array.Array
The start indices of the time bins of shape
(utime)
time_bin_counts :
dask.array.Array
The counts of unique time in each time bin of shape
(utime)
antenna1 :
dask.array.Array
First antenna indices of shape
(row,)
.antenna2 :
dask.array.Array
Second antenna indices of shape
(row,)
jones :
dask.array.Array
Gain solutions of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.model :
dask.array.Array
Model data values of shape
(row, chan, dir, corr)
or(row, chan, dir, corr, corr)
.flag :
dask.array.Array
Flag data of shape
(row, chan, corr)
or(row, chan, corr, corr)
Returns: jhj :
dask.array.Array
The diagonal of the Hessian of shape
(time, ant, chan, dir, corr)
or(time, ant, chan, dir, corr, corr)
.