Welcome to Codex Africanus’s documentation!¶

Codex Africanus¶

Radio Astronomy Building Blocks

Documentation¶

https://codex-africanus.readthedocs.io.

Installation¶

Stable release¶

To install Codex Africanus, run this command in your terminal:

$ pip install codex-africanus

This is the preferred method to install Codex Africanus, as it will always install the most recent stable release.

If you don’t have pip installed, this Python installation guide can guide you through the process.

By default, Codex Africanus will install with a minimal set of dependencies, numpy and numba.

Further functionality can be enabled by installing extra requirements as follows:

$ pip install codex-africanus[dask]
$ pip install codex-africanus[scipy]
$ pip install codex-africanus[astropy]
$ pip install codex-africanus[python-casacore]

To install the complete set of dependencies for the CPU:

$ pip install codex-africanus[complete]

To install the complete set of dependencies including CUDA:

$ pip install codex-africanus[complete-cuda]

From sources¶

The sources for Codex Africanus can be downloaded from the Github repo.

You can either clone the public repository:

$ git clone git://github.com/ska-sa/codex-africanus

Or download the tarball:

$ curl  -OL https://github.com/ska-sa/codex-africanus/tarball/master

Once you have a copy of the source, you can install it with:

$ python setup.py install

Usage¶

To use Codex Africanus in a project:

import africanus

Command Line Utilities¶

The following command line utilities are installed. Run each utility’s help for further information.

$ utility --help

plot-filter¶

Plots convolution filters.

plot-taper¶

Plots tapers associated with convolution filters.

API¶

Radio Interferometer Measurement Equation¶

Functions used to compute the terms of the Radio Interferometer Measurement Equation (RIME). It describes the response of an interferometer to a sky model.

\[V_{pq} = G_{p} \left( \sum_{s} E_{ps} L_{p} K_{ps} B_{s} K_{qs}^H L_{q}^H E_{qs}^H \right) G_{q}^H\]

where for antenna $p$ and $q$, and source $s$:

$G_{p}$ represents direction-independent effects.
$E_{ps}$ represents direction-dependent effects.
$L_{p}$ represents the feed rotation.
$K_{ps}$ represents the phase delay term.
$B_{s}$ represents the brightness matrix.

The RIME is more formally described in the following four papers:

Numpy¶

`predict_vis`(time_index, antenna1, antenna2)	Multiply Jones terms together to form model visibilities according to the following formula:
`phase_delay`(lm, uvw, frequency[, convention])	Computes the phase delay (K) term:
`parallactic_angles`(times, antenna_positions, ...)	Computes parallactic angles per timestep for the given reference antenna position and field centre.
`feed_rotation`(parallactic_angles[, feed_type])	Computes the 2x2 feed rotation (L) matrix from the `parallactic_angles`.
`transform_sources`(lm, parallactic_angles, ...)	Creates beam sampling coordinates suitable for use in `beam_cube_dde()` by:
`beam_cube_dde`(beam, beam_lm_extents, ...)	Evaluates Direction Dependent Effects along a source's path by interpolating the values of a complex beam cube at the source location.
`zernike_dde`(coords, coeffs, noll_index, ...)	Computes Direction Dependent Effects by evaluating Zernicke Polynomials defined by coefficients `coeffs` and noll indexes `noll_index` at the specified coordinates `coords`.
`wsclean_predict`(uvw, lm, source_type, flux, ...)	Predict visibilities from a WSClean sky model.

africanus.rime.predict_vis(time_index, antenna1, antenna2, dde1_jones=None, source_coh=None, dde2_jones=None, die1_jones=None, base_vis=None, die2_jones=None)[source]¶

Multiply Jones terms together to form model visibilities according to the following formula:

\[V_{pq} = G_{p} \left( B_{pq} + \sum_{s} E_{ps} X_{pqs} E_{qs}^H \right) G_{q}^H\]

where for antenna $p$ and $q$, and source $s$:

$B_{{pq}}$ represent base coherencies.
$E_{{ps}}$ represents Direction-Dependent Jones terms.
$X_{{pqs}}$ represents a coherency matrix (per-source).
$G_{{p}}$ represents Direction-Independent Jones terms.

Generally, $E_{ps}$, $G_{p}$, $X_{pqs}$ should be formed by using the RIME API functions and combining them together with einsum().

Please read the Notes

Parameters

time_indexnumpy.ndarray: Time index used to look up the antenna Jones index for a particular baseline with shape (row,). Obtainable via np.unique(time, return_inverse=True)[1].
antenna1numpy.ndarray: Antenna 1 index used to look up the antenna Jones for a particular baseline. with shape (row,).
antenna2numpy.ndarray: Antenna 2 index used to look up the antenna Jones for a particular baseline. with shape (row,).
dde1_jonesnumpy.ndarray, optional: $E_{ps}$ Direction-Dependent Jones terms for the first antenna. shape (source,time,ant,chan,corr_1,corr_2)
source_cohnumpy.ndarray, optional: $X_{pqs}$ Direction-Dependent Coherency matrix for the baseline. with shape (source,row,chan,corr_1,corr_2)
dde2_jonesnumpy.ndarray, optional: $E_{qs}$ Direction-Dependent Jones terms for the second antenna. This is usually the same array as dde1_jones as this preserves the symmetry of the RIME. predict_vis will perform the conjugate transpose internally. shape (source,time,ant,chan,corr_1,corr_2)
die1_jonesnumpy.ndarray, optional: $G_{ps}$ Direction-Independent Jones terms for the first antenna of the baseline. with shape (time,ant,chan,corr_1,corr_2)
base_visnumpy.ndarray, optional: $B_{pq}$ base coherencies, added to source coherency summation before multiplication with die1_jones and die2_jones. shape (row,chan,corr_1,corr_2).
die2_jonesnumpy.ndarray, optional: $G_{ps}$ Direction-Independent Jones terms for the second antenna of the baseline. This is usually the same array as die1_jones as this preserves the symmetry of the RIME. predict_vis will perform the conjugate transpose internally. shape (time,ant,chan,corr_1,corr_2)

Returns

visibilitiesnumpy.ndarray: Model visibilities of shape (row,chan,corr_1,corr_2)

Notes

Direction-Dependent terms (dde{1,2}_jones) and Independent (die{1,2}_jones) are optional, but if one is present, the other must be present.
The inputs to this function involve row, time and ant (antenna) dimensions.
Each row is associated with a pair of antenna Jones matrices at a particular timestep via the time_index, antenna1 and antenna2 inputs.
The row dimension must be an increasing partial order in time.

africanus.rime.phase_delay(lm, uvw, frequency, convention='fourier')[source]¶

Computes the phase delay (K) term:

\[ \begin{align}\begin{aligned}& {\Large e^{-2 \pi i (u l + v m + w (n - 1))} }\\& \textrm{where } n = \sqrt{1 - l^2 - m^2}\end{aligned}\end{align} \]

Parameters

lmnumpy.ndarray: LM coordinates of shape (source, 2) with L and M components in the last dimension.
uvwnumpy.ndarray: UVW coordinates of shape (row, 3) with U, V and W components in the last dimension.
frequencynumpy.ndarray: frequencies of shape (chan,)
convention{‘fourier’, ‘casa’}: Uses the $e^{-2 \pi \mathit{i}}$ sign convention if fourier and $e^{2 \pi \mathit{i}}$ if casa.

Returns

complex_phasenumpy.ndarray: complex of shape (source, row, chan)

Notes

Corresponds to the complex exponential of the Van Cittert-Zernike Theorem.

MeqTrees uses the CASA sign convention.

africanus.rime.parallactic_angles(times, antenna_positions, field_centre, backend='casa')[source]¶

Computes parallactic angles per timestep for the given reference antenna position and field centre.

Parameters

timesnumpy.ndarray

Array of Mean Julian Date times in seconds with shape (time,),

antenna_positionsnumpy.ndarray

Antenna positions of shape (ant, 3) in metres in the ITRF frame.

field_centrenumpy.ndarray

Field centre of shape (2,) in radians

backend{‘casa’, ‘test’}, optional

Backend to use for calculating the parallactic angles.

casa defers to an implementation depending on python-casacore. This backend should be used by default.
test creates parallactic angles by multiplying the times and antenna_position arrays. It exist solely for testing.

Returns

parallactic_anglesnumpy.ndarray: Parallactic angles of shape (time,ant)

africanus.rime.feed_rotation(parallactic_angles, feed_type='linear')[source]¶

Computes the 2x2 feed rotation (L) matrix from the parallactic_angles.

\[\begin{split}\textrm{linear} \begin{bmatrix} cos(pa) & sin(pa) \\ -sin(pa) & cos(pa) \end{bmatrix} \qquad \textrm{circular} \begin{bmatrix} e^{-i pa} & 0 \\ 0 & e^{i pa} \end{bmatrix}\end{split}\]

Parameters

parallactic_anglesnumpy.ndarray: floating point parallactic angles. Of shape (pa0, pa1, ..., pan).
feed_type{‘linear’, ‘circular’}: The type of feed

Returns

feed_matrixnumpy.ndarray: Feed rotation matrix of shape (pa0, pa1,...,pan,2,2)

africanus.rime.transform_sources(lm, parallactic_angles, pointing_errors, antenna_scaling, frequency, dtype=None)[source]¶

Creates beam sampling coordinates suitable for use in beam_cube_dde() by:

Rotating lm coordinates by the parallactic_angles
Adding pointing_errors
Scaling by antenna_scaling

Parameters

lmnumpy.ndarray: LM coordinates of shape (src,2) in radians offset from the phase centre.
parallactic_anglesnumpy.ndarray: parallactic angles of shape (time, antenna) in radians.
pointing_errorsnumpy.ndarray: LM pointing errors for each antenna at each timestep in radians. Has shape (time, antenna, 2)
antenna_scalingnumpy.ndarray: antenna scaling factor for each channel and each antenna. Has shape (antenna, chan)
frequencynumpy.ndarray: frequencies for each channel. Has shape (chan,)
dtypenumpy.dtype, optional: Numpy dtype of result array. Should be float32 or float64. Defaults to float64

Returns

coordsnumpy.ndarray: coordinates of shape (3, src, time, antenna, chan) where each coordinate component represents l, m and frequency, respectively.

africanus.rime.beam_cube_dde(beam, beam_lm_extents, beam_freq_map, lm, parallactic_angles, point_errors, antenna_scaling, frequency)[source]¶

Evaluates Direction Dependent Effects along a source’s path by interpolating the values of a complex beam cube at the source location.

Parameters

beamnumpy.ndarray

Complex beam cube of shape (beam_lw, beam_mh, beam_nud, corr, corr). beam_lw, beam_mh and beam_nud define the size of the cube in the l, m and frequency dimensions, respectively.

beam_lm_extentsnumpy.ndarray

lm extents of the beam cube of shape (2, 2). [[lower_l, upper_l], [lower_m, upper_m]].

beam_freq_mapnumpy.ndarray

Beam frequency map of shape (beam_nud,). This array is used to define interpolation along the (chan,) dimension.

lmnumpy.ndarray

Source lm coordinates of shape (source, 2). These coordinates are:

Scaled if the associated frequency lies outside the beam cube.

Offset by pointing errors: point_errors

Rotated by parallactic angles: parallactic_angles.

Scaled by antenna scaling factors: antenna_scaling.

parallactic_anglesnumpy.ndarray

Parallactic angles of shape (time, ant).

point_errorsnumpy.ndarray

Pointing errors of shape (time, ant, chan, 2).

antenna_scalingnumpy.ndarray

Antenna scaling factors of shape (ant, chan, 2)

frequencynumpy.ndarray

Frequencies of shape (chan,).

Returns

ddesnumpy.ndarray: Direction Dependent Effects of shape (source, time, ant, chan, corr, corr)

Notes

Sources are clamped to the provided beam_lm_extents.
Frequencies outside the cube (i.e. outside beam_freq_map) introduce linear scaling to the lm coordinates of a source.

africanus.rime.zernike_dde(coords, coeffs, noll_index, parallactic_angles, frequency_scaling, antenna_scaling, pointing_errors)[source]¶

Computes Direction Dependent Effects by evaluating Zernicke Polynomials defined by coefficients coeffs and noll indexes noll_index at the specified coordinates coords.

Decomposition of a voxel beam cube into Zernicke polynomial coefficients can be achieved through the use of the eidos package.

Parameters

coordsnumpy.ndarray: Float coordinates at which to evaluate the zernike polynomials. Has shape (3, source, time, ant, chan). The three components in the first dimension represent l, m and frequency coordinates, respectively.
coeffsnumpy.ndarray: complex Zernicke polynomial coefficients. Has shape (ant, chan, corr_1, ..., corr_n, poly) where poly is the number of polynomial coefficients and corr_1, ..., corr_n are a variable number of correlation dimensions.
noll_indexnumpy.ndarray: Noll index associated with each polynomial coefficient. Has shape (ant, chan, corr_1, ..., corr_n, poly). correlation dimensions.
parallactic_anglesnumpy.ndarray: Parallactic angle rotation. Has shape (time, ant).
frequency_scalingnumpy.ndarray: The scaling of frequency of the beam. Has shape (chan,).
antenna_scalingnumpy.ndarray: The antenna scaling. Has shape (ant, chan, 2).
pointing_errorsnumpy.ndarray: The pointing error. Has shape (time, ant, chan, 2).

Returns

ddenumpy.ndarray: complex values with shape (source, time, ant, chan, corr_1, ..., corr_n)

africanus.rime.wsclean_predict(uvw, lm, source_type, flux, coeffs, log_poly, ref_freq, gauss_shape, frequency)[source]¶

Predict visibilities from a WSClean sky model.

Parameters

uvwnumpy.ndarray: UVW coordinates of shape (row, 3)
lmnumpy.ndarray: Source LM coordinates of shape (source, 2), in radians. Derived from the Ra and Dec fields.
source_typenumpy.ndarray: Strings defining the source type of shape (source,). Should be either "POINT" or "GAUSSIAN". Contains the Type field.
fluxnumpy.ndarray: Source flux of shape (source,). Contains the I field.
coeffsnumpy.ndarray: Source Polynomial coefficients of shape (source, coeffs). Contains the SpectralIndex field.
log_polynumpy.ndarray: Source polynomial type of shape (source,). If True, logarithmic polynomials are used. If False, standard polynomials are used. Contains the LogarithmicSI field.
ref_freqnumpy.ndarray: Source Reference frequency of shape (source,). Contains the ReferenceFrequency field.
gauss_shapenumpy.ndarray: Gaussian shape parameters of shape (source, 3) used when the corresponding source_type is "GAUSSIAN". The 3 components should contain the MajorAxis, MinorAxis and Orientation fields in radians, respectively.
frequencynumpy.ndarray: Frequency of shape (chan,).

Returns

visibilitiesnumpy.ndarray: Complex visibilities of shape (row, chan, 1)

Cuda¶

`predict_vis`(time_index, antenna1, antenna2)	Multiply Jones terms together to form model visibilities according to the following formula:
`phase_delay`(lm, uvw, frequency)	Computes the phase delay (K) term:
`feed_rotation`(parallactic_angles[, feed_type])	Computes the 2x2 feed rotation (L) matrix from the `parallactic_angles`.
`beam_cube_dde`(beam, beam_lm_ext, ...)	Evaluates Direction Dependent Effects along a source's path by interpolating the values of a complex beam cube at the source location.

africanus.rime.cuda.predict_vis(time_index, antenna1, antenna2, dde1_jones=None, source_coh=None, dde2_jones=None, die1_jones=None, base_vis=None, die2_jones=None)[source]¶

Multiply Jones terms together to form model visibilities according to the following formula:

\[V_{pq} = G_{p} \left( B_{pq} + \sum_{s} E_{ps} X_{pqs} E_{qs}^H \right) G_{q}^H\]

where for antenna $p$ and $q$, and source $s$:

$B_{{pq}}$ represent base coherencies.
$E_{{ps}}$ represents Direction-Dependent Jones terms.
$X_{{pqs}}$ represents a coherency matrix (per-source).
$G_{{p}}$ represents Direction-Independent Jones terms.

Generally, $E_{ps}$, $G_{p}$, $X_{pqs}$ should be formed by using the RIME API functions and combining them together with einsum().

Please read the Notes

Parameters

time_indexcupy.ndarray: Time index used to look up the antenna Jones index for a particular baseline with shape (row,). Obtainable via cp.unique(time, return_inverse=True)[1].
antenna1cupy.ndarray: Antenna 1 index used to look up the antenna Jones for a particular baseline. with shape (row,).
antenna2cupy.ndarray: Antenna 2 index used to look up the antenna Jones for a particular baseline. with shape (row,).
dde1_jonescupy.ndarray, optional: $E_{ps}$ Direction-Dependent Jones terms for the first antenna. shape (source,time,ant,chan,corr_1,corr_2)
source_cohcupy.ndarray, optional: $X_{pqs}$ Direction-Dependent Coherency matrix for the baseline. with shape (source,row,chan,corr_1,corr_2)
dde2_jonescupy.ndarray, optional: $E_{qs}$ Direction-Dependent Jones terms for the second antenna. This is usually the same array as dde1_jones as this preserves the symmetry of the RIME. predict_vis will perform the conjugate transpose internally. shape (source,time,ant,chan,corr_1,corr_2)
die1_jonescupy.ndarray, optional: $G_{ps}$ Direction-Independent Jones terms for the first antenna of the baseline. with shape (time,ant,chan,corr_1,corr_2)
base_viscupy.ndarray, optional: $B_{pq}$ base coherencies, added to source coherency summation before multiplication with die1_jones and die2_jones. shape (row,chan,corr_1,corr_2).
die2_jonescupy.ndarray, optional: $G_{ps}$ Direction-Independent Jones terms for the second antenna of the baseline. This is usually the same array as die1_jones as this preserves the symmetry of the RIME. predict_vis will perform the conjugate transpose internally. shape (time,ant,chan,corr_1,corr_2)

Returns

visibilitiescupy.ndarray: Model visibilities of shape (row,chan,corr_1,corr_2)

Notes

Direction-Dependent terms (dde{1,2}_jones) and Independent (die{1,2}_jones) are optional, but if one is present, the other must be present.
The inputs to this function involve row, time and ant (antenna) dimensions.
Each row is associated with a pair of antenna Jones matrices at a particular timestep via the time_index, antenna1 and antenna2 inputs.
The row dimension must be an increasing partial order in time.

africanus.rime.cuda.phase_delay(lm, uvw, frequency)[source]¶

Computes the phase delay (K) term:

\[ \begin{align}\begin{aligned}& {\Large e^{-2 \pi i (u l + v m + w (n - 1))} }\\& \textrm{where } n = \sqrt{1 - l^2 - m^2}\end{aligned}\end{align} \]

Parameters

lmcupy.ndarray: LM coordinates of shape (source, 2) with L and M components in the last dimension.
uvwcupy.ndarray: UVW coordinates of shape (row, 3) with U, V and W components in the last dimension.
frequencycupy.ndarray: frequencies of shape (chan,)
convention{‘fourier’, ‘casa’}: Uses the $e^{-2 \pi \mathit{i}}$ sign convention if fourier and $e^{2 \pi \mathit{i}}$ if casa.

Returns

complex_phasecupy.ndarray: complex of shape (source, row, chan)

Notes

Corresponds to the complex exponential of the Van Cittert-Zernike Theorem.

MeqTrees uses the CASA sign convention.

africanus.rime.cuda.feed_rotation(parallactic_angles, feed_type='linear')[source]¶

Computes the 2x2 feed rotation (L) matrix from the parallactic_angles.

\[\begin{split}\textrm{linear} \begin{bmatrix} cos(pa) & sin(pa) \\ -sin(pa) & cos(pa) \end{bmatrix} \qquad \textrm{circular} \begin{bmatrix} e^{-i pa} & 0 \\ 0 & e^{i pa} \end{bmatrix}\end{split}\]

Parameters

parallactic_anglescupy.ndarray: floating point parallactic angles. Of shape (pa0, pa1, ..., pan).
feed_type{‘linear’, ‘circular’}: The type of feed

Returns

feed_matrixcupy.ndarray: Feed rotation matrix of shape (pa0, pa1,...,pan,2,2)

africanus.rime.cuda.beam_cube_dde(beam, beam_lm_ext, beam_freq_map, lm, parangles, pointing_errors, antenna_scaling, frequencies)[source]¶

Evaluates Direction Dependent Effects along a source’s path by interpolating the values of a complex beam cube at the source location.

Parameters

beamcupy.ndarray

Complex beam cube of shape (beam_lw, beam_mh, beam_nud, corr, corr). beam_lw, beam_mh and beam_nud define the size of the cube in the l, m and frequency dimensions, respectively.

beam_lm_extentscupy.ndarray

lm extents of the beam cube of shape (2, 2). [[lower_l, upper_l], [lower_m, upper_m]].

beam_freq_mapcupy.ndarray

Beam frequency map of shape (beam_nud,). This array is used to define interpolation along the (chan,) dimension.

lmcupy.ndarray

Source lm coordinates of shape (source, 2). These coordinates are:

Scaled if the associated frequency lies outside the beam cube.

Offset by pointing errors: point_errors

Rotated by parallactic angles: parallactic_angles.

Scaled by antenna scaling factors: antenna_scaling.

parallactic_anglescupy.ndarray

Parallactic angles of shape (time, ant).

point_errorscupy.ndarray

Pointing errors of shape (time, ant, chan, 2).

antenna_scalingcupy.ndarray

Antenna scaling factors of shape (ant, chan, 2)

frequencycupy.ndarray

Frequencies of shape (chan,).

Returns

ddescupy.ndarray: Direction Dependent Effects of shape (source, time, ant, chan, corr, corr)

Notes

Sources are clamped to the provided beam_lm_extents.
Frequencies outside the cube (i.e. outside beam_freq_map) introduce linear scaling to the lm coordinates of a source.

Dask¶

`predict_vis`(time_index, antenna1, antenna2)	Multiply Jones terms together to form model visibilities according to the following formula:
`phase_delay`(lm, uvw, frequency[, convention])	Computes the phase delay (K) term:
`parallactic_angles`(times, antenna_positions, ...)	Computes parallactic angles per timestep for the given reference antenna position and field centre.
`feed_rotation`(parallactic_angles, feed_type)	Computes the 2x2 feed rotation (L) matrix from the `parallactic_angles`.
`transform_sources`(lm, parallactic_angles, ...)	Creates beam sampling coordinates suitable for use in `beam_cube_dde()` by:
`beam_cube_dde`(beam, beam_lm_extents, ...)	Evaluates Direction Dependent Effects along a source's path by interpolating the values of a complex beam cube at the source location.
`zernike_dde`(coords, coeffs, noll_index, ...)	Computes Direction Dependent Effects by evaluating Zernicke Polynomials defined by coefficients `coeffs` and noll indexes `noll_index` at the specified coordinates `coords`.
`wsclean_predict`(uvw, lm, source_type, flux, ...)	Predict visibilities from a WSClean sky model.

africanus.rime.dask.predict_vis(time_index, antenna1, antenna2, dde1_jones=None, source_coh=None, dde2_jones=None, die1_jones=None, base_vis=None, die2_jones=None, streams=None)[source]¶

Multiply Jones terms together to form model visibilities according to the following formula:

\[V_{pq} = G_{p} \left( B_{pq} + \sum_{s} E_{ps} X_{pqs} E_{qs}^H \right) G_{q}^H\]

where for antenna $p$ and $q$, and source $s$:

$B_{{pq}}$ represent base coherencies.
$E_{{ps}}$ represents Direction-Dependent Jones terms.
$X_{{pqs}}$ represents a coherency matrix (per-source).
$G_{{p}}$ represents Direction-Independent Jones terms.

Generally, $E_{ps}$, $G_{p}$, $X_{pqs}$ should be formed by using the RIME API functions and combining them together with einsum().

Please read the Notes

Parameters

time_indexdask.array.Array: Time index used to look up the antenna Jones index for a particular baseline with shape (row,). Obtainable via time.map_blocks(lambda a: np.unique(a, return_inverse=True)[1]).
antenna1dask.array.Array: Antenna 1 index used to look up the antenna Jones for a particular baseline. with shape (row,).
antenna2dask.array.Array: Antenna 2 index used to look up the antenna Jones for a particular baseline. with shape (row,).
dde1_jonesdask.array.Array, optional: $E_{ps}$ Direction-Dependent Jones terms for the first antenna. shape (source,time,ant,chan,corr_1,corr_2)
source_cohdask.array.Array, optional: $X_{pqs}$ Direction-Dependent Coherency matrix for the baseline. with shape (source,row,chan,corr_1,corr_2)
dde2_jonesdask.array.Array, optional: $E_{qs}$ Direction-Dependent Jones terms for the second antenna. This is usually the same array as dde1_jones as this preserves the symmetry of the RIME. predict_vis will perform the conjugate transpose internally. shape (source,time,ant,chan,corr_1,corr_2)
die1_jonesdask.array.Array, optional: $G_{ps}$ Direction-Independent Jones terms for the first antenna of the baseline. with shape (time,ant,chan,corr_1,corr_2)
base_visdask.array.Array, optional: $B_{pq}$ base coherencies, added to source coherency summation before multiplication with die1_jones and die2_jones. shape (row,chan,corr_1,corr_2).
die2_jonesdask.array.Array, optional: $G_{ps}$ Direction-Independent Jones terms for the second antenna of the baseline. This is usually the same array as die1_jones as this preserves the symmetry of the RIME. predict_vis will perform the conjugate transpose internally. shape (time,ant,chan,corr_1,corr_2)
streams{False, True}: If True the coherencies are serially summed in a linear chain. If False, dask uses a tree style reduction algorithm.

Returns

visibilitiesdask.array.Array: Model visibilities of shape (row,chan,corr_1,corr_2)

Notes

Direction-Dependent terms (dde{1,2}_jones) and Independent (die{1,2}_jones) are optional, but if one is present, the other must be present.
The inputs to this function involve row, time and ant (antenna) dimensions.
Each row is associated with a pair of antenna Jones matrices at a particular timestep via the time_index, antenna1 and antenna2 inputs.
The row dimension must be an increasing partial order in time.
The ant dimension should only contain a single chunk equal to the number of antenna. Since each row can contain any antenna, random access must be preserved along this dimension.
The chunks in the row and time dimension must align. This subtle point must be understood otherwise invalid results will be produced by the chunking scheme. In the example below we have four unique time indices [0,1,2,3], and four unique antenna [0,1,2,3] indexing 10 rows.
```
#  Row indices into the time/antenna indexed arrays
time_idx = np.asarray([0,0,1,1,2,2,2,2,3,3])
ant1 = np.asarray(    [0,0,0,0,1,1,1,2,2,3]
ant2 = np.asarray(    [0,1,2,3,1,2,3,2,3,3])
```
A reasonable chunking scheme for the row and time dimension would be (4,4,2) and (2,1,1) respectively. Another way of explaining this is that the first four rows contain two unique timesteps, the second four rows contain one unique timestep and the last two rows contain one unique timestep.

Some rules of thumb:
1. The number chunks in row and time must match although the individual chunk sizes need not.
2. Unique timesteps should not be split across row chunks.
3. For a Measurement Set whose rows are ordered on the TIME column, the following is a good way of obtaining the row chunking strategy:
```
import numpy as np
import pyrap.tables as pt

ms = pt.table("data.ms")
times = ms.getcol("TIME")
unique_times, chunks = np.unique(times, return_counts=True)
```
4. Use aggregate_chunks() to aggregate multiple row and time chunks into chunks large enough such that functions operating on the resulting data can drop the GIL and spend time processing the data. Expanding the previous example:
```
# Aggregate row
utimes = unique_times.size
# Single chunk for each unique time
time_chunks = (1,)*utimes
# Aggregate row chunks into chunks <= 10000
aggregate_chunks((chunks, time_chunks), (10000, utimes))
```

africanus.rime.dask.phase_delay(lm, uvw, frequency, convention='fourier')[source]¶

Computes the phase delay (K) term:

\[ \begin{align}\begin{aligned}& {\Large e^{-2 \pi i (u l + v m + w (n - 1))} }\\& \textrm{where } n = \sqrt{1 - l^2 - m^2}\end{aligned}\end{align} \]

Parameters

lmdask.array.Array: LM coordinates of shape (source, 2) with L and M components in the last dimension.
uvwdask.array.Array: UVW coordinates of shape (row, 3) with U, V and W components in the last dimension.
frequencydask.array.Array: frequencies of shape (chan,)
convention{‘fourier’, ‘casa’}: Uses the $e^{-2 \pi \mathit{i}}$ sign convention if fourier and $e^{2 \pi \mathit{i}}$ if casa.

Returns

complex_phasedask.array.Array: complex of shape (source, row, chan)

Notes

Corresponds to the complex exponential of the Van Cittert-Zernike Theorem.

MeqTrees uses the CASA sign convention.

africanus.rime.dask.parallactic_angles(times, antenna_positions, field_centre, **kwargs)[source]¶

Computes parallactic angles per timestep for the given reference antenna position and field centre.

Parameters

timesdask.array.Array

Array of Mean Julian Date times in seconds with shape (time,),

antenna_positionsdask.array.Array

Antenna positions of shape (ant, 3) in metres in the ITRF frame.

field_centredask.array.Array

Field centre of shape (2,) in radians

backend{‘casa’, ‘test’}, optional

Backend to use for calculating the parallactic angles.

casa defers to an implementation depending on python-casacore. This backend should be used by default.
test creates parallactic angles by multiplying the times and antenna_position arrays. It exist solely for testing.

Returns

parallactic_anglesdask.array.Array: Parallactic angles of shape (time,ant)

africanus.rime.dask.feed_rotation(parallactic_angles, feed_type)[source]¶

Computes the 2x2 feed rotation (L) matrix from the parallactic_angles.

\[\begin{split}\textrm{linear} \begin{bmatrix} cos(pa) & sin(pa) \\ -sin(pa) & cos(pa) \end{bmatrix} \qquad \textrm{circular} \begin{bmatrix} e^{-i pa} & 0 \\ 0 & e^{i pa} \end{bmatrix}\end{split}\]

Parameters

parallactic_anglesnumpy.ndarray: floating point parallactic angles. Of shape (pa0, pa1, ..., pan).
feed_type{‘linear’, ‘circular’}: The type of feed

Returns

feed_matrixnumpy.ndarray: Feed rotation matrix of shape (pa0, pa1,...,pan,2,2)

africanus.rime.dask.transform_sources(lm, parallactic_angles, pointing_errors, antenna_scaling, frequency, dtype=None)[source]¶

Creates beam sampling coordinates suitable for use in beam_cube_dde() by:

Rotating lm coordinates by the parallactic_angles
Adding pointing_errors
Scaling by antenna_scaling

Parameters

lmdask.array.Array: LM coordinates of shape (src,2) in radians offset from the phase centre.
parallactic_anglesdask.array.Array: parallactic angles of shape (time, antenna) in radians.
pointing_errorsdask.array.Array: LM pointing errors for each antenna at each timestep in radians. Has shape (time, antenna, 2)
antenna_scalingdask.array.Array: antenna scaling factor for each channel and each antenna. Has shape (antenna, chan)
frequencydask.array.Array: frequencies for each channel. Has shape (chan,)
dtypenumpy.dtype, optional: Numpy dtype of result array. Should be float32 or float64. Defaults to float64

Returns

coordsdask.array.Array: coordinates of shape (3, src, time, antenna, chan) where each coordinate component represents l, m and frequency, respectively.

africanus.rime.dask.beam_cube_dde(beam, beam_lm_extents, beam_freq_map, lm, parallactic_angles, point_errors, antenna_scaling, frequencies)[source]¶

Evaluates Direction Dependent Effects along a source’s path by interpolating the values of a complex beam cube at the source location.

Parameters

beamdask.array.Array

Complex beam cube of shape (beam_lw, beam_mh, beam_nud, corr, corr). beam_lw, beam_mh and beam_nud define the size of the cube in the l, m and frequency dimensions, respectively.

beam_lm_extentsdask.array.Array

lm extents of the beam cube of shape (2, 2). [[lower_l, upper_l], [lower_m, upper_m]].

beam_freq_mapdask.array.Array

Beam frequency map of shape (beam_nud,). This array is used to define interpolation along the (chan,) dimension.

lmdask.array.Array

Source lm coordinates of shape (source, 2). These coordinates are:

Scaled if the associated frequency lies outside the beam cube.

Offset by pointing errors: point_errors

Rotated by parallactic angles: parallactic_angles.

Scaled by antenna scaling factors: antenna_scaling.

parallactic_anglesdask.array.Array

Parallactic angles of shape (time, ant).

point_errorsdask.array.Array

Pointing errors of shape (time, ant, chan, 2).

antenna_scalingdask.array.Array

Antenna scaling factors of shape (ant, chan, 2)

frequencydask.array.Array

Frequencies of shape (chan,).

Returns

ddesdask.array.Array: Direction Dependent Effects of shape (source, time, ant, chan, corr, corr)

Notes

Sources are clamped to the provided beam_lm_extents.
Frequencies outside the cube (i.e. outside beam_freq_map) introduce linear scaling to the lm coordinates of a source.

africanus.rime.dask.zernike_dde(coords, coeffs, noll_index, parallactic_angle, frequency_scaling, antenna_scaling, pointing_errors)[source]¶

Computes Direction Dependent Effects by evaluating Zernicke Polynomials defined by coefficients coeffs and noll indexes noll_index at the specified coordinates coords.

Decomposition of a voxel beam cube into Zernicke polynomial coefficients can be achieved through the use of the eidos package.

Parameters

coordsdask.array.Array: Float coordinates at which to evaluate the zernike polynomials. Has shape (3, source, time, ant, chan). The three components in the first dimension represent l, m and frequency coordinates, respectively.
coeffsdask.array.Array: complex Zernicke polynomial coefficients. Has shape (ant, chan, corr_1, ..., corr_n, poly) where poly is the number of polynomial coefficients and corr_1, ..., corr_n are a variable number of correlation dimensions.
noll_indexdask.array.Array: Noll index associated with each polynomial coefficient. Has shape (ant, chan, corr_1, ..., corr_n, poly). correlation dimensions.
parallactic_anglesdask.array.Array: Parallactic angle rotation. Has shape (time, ant).
frequency_scalingdask.array.Array: The scaling of frequency of the beam. Has shape (chan,).
antenna_scalingdask.array.Array: The antenna scaling. Has shape (ant, chan, 2).
pointing_errorsdask.array.Array: The pointing error. Has shape (time, ant, chan, 2).

Returns

ddedask.array.Array: complex values with shape (source, time, ant, chan, corr_1, ..., corr_n)

africanus.rime.dask.wsclean_predict(uvw, lm, source_type, flux, coeffs, log_poly, ref_freq, gauss_shape, frequency)[source]¶

Predict visibilities from a WSClean sky model.

Parameters

uvwdask.array.Array: UVW coordinates of shape (row, 3)
lmdask.array.Array: Source LM coordinates of shape (source, 2), in radians. Derived from the Ra and Dec fields.
source_typedask.array.Array: Strings defining the source type of shape (source,). Should be either "POINT" or "GAUSSIAN". Contains the Type field.
fluxdask.array.Array: Source flux of shape (source,). Contains the I field.
coeffsdask.array.Array: Source Polynomial coefficients of shape (source, coeffs). Contains the SpectralIndex field.
log_polydask.array.Array: Source polynomial type of shape (source,). If True, logarithmic polynomials are used. If False, standard polynomials are used. Contains the LogarithmicSI field.
ref_freqdask.array.Array: Source Reference frequency of shape (source,). Contains the ReferenceFrequency field.
gauss_shapedask.array.Array: Gaussian shape parameters of shape (source, 3) used when the corresponding source_type is "GAUSSIAN". The 3 components should contain the MajorAxis, MinorAxis and Orientation fields in radians, respectively.
frequencydask.array.Array: Frequency of shape (chan,).

Returns

visibilitiesdask.array.Array: Complex visibilities of shape (row, chan, 1)

Direct Fourier Transform¶

Functions used to compute the discretised direct Fourier transform (DFT) for an ideal interferometer. The DFT for an ideal interferometer is defined as

\[V(u,v,w) = \int B(l,m) e^{-2\pi i \left( ul + vm + w(n-1)\right)} \frac{dl dm}{n}\]

where $u,v,w$ are data space coordinates and where visibilities $V$ have been obtained. The $l,m,n$ are signal space coordinates at which we wish to reconstruct the signal $B$. Note that the signal correspondes to the brightness matrix and not the Stokes parameters. We adopt the convention where we absorb the fixed coordinate $n$ in the denominator into the image. Note that the data space coordinates have an implicit dependence on frequency and time and that the image has an implicit dependence on frequency. The discretised form of the DFT can be written as

\[V(u,v,w) = \sum_s e^{-2 \pi i (u l_s + v m_s + w (n_s - 1))} \cdot B_s\]

where $s$ labels the source (or pixel) location. If only a single correlation is present $B = I$, this can be cast into a matrix equation as follows

\[V = R I\]

where $R$ is the operator that maps an image to visibility space. This mapping is implemented by the im_to_vis() function. If multiple correlations are present then each one is mapped to its corresponding visibility. An imaging algorithm also requires the adjoint denoted $R^\dagger$ which is simply the complex conjugate transpose of $R$. The dirty image is obtained by applying the adjoint operator to the visibilities

\[I^D = R^\dagger V\]

This is implemented by the vis_to_im() function. Note that an imaging algorithm using these operators will actually reconstruct $\frac{I}{n}$ but that it is trivial to obtain $I$ since $n$ is known at each location in the image.

Numpy¶

`im_to_vis`(image, uvw, lm, frequency[, ...])	Computes the discrete image to visibility mapping of an ideal interferometer:
`vis_to_im`(vis, uvw, lm, frequency, flags[, ...])	Computes visibility to image mapping of an ideal interferometer:

africanus.dft.im_to_vis(image, uvw, lm, frequency, convention='fourier', dtype=None)[source]¶

Computes the discrete image to visibility mapping of an ideal interferometer:

\[{\Large \sum_s e^{-2 \pi i (u l_s + v m_s + w (n_s - 1))} \cdot I_s }\]

Parameters

imagenumpy.ndarray: image of shape (source, chan, corr) The brighness matrix in each pixel (flatten 2D array per channel and corr). Note not Stokes terms
uvwnumpy.ndarray: uvw coordinates of shape (row, 3) with u, v and w components in the last dimension.
lmnumpy.ndarray: lm coordinates of shape (source, 2) with l and m components in the last dimension.
frequencynumpy.ndarray: frequencies of shape (chan,)
convention{‘fourier’, ‘casa’}: Uses the $e^{-2 \pi \mathit{i}}$ sign convention if fourier and $e^{2 \pi \mathit{i}}$ if casa.
dtypenp.dtype, optional: Datatype of result. Should be either np.complex64 or np.complex128. If None, numpy.result_type() is used to infer the data type from the inputs.

Returns

visibiltiesnumpy.ndarray: complex of shape (row, chan, corr)

africanus.dft.vis_to_im(vis, uvw, lm, frequency, flags, convention='fourier', dtype=None)[source]¶

Computes visibility to image mapping of an ideal interferometer:

\[{\Large \sum_k e^{ 2 \pi i (u_k l + v_k m + w_k (n - 1))} \cdot V_k}\]

Parameters

visnumpy.ndarray: visibilities of shape (row, chan, corr) Visibilities corresponding to brightness terms. Note the dirty images produced do not necessarily correspond to Stokes terms and need to be converted.
uvwnumpy.ndarray: uvw coordinates of shape (row, 3) with u, v and w components in the last dimension.
lmnumpy.ndarray: lm coordinates of shape (source, 2) with l and m components in the last dimension.
frequencynumpy.ndarray: frequencies of shape (chan,)
flagsnumpy.ndarray: Boolean array of shape (row, chan, corr) Note that if one correlation is flagged we discard all of them otherwise we end up irretrievably mixing Stokes terms.
convention{‘fourier’, ‘casa’}: Uses the $e^{-2 \pi \mathit{i}}$ sign convention if fourier and $e^{2 \pi \mathit{i}}$ if casa.
dtypenp.dtype, optional: Datatype of result. Should be either np.float32 or np.float64. If None, numpy.result_type() is used to infer the data type from the inputs.

Returns

imagenumpy.ndarray: float of shape (source, chan, corr)

Dask¶

`im_to_vis`(image, uvw, lm, frequency[, ...])	Computes the discrete image to visibility mapping of an ideal interferometer:
`vis_to_im`(vis, uvw, lm, frequency, flags[, ...])	Computes visibility to image mapping of an ideal interferometer:

africanus.dft.dask.im_to_vis(image, uvw, lm, frequency, convention='fourier', dtype=numpy.complex128)[source]¶

Computes the discrete image to visibility mapping of an ideal interferometer:

\[{\Large \sum_s e^{-2 \pi i (u l_s + v m_s + w (n_s - 1))} \cdot I_s }\]

Parameters

imagedask.array.Array: image of shape (source, chan, corr) The brighness matrix in each pixel (flatten 2D array per channel and corr). Note not Stokes terms
uvwdask.array.Array: uvw coordinates of shape (row, 3) with u, v and w components in the last dimension.
lmdask.array.Array: lm coordinates of shape (source, 2) with l and m components in the last dimension.
frequencydask.array.Array: frequencies of shape (chan,)
convention{‘fourier’, ‘casa’}: Uses the $e^{-2 \pi \mathit{i}}$ sign convention if fourier and $e^{2 \pi \mathit{i}}$ if casa.
dtypenp.dtype, optional: Datatype of result. Should be either np.complex64 or np.complex128. If None, numpy.result_type() is used to infer the data type from the inputs.

Returns

visibiltiesdask.array.Array: complex of shape (row, chan, corr)

africanus.dft.dask.vis_to_im(vis, uvw, lm, frequency, flags, convention='fourier', dtype=numpy.float64)[source]¶

Computes visibility to image mapping of an ideal interferometer:

\[{\Large \sum_k e^{ 2 \pi i (u_k l + v_k m + w_k (n - 1))} \cdot V_k}\]

Parameters

visdask.array.Array: visibilities of shape (row, chan, corr) Visibilities corresponding to brightness terms. Note the dirty images produced do not necessarily correspond to Stokes terms and need to be converted.
uvwdask.array.Array: uvw coordinates of shape (row, 3) with u, v and w components in the last dimension.
lmdask.array.Array: lm coordinates of shape (source, 2) with l and m components in the last dimension.
frequencydask.array.Array: frequencies of shape (chan,)
flagsdask.array.Array: Boolean array of shape (row, chan, corr) Note that if one correlation is flagged we discard all of them otherwise we end up irretrievably mixing Stokes terms.
convention{‘fourier’, ‘casa’}: Uses the $e^{-2 \pi \mathit{i}}$ sign convention if fourier and $e^{2 \pi \mathit{i}}$ if casa.
dtypenp.dtype, optional: Datatype of result. Should be either np.float32 or np.float64. If None, numpy.result_type() is used to infer the data type from the inputs.

Returns

imagedask.array.Array: float of shape (source, chan, corr)

Gridding and Degridding¶

This section contains routines for

Gridding complex visibilities onto an image.
Degridding complex visibilities from an image.

Nifty¶

Dask wrappers around Nifty’s Gridder.

Dask¶

`grid_config`([nx, ny, eps, cell_size_x, ...])	Returns a wrapper around a NIFTY GridderConfiguration object.
`grid`(vis, uvw, flags, weights, frequencies, ...)	Grids the supplied visibilities in parallel.
`dirty`(grid, grid_config)	Computes the dirty image from gridded visibilities and the gridding configuration.
`degrid`(grid, uvw, flags, weights, ...[, ...])	Degrids the visibilities from the supplied grid in parallel.
`model`(image, grid_config)	Computes model visibilities from an image and a gridding configuration.

africanus.gridding.nifty.dask.grid_config(nx=1024, ny=1024, eps=2e-13, cell_size_x=2.0, cell_size_y=2.0)[source]¶

Returns a wrapper around a NIFTY GridderConfiguration object.

Parameters

nxint, optional: Number of X pixels in the grid. Defaults to 1024.
nyint, optional: Number of Y pixels in the grid. Defaults to 1024.
cell_size_xfloat, optional: Cell size of the X pixel in arcseconds. Defaults to 2.0.
cell_size_yfloat, optional: Cell size of the Y pixel in arcseconds. Defaults to 2.0.
epsfloat: Gridder accuracy error. Defaults to 2e-13

Returns

grid_configGridderConfigWrapper: The NIFTY Gridder Configuration

africanus.gridding.nifty.dask.grid(vis, uvw, flags, weights, frequencies, grid_config, wmin=- 1e+30, wmax=1e+30, streams=None)[source]¶

Grids the supplied visibilities in parallel. Note that a grid is create for each visibility chunk.

Parameters

visdask.array.Array: visibilities of shape (row, chan, corr)
uvwdask.array.Array: uvw coordinates of shape (row, 3)
flagsdask.array.Array: flags of shape (row, chan, corr)
weightsdask.array.Array: weights of shape (row, chan, corr).
frequenciesdask.array.Array: frequencies of shape (chan,)
grid_configGridderConfigWrapper: Gridding Configuration
wminfloat: Minimum W coordinate to grid. Defaults to -1e30.
wmaxfloat: Maximum W coordinate to grid. Default to 1e30.
streamsint, optional: Number of parallel gridding operations. Default to None, in which case as many grids as visibility chunks will be created.

Returns

griddask.array.Array: grid of shape (ny, nx, corr)

africanus.gridding.nifty.dask.dirty(grid, grid_config)[source]¶

Computes the dirty image from gridded visibilities and the gridding configuration.

Parameters

griddask.array.Array: Gridded visibilities of shape (nv, nu, ncorr)
grid_configGridderConfigWrapper: Gridding configuration

Returns

dirtydask.array.Array: dirty image of shape (ny, nx, corr)

africanus.gridding.nifty.dask.degrid(grid, uvw, flags, weights, frequencies, grid_config, wmin=- 1e+30, wmax=1e+30)[source]¶

Degrids the visibilities from the supplied grid in parallel.

Parameters

griddask.array.Array: gridded visibilities of shape (ny, nx, corr)
uvwdask.array.Array: uvw coordinates of shape (row, 3)
flagsdask.array.Array: flags of shape (row, chan, corr)
weightsdask.array.Array: weights of shape (row, chan, corr). Currently unsupported and ignored.
frequenciesdask.array.Array: frequencies of shape (chan,)
grid_configGridderConfigWrapper: Gridding Configuration
wminfloat: Minimum W coordinate to grid. Defaults to -1e30.
wmaxfloat: Maximum W coordinate to grid. Default to 1e30.

Returns

griddask.array.Array: grid of shape (ny, nx, corr)

africanus.gridding.nifty.dask.model(image, grid_config)[source]¶

Computes model visibilities from an image and a gridding configuration.

Parameters

imagedask.array.Array: Image of shape (ny, nx, corr).
grid_configGridderConfigWrapper: nifty gridding configuration object

Returns

model_visdask.array.Array: Model visibilities of shape (nu, nv, corr).

wgridder¶

Wrappers around ‘ducc.wgridder <https://gitlab.mpcdf.mpg.de/mtr/ducc>`_.

Numpy¶

`dirty`(uvw, freq, vis, freq_bin_idx, ...[, ...])	Compute visibility to image mapping using ducc gridder i.e.
`model`(uvw, freq, image, freq_bin_idx, ...[, ...])	Compute image to visibility mapping using ducc degridder i.e.
`residual`(uvw, freq, image, vis, ...[, ...])	Compute residual image given a model and visibilities using ducc degridder i.e.
`hessian`(uvw, freq, image, freq_bin_idx, ...)	Compute action of Hessian on an image using ducc

africanus.gridding.wgridder.dirty(uvw, freq, vis, freq_bin_idx, freq_bin_counts, nx, ny, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True, double_accum=False)[source]¶

Compute visibility to image mapping using ducc gridder i.e.

\[I^D = R^\dagger \Sigma^{-1} V\]

where $R^\dagger$ is an implicit gridding operator, $V$ denotes visibilities of shape (row, chan) and $I^D$ is the dirty image of shape (band, nx, ny).

The number of imaging bands (band) must be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

Note that, if self adjoint gridding and degridding operators are required then weights should be the square root of what is typically referred to as imaging weights and should also be passed into the degridder. In this case, the data needs to be pre-whitened.

Parameters

uvwnumpy.ndarray: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqnumpy.ndarray: Observational frequencies of shape (chan,).
visnumpy.ndarray: Visibilities of shape (row,chan).
freq_bin_idxnumpy.ndarray: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsnumpy.ndarray: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
weightsnumpy.ndarray, optional: Imaging weights of shape (row, chan).
flag:class:numpy.ndarray, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one. If set to zero will use all available cores.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True
double_accumbool, optional: If true ducc will accumulate in double precision regardless of the input type.

Returns

modelnumpy.ndarray: Dirty image corresponding to visibilities of shape (nband, nx, ny).

africanus.gridding.wgridder.model(uvw, freq, image, freq_bin_idx, freq_bin_counts, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True)[source]¶

Compute image to visibility mapping using ducc degridder i.e.

\[V = Rx\]

where $R$ is an implicit degridding operator, $V$ denotes visibilities of shape (row, chan) and $x$ is the image of shape (band, nx, ny).

The number of imaging bands (band) has to be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

There is an option to provide weights during degridding to cater for self adjoint gridding and degridding operators. In this case weights should actually be the square root of what is typically referred to as imaging weights. In this case the degridder computes the whitened model visibilities i.e.

\[V = \Sigma^{-\frac{1}{2}} R x\]

where $\Sigma$ refers to the inverse of the weights (i.e. the data covariance matrix when using natural weighting).

Parameters

uvwnumpy.ndarray: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqnumpy.ndarray: Observational frequencies of shape (chan,).
modelnumpy.ndarray: Model image to degrid of shape (nband, nx, ny).
freq_bin_idxnumpy.ndarray: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsnumpy.ndarray: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
weightsnumpy.ndarray, optional: Imaging weights of shape (row, chan).
flag:class:numpy.ndarray, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one. If set to zero will use all available cores.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True

Returns

visnumpy.ndarray: Visibilities corresponding to model of shape (row,chan).

africanus.gridding.wgridder.residual(uvw, freq, image, vis, freq_bin_idx, freq_bin_counts, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True, double_accum=False)[source]¶

Compute residual image given a model and visibilities using ducc degridder i.e.

\[I^R = R^\dagger \Sigma^{-1}(V - Rx)\]

where $R$ is an implicit degridding operator, $V$ denotes visibilities of shape (row, chan) and $x$ is the image of shape (band, nx, ny).

The number of imaging bands (band) must be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

Note that, if the gridding and degridding operators both apply the square root of the imaging weights then the visibilities that are passed in should be pre-whitened. In this case the function computes

\[I^R = R^\dagger \Sigma^{-\frac{1}{2}}(\tilde{V} - \Sigma^{-\frac{1}{2}}Rx)\]

which is identical to the above expression if $\tilde{V} = \Sigma^{-\frac{1}{2}}V$.

Parameters

uvwnumpy.ndarray: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqnumpy.ndarray: Observational frequencies of shape (chan,).
modelnumpy.ndarray: Model image to degrid of shape (band, nx, ny).
visnumpy.ndarray: Visibilities of shape (row,chan).
weightsnumpy.ndarray: Imaging weights of shape (row, chan).
freq_bin_idxnumpy.ndarray: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsnumpy.ndarray: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
flag:class:numpy.ndarray, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
nuint, optional: The number of pixels in the padded grid along the $x$ direction. Chosen automatically by default.
nvint, optional: The number of pixels in the padded grid along the $y$ direction. Chosen automatically by default.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True
double_accumbool, optional: If true ducc will accumulate in double precision regardless of the input type.

Returns

residualnumpy.ndarray: Residual image corresponding to model of shape (band, nx, ny).

africanus.gridding.wgridder.hessian(uvw, freq, image, freq_bin_idx, freq_bin_counts, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True, double_accum=False)[source]¶

Compute action of Hessian on an image using ducc

\[R^\dagger \Sigma^{-1} R x\]

where $R$ is an implicit degridding operator and $x$ is the image of shape (band, nx, ny).

The number of imaging bands (band) must be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

Parameters

uvwnumpy.ndarray: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqnumpy.ndarray: Observational frequencies of shape (chan,).
modelnumpy.ndarray: Model image to degrid of shape (band, nx, ny).
weightsnumpy.ndarray: Imaging weights of shape (row, chan).
freq_bin_idxnumpy.ndarray: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsnumpy.ndarray: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
flag:class:numpy.ndarray, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
nuint, optional: The number of pixels in the padded grid along the $x$ direction. Chosen automatically by default.
nvint, optional: The number of pixels in the padded grid along the $y$ direction. Chosen automatically by default.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True
double_accumbool, optional: If true ducc will accumulate in double precision regardless of the input type.

Returns

residualnumpy.ndarray: Residual image corresponding to model of shape (band, nx, ny).

Dask¶

`dirty`(uvw, freq, vis, freq_bin_idx, ...[, ...])	Compute visibility to image mapping using ducc gridder i.e.
`model`(uvw, freq, image, freq_bin_idx, ...[, ...])	Compute image to visibility mapping using ducc degridder i.e.
`residual`(uvw, freq, image, vis, ...[, ...])	Compute residual image given a model and visibilities using ducc degridder i.e.
`hessian`(uvw, freq, image, freq_bin_idx, ...)	Compute action of Hessian on an image using ducc

africanus.gridding.wgridder.dask.dirty(uvw, freq, vis, freq_bin_idx, freq_bin_counts, nx, ny, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True, double_accum=False)[source]¶

Compute visibility to image mapping using ducc gridder i.e.

\[I^D = R^\dagger \Sigma^{-1} V\]

where $R^\dagger$ is an implicit gridding operator, $V$ denotes visibilities of shape (row, chan) and $I^D$ is the dirty image of shape (band, nx, ny).

The number of imaging bands (band) must be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

Note that, if self adjoint gridding and degridding operators are required then weights should be the square root of what is typically referred to as imaging weights and should also be passed into the degridder. In this case, the data needs to be pre-whitened.

Parameters

uvwdask.array.Array: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqdask.array.Array: Observational frequencies of shape (chan,).
visdask.array.Array: Visibilities of shape (row,chan).
freq_bin_idxdask.array.Array: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsdask.array.Array: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
weightsdask.array.Array, optional: Imaging weights of shape (row, chan).
flag:class:dask.array.Array, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one. If set to zero will use all available cores.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True
double_accumbool, optional: If true ducc will accumulate in double precision regardless of the input type.

Returns

modeldask.array.Array: Dirty image corresponding to visibilities of shape (nband, nx, ny).

africanus.gridding.wgridder.dask.model(uvw, freq, image, freq_bin_idx, freq_bin_counts, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True)[source]¶

Compute image to visibility mapping using ducc degridder i.e.

\[V = Rx\]

where $R$ is an implicit degridding operator, $V$ denotes visibilities of shape (row, chan) and $x$ is the image of shape (band, nx, ny).

The number of imaging bands (band) has to be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

There is an option to provide weights during degridding to cater for self adjoint gridding and degridding operators. In this case weights should actually be the square root of what is typically referred to as imaging weights. In this case the degridder computes the whitened model visibilities i.e.

\[V = \Sigma^{-\frac{1}{2}} R x\]

where $\Sigma$ refers to the inverse of the weights (i.e. the data covariance matrix when using natural weighting).

Parameters

uvwdask.array.Array: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqdask.array.Array: Observational frequencies of shape (chan,).
modeldask.array.Array: Model image to degrid of shape (nband, nx, ny).
freq_bin_idxdask.array.Array: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsdask.array.Array: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
weightsdask.array.Array, optional: Imaging weights of shape (row, chan).
flag:class:dask.array.Array, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one. If set to zero will use all available cores.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True

Returns

visdask.array.Array: Visibilities corresponding to model of shape (row,chan).

africanus.gridding.wgridder.dask.residual(uvw, freq, image, vis, freq_bin_idx, freq_bin_counts, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True, double_accum=False)[source]¶

Compute residual image given a model and visibilities using ducc degridder i.e.

\[I^R = R^\dagger \Sigma^{-1}(V - Rx)\]

where $R$ is an implicit degridding operator, $V$ denotes visibilities of shape (row, chan) and $x$ is the image of shape (band, nx, ny).

The number of imaging bands (band) must be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

Note that, if the gridding and degridding operators both apply the square root of the imaging weights then the visibilities that are passed in should be pre-whitened. In this case the function computes

\[I^R = R^\dagger \Sigma^{-\frac{1}{2}}(\tilde{V} - \Sigma^{-\frac{1}{2}}Rx)\]

which is identical to the above expression if $\tilde{V} = \Sigma^{-\frac{1}{2}}V$.

Parameters

uvwdask.array.Array: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqdask.array.Array: Observational frequencies of shape (chan,).
modeldask.array.Array: Model image to degrid of shape (band, nx, ny).
visdask.array.Array: Visibilities of shape (row,chan).
weightsdask.array.Array: Imaging weights of shape (row, chan).
freq_bin_idxdask.array.Array: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsdask.array.Array: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
flag:class:dask.array.Array, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
nuint, optional: The number of pixels in the padded grid along the $x$ direction. Chosen automatically by default.
nvint, optional: The number of pixels in the padded grid along the $y$ direction. Chosen automatically by default.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True
double_accumbool, optional: If true ducc will accumulate in double precision regardless of the input type.

Returns

residualdask.array.Array: Residual image corresponding to model of shape (band, nx, ny).

africanus.gridding.wgridder.dask.hessian(uvw, freq, image, freq_bin_idx, freq_bin_counts, cell, weights=None, flag=None, celly=None, epsilon=1e-05, nthreads=1, do_wstacking=True, double_accum=False)[source]¶

Compute action of Hessian on an image using ducc

\[R^\dagger \Sigma^{-1} R x\]

where $R$ is an implicit degridding operator and $x$ is the image of shape (band, nx, ny).

The number of imaging bands (band) must be less than or equal to the number of channels (chan) at which the data were obtained. The mapping from (chan) to (band) is described by freq_bin_idx and freq_bin_counts as described below.

Parameters

uvwdask.array.Array: uvw coordinates at which visibilities were obtained with shape (row, 3).
freqdask.array.Array: Observational frequencies of shape (chan,).
modeldask.array.Array: Model image to degrid of shape (band, nx, ny).
weightsdask.array.Array: Imaging weights of shape (row, chan).
freq_bin_idxdask.array.Array: Starting indices of frequency bins for each imaging band of shape (band,).
freq_bin_countsdask.array.Array: The number of channels in each imaging band of shape (band,).
cellfloat: The cell size of a pixel along the $x$ direction in radians.
flag:class:dask.array.Array, optional: Flags of shape (row,chan). Will only process visibilities for which flag!=0
cellyfloat, optional: The cell size of a pixel along the $y$ direction in radians. By default same as cell size along $x$ direction.
nuint, optional: The number of pixels in the padded grid along the $x$ direction. Chosen automatically by default.
nvint, optional: The number of pixels in the padded grid along the $y$ direction. Chosen automatically by default.
epsilonfloat, optional: The precision of the gridder with respect to the direct Fourier transform. By deafult, this is set to 1e-5 for single precision and 1e-7 for double precision.
nthreadsint, optional: The number of threads to use. Defaults to one.
do_wstackingbool, optional: Whether to correct for the w-term or not. Defaults to True
double_accumbool, optional: If true ducc will accumulate in double precision regardless of the input type.

Returns

residualdask.array.Array: Residual image corresponding to model of shape (band, nx, ny).

Utilities¶

estimate_cell_size(u, v, wavelength[, ...])

Estimate the cell size in arcseconds given baseline u and v coordinates, as well as the wavelengths, $\lambda$.

africanus.gridding.util.estimate_cell_size(u, v, wavelength, factor=3.0, ny=None, nx=None)[source]¶

Estimate the cell size in arcseconds given baseline u and v coordinates, as well as the wavelengths, $\lambda$.

The cell size is computed as:

\[ \begin{align}\begin{aligned}\Delta u = 1.0 / \left( 2 \times \text{ factor } \times \max (\vert u \vert) / \min( \lambda) \right)\\\Delta v = 1.0 / \left( 2 \times \text{ factor } \times \max (\vert v \vert) / \min( \lambda) \right)\end{aligned}\end{align} \]

If ny and nx are provided the following checks are performed and exceptions are raised on failure:

\[ \begin{align}\begin{aligned}\Delta u * \text{ ny } \leq \min (\lambda) / \min (\vert u \vert)\\\Delta v * \text{ nx } \leq \min (\lambda) / \min (\vert v \vert)\end{aligned}\end{align} \]

Parameters

unumpy.ndarray or float: Maximum u coordinate in metres.
vnumpy.ndarray or float: Maximum v coordinate in metres.
wavelengthnumpy.ndarray or float: Wavelengths, in metres.
factorfloat, optional: Scaling factor
nyint, optional: Grid y dimension
nxint, optional: Grid x dimension

Returns

numpy.ndarray: Cell size of u and v in arcseconds with shape (2,)

Raises

ValueError: If the cell size criteria are not matched.

Deconvolution Algorithms¶

africanus.deconv.hogbom.hogbom_clean(dirty, psf, gamma=0.1, threshold='default', niter='default')[source]¶

Performs Hogbom Clean on the dirty image given the psf.

Parameters

dirtynp.ndarray: float64 dirty image of shape (ny, nx)
psfnp.ndarray: float64 Point Spread Function of shape (2*ny, 2*nx)
gamma (optional) float: the gain factor (must be less than one)
threshold (optional)float or str: the threshold to clean to
niter (optionalinteger: the maximum number of iterations allowed

Returns

np.ndarray: float64 clean image of shape (ny, nx)
np.ndarray: float64 residual image of shape (ny, nx)

Coordinate Transforms¶

Numpy¶

`radec_to_lm`(radec[, phase_centre])	Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.
`radec_to_lmn`(radec[, phase_centre])	Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.
`lm_to_radec`(lm[, phase_centre])	Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.
`lmn_to_radec`(lmn[, phase_centre])	Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.

africanus.coordinates.radec_to_lm(radec, phase_centre=None)[source]¶

Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.

\begin{eqnarray} & l =& \, \cos \, \delta \sin \, \Delta \alpha \\ & m =& \, \sin \, \delta \cos \, \delta 0 - \cos \delta \sin \delta 0 \cos \Delta \alpha \\ & n =& \, \sqrt{1 - l^2 - m^2} - 1 \end{eqnarray}

where $\Delta \alpha = \alpha - \alpha 0$ is the difference between the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

radecnumpy.ndarray: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.
phase_centrenumpy.ndarray, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

numpy.ndarray: lm Direction Cosines of shape (coord, 2)

africanus.coordinates.radec_to_lmn(radec, phase_centre=None)[source]¶

Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.

\begin{eqnarray} & l =& \, \cos \, \delta \sin \, \Delta \alpha \\ & m =& \, \sin \, \delta \cos \, \delta 0 - \cos \delta \sin \delta 0 \cos \Delta \alpha \\ & n =& \, \sqrt{1 - l^2 - m^2} - 1 \end{eqnarray}

where $\Delta \alpha = \alpha - \alpha 0$ is the difference between the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

radecnumpy.ndarray: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.
phase_centrenumpy.ndarray, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

numpy.ndarray: lm Direction Cosines of shape (coord, 3)

africanus.coordinates.lm_to_radec(lm, phase_centre=None)[source]¶

Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.

\begin{eqnarray} & \delta = & \, \arcsin \left( m \cos \delta 0 + n \sin \delta 0 \right) \\ & \alpha = & \, \arctan \left( \frac{l}{n \cos \delta 0 - m \sin \delta 0} \right) \\ \end{eqnarray}

where $\alpha$ is the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

lmnumpy.ndarray: lm Direction Cosines of shape (coord, 2)
phase_centrenumpy.ndarray, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

numpy.ndarray: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.

africanus.coordinates.lmn_to_radec(lmn, phase_centre=None)[source]¶

Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.

\begin{eqnarray} & \delta = & \, \arcsin \left( m \cos \delta 0 + n \sin \delta 0 \right) \\ & \alpha = & \, \arctan \left( \frac{l}{n \cos \delta 0 - m \sin \delta 0} \right) \\ \end{eqnarray}

where $\alpha$ is the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

lmnnumpy.ndarray: lm Direction Cosines of shape (coord, 3)
phase_centrenumpy.ndarray, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

numpy.ndarray: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.

Dask¶

`radec_to_lm`(radec[, phase_centre])	Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.
`radec_to_lmn`(radec[, phase_centre])	Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.
`lm_to_radec`(lm[, phase_centre])	Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.
`lmn_to_radec`(lmn[, phase_centre])	Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.

africanus.coordinates.dask.radec_to_lm(radec, phase_centre=None)[source]¶

Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.

\begin{eqnarray} & l =& \, \cos \, \delta \sin \, \Delta \alpha \\ & m =& \, \sin \, \delta \cos \, \delta 0 - \cos \delta \sin \delta 0 \cos \Delta \alpha \\ & n =& \, \sqrt{1 - l^2 - m^2} - 1 \end{eqnarray}

where $\Delta \alpha = \alpha - \alpha 0$ is the difference between the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

radecdask.array.Array: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.
phase_centredask.array.Array, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

dask.array.Array: lm Direction Cosines of shape (coord, 2)

africanus.coordinates.dask.radec_to_lmn(radec, phase_centre=None)[source]¶

Converts Right-Ascension/Declination coordinates in radians to a Direction Cosine lm coordinates, relative to the Phase Centre.

\begin{eqnarray} & l =& \, \cos \, \delta \sin \, \Delta \alpha \\ & m =& \, \sin \, \delta \cos \, \delta 0 - \cos \delta \sin \delta 0 \cos \Delta \alpha \\ & n =& \, \sqrt{1 - l^2 - m^2} - 1 \end{eqnarray}

where $\Delta \alpha = \alpha - \alpha 0$ is the difference between the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

radecdask.array.Array: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.
phase_centredask.array.Array, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

dask.array.Array: lm Direction Cosines of shape (coord, 3)

africanus.coordinates.dask.lm_to_radec(lm, phase_centre=None)[source]¶

Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.

\begin{eqnarray} & \delta = & \, \arcsin \left( m \cos \delta 0 + n \sin \delta 0 \right) \\ & \alpha = & \, \arctan \left( \frac{l}{n \cos \delta 0 - m \sin \delta 0} \right) \\ \end{eqnarray}

where $\alpha$ is the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

lmdask.array.Array: lm Direction Cosines of shape (coord, 2)
phase_centredask.array.Array, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

dask.array.Array: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.

africanus.coordinates.dask.lmn_to_radec(lmn, phase_centre=None)[source]¶

Convert Direction Cosine lm coordinates to Right Ascension/Declination coordinates in radians, relative to the Phase Centre.

\begin{eqnarray} & \delta = & \, \arcsin \left( m \cos \delta 0 + n \sin \delta 0 \right) \\ & \alpha = & \, \arctan \left( \frac{l}{n \cos \delta 0 - m \sin \delta 0} \right) \\ \end{eqnarray}

where $\alpha$ is the Right Ascension of each coordinate and the phase centre and $\delta 0$ is the Declination of the phase centre.

Parameters

lmndask.array.Array: lm Direction Cosines of shape (coord, 3)
phase_centredask.array.Array, optional: radec coordinates of the Phase Centre. Shape (2,)

Returns

dask.array.Array: radec coordinates of shape (coord, 2) where Right-Ascension and Declination are in the last 2 components, respectively.

Sky Model¶

Functionality related to the Sky Model.

Coherency Conversion¶

Utilities for converting back and forth between stokes parameters and correlations

Numpy¶

convert(input, input_schema, output_schema)

This function converts forward and backward from stokes I,Q,U,V to both linear XX,XY,YX,YY and circular RR, RL, LR, LL correlations.

africanus.model.coherency.convert(input, input_schema, output_schema)[source]¶

This function converts forward and backward from stokes I,Q,U,V to both linear XX,XY,YX,YY and circular RR, RL, LR, LL correlations.

For example, we can convert from stokes parameters to linear correlations:

stokes.shape == (10, 4, 4)
corrs = convert(stokes, ["I", "Q", "U", "V"],
                [['XX', 'XY'], ['YX', 'YY'])

assert corrs.shape == (10, 4, 2, 2)

Or circular correlations to stokes:

vis.shape == (10, 4, 2, 2)

stokes = convert(vis, [['RR', 'RL'], ['LR', 'LL']],
                        ['I', 'Q', 'U', 'V'])

assert stokes.shape == (10, 4, 4)

input can output can be arbitrarily nested or ordered lists, but the appropriate inputs must be present to produce the requested outputs.

The elements of input and output may be strings or integers representing stokes parameters or correlations. See the Notes for a full list.

Parameters

inputnumpy.ndarray: Complex or floating point input data of shape (dim_1, ..., dim_n, icorr_1, ..., icorr_m)
input_schemalist of str or int: A schema describing the icorr_1, ..., icorr_m dimension of input. Must have the same shape as the last dimensions of input.
output_schemalist of str or int: A schema describing the ocorr_1, ..., ocorr_n dimension of the return value.

Returns

resultnumpy.ndarray: Result of shape (dim_1, ..., dim_n, ocorr_1, ..., ocorr_m) The type may be floating point or promoted to complex depending on the combinations in output.

Notes

Only stokes parameters, linear and circular correlations are currently handled, but the full list of id’s and strings as defined in the CASA documentation is:

{{ Undefined: 0, I: 1, Q: 2, U: 3, V: 4, RR: 5, RL: 6, LR: 7, LL: 8,
    XX: 9, XY: 10, YX: 11, YY: 12, RX: 13, RY: 14, LX: 15, LY: 16,
    XR: 17, XL: 18, YR: 19, YL: 20, PP: 21, PQ: 22, QP: 23, QQ:
    24, RCircular: 25, LCircular: 26, Linear: 27, Ptotal: 28,
    Plinear: 29, PFtotal: 30, PFlinear: 31, Pangle: 32 }}

Cuda¶

convert(inputs, input_schema, output_schema)

This function converts forward and backward from stokes I,Q,U,V to both linear XX,XY,YX,YY and circular RR, RL, LR, LL correlations.

africanus.model.coherency.cuda.convert(inputs, input_schema, output_schema)[source]¶

This function converts forward and backward from stokes I,Q,U,V to both linear XX,XY,YX,YY and circular RR, RL, LR, LL correlations.

For example, we can convert from stokes parameters to linear correlations:

stokes.shape == (10, 4, 4)
corrs = convert(stokes, ["I", "Q", "U", "V"],
                [['XX', 'XY'], ['YX', 'YY'])

assert corrs.shape == (10, 4, 2, 2)

Or circular correlations to stokes:

vis.shape == (10, 4, 2, 2)

stokes = convert(vis, [['RR', 'RL'], ['LR', 'LL']],
                        ['I', 'Q', 'U', 'V'])

assert stokes.shape == (10, 4, 4)

input can output can be arbitrarily nested or ordered lists, but the appropriate inputs must be present to produce the requested outputs.

The elements of input and output may be strings or integers representing stokes parameters or correlations. See the Notes for a full list.

Parameters

inputcupy.ndarray: Complex or floating point input data of shape (dim_1, ..., dim_n, icorr_1, ..., icorr_m)
input_schemalist of str or int: A schema describing the icorr_1, ..., icorr_m dimension of input. Must have the same shape as the last dimensions of input.
output_schemalist of str or int: A schema describing the ocorr_1, ..., ocorr_n dimension of the return value.

Returns

resultcupy.ndarray: Result of shape (dim_1, ..., dim_n, ocorr_1, ..., ocorr_m) The type may be floating point or promoted to complex depending on the combinations in output.

Notes

Only stokes parameters, linear and circular correlations are currently handled, but the full list of id’s and strings as defined in the CASA documentation is:

{{ Undefined: 0, I: 1, Q: 2, U: 3, V: 4, RR: 5, RL: 6, LR: 7, LL: 8,
    XX: 9, XY: 10, YX: 11, YY: 12, RX: 13, RY: 14, LX: 15, LY: 16,
    XR: 17, XL: 18, YR: 19, YL: 20, PP: 21, PQ: 22, QP: 23, QQ:
    24, RCircular: 25, LCircular: 26, Linear: 27, Ptotal: 28,
    Plinear: 29, PFtotal: 30, PFlinear: 31, Pangle: 32 }}

Dask¶

convert(input, input_schema, output_schema)

This function converts forward and backward from stokes I,Q,U,V to both linear XX,XY,YX,YY and circular RR, RL, LR, LL correlations.

africanus.model.coherency.dask.convert(input, input_schema, output_schema)[source]¶

This function converts forward and backward from stokes I,Q,U,V to both linear XX,XY,YX,YY and circular RR, RL, LR, LL correlations.

For example, we can convert from stokes parameters to linear correlations:

stokes.shape == (10, 4, 4)
corrs = convert(stokes, ["I", "Q", "U", "V"],
                [['XX', 'XY'], ['YX', 'YY'])

assert corrs.shape == (10, 4, 2, 2)

Or circular correlations to stokes:

vis.shape == (10, 4, 2, 2)

stokes = convert(vis, [['RR', 'RL'], ['LR', 'LL']],
                        ['I', 'Q', 'U', 'V'])

assert stokes.shape == (10, 4, 4)

input can output can be arbitrarily nested or ordered lists, but the appropriate inputs must be present to produce the requested outputs.

The elements of input and output may be strings or integers representing stokes parameters or correlations. See the Notes for a full list.

Parameters

inputdask.array.Array: Complex or floating point input data of shape (dim_1, ..., dim_n, icorr_1, ..., icorr_m)
input_schemalist of str or int: A schema describing the icorr_1, ..., icorr_m dimension of input. Must have the same shape as the last dimensions of input.
output_schemalist of str or int: A schema describing the ocorr_1, ..., ocorr_n dimension of the return value.

Returns

resultdask.array.Array: Result of shape (dim_1, ..., dim_n, ocorr_1, ..., ocorr_m) The type may be floating point or promoted to complex depending on the combinations in output.

Notes

Only stokes parameters, linear and circular correlations are currently handled, but the full list of id’s and strings as defined in the CASA documentation is:

{{ Undefined: 0, I: 1, Q: 2, U: 3, V: 4, RR: 5, RL: 6, LR: 7, LL: 8,
    XX: 9, XY: 10, YX: 11, YY: 12, RX: 13, RY: 14, LX: 15, LY: 16,
    XR: 17, XL: 18, YR: 19, YL: 20, PP: 21, PQ: 22, QP: 23, QQ:
    24, RCircular: 25, LCircular: 26, Linear: 27, Ptotal: 28,
    Plinear: 29, PFtotal: 30, PFlinear: 31, Pangle: 32 }}

Spectral Model¶

Functionality for computing a Spectral Model.

Numpy¶

spectral_model(stokes, spi, ref_freq, frequency)

Compute a spectral model, per polarisation.

africanus.model.spectral.spectral_model(stokes, spi, ref_freq, frequency, base=0)[source]¶

Compute a spectral model, per polarisation.

\begin{eqnarray} I(\lambda) & = & I_0 \prod_{i=1} (\lambda / \lambda_0)^{\alpha_{i}} \\ \ln( I(\lambda) ) & = & \sum_{i=0} \alpha_{i} \ln (\lambda / \lambda_0)^i \, \textrm{where} \, \alpha_0 = \ln I_0 \\ \log_{10}( I(\lambda) ) & = & \sum_{i=0} \alpha_{i} \log_{10} (\lambda / \lambda_0)^i \, \textrm{where} \, \alpha_0 = \log_{10} I_0 \\ \end{eqnarray}

Parameters

stokesnumpy.ndarray

Stokes parameters of shape (source,) or (source, pol). If a pol dimension is present, then it must also be present on spi.

spinumpy.ndarray

Spectral index of shape (source, spi-comps) or (source, spi-comps, pol).

ref_freqnumpy.ndarray

Reference frequencies of shape (source,)

frequenciesnumpy.ndarray

Frequencies of shape (chan,)

base{“std”, “log”, “log10”} or {0, 1, 2} or list.

string or corresponding enumeration specifying the polynomial base. Defaults to 0.

If a list is provided, a polynomial base can be specified for each stokes parameter or polarisation in the pol dimension.

string specification of the base is only supported in python 3. while the corresponding integer enumerations are supported on all python versions.

Returns

spectral_modelnumpy.ndarray: Spectral Model of shape (source, chan) or (source, chan, pol).

Dask¶

spectral_model(stokes, spi, ref_freq, ...[, ...])

Compute a spectral model, per polarisation.

africanus.model.spectral.dask.spectral_model(stokes, spi, ref_freq, frequencies, base=0)[source]¶

Compute a spectral model, per polarisation.

\begin{eqnarray} I(\lambda) & = & I_0 \prod_{i=1} (\lambda / \lambda_0)^{\alpha_{i}} \\ \ln( I(\lambda) ) & = & \sum_{i=0} \alpha_{i} \ln (\lambda / \lambda_0)^i \, \textrm{where} \, \alpha_0 = \ln I_0 \\ \log_{10}( I(\lambda) ) & = & \sum_{i=0} \alpha_{i} \log_{10} (\lambda / \lambda_0)^i \, \textrm{where} \, \alpha_0 = \log_{10} I_0 \\ \end{eqnarray}

Parameters

stokesdask.array.Array

Stokes parameters of shape (source,) or (source, pol). If a pol dimension is present, then it must also be present on spi.

spidask.array.Array

Spectral index of shape (source, spi-comps) or (source, spi-comps, pol).

ref_freqdask.array.Array

Reference frequencies of shape (source,)

frequenciesdask.array.Array

Frequencies of shape (chan,)

base{“std”, “log”, “log10”} or {0, 1, 2} or list.

string or corresponding enumeration specifying the polynomial base. Defaults to 0.

If a list is provided, a polynomial base can be specified for each stokes parameter or polarisation in the pol dimension.

string specification of the base is only supported in python 3. while the corresponding integer enumerations are supported on all python versions.

Returns

spectral_modeldask.array.Array: Spectral Model of shape (source, chan) or (source, chan, pol).

Spectral Index¶

Functionality related to the spectral index.

For example, we may want to compute the spectral indices of components in a sky model defined by

\[I(\nu) = I(\nu_0) \left(\frac{\nu}{\nu_0}\right)^\alpha\]

where $\nu$ are frequencies ay which we want to construct the intensity of a Stokes I image and the $\nu_0$ is the corresponding reference frequency. The spectral index $\alpha$ determines how quickly the intensity grows or decays as a function of frequency. Given a list of model image components (preferably with the residuals added back in) we can recover the corresponding spectral indices and reference intensities using the fit_spi_components() function. This will also return a lower bound on the associated uncertainties on these components.

Numpy¶

fit_spi_components(data, weights, freqs, freq0)

Computes the spectral indices and the intensity at the reference frequency of a spectral index model:

africanus.model.spi.fit_spi_components(data, weights, freqs, freq0, alphai=None, I0i=None, beam=None, tol=0.0001, maxiter=100)[source]¶

Computes the spectral indices and the intensity at the reference frequency of a spectral index model:

\[I(\nu) = A(\nu) I(\nu_0) \left( \frac{\nu}{\nu_0} \right) ^ \alpha\]

where $I(\nu)$ is the apparent source spectrum, $A(\nu)$ is the beam model for each component as a function of frequency.

Parameters

datanumpy.ndarray: array of shape (comps, chan) The noisy data as a function of frequency.
weightsnumpy.ndarray: array of shape (chan,) Inverse of variance on each frequency axis.
freqsnumpy.ndarray: frequencies of shape (chan,)
freq0float: Reference frequency
alphainumpy.ndarray, optional: array of shape (comps,) Initial guess for the alphas. Defaults to -0.7.
I0inumpy.ndarray, optional: array of shape (comps,) Initial guess for the intensities at the reference frequency. Defaults to 1.0.
beam_compsnumpy.ndarray, optional: array of shape (comps, chan) Power beam for each component as a function of frequency.
tolfloat, optional: Solver absolute tolerance (optional). Defaults to 1e-6.
maxiterint, optional: Solver maximum iterations (optional). Defaults to 100.
dtypenp.dtype, optional: Datatype of result. Should be either np.float32 or np.float64. Defaults to np.float64.

Returns

outnumpy.ndarray: array of shape (4, comps) The fitted components arranged as [alphas, alphavars, I0s, I0vars]

Dask¶

fit_spi_components(data, weights, freqs, freq0)

Computes the spectral indices and the intensity at the reference frequency of a spectral index model:

africanus.model.spi.dask.fit_spi_components(data, weights, freqs, freq0, alphai=None, I0i=None, beam=None, tol=1e-05, maxiter=100)[source]¶

Computes the spectral indices and the intensity at the reference frequency of a spectral index model:

\[I(\nu) = A(\nu) I(\nu_0) \left( \frac{\nu}{\nu_0} \right) ^ \alpha\]

where $I(\nu)$ is the apparent source spectrum, $A(\nu)$ is the beam model for each component as a function of frequency.

Parameters

datadask.array.Array: array of shape (comps, chan) The noisy data as a function of frequency.
weightsdask.array.Array: array of shape (chan,) Inverse of variance on each frequency axis.
freqsdask.array.Array: frequencies of shape (chan,)
freq0float: Reference frequency
alphaidask.array.Array, optional: array of shape (comps,) Initial guess for the alphas. Defaults to -0.7.
I0idask.array.Array, optional: array of shape (comps,) Initial guess for the intensities at the reference frequency. Defaults to 1.0.
beam_compsdask.array.Array, optional: array of shape (comps, chan) Power beam for each component as a function of frequency.
tolfloat, optional: Solver absolute tolerance (optional). Defaults to 1e-6.
maxiterint, optional: Solver maximum iterations (optional). Defaults to 100.
dtypenp.dtype, optional: Datatype of result. Should be either np.float32 or np.float64. Defaults to np.float64.

Returns

outdask.array.Array: array of shape (4, comps) The fitted components arranged as [alphas, alphavars, I0s, I0vars]

Source Morphology¶

Shape functions for different Source Morphologies

Numpy¶

gaussian(uvw, frequency, shape_params)

Computes the Gaussian Shape Function.

africanus.model.shape.gaussian(uvw, frequency, shape_params)[source]¶

Computes the Gaussian Shape Function.

\[\begin{split}& \lambda^\prime = 2 \lambda \pi \\ & r = \frac{e_{min}}{e_{maj}} \\ & u_{1} = (u \, e_{maj} \, cos(\alpha) - v \, e_{maj} \, sin(\alpha)) r \lambda^\prime \\ & v_{1} = (u \, e_{maj} \, sin(\alpha) - v \, e_{maj} \, cos(\alpha)) \lambda^\prime \\ & \textrm{shape} = e^{(-u_{1}^2 - v_{1}^2)}\end{split}\]

where:

$u$ and $v$ are the UV coordinates and $\lambda$ the frequency.
$e_{maj}$ and $e_{min}$ are the major and minor axes and $\alpha$ the position angle.

Parameters

uvwnumpy.ndarray: UVW coordinates of shape (row, 3)
frequencynumpy.ndarray: frequencies of shape (chan,)
shape_paramnumpy.ndarray: Gaussian Shape Parameters of shape (source, 3) where the second dimension contains the (emajor, eminor, angle) parameters describing the shape of the Gaussian

Returns

gauss_shapenumpy.ndarray: Shape parameters of shape (source, row, chan)

Dask¶

gaussian(uvw, frequency, shape_params)

Computes the Gaussian Shape Function.

africanus.model.shape.dask.gaussian(uvw, frequency, shape_params)[source]¶

Computes the Gaussian Shape Function.

\[\begin{split}& \lambda^\prime = 2 \lambda \pi \\ & r = \frac{e_{min}}{e_{maj}} \\ & u_{1} = (u \, e_{maj} \, cos(\alpha) - v \, e_{maj} \, sin(\alpha)) r \lambda^\prime \\ & v_{1} = (u \, e_{maj} \, sin(\alpha) - v \, e_{maj} \, cos(\alpha)) \lambda^\prime \\ & \textrm{shape} = e^{(-u_{1}^2 - v_{1}^2)}\end{split}\]

where:

$u$ and $v$ are the UV coordinates and $\lambda$ the frequency.
$e_{maj}$ and $e_{min}$ are the major and minor axes and $\alpha$ the position angle.

Parameters

uvwdask.array.Array: UVW coordinates of shape (row, 3)
frequencydask.array.Array: frequencies of shape (chan,)
shape_paramdask.array.Array: Gaussian Shape Parameters of shape (source, 3) where the second dimension contains the (emajor, eminor, angle) parameters describing the shape of the Gaussian

Returns

gauss_shapedask.array.Array: Shape parameters of shape (source, row, chan)

WSClean Spectral Model¶

Utilities for creating a spectral model from a wsclean component file.

Numpy¶

`load`(filename)	Loads wsclean component model.
`spectra`(I, coeffs, log_poly, ref_freq, frequency)	Produces a spectral model from a polynomial expansion of a wsclean file model.

africanus.model.wsclean.load(filename)[source]¶

Loads wsclean component model.

sources = load("components.txt")
sources = dict(sources)  # Convert to dictionary

I = sources["I"]
ref_freq = sources["ReferenceFrequency"]

See the WSClean Component List for further details.

Parameters

filenamestr or iterable: Filename of wsclean model file or iterable producing the lines of the file.

Returns

list of (name, list of values) tuples: list of column (name, value) tuples

Dask¶

spectra(stokes, spi, log_si, ref_freq, frequency)

Produces a spectral model from a polynomial expansion of a wsclean file model.

africanus.model.wsclean.dask.spectra(stokes, spi, log_si, ref_freq, frequency)[source]¶

Produces a spectral model from a polynomial expansion of a wsclean file model. Depending on how log_poly is set ordinary or logarithmic polynomials are used to produce the expansion:

\[\begin{split}& flux(\lambda) = I_{0} + \sum\limits_{c=0} \textrm{coeffs}(c) ({\lambda/\lambda_{ref}} - 1)^{c+1} \\ & flux(\lambda) = \exp \left( \log I_{0} + \sum\limits_{c=0} \textrm{coeffs}(c) \log({\lambda/\lambda_{ref}})^{c+1} \right) \\\end{split}\]

See the WSClean Component List for further details.

Parameters

Idask.array.Array: flux density in Janskys at the reference frequency of shape (source,)
coeffsdask.array.Array: Polynomial coefficients for each source of shape (source, comp)
log_polydask.array.Array or bool: boolean array of shape (source, ) indicating whether logarithmic (True) or ordinary (False) polynomials should be used.
ref_freqdask.array.Array: Source reference frequencies of shape (source,)
frequencydask.array.Array: frequencies of shape (chan,)

Returns

spectral_modeldask.array.Array: Spectral Model of shape (source, chan)

Averaging¶

Routines for averaging visibility data.

Time and Channel Averaging¶

The routines in this section average row-based samples by:

Averaging samples of consecutive time values into bins defined by an period of time_bin_secs seconds.
Averaging channel data into equally sized bins of chan_bin_size.

In order to achieve this, a baseline x time ordering is established over the input data where baseline corresponds to the unique (ANTENNA1, ANTENNA2) pairs and time corresponds to the unique, monotonically increasing TIME values associated with the rows of a Measurement Set.

Baseline	T0	T1	T2	T3	T4
(0, 0)	0.1	0.2	0.3	0.4	0.5
(0, 1)	0.1	0.2	0.3	0.4	0.5
(0, 2)	0.1	0.2	X	0.4	0.5
(1, 1)	0.1	0.2	0.3	0.4	0.5
(1, 2)	0.1	0.2	0.3	0.4	0.5
(2, 2)	0.1	0.2	0.3	0.4	0.5

It is possible for times or baselines to be missing. In the above example, T2 is missing for baseline (0, 2).

Warning

The above requires unique lexicographical combinations of (TIME, ANTENNA1, ANTENNA2). This can usually be achieved by suitably partitioning input data on indexing rows, DATA_DESC_ID and SCAN_NUMBER in particular.

For each baseline, adjacent time’s are assigned to a bin if $h_c - h_e/2 - (l_c - l_e/2) <$ time_bin_secs, where $h_c$ and $l_c$ are the upper and lower time and $h_e$ and $l_e$ are the upper and lower intervals, taken from the INTERVAL column. Note that no distinction is made between flagged and unflagged data when establishing the endpoints in the bin.

The reason for this is that the Measurement Set v2.0 Specification specifies that TIME and INTERVAL columns are defined as containing the nominal time and period at which the visibility was sampled. This means that their values includie valid, flagged and missing data. Thus, averaging a regular high-resolution baseline x htime grid should produce a regular low-resolution baseline x ltime grid (htime > ltime) in the presence of bad data

By contrast, other columns such as TIME_CENTROID and EXPOSURE contain the effective time and period as they exclude missing and bad data. Their increased accuracy, and therefore variability means that they are unsuitable for establishing a grid over the data.

To summarise, the averaged times in each bin establish a map:

from possibly unordered input rows.
to a reduced set of output rows ordered by averaged (TIME, ANTENNA1, ANTENNA2).

Flagged Data Handling¶

Both FLAG_ROW and FLAG columns may be supplied to the averager, but they should be consistent with each other. The averager will throw an exception if this is not the case, rather than making an assumption as to which is correct.

When provided with flags, the averager will output averages for bins that are completely flagged.

Part of the reason for this is that the specifies that the TIME and INTERVAL columns represent the nominal time and interval values. This means that they should represent valid as well as flagged or missing data in their computation.

By contrast, most other columns such as TIME_CENTROID and EXPOSURE, contain the effective values and should only include valid, unflagged data.

To support this:

TIME and INTERVAL are averaged using both flagged and unflagged samples.
Other columns, such as TIME_CENTROID are handled as follows:
1. If the bin contains some unflagged data, only this data is used to calculate average.
2. If the bin is completely flagged, the average of all samples (which are all flagged) will be used.
In both cases, a completely flagged bin will have it’s flag set.
To support the two cases, twice the memory of the output array is required to track both averages, but only one array of merged values is returned.

Guarantees¶

Averaged output data will be lexicographically ordered by (TIME, ANTENNA1, ANTENNA2)
TIME and INTERVAL columns always contain the nominal average and sum and therefore contain both and missing or unflagged data.
Other columns will contain the effective average and will contain only valid data except when all data in the bin is flagged.
Completely flagged bins will be set as flagged in both the nominal and effective case.
Certain columns are averaged, while others are summed, or simply assigned to the last value in the bin in the case of antenna indices.
Visibility data is averaged by multiplying and dividing by WEIGHT_SPECTRUM or WEIGHT or natural weighting, in order of priority.

\[\frac{\sum v_i w_i}{\sum w_i}\]

SIGMA_SPECTRUM is averaged by multiplying and dividing by WEIGHT_SPECTRUM or WEIGHT or natural weighting, in order of priority and availability.

SIGMA is only averaged with WEIGHT or natural weighting.

\[\sqrt{\frac{\sum w_i^2 \sigma_i^2}{(\sum w_i)^2}}\]

The following table summarizes the handling of each column in the main Measurement Set table:

Column	Unflagged/Flagged sample handling	Aggregation Method	Required
TIME	Nominal	Mean	Yes
INTERVAL	Nominal	Sum	Yes
ANTENNA1	Nominal	Assigned to Last Input	Yes
ANTENNA2	Nominal	Assigned to Last Input	Yes
TIME_CENTROID	Effective	Mean	No
EXPOSURE	Effective	Sum	No
FLAG_ROW	Effective	Set if All Inputs Flagged	No
UVW	Effective	Mean	No
WEIGHT	Effective	Sum	No
SIGMA	Effective	Weighted Mean	No
DATA (vis)	Effective	Weighted Mean	No
FLAG	Effective	Set if All Inputs Flagged	No
WEIGHT_SPECTRUM	Effective	Sum	No
SIGMA_SPECTRUM	Effective	Weighted Mean	No

The following SPECTRAL_WINDOW sub-table columns are averaged as follows:

Column	Aggregation Method
CHAN_FREQ	Mean
CHAN_WIDTH	Sum
EFFECTIVE_BW	Sum
RESOLUTION	Sum

Dask Implementation¶

The dask implementation chunks data up by row and channel and averages each chunk independently of values in other chunks. This should be kept in mind if one wishes to maintain a particular ordering in the output dask arrays.

Typically, Measurement Set data is monotonically ordered in time. To maintain this guarantee in output dask arrays, the chunks will need to be separated by distinct time values. Practically speaking this means that the first and second chunk should not both contain value time 0.1, for example.

Numpy¶

`time_and_channel`(time, interval, antenna1, ...)	Averages in time and channel.
`bda`(time, interval, antenna1, antenna2[, ...])	Averages in time and channel, dependent on baseline length.

africanus.averaging.time_and_channel(time, interval, antenna1, antenna2, time_centroid=None, exposure=None, flag_row=None, uvw=None, weight=None, sigma=None, chan_freq=None, chan_width=None, effective_bw=None, resolution=None, visibilities=None, flag=None, weight_spectrum=None, sigma_spectrum=None, time_bin_secs=1.0, chan_bin_size=1)[source]¶

Averages in time and channel.

Parameters

timenumpy.ndarray: Time values of shape (row,).
intervalnumpy.ndarray: Interval values of shape (row,).
antenna1numpy.ndarray: First antenna indices of shape (row,)
antenna2numpy.ndarray: Second antenna indices of shape (row,)
time_centroidnumpy.ndarray, optional: Time centroid values of shape (row,)
exposurenumpy.ndarray, optional: Exposure values of shape (row,)
flag_rownumpy.ndarray, optional: Flagged rows of shape (row,).
uvwnumpy.ndarray, optional: UVW coordinates of shape (row, 3).
weightnumpy.ndarray, optional: Weight values of shape (row, corr).
sigmanumpy.ndarray, optional: Sigma values of shape (row, corr).
chan_freqnumpy.ndarray, optional: Channel frequencies of shape (chan,).
chan_widthnumpy.ndarray, optional: Channel widths of shape (chan,).
effective_bwnumpy.ndarray, optional: Effective channel bandwidth of shape (chan,).
resolutionnumpy.ndarray, optional: Effective channel resolution of shape (chan,).
visibilitiesnumpy.ndarray or tuple of numpy.ndarray, optional: Visibility data of shape (row, chan, corr). Tuples of visibilities arrays may be supplied, in which case tuples will be output.
flagnumpy.ndarray, optional: Flag data of shape (row, chan, corr).
weight_spectrumnumpy.ndarray, optional: Weight spectrum of shape (row, chan, corr).
sigma_spectrumnumpy.ndarray, optional: Sigma spectrum of shape (row, chan, corr).
time_bin_secsfloat, optional: Maximum summed interval in seconds to include within a bin. Defaults to 1.0.
chan_bin_sizeint, optional: Number of bins to average together. Defaults to 1.

Returns

namedtuple: A namedtuple whose entries correspond to the input arrays. Output arrays will be None if the inputs were None.

Notes

The implementation currently requires unique lexicographical combinations of (TIME, ANTENNA1, ANTENNA2). This can usually be achieved by suitably partitioning input data on indexing rows, DATA_DESC_ID and SCAN_NUMBER in particular.

africanus.averaging.bda(time, interval, antenna1, antenna2, time_centroid=None, exposure=None, flag_row=None, uvw=None, weight=None, sigma=None, chan_freq=None, chan_width=None, effective_bw=None, resolution=None, visibilities=None, flag=None, weight_spectrum=None, sigma_spectrum=None, max_uvw_dist=None, max_fov=3.0, decorrelation=0.98, time_bin_secs=None, min_nchan=1)[source]¶

Averages in time and channel, dependent on baseline length.

Parameters

timenumpy.ndarray: Time values of shape (row,).
intervalnumpy.ndarray: Interval values of shape (row,).
antenna1numpy.ndarray: First antenna indices of shape (row,)
antenna2numpy.ndarray: Second antenna indices of shape (row,)
time_centroidnumpy.ndarray, optional: Time centroid values of shape (row,)
exposurenumpy.ndarray, optional: Exposure values of shape (row,)
flag_rownumpy.ndarray, optional: Flagged rows of shape (row,).
uvwnumpy.ndarray, optional: UVW coordinates of shape (row, 3).
weightnumpy.ndarray, optional: Weight values of shape (row, corr).
sigmanumpy.ndarray, optional: Sigma values of shape (row, corr).
chan_freqnumpy.ndarray, optional: Channel frequencies of shape (chan,).
chan_widthnumpy.ndarray, optional: Channel widths of shape (chan,).
effective_bwnumpy.ndarray, optional: Effective channel bandwidth of shape (chan,).
resolutionnumpy.ndarray, optional: Effective channel resolution of shape (chan,).
visibilitiesnumpy.ndarray or tuple of numpy.ndarray, optional: Visibility data of shape (row, chan, corr). Tuples of visibilities arrays may be supplied, in which case tuples will be output.
flagnumpy.ndarray, optional: Flag data of shape (row, chan, corr).
weight_spectrumnumpy.ndarray, optional: Weight spectrum of shape (row, chan, corr).
sigma_spectrumnumpy.ndarray, optional: Sigma spectrum of shape (row, chan, corr).
max_uvw_distfloat, optional: Maximum UVW distance. Will be inferred from the UVW coordinates if not supplied.
max_fovfloat: Maximum Field of View Radius. Defaults to 3 degrees.
decorrelationfloat: Acceptable amount of decorrelation. This is a floating point value between 0.0 and 1.0.
time_bin_secsfloat, optional: Maximum number of seconds worth of data that can be aggregated into a bin. Defaults to None in which case the value is only bounded by the decorrelation factor and the field of view.
min_nchanint, optional: Minimum number of channels in an averaged sample. Useful in cases where imagers expect at least min_nchan channels. Defaults to 1.

Returns

namedtuple: A namedtuple whose entries correspond to the input arrays. Output arrays will be None if the inputs were None. See the Notes for an explanation of the output formats.

Notes

In all cases arrays starting with (row, chan) and (row,) dimensions are respectively averaged and expanded into a (rowchan,) dimension, as the number of channels varies per output row.

The output namedtuple contains an offsets array of shape (out_rows + 1,) encoding the starting offsets of each output row, as well as a single entry at the end such that np.diff(offsets) produces the number of channels for each output row.

avg = bda(...)
time = avg.time[avg.offsets[:-1]]
out_chans = np.diff(avg.offsets)

The implementation currently requires unique lexicographical combinations of (TIME, ANTENNA1, ANTENNA2). This can usually be achieved by suitably partitioning input data on indexing rows, DATA_DESC_ID and SCAN_NUMBER in particular.

Dask¶

`time_and_channel`(time, interval, antenna1, ...)	Averages in time and channel.
`bda`(time, interval, antenna1, antenna2[, ...])	Averages in time and channel, dependent on baseline length.

africanus.averaging.dask.time_and_channel(time, interval, antenna1, antenna2, time_centroid=None, exposure=None, flag_row=None, uvw=None, weight=None, sigma=None, chan_freq=None, chan_width=None, effective_bw=None, resolution=None, visibilities=None, flag=None, weight_spectrum=None, sigma_spectrum=None, time_bin_secs=1.0, chan_bin_size=1)[source]¶

Averages in time and channel.

Parameters

timedask.array.Array: Time values of shape (row,).
intervaldask.array.Array: Interval values of shape (row,).
antenna1dask.array.Array: First antenna indices of shape (row,)
antenna2dask.array.Array: Second antenna indices of shape (row,)
time_centroiddask.array.Array, optional: Time centroid values of shape (row,)
exposuredask.array.Array, optional: Exposure values of shape (row,)
flag_rowdask.array.Array, optional: Flagged rows of shape (row,).
uvwdask.array.Array, optional: UVW coordinates of shape (row, 3).
weightdask.array.Array, optional: Weight values of shape (row, corr).
sigmadask.array.Array, optional: Sigma values of shape (row, corr).
chan_freqdask.array.Array, optional: Channel frequencies of shape (chan,).
chan_widthdask.array.Array, optional: Channel widths of shape (chan,).
effective_bwdask.array.Array, optional: Effective channel bandwidth of shape (chan,).
resolutiondask.array.Array, optional: Effective channel resolution of shape (chan,).
visibilitiesdask.array.Array or tuple of dask.array.Array, optional: Visibility data of shape (row, chan, corr). Tuples of visibilities arrays may be supplied, in which case tuples will be output.
flagdask.array.Array, optional: Flag data of shape (row, chan, corr).
weight_spectrumdask.array.Array, optional: Weight spectrum of shape (row, chan, corr).
sigma_spectrumdask.array.Array, optional: Sigma spectrum of shape (row, chan, corr).
time_bin_secsfloat, optional: Maximum summed interval in seconds to include within a bin. Defaults to 1.0.
chan_bin_sizeint, optional: Number of bins to average together. Defaults to 1.

Returns

namedtuple: A namedtuple whose entries correspond to the input arrays. Output arrays will be None if the inputs were None.

Notes

The implementation currently requires unique lexicographical combinations of (TIME, ANTENNA1, ANTENNA2). This can usually be achieved by suitably partitioning input data on indexing rows, DATA_DESC_ID and SCAN_NUMBER in particular.

africanus.averaging.dask.bda(time, interval, antenna1, antenna2, time_centroid=None, exposure=None, flag_row=None, uvw=None, weight=None, sigma=None, chan_freq=None, chan_width=None, effective_bw=None, resolution=None, visibilities=None, flag=None, weight_spectrum=None, sigma_spectrum=None, max_uvw_dist=None, max_fov=3.0, decorrelation=0.98, time_bin_secs=None, min_nchan=1, format='flat')[source]¶

Averages in time and channel, dependent on baseline length.

Parameters

timedask.array.Array: Time values of shape (row,).
intervaldask.array.Array: Interval values of shape (row,).
antenna1dask.array.Array: First antenna indices of shape (row,)
antenna2dask.array.Array: Second antenna indices of shape (row,)
time_centroiddask.array.Array, optional: Time centroid values of shape (row,)
exposuredask.array.Array, optional: Exposure values of shape (row,)
flag_rowdask.array.Array, optional: Flagged rows of shape (row,).
uvwdask.array.Array, optional: UVW coordinates of shape (row, 3).
weightdask.array.Array, optional: Weight values of shape (row, corr).
sigmadask.array.Array, optional: Sigma values of shape (row, corr).
chan_freqdask.array.Array, optional: Channel frequencies of shape (chan,).
chan_widthdask.array.Array, optional: Channel widths of shape (chan,).
effective_bwdask.array.Array, optional: Effective channel bandwidth of shape (chan,).
resolutiondask.array.Array, optional: Effective channel resolution of shape (chan,).
visibilitiesdask.array.Array or tuple of dask.array.Array, optional: Visibility data of shape (row, chan, corr). Tuples of visibilities arrays may be supplied, in which case tuples will be output.
flagdask.array.Array, optional: Flag data of shape (row, chan, corr).
weight_spectrumdask.array.Array, optional: Weight spectrum of shape (row, chan, corr).
sigma_spectrumdask.array.Array, optional: Sigma spectrum of shape (row, chan, corr).
max_uvw_distfloat, optional: Maximum UVW distance. Will be inferred from the UVW coordinates if not supplied.
max_fovfloat: Maximum Field of View Radius. Defaults to 3 degrees.
decorrelationfloat: Acceptable amount of decorrelation. This is a floating point value between 0.0 and 1.0.
time_bin_secsfloat, optional: Maximum number of seconds worth of data that can be aggregated into a bin. Defaults to None in which case the value is only bounded by the decorrelation factor and the field of view.
min_nchanint, optional: Minimum number of channels in an averaged sample. Useful in cases where imagers expect at least min_nchan channels. Defaults to 1.

Returns

namedtuple: A namedtuple whose entries correspond to the input arrays. Output arrays will be None if the inputs were None. See the Notes for an explanation of the output formats.

Notes

In all cases arrays starting with (row, chan) and (row,) dimensions are respectively averaged and expanded into a (rowchan,) dimension, as the number of channels varies per output row.

The output namedtuple contains an offsets array of shape (out_rows + 1,) encoding the starting offsets of each output row, as well as a single entry at the end such that np.diff(offsets) produces the number of channels for each output row.

avg = bda(...)
time = avg.time[avg.offsets[:-1]]
out_chans = np.diff(avg.offsets)

The implementation currently requires unique lexicographical combinations of (TIME, ANTENNA1, ANTENNA2). This can usually be achieved by suitably partitioning input data on indexing rows, DATA_DESC_ID and SCAN_NUMBER in particular.

Utilities¶

Command Line¶

parse_python_assigns(assign_str)

Parses a string, containing assign statements into a dictionary.

africanus.util.cmdline.parse_python_assigns(assign_str)[source]¶

Parses a string, containing assign statements into a dictionary.

data = parse_python_assigns("beta=5.6; l=[2,3], s='hello, world'")

assert data == {
    'beta': 5.6,
    'l': [2, 3],
    's': 'hello, world'
}

Parameters

assign_str: str: Assignment string. Should only contain assignment statements assigning python literals or builtin function calls, to variable names. Multiple assignment statements should be separated by semi-colons.

Returns

dict: Dictionary { name: value } containing assignment results.

Requirements Handling¶

requires_optional(*requirements)

Decorator returning either the original function, or a dummy function raising a MissingPackageException when called, depending on whether the supplied requirements are present.

africanus.util.requirements.requires_optional(*requirements)[source]¶

Decorator returning either the original function, or a dummy function raising a MissingPackageException when called, depending on whether the supplied requirements are present.

If packages are missing and called within a test, the dummy function will call pytest.skip().

Used in the following way:

try:
    from scipy import interpolate
except ImportError as e:
    # https://stackoverflow.com/a/29268974/1611416, pep 3110 and 344
    scipy_import_error = e
else:
    scipy_import_error = None

@requires_optional('scipy', scipy_import_error)
def function(*args, **kwargs):
    return interpolate(...)

Parameters

requirementsiterable of string, None or ImportError: Sequence of package names required by the decorated function. ImportError exceptions (or None, indicating their absence) may also be supplied and will be immediately re-raised within the decorator. This is useful for tracking down problems in user import logic.

Returns

callable: Either the original function if all requirements are available or a dummy function that throws a MissingPackageException or skips a pytest.

Shapes¶

`aggregate_chunks`(chunks, max_chunks)	Aggregate dask `chunks` together into chunks no larger than `max_chunks`.
`corr_shape`(ncorr, corr_shape)	Returns the shape of the correlations, given `ncorr` and the type of correlation shape requested

africanus.util.shapes.aggregate_chunks(chunks, max_chunks)[source]¶

Aggregate dask chunks together into chunks no larger than max_chunks.

chunks, max_c = ((3,4,6,3,6,7),(1,1,1,1,1,1)), (10,3)
expected = ((7,9,6,7), (2,2,1,1))
assert aggregate_chunks(chunks, max_c) == expected

Parameters

chunkssequence of tuples or tuple
max_chunkssequence of ints or int

Returns

sequence of tuples or tuple

africanus.util.shapes.corr_shape(ncorr, corr_shape)[source]¶

Returns the shape of the correlations, given ncorr and the type of correlation shape requested

Parameters

ncorrinteger: Number of correlations
corr_shape{‘flat’, ‘matrix’}: Shape of output correlations

Returns

tuple

Shape tuple describing the correlation dimensions

If flat returns (ncorr,)
If matrix returns
- (1,) if ncorr == 1
- (2,) if ncorr == 2
- (2,2) if ncorr == 4

Beams¶

`beam_filenames`(filename_schema, corr_types)	Returns a dictionary of beam filename pairs, keyed on correlation,from the cartesian product of correlations and real, imaginary pairs
`beam_grids`(header[, l_axis, m_axis])	Extracts the FITS indices and grids for the beam dimensions in the supplied FITS `header`.

africanus.util.beams.beam_filenames(filename_schema, corr_types)[source]¶

Returns a dictionary of beam filename pairs, keyed on correlation,from the cartesian product of correlations and real, imaginary pairs

Given beam_$(corr)_$(reim).fits returns:

{
  'xx' : ['beam_xx_re.fits', 'beam_xx_im.fits'],
  'xy' : ['beam_xy_re.fits', 'beam_xy_im.fits'],
  ...
  'yy' : ['beam_yy_re.fits', 'beam_yy_im.fits'],
}

Given beam_$(CORR)_$(REIM).fits returns:

{
  'xx' : ['beam_XX_RE.fits', 'beam_XX_IM.fits'],
  'xy' : ['beam_XY_RE.fits', 'beam_XY_IM.fits'],
  ...
  'yy' : ['beam_YY_RE.fits', 'beam_YY_IM.fits']),
}

Parameters

filename_schemastr: String containing the filename schema.
corr_typeslist of integers: list of integers defining the correlation type.

Returns

dict: Dictionary of schema {correlation : (refile, imfile)} mapping correlations to real and imaginary filename pairs

africanus.util.beams.beam_grids(header, l_axis=None, m_axis=None)[source]¶

Extracts the FITS indices and grids for the beam dimensions in the supplied FITS header. Specifically the axes specified by

L or X CTYPE
M or Y CTYPE
FREQ CTYPE

If the first two axes have a negative sign, such as -L, the grid will be inverted.

Any grids corresponding to axes with a CUNIT type of DEG will be converted to radians.

Parameters

headerHeader or dict: FITS header object.
l_axisstr: FITS axis interpreted as the L axis. L and X are sensible values here. -L will invert the coordinate system on that axis.
m_axisstr: FITS axis interpreted as the M axis. M and Y are sensible values here. -M will invert the coordinate system on that axis.

Returns

tuple: Returns ((l_axis, l_grid), (m_axis, m_grid), (freq_axis, freq_grid)) where the axis is the FORTRAN indexed FITS axis (1-indexed) and grid contains the values at each pixel along the axis.

Code¶

`format_code`(code)	Formats some code with line numbers
`memoize_on_key`(key_fn)	Memoize based on a key function supplied by the user.

africanus.util.code.format_code(code)[source]¶

Formats some code with line numbers

Parameters

codestr: Code

Returns

str: Code prefixed with line numbers

class africanus.util.code.memoize_on_key(key_fn)[source]¶

Memoize based on a key function supplied by the user. The key function should return a custom key for memoizing the decorated function, based on the arguments passed to it.

In the following example, the arguments required to generate the _generate_phase_delay_kernel function are the types of the lm, uvw and frequency arrays, as well as the number of correlations, ncorr.

The supplied key_fn produces a unique key based on these types and the number of correlations, which is used to cache the generated function.

def key_fn(lm, uvw, frequency, ncorrs=4):
    '''
    Produce a unique key for the arguments of
     _generate_phase_delay_kernel
    '''
    return (lm.dtype, uvw.dtype, frequency.dtype, ncorrs)

_code_template = jinja2.Template('''
#define ncorrs {{ncorrs}}

__global__ void phase_delay(
    const {{lm_type}} * lm,
    const {{uvw_type}} * uvw,
    const {{freq_type}} * frequency,
    {{out_type}} * out)
{
    ...
}
''')

_type_map = {
    np.float32: 'float',
    np.float64: 'double'
}

@memoize_on_key(key_fn)
def _generate_phase_delay_kernel(lm, uvw, frequency, ncorrs=4):
    ''' Generate the phase delay kernel '''
    out_dtype = np.result_type(lm.dtype, uvw.dtype, frequency.dtype)
    code = _code_template.render(lm_type=_type_map[lm.dtype],
                                 uvw_type=_type_map[uvw.dtype],
                                 freq_type=_type_map[frequency.dtype],
                                 ncorrs=ncorrs)
    return cp.RawKernel(code, "phase_delay")

Methods

__call__(fn)

Call self as a function.

dask¶

EstimatingProgressBar([minimum, width, dt, out])

Progress Bar that displays elapsed time as well as an estimate of total time taken.

class africanus.util.dask_util.EstimatingProgressBar(minimum=0, width=42, dt=1.0, out=sys.stdout)[source]¶

Progress Bar that displays elapsed time as well as an estimate of total time taken.

When starting a dask computation, the bar examines the graph and determines the number of chunks contained by a dask collection.

During computation the number of completed chunks and their the total time taken to complete them are tracked. The average derived from these numbers are used to estimate total compute time, relative to the current elapsed time.

The bar is not particularly accurate and will underestimate near the beginning of computation and seems to slightly overestimate during the buk of computation. However, it may be more accurate than the default dask task bar which tracks number of tasks completed by total tasks.

Parameters

minimumint, optional: Minimum time threshold in seconds before displaying a progress bar. Default is 0 (always display)
widthint, optional: Width of the bar, default is 42 characters.
dtfloat, optional: Update resolution in seconds, default is 1.0 seconds.

CUDA¶

grids(dims, blocks)

Determine the grid size, given space dimensions sizes and blocks

africanus.util.cuda.grids(dims, blocks)[source]¶

Determine the grid size, given space dimensions sizes and blocks

Parameters

dimstuple of ints: (x, y, z) tuple

Returns

tuple: (x, y, z) grid size tuple

Patterns¶

`Multiton`(args, *kwargs)	General Multiton metaclass
`LazyProxy`(fn, args, *kwargs)	Lazy instantiation of a proxied object.
`LazyProxyMultiton`(args, *kwargs)	Combination of a `LazyProxy` with a `Multiton`

class africanus.util.patterns.Multiton(*args, **kwargs)[source]¶

General Multiton metaclass

Implementation of the Multiton pattern, which always returns a unique object for a unique set of arguments provided to a class constructor. For example, in the following, only a single instance of A with argument 1 is ever created.

class A(metaclass=Multiton):
    def __init__(self, *args, **kw):
        self.args = args
        self.kw = kw

assert A(1) is A(1)
assert A(1, "bob") is not A(1)

This is useful for ensuring that only a single instance of a heavy-weight resource such as files, sockets, thread/process pools or database connections is created in a single process, for a unique set of arguments.

Notes

Instantiation of object instances is thread-safe.

class africanus.util.patterns.LazyProxy(fn, *args, **kwargs)[source]¶

Lazy instantiation of a proxied object.

A LazyProxy proxies an object which is lazily instantiated on first use. It is primarily useful for embedding references to heavy-weight resources in a dask graph, so they can be pickled and sent to other workers without immediately instantiating those resources.

To this end, the proxy takes as arguments:

a class or factory function that instantiates the desired resource.
*args and **kwargs that should be supplied to the instantiator.

The function and arguments for creating a file are wrapped in a LazyProxy. It is only instantiated when f.write is called.¶

f = LazyProxy(open, "test.txt", mode="r")
f.write("Hello World!")
f.close()

In addition to the class/factory function, it is possible to specifiy a Finaliser supplied to weakref.finalize that is called to cleanup the resource when the LazyProxy is garbage collected. In this case, the first argument should be a tuple of two elements: the factory and the finaliser.

# LazyProxy defined with factory function and finaliser function
def finalise_file(file):
    file.close()

f2 = LazyProxy((open, finalise_file), "test.txt", mode="r")

class WrappedFile:
    def __init__(self, *args, **kwargs):
        self.handle = open(*args, **kwargs)

    def close(self):
        self.handle.close()

# LazyProxy defined with class
f1 = LazyProxy((WrappedFile, WrappedFile.close), "test.txt", mode="r")

LazyProxy objects are designed to be embedded in dask.array.blockwise() calls. For example:

# Specify the start and length of each range
file_ranges = np.array([[0, 5], [5, 10], [15, 5] [20, 10]])
# Chunk each range individually
da_file_ranges = dask.array(file_ranges, chunks=(1, 2))
# Reference a binary file
file_proxy = LazyProxy(open, "data.dat", "rb")

def _read(file_proxy, file_range):
    # Seek to range start and read the length of data
    start, length = file_range
    file_proxy.seek(start)
    return np.asarray(file_proxy.read(length), np.uint8)

data = da.blockwise(_read, "x",
                    # Embed the file_proxy in the graph
                    file_proxy, None,
                    # Pass each file range to the _read
                    da_file_ranges, "xy",
                    # output chunks should have the length
                    # of each range
                    adjust_chunks={"x": tuple(file_ranges[:, 1])},
                    concatenate=True)

print(data.compute(processes=True))

Parameters

fnclass or callable or tuple: A callable object that used to create the proxied object. In tuple form, this should consist of two callables. The first should create the proxied object and the second should be a finaliser that performs cleanup on the proxied object when the LazyProxy is garbage collected: it is passed directly to weakref.finalize.
*argstuple: Positional arguments passed to the callable object specified in fn that will create the proxied object. The contents of *args should be pickleable.
**kwargsdict: Keyword arguments passed to the callable object specified in fn that will create the proxied object. The contents of **kwargs should be pickleable.

Notes

Instantiation of the proxied object is thread-safe.
LazyProxy’s are configured to never instantiate within dask.array.blockwise() and dask.blockwise.blockwise() calls.

class africanus.util.patterns.LazyProxyMultiton(*args, **kwargs)[source]¶

Combination of a LazyProxy with a Multiton

Ensures that only a single LazyProxy is ever created for the given constructor arguments.

class A:
    def __init__(self, value):
        self.value = value

assert LazyProxyMultiton("foo") is LazyProxyMultiton("foo")

See LazyProxy and Multiton for further details

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 self-calibration.
Third generation calibration (3GC): using a partially incomplete sky model to perform direction dependent calibration. Also known as direction dependent self-calibration.

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 diag-diag 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_indicesnumpy.ndarray: The start indices of the time bins of shape (utime)
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime)
antenna1numpy.ndarray: First antenna indices of shape (row,).
antenna2numpy.ndarray: Second antenna indices of shape (row,)
jonesnumpy.ndarray: Gains of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
modelnumpy.ndarray: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).

Returns

visnumpy.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_indicesnumpy.ndarray: The start indices of the time bins of shape (utime)
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime)
antenna1numpy.ndarray: First antenna indices of shape (row,).
antenna2numpy.ndarray: Second antenna indices of shape (row,)
jonesnumpy.ndarray: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
visnumpy.ndarray: Data values of shape (row, chan, corr). or (row, chan, corr, corr).
flagnumpy.ndarray: Flag data of shape (row, chan, corr) or (row, chan, corr, corr)
modelnumpy.ndarray: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).

Returns

residualnumpy.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 non-trivial 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_indicesnumpy.ndarray: The start indices of the time bins of shape (utime).
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime).
antenna1numpy.ndarray: Antenna 1 index used to look up the antenna Jones for a particular baseline with shape (row,).
antenna2numpy.ndarray: Antenna 2 index used to look up the antenna Jones for a particular baseline with shape (row,).
jonesnumpy.ndarray: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
visnumpy.ndarray: Data values of shape (row, chan, corr) or (row, chan, corr, corr).
flagnumpy.ndarray: Flag data of shape (row, chan, corr) or (row, chan, corr, corr).
Returns
——-
corrected_visnumpy.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_indicesnumpy.ndarray: The start indices of the time bins of shape (utime)
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime)
antenna1numpy.ndarray: First antenna indices of shape (row,).
antenna2numpy.ndarray: Second antenna indices of shape (row,)
jonesnumpy.ndarray: Gains of shape (utime, ant, chan, dir, corr) or (utime, ant, chan, dir, corr, corr).
modelnumpy.ndarray: Model image as a function of time with shape (utime, chan, dir, corr) or (utime, chan, dir, corr, corr).
uvwnumpy.ndarray: uvw coordinates of shape (row, 3)
lmnumpy.ndarray: Source lm coordinates as a function of time (utime, dir, 2)

Returns

visnumpy.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_indicesdask.array.Array: The start indices of the time bins of shape (utime)
time_bin_countsdask.array.Array: The counts of unique time in each time bin of shape (utime)
antenna1dask.array.Array: First antenna indices of shape (row,).
antenna2dask.array.Array: Second antenna indices of shape (row,)
jonesdask.array.Array: Gains of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
modeldask.array.Array: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).

Returns

visdask.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_indicesdask.array.Array: The start indices of the time bins of shape (utime)
time_bin_countsdask.array.Array: The counts of unique time in each time bin of shape (utime)
antenna1dask.array.Array: First antenna indices of shape (row,).
antenna2dask.array.Array: Second antenna indices of shape (row,)
jonesdask.array.Array: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
visdask.array.Array: Data values of shape (row, chan, corr). or (row, chan, corr, corr).
flagdask.array.Array: Flag data of shape (row, chan, corr) or (row, chan, corr, corr)
modeldask.array.Array: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).

Returns

residualdask.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 non-trivial 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_indicesdask.array.Array: The start indices of the time bins of shape (utime).
time_bin_countsdask.array.Array: The counts of unique time in each time bin of shape (utime).
antenna1dask.array.Array: Antenna 1 index used to look up the antenna Jones for a particular baseline with shape (row,).
antenna2dask.array.Array: Antenna 2 index used to look up the antenna Jones for a particular baseline with shape (row,).
jonesdask.array.Array: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
visdask.array.Array: Data values of shape (row, chan, corr) or (row, chan, corr, corr).
flagdask.array.Array: Flag data of shape (row, chan, corr) or (row, chan, corr, corr).
Returns
——-
corrected_visdask.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_indicesdask.array.Array: The start indices of the time bins of shape (utime)
time_bin_countsdask.array.Array: The counts of unique time in each time bin of shape (utime)
antenna1dask.array.Array: First antenna indices of shape (row,).
antenna2dask.array.Array: Second antenna indices of shape (row,)
jonesdask.array.Array: Gains of shape (utime, ant, chan, dir, corr) or (utime, ant, chan, dir, corr, corr).
modeldask.array.Array: Model image as a function of time with shape (utime, chan, dir, corr) or (utime, chan, dir, corr, corr).
uvwdask.array.Array: uvw coordinates of shape (row, 3)
lmdask.array.Array: Source lm coordinates as a function of time (utime, dir, 2)

Returns

visdask.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 phase-only 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 phase-only maximum likelihood calibration using a Gauss-Newton 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_indicesnumpy.ndarray: The start indices of the time bins of shape (utime)
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime)
antenna1numpy.ndarray: First antenna indices of shape (row,).
antenna2numpy.ndarray: Second antenna indices of shape (row,)
jonesnumpy.ndarray: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
residualnumpy.ndarray: Residual values of shape (row, chan, corr). or (row, chan, corr, corr).
modelnumpy.ndarray: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).
flagnumpy.ndarray: Flag data of shape (row, chan, corr) or (row, chan, corr, corr)

Returns

jhrnumpy.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 phase-only maximum likelihood calibration. Currently assumes scalar or diagonal inputs.

Parameters

time_bin_indicesnumpy.ndarray: The start indices of the time bins of shape (utime)
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime)
antenna1numpy.ndarray: First antenna indices of shape (row,).
antenna2numpy.ndarray: Second antenna indices of shape (row,)
jonesnumpy.ndarray: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
modelnumpy.ndarray: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).
flagnumpy.ndarray: Flag data of shape (row, chan, corr) or (row, chan, corr, corr)

Returns

jhjnumpy.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_indicesnumpy.ndarray: The start indices of the time bins of shape (utime)
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime)
antenna1numpy.ndarray: First antenna indices of shape (row,).
antenna2numpy.ndarray: Second antenna indices of shape (row,)
jonesnumpy.ndarray: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
residualnumpy.ndarray: Residual values of shape (row, chan, corr). or (row, chan, corr, corr).
modelnumpy.ndarray: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).
flagnumpy.ndarray: Flag data of shape (row, chan, corr) or (row, chan, corr, corr)

Returns

jhjnumpy.ndarray: The diagonal of the Hessian of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
jhrnumpy.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 phase-only maximum likelihood calibration using a Gauss-Newton optimisation algorithm. Currently only DIAG mode is supported.

Parameters

time_bin_indicesnumpy.ndarray: The start indices of the time bins of shape (utime)
time_bin_countsnumpy.ndarray: The counts of unique time in each time bin of shape (utime)
antenna1numpy.ndarray: First antenna indices of shape (row,).
antenna2numpy.ndarray: Second antenna indices of shape (row,).
jonesnumpy.ndarray: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
visnumpy.ndarray: Data values of shape (row, chan, corr) or (row, chan, corr, corr).
flagnumpy.ndarray: Flag data of shape (row, chan, corr) or (row, chan, corr, corr).
modelnumpy.ndarray: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).
weightnumpy.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 1e-4.
maxiter: int, optional: The maximum number of iterations. Defaults to 100.

Returns

gainsnumpy.ndarray: Gain solutions of shape (time, ant, chan, dir, corr) or shape (time, ant, chan, dir, corr, corr)
jhjnumpy.ndarray: The diagonal of the Hessian of shape (time, ant, chan, dir, corr) or shape (time, ant, chan, dir, corr, corr)
jhrnumpy.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 phase-only 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_indicesdask.array.Array: The start indices of the time bins of shape (utime)
time_bin_countsdask.array.Array: The counts of unique time in each time bin of shape (utime)
antenna1dask.array.Array: First antenna indices of shape (row,).
antenna2dask.array.Array: Second antenna indices of shape (row,)
jonesdask.array.Array: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
residualdask.array.Array: Residual values of shape (row, chan, corr). or (row, chan, corr, corr).
modeldask.array.Array: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).
flagdask.array.Array: Flag data of shape (row, chan, corr) or (row, chan, corr, corr)

Returns

jhrdask.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 phase-only maximum likelihood calibration. Currently assumes scalar or diagonal inputs.

Parameters

time_bin_indicesdask.array.Array: The start indices of the time bins of shape (utime)
time_bin_countsdask.array.Array: The counts of unique time in each time bin of shape (utime)
antenna1dask.array.Array: First antenna indices of shape (row,).
antenna2dask.array.Array: Second antenna indices of shape (row,)
jonesdask.array.Array: Gain solutions of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).
modeldask.array.Array: Model data values of shape (row, chan, dir, corr) or (row, chan, dir, corr, corr).
flagdask.array.Array: Flag data of shape (row, chan, corr) or (row, chan, corr, corr)

Returns

jhjdask.array.Array: The diagonal of the Hessian of shape (time, ant, chan, dir, corr) or (time, ant, chan, dir, corr, corr).

Linear Algebra¶

This module contains specialised linear algebra tools that are not currently available in the python standard scientific libraries.

Kronecker tools¶

A kronecker matrix is matrix that can be written as a kronecker matrix of the individual matrices i.e.

\[\begin{split}K = K_0 \\otimes K_1 \\otimes K_2 \\otimes \\cdots\end{split}\]

Matrices which exhibit this structure can exploit properties of the kronecker product to avoid explicitly expanding the matrix $K$. This module implements some common linear algebra operations which leverages this property for computational gains and a reduced memory footprint.

Numpy¶

`kron_matvec`(A, b)	Computes the matrix vector product of a kronecker matrix in linear time.
`kron_cholesky`(A)	Computes the Cholesky decomposition of a kronecker matrix as a kronecker matrix of Cholesky factors.

africanus.linalg.kron_matvec(A, b)[source]¶

Computes the matrix vector product of a kronecker matrix in linear time. Assumes A consists of kronecker product of square matrices.

Parameters

Anumpy.ndarray: An array of arrays holding matrices [K0, K1, …] where $A = K_0 \otimes K_1 \otimes \cdots$
bnumpy.ndarray: The right hand side vector

Returns

xnumpy.ndarray: The result of A.dot(b)

africanus.linalg.kron_cholesky(A)[source]¶

Computes the Cholesky decomposition of a kronecker matrix as a kronecker matrix of Cholesky factors.

Parameters

Anumpy.ndarray: An array of arrays holding matrices [K0, K1, …] where $A = K_0 \otimes K_1 \otimes \cdots$

Returns

Lnumpy.ndarray: An array of arrays holding matrices [L0, L1, …] where $L = L_0 \otimes L_1 \otimes \cdots$ and each Li = cholesky(Ki)

Gaussian processes¶

This module provides a collection of tools that are useful when performing Gaussian process regression.

Numpy¶

`abs_diff`(x, xp)	Gets matrix of differences between $D$-dimensional vectors x and xp i.e.
`exponential_squared`(x, xp, sigmaf, l[, pspec])	Create exponential squared covariance function between $D$ dimensional vectors $x$ and $x_p$ i.e.

africanus.gps.abs_diff(x, xp)[source]¶

Gets matrix of differences between $D$-dimensional vectors x and xp i.e.

\[X_{ij} = |x_i - x_j|\]

Parameters

xnumpy.ndarray: Array of inputs of shape (N, D).
xpnumpy.ndarray: Array of inputs of shape (Np, D).

Returns

XXnumpy.ndarray: Array of differences of shape (N, Np).

africanus.gps.exponential_squared(x, xp, sigmaf, l, pspec=False)[source]¶

Create exponential squared covariance function between $D$ dimensional vectors $x$ and $x_p$ i.e.

\[k(x, x_p) = \sigma_f^2 \exp\left(-\frac{(x-x_p)^2}{2l^2}\right)\]

Parameters

xnumpy.ndarray: Array of shape (N, D).
xpnumpy.ndarray: Array of shape (Np, D).
sigmaffloat: The signal variance hyper-parameter
lfloat: The length scale hyper-parameter

Returns

Knumpy.ndarray: Array of shape (N, Np)

Fused Radio Interferometer Measurement Equation¶

Radio Interferometer Measurement Equation¶

The Radio Interferometer Measurement Equation (RIME) describes the response of an interferometer to a sky model. As described in A full-sky Jones formalism, a RIME could be written as follows:

\[V_{pq} = G_{p} \left( \sum_{s} E_{ps} L_{p} K_{ps} B_{s} K_{qs}^H L_{q}^H E_{qs}^H \right) G_{q}^H\]

where for antenna $p$ and $q$, and source $s$:

$G_{p}$ represents direction-independent effects.
$E_{ps}$ represents direction-dependent effects.
$L_{p}$ represents the feed rotation.
$K_{ps}$ represents the phase delay term.
$B_{s}$ represents the brightness matrix.

The RIME is more formally described in the following four papers:

The Fused RIME¶

The RIME poses a number of implementation challenges which focus on flexibility, speed and ease of use.

Firstly, the RIME can be composed of many terms representing various physical effects. It is useful for scientist to be able to specify many different terms in the above Equation, for example.

Secondly, the computational complexity of the RIME O(S x V) where S is the number of source and V is the number of visibilities. This is computionationally expensive relative to degridding strategies.

Thirdly, it should be as easy as possible to define the RIME, but not at the cost of the previous two constraints.

The Fused RIME therefore implements a “RIME Compiler” using Numba for speed, which compiles a RIME Specification defined by a number of Terms into a single, optimal unit of execution.

A Simple Example¶

In the following example, we will define a simple RIME using the Fused RIME API to define terms for computing:

the Phase Delay.
the Brightness Matrix.

The RIME Specification¶

The specification for this RIME is as follows:

rime_spec = RimeSpecification("(Kpq, Bpq): [I,Q,U,V] -> [XX,XY,YX,YY]",
                              terms={"K": Phase},
                              transformers=[LMTransformer])

(Kpq, Bpq) specifies the onion including the Phase Delay and Brightness more formally defined here, while the the pq in both terms signifies that they are calculated per-baseline. [I,Q,U,V] -> [XX,XY,YX,YY] defines the stokes to correlation conversion within the RIME and also identifies whether the RIME is handling linear or circular feeds. terms={"K": Phase} indicates that the K term is implemented as a custom Phase term, described in the next section. Finally, LMTransformer is a Transformer that precomputes lm coordinates for use by all terms.

Custom Phase Term¶

Within the RIME, each term is sampled at an individual source, row and channel.

Therefore each term must provide a sampling function that will provide the necessary data for multiplication within the RIME. Consider the following Phase Term:

from africanus.experimental.rime.fused.terms.core import Term

class Phase(Term):
    def sampler(self):
        def phase_sample(state, s, r, t, f1, f2, a1, a2, c):
            p = state.real_phase[s, r] * state.chan_freq[c]
            return np.cos(p) + np.sin(p)*1j

        return phase_sample

This may look simple: we compute the complex phase by multiplying the real phase at each source and row by the channel frequency and return the complex exponential of this value.

However, questions remain: What is the state object and how do we know that the real_phase and chan_freq are members? To answer this, we must define (and understand) a second method defined on the Phase term, called init_fields.

import numba
from africanus.experimental.rime.fused.terms.core import Term

class Phase(Term)
    def init_fields(self, typingctx, lm, uvw, chan_freq):
        # Given the numba types of the lm, uvw and chan_freq
        # arrays, derive a unified output numba type
        numba_type = typingctx.unify_types(lm.dtype,
                                           uvw.dtype,
                                           chan_freq.dtype)

        # Define the type of new fields on the state object
        # in this case a 2D Numba array with dtype numba_type
        fields = [("real_phase", numba_type[:, :])]

        def real_phase(lm, uvw, chan_freq):
            """Compute the real_phase upfront, instead of in
            the sampling function"""
            real_phase = np.empty((lm.shape[0], uvw.shape[0]), numba_type)

            for s in range(lm.shape[0]):
                l, m = lm[s]
                n = 1.0 - l**2 - m**2
                n = np.sqrt(0.0 if n <= 0.0 else n) - 1.0

                for r in range(uvw.shape[0]):
                    u, v, w = uvw[r]
                    real_phase[s, r] = -2.0*np.pi*(l*u + m*v + n*w)/3e8

            return real_phase

        # Return the new field definition and
        # the function for creating it
        return fields, real_phase

init_fields serves multiple purposes:

It requests input for the Phase term. The above definition of init_fields signifies that the Phase term desires the lm, uvw and chan_freq arrays. Additionally, these arrays will be stored on the state object provided to the sampling function.
It supports reasoning about Numba types in a manner similar to numba.generated_jit(). The lm, uvw and chan_freq arguments contain the Numba types of the variables supplied to the RIME, while the typingctx argument contains a Numba Typing Context which can be useful for reasoning about these types. For example typingctx.unify_types(lm.dtype, uvw.dtype, chan_freq.dtype) returns a type with sufficient precision, given the input types, similar to numpy.result_type().
It allows the user to define new fields, as well as a function for defining those fields on the state object. The above definition of init_fields returns a list of (name, type) tuples defining the new field names and their types, while real_phase defines the creation of this new field.

This is useful for optimising the sampling function by pre-computing values. For example, it is wasteful to compute the real phase for each source, row and channel.

Returning to our definition of the Phase Term sampling function, we can see that it uses the new field real_phase defined in init_fields, as well as the chan_freq array requested in init_fields to compute a complex exponential.

class Phase(Term):
    def sampler(self):
        def phase_sample(state, s, r, t, f1, f2, a1, a2, c):
            p = state.real_phase[s, r] * state.chan_freq[c]
            return np.cos(p) + np.sin(p)*1j

        return phase_sample

Transformers¶

Using Term.init_fields(), we can precompute data for use in sampling functions, within a single Term. However, sometimes we wish to precompute data for use by multiple Terms. This can be achieved through the use of Transformers. A good example of data that it is useful to precompute for multiple Terms are lm coordinates, which are in turn, derived from phase_dir and radec which are the phase centre of an observation and the position of a source, respectively. In the following code snippet, LMTransformer.init_fields

from africanus.experimental.rime.fused.transformers import Transformer

class LMTransformer(Transformer):
    # Must specify list of outputs produced by this transformer on the
    # OUTPUTS class attribute
    OUTPUTS = ["lm"]

    def init_fields(self, typingctx, radec, phase_dir):
        # Type and provide method for initialising the lm output
        dt = typingctx.unify_types(radec.dtype, phase_dir.dtype)
        fields = [("lm", dt[:, :])]

        def lm(radec, phase_dir):
            lm = np.empty_like(radec)
            pc_ra = phase_dir[0]
            pc_dec = phase_dir[1]

            sin_pc_dec = np.sin(pc_dec)
            cos_pc_dec = np.cos(pc_dec)

            for s in range(radec.shape[0]):
                da = radec[s, 0] - pc_ra
                sin_ra_delta = np.sin(da)
                cos_ra_delta = np.cos(da)

                sin_dec = np.sin(radec[s, 1])
                cos_dec = np.cos(radec[s, 1])

                lm[s, 0] = cos_dec*sin_ra_delta
                lm[s, 1] = sin_dec*cos_pc_dec - cos_dec*sin_pc_dec*cos_ra_delta

            return lm

        return fields, lm

The lm array will be available on the state object and as a valid input for Term.init_fields().

Invoking the RIME¶

We then invoke the RIME by passing in the RimeSpecification, as well as a dataset containing the required arguments:

from africanus.experimental.rime.fused.core import rime
import numpy as np

dataset = {
    "radec": np.random.random((10, 2))*1e-5,
    "phase_dir": np.random.random((2,))*1e-5,
    "uvw": np.random.random((100, 3))*1e5,
    "chan_freq:" np.linspace(.856e9, 2*.856e9, 16),
    ...,
    "stokes": np.random.random((10, 4)),
    # other required data
}

rime_spec = RimeSpecification("(Kpq, Bpq)",
                              terms={"K": Phase},
                              transformers=LMTransformer)
model_visibilities = rime(rime_spec, dataset)

Dask Support¶

Dask wrappers are provided for the africanus.experimental.rime.fused.core.rime() function. In order to support this, both Term and Transformer classes need to supply a dask_schema function which is used to define the schema for each supplied argument, which in turn is supplied to a dask.array.blockwise() call.

The schema should be a tuple of dimension string names. In particular, the rime function assigns special meaning to source, row, chan and corr – These names are are associated with individual sources (fields) and Measurement Set rows, channels and correlations, respectively. Dask Array chunking is supported along these dimensions in the sense that the rime will be computed for each chunk along these dimensions.

Note

Chunks in dimensions other than source, row, chan and corr will be contracted into a single array within the rime function. It is recommended that other dimensions contain a single chunk, or contain small quantities of data relative to the special dimensions.

Therefore, Phase.dask_schema could be implemented as follows:

class Phase(Term):
    def dask_schema(self, lm, uvw, chan_freq):
        assert lm.ndim == 2
        assert uvw.ndim == 2
        assert chan_freq.ndim == 1

        return {
            "lm": ("source", "lm-component"),
            "uvw": ("row", "uvw-component"),
            "chan_freq": ("chan",),
        }

The dask_schema for a Transformer is slightly different as, in addition a schema for the inputs, it must also provide an array_like variable describing the number of dimensions and data type of the output arrays. The array_like variables are in turn passed into Term.dask_schema. Thus, LMTransformer.dask_schema could be implemented as follows;

class LMTransformer(Transformer):
    OUTPUTS = ["lm"]

    def dask_schema(self, phase_dir, radec):
        dt = np.result_type(phase_dir.dtype, radec.dtype)
        return ({
            "phase_dir": ("radec-component",),
            "radec": ("source", "radec-component",),
        },
        {
            "lm": np.empty((0,0), dtype=dt)
        })

Then, in a paradigm very similar to the non-dask case, we create a RimeSpecification and supply it, along with a dictionary or dataset of dask arrays, to the rime() function. This will produce a dask array representing the model visibilities.

from africanus.experimental.rime.fused.dask import rime
import dask.array as da
import numpy as np

dataset = {
    "radec": da.random.random((10, 2), chunks=(2, 2))*1e-5,
    "phase_dir": da.random.random((2,), chunks=(2,))*1e-5,
    "uvw": da.random.random((100, 3), chunks=(10, 3))*1e5,
    "chan_freq:" da.linspace(.856e9, 2*.856e9, 16, chunks=(4,)),
    ...,
    "stokes": da.random.random((10, 4), chunks=(2, 4)),
    # other required data
}

rime_spec = RimeSpecification("(Kpq, Bpq)",
                              terms={"K": Phase},
                              transformers=LMTransformer)
model_visibilities = rime(rime_spec, dataset)
model_visibilities.compute()

API¶

class africanus.experimental.rime.fused.specification.RimeSpecification(specification, terms=None, transformers=None)[source]¶

Defines a unique Radio Interferometer Measurement Equation (RIME)

The RIME is composed of a number of Jones Terms, which are multiplied together and combined to produce model visibilities.

The RimeSpecification specifies the order of these Jones Terms and supports custom Jones terms specified by the user.

One of the simplest RIME’s that can be expressed involve a Phase (Kpq) and a Brightness (Bpq) term. The specification for this RIME is as follows:

rime_spec = RimeSpecification("(Kpq, Bpq): [I,Q,U,V] -> [XX,XY,YX,YY]")

(Kpq, Bpq) specifies the onion more formally defined here, while [I,Q,U,V] -> [XX,XY,YX,YY] defines the stokes to correlation conversion within the RIME. It also identifies whether the RIME is handling linear or circular feeds.

Term Configuration

The pq in Kpq and Bpq signifies that their values are calculated per-baseline. It is possible to specify per-antenna terms: Kp and Kq for example which represent left (ANTENNA1) and right (ANTENNA2) terms respectively. Not that the hermitian transpose of the right term is automatically performed and does not need to be implemented in the Term itself. Thus, for example, (Kp, Bpq, Kq) specifies a RIME where the Phase Term is separated into left and right terms, while the Brightness Matrix is calculated per-baseline.

Stokes to Correlation Mapping

[I,Q,U,V] -> [XX,XY,YX,YY] specifies a mapping from four stokes parameters to four correlations. Both linear [XX,XY,YX,YY] and circular [RR,RL,LR,LL] feed types are supported. A variety of mappings are possible:

[I,Q,U,V] -> [XX,XY,YX,YY]
[I,Q] -> [XX,YY]
[I,Q] -> [RR,LL]

Custom Terms

Custom Term classes implemented by a user can be added to the RIME as follows:

class CustomJones(Term):
    ...

spec = RimeSpecification("(Apq,Kpq,Bpq)", terms={"A": CustomJones})

Parameters

specificationstr: A string specifying the terms in the RIME and the stokes to correlation conversion.
termsdict of str or Terms: A map describing custom Term implementations. If one has defined a custom Gaussian Term class, for use in RIME (Cpq, Kpq, Bpq), this should be supplied as terms={"C": Gaussian}. strings can be supplied for predefined RIME classes.
transformerslist of Transformers: A list of Transformer classes.

class africanus.experimental.rime.fused.terms.core.Term[source]¶

Base class for Terms which describe parts of the Fused RIME. Implementors of a RIME Term should inherit from it.

A Term is an object that defines how a term in the RIME should be sampled to produces the Jones Terms that make up the RIME. It therefore defines a sampling function, which in turn depends on arbitrary inputs for performing the sampling.

A high degree of flexibility and leeway is afforded when implementing a Term. It might be implemented by merely indexing an array of Jones Matrices, or by implementing some computational model describing the Jones Terms.

class Phase(Term):
    def __init__(self, configuration):
        super().__init__(configuration)

init_fields(self, typing_ctx, arg1, ..., argn, kwarg1=None, ..., kwargn=None)¶

Requests inputs to the RIME term, ensuring that they are stored on a state object supplied to the sampling function and allows for new fields to be initialised and stored on the state object.

Requested inputs arg1...argn are required to be passed to the Fused RIME by the caller and are supplied to init_fields as Numba types. kwarg1...kwargn are optional – if omitted by the caller, their default types (and values) will be supplied.

init_fields should return a (fields, function) tuple. fields should be a list of the form [(name, numba_type)], while function should be a function of the form fn(arg1, ..., argn, kwarg1=None, .., kwargn=None) and should return the variables of the type defined in fields. Note that it’s signature therefore matches that of init_fields from after the typingctx argument. See the Simple Example.

Parameters

typingctx – A Numba typing context.
arg1...argn – Required RIME inputs for this Term.
kwarg1...kwargn – Optional RIME inputs for this Term. Types here should be simple: ints, floats, complex numbers and strings are ideal.

Return type

tuple

Returns

A (fields, function) tuple.

Warning

The function returned by init_fields must be compileable in Numba’s nopython mode.

sampler(self)¶

Return a sampling function of the following form:

def sampler(self):
    def sample(state, s, r, t, f1, f2, a1, a2, c):
        ...

return sample

Parameters

state – A state object containing the inputs requested by all Term objects in the RIME, as well as any fields created by Term.init_fields.
s – Source index.
r – Row index.
t – Time index.
f1 – Feed 1 index.
f2 – Feed 2 index.
a1 – Antenna 1 index.
a2 – Antenna2 index.
c – Channel index.

Return type

scalar or a tuple

Returns

a scalar or a tuple of two scalars or a tuple of four scalars.

Warning

The sampling function returned by sampler must be compileable in Numba’s nopython mode.

dask_schema(self, arg1, ..., argn, kwargs1=None, ..., kwargn=None)¶

Parameters

arg1...argn – Required RIME inputs for this Transformer.
kwarg1...kwargn – Optional RIME inputs for this Transformer. Types here should be simple: ints, floats, complex numbers and strings are ideal.

Return type

dict

Returns

A dictionary of the form {name: schema} defining the blockwise() dimension schema of each supplied argument and keyword argument.

class africanus.experimental.rime.fused.transformers.core.Transformer[source]¶

Base class for precomputing data for consumption by Term’s.

OUTPUTS¶: This class attributes should contain names of the outputs produced by the Transformer class. This should correspond to the fields produced by Transformer.init_fields().

init_fields(self, typing_ctx, arg1, ..., argn, kwarg1=None, ..., kwargn=None)¶

Requests inputs to the Transformer, and specifies new fields and the function for creating them on the state object. Functionally, this method behaves exactly the same as the init_fields() method, the difference being that the outputs are available to all Terms.

Return type: tuple
Returns: A (fields, function) tuple.

Warning

The function returned by init_fields must be compileable in Numba’s nopython mode.

dask_schema(self, arg1, ..., argn, kwargs1=None, ..., kwargn=None)¶

Return type

tuple

Returns

A (inputs, outputs) tuple.

inputs should be a dictionary of the form {name: schema} where schema is a dimension schema suitable for use in dask.array.blockwise(). A suitable schema for visibility data would be (row, chan, corr), while a uvw coordinate schema could be (row, uvw-component).

outputs should be a dictionary of the form {name: array_like}, where array_like is an object with dtype and ndim attributes. A suitable array_like for lm data could be np.empty((0,0), dtype=np.float64).

Predefined Terms¶

class africanus.experimental.rime.fused.terms.phase.Phase(configuration)[source]¶

Phase Delay Term

Attributes

configuration

class africanus.experimental.rime.fused.terms.brightness.Brightness(configuration, stokes, corrs)[source]¶

Brightness Matrix Term

Attributes

configuration

class africanus.experimental.rime.fused.terms.gaussian.Gaussian(configuration)[source]¶

Gaussian Amplitude Term

Attributes

configuration

class africanus.experimental.rime.fused.terms.feed_rotation.FeedRotation(configuration, feed_type, corrs)[source]¶

Feed Rotation Term

Attributes

configuration

class africanus.experimental.rime.fused.terms.cube_dde.BeamCubeDDE(configuration, corrs)[source]¶

Voxel Beam Cube Term

Attributes

configuration

Predefined Transformers¶

class africanus.experimental.rime.fused.transformers.lm.LMTransformer[source]¶

class africanus.experimental.rime.fused.transformers.parangle.ParallacticTransformer(process_pool)[source]¶

Numpy¶

rime(rime_spec, *args, **kw)

Evaluates the Radio Interferometer Measurement Equation (RIME), given the Specification of the RIME rime_spec, as well as the inputs to the RIME given in *args and **kwargs.

africanus.experimental.rime.fused.core.rime(rime_spec, *args, **kw)[source]¶: Evaluates the Radio Interferometer Measurement Equation (RIME), given the Specification of the RIME rime_spec, as well as the inputs to the RIME given in *args and **kwargs.

Dask¶

rime(rime_spec, *args, **kw)

Like rime(), but for a dask paradigm

africanus.experimental.rime.fused.dask.rime(rime_spec, *args, **kw)[source]¶: Like rime(), but for a dask paradigm

Contributing¶

Contributions are welcome, and they are greatly appreciated! Every little bit helps, and credit will always be given.

You can contribute in many ways:

Types of Contributions¶

Report Bugs¶

Report bugs at https://github.com/ska-sa/codex-africanus/issues.

If you are reporting a bug, please include:

Your operating system name and version.
Any details about your local setup that might be helpful in troubleshooting.
Detailed steps to reproduce the bug.

Fix Bugs¶

Look through the GitHub issues for bugs. Anything tagged with “bug” and “help wanted” is open to whoever wants to implement it.

Implement Features¶

Look through the GitHub issues for features. Anything tagged with “enhancement” and “help wanted” is open to whoever wants to implement it.

Write Documentation¶

Codex Africanus could always use more documentation, whether as part of the official Codex Africanus docs, in docstrings, or even on the web in blog posts, articles, and such.

Submit Feedback¶

The best way to send feedback is to file an issue at https://github.com/ska-sa/codex-africanus/issues.

If you are proposing a feature:

Explain in detail how it would work.
Keep the scope as narrow as possible, to make it easier to implement.
Remember that this is a volunteer-driven project, and that contributions are welcome :)

Get Started!¶

Ready to contribute? Here’s how to set up codex-africanus for local development.

Fork the codex-africanus repo on GitHub.

Clone your fork locally:

$ git clone git@github.com:your_name_here/codex-africanus.git

Install your local copy into a virtualenv. Assuming you have virtualenvwrapper installed, this is how you set up your fork for local development:
```
$ mkvirtualenv codex-africanus
$ cd codex-africanus/
$ pip install -e .
```
Create a branch for local development:
```
$ git checkout -b name-of-your-bugfix-or-feature
```
Now you can make your changes locally.
When you’re done making changes, check that your changes pass the test cases, fixup your PEP8 compliance, and check for any code style issues:

$ py.test -v africanus $ autopep8 -r -i africanus $ flake8 africanus $ pycodestyle africanus

To get autopep8 and pycodestyle, just pip install them into your virtualenv.

Commit your changes and push your branch to GitHub:

$ git add .
$ git commit -m "Your detailed description of your changes."
$ git push origin name-of-your-bugfix-or-feature

Submit a pull request through the GitHub website.

Pull Request Guidelines¶

Before you submit a pull request, check that it meets these guidelines:

The pull request should include tests.
If the pull request adds functionality, the docs should be updated. Put your new functionality into a function with a docstring, and add the feature to the list in HISTORY.rst.
The pull request should work for Python 2.7, 3.5 and 3.6. Check https://travis-ci.org/ska-sa/codex-africanus/pull_requests and make sure that the tests pass for all supported Python versions.

Tips¶

To run the tests:

$ py.test -vvv africanus/

Deploying¶

A reminder for the maintainers on how to deploy.

Update HISTORY.rst with the intended release number Z.Y.X and commit to git.
Bump the version number with bumpversion. This creates a new git commit, as well as an annotated tag Z.Y.X for the release. If your current version is Z.Y.W and the new version is Z.Y.X call:
```
$ python -m pip install bump2version
$ bump2version --current-version Z.Y.W --new-version Z.Y.X patch
```
Push the release commit and new tag up:
```
$ git push --follow-tags
```
Travis should automatically deploy the tagged release to PyPI if the automated tests pass.

Credits¶

Development Lead¶

Simon Perkins <sperkins@ska.ac.za>

Contributors¶

Landman Bester <lbester@ska.ac.za>
Benjamin Hugo <bhugo@ska.ac.za>
Jonathan Kenyon <jkenyon@ska.ac.za>
Gijs Molenaar <gijs@pythonic.nl>
Joshua van Staden <joshvstaden14@gmail.com>
Oleg Smirnov <oms@ska.ac.za, osmirnov@gmail.com>

History¶

0.3.4 (2023-10-03)¶

Separate stokes and correlation dimensions in dask fused RIME (GH#273)
Disallow feed rotation terms for RIME’s containing less than four correlations (GH#273)
Update trove hash (GH#274)

0.3.3 (2022-08-03)¶

Deprecate Python 3.7 and test on Python 3.10 (GH#271)
Pin flake8 to >= 4.0.0 and < 5.0.0 (GH#272)
Document Fused RIME (GH#270)
Add Multiton, LazyProxy and LazyProxyMultiton patterns (GH#269)

0.3.2 (2022-01-13)¶

Support numba >= 0.54 (GH#264)
Fused RIME (GH#239)
Restrict numba version to <= 0.54.0 (GH#259)
BDA fix typos in numba wrapper (GH#261)
BDA Time-smearing fixes (GH#253)

0.3.1 (2021-09-09)¶

Handle empty spectral indices in WSClean Model (GH#258)
Support missing data during BDA (GH#252)

0.3.0 (2021-09-09)¶

Deprecate Python 3.6 support, add Python 3.9 support (GH#248)
Using contextlib.suppress instead of deprecated dask.util.ignoring in EstimatingProgressBar (GH#256)
Disallow numba 0.54.0 (GH#254)
Upgrade to CuPy 9.0 and fix template encoding (GH#251)
Parse and zero spectral models containing ‘nan’ and ‘inf’ in wsclean model files (GH#250)
Clarify _wrapper names (GH#247)
Baseline-Dependent Time-and-Channel Averaging (GH#173, GH#243)

0.2.10 (2021-02-09)¶

Don’t let dof go to zero during spi fitting (GH#240)
Add support for Shapelets and Zernike Polynomials (GH#231)
Add beam model during SPI fitting (GH#238)
Add double accumulation option and Hessian function to wgridder (GH#237)
Upgrade ducc0 to version 0.8.0 (GH#236)
Add mindet to avoid div0 errors in spi fitter and fix alpha and I0 variance estimates (GH#234)

0.2.9 (2020-12-15)¶

Upgrade ducc0 to version 0.7.0 (GH#233)
Fix manually specifying wgridder precision (GH#230)

0.2.8 (2020-10-08)¶

Fix NoneType issue in wgridder when weights are None (GH#228)
Bounding hull geometric and image manipulation routines (GH#192, GH#154)
Fix row chunk chunking in Perley Polyhedron Degridder Dask Interface

0.2.7 (2020-09-23)¶

Deprecate old gridder and filters (GH#224)
Upgrade to ducc0 0.6.0 (GH#223)
Add Perley Polyhedron Faceting Gridder/Degridder (GH#202, GH#215, GH#222)

0.2.6 (2020-08-07)¶

Add wrapper for ducc0.wgridder (GH#204)
Correct Irregular Grid nesting in BeamAxes (GH#217)

0.2.5 (2020-07-01)¶

Convert WSClean Gaussian arcsecond and degree quantities to radians (GH#206)
Update classifiers and correct license in setup.py to BSD3 (GH#201)

0.2.4 (2020-05-29)¶

Support overriding the l and m axis sign in beam_grids (GH#199)
Upgrade to python-casacore 3.3.1 (GH#197)
Upgrade to jax 0.1.68 and jaxlib 0.1.47 (GH#197)
Upgrade to scipy 1.4.0 (GH#197)
Use github workflows (GH#196, GH#197, GH#198, GH#199)
Make CASA parallactic angles thread-safe (GH#195)
Fix spectral model documentation (GH#190), to match changes in (GH#189)

0.2.3 (2020-05-14)¶

Fix incorrect SPI calculation and make predict defaults MeqTree equivalent (GH#189)
Depend on pytest-flake8 >= 1.0.6 (GH#187, GH#188)
MeqTrees Comparison Script Updates (GH#160)
Improve requirements handling (GH#187)
Use python-casacore wheels for travis testing, instead of kernsuite packages (GH#185)

0.2.2 (2020-04-09)¶

Add a dask Estimating Progress Bar (GH#182, GH#183)

0.2.1 (2020-04-03)¶

Update trove to latest master commit (GH#178)
Added Cubic Spline support (GH#174)
Depend on python-casacore >= 3.2.0 (GH#172)
Drop Python 3.5 support and test Python 3.7 (GH#168)
Implement optimised WSClean predict (GH#166, GH#167, GH#177, GH#179, GH#180, GH#181)
Simplify dask predict_vis code (GH#164, GH#165)
Document and check weight shapes in simple gridder and degridder (GH#162, GH#163)
Restructuring calibration module (GH#127)
Upgrade to numba 0.46.0, using new inlining functionality in the RIME and averaging code.
Modified predict to be compatible with eidos fits headers (GH#158)

0.2.0 (2019-09-30)¶

Added standalone SPI fitter (GH#153)
Fail earlier and explain duplicate averaging rows (GH#155)
CUDA Beam Implementation (GH#152)
Fix documentation package versions (GH#151)
Deprecate experimental w-stacking gridder in favour of nifty gridder (GH#148)
Expand travis build matrix (GH#147)
Drop Python 2 support (GH#146, GH#149, GH#150)
Support the beam in the predict example (GH#145)
Fix weight indexing in averaging (GH#144)
Support EFFECTIVE_BW and RESOLUTION in averaging (GH#144)
Optimise predict_vis jones coherency summation (GH#143)
Remove use of @wraps (GH#141, GH#142)
Set row chunks to nan in dask averaging code. (GH#139)
predict_vis documentation improvements (GH#135, GH#140)
Upgrade to dask-ms in the examples (GH#134, GH#138)
Explain how to obtain predict_vis time_index argument (GH#130)
Update RIME predict example to support Tigger LSM’s and Gaussians (GH#129)
Add dask wrappers for the nifty gridder (GH#116, GH#136, GH#146)
Testing and requirement updates. (GH#124)
Upgraded DFT kernels to have a correlation axis and added flags for vis_to_im. Added predict_from_fits example. (GH#122)
Fixed segfault when using _unique_internal on empty ndarrays (GH#123)
Removed apply_gains. Use africanus.calibration.utils.correct_vis instead (GH#118)
Add streams parameter to dask predict_vis (GH#118)
Implement the beam in numba (GH#112)
Add residual_vis, correct_vis, phase_only_GN (GH#113)

0.1.8 (2019-05-28)¶

Use environment markers in setup.py (GH#110)
Add apply_gains, a wrapper around predict_vis (GH#108)
Fix testing extras_require (GH#107)
Fix WEIGHT_SPECTRUM averaging and add more averaging tests (GH#106)

0.1.7 (2019-05-09)¶

Even more support for automated travis deploys.

0.1.6 (2019-05-09)¶

Support automated travis deploys.

0.1.5 (2019-05-09)¶

Predict script enhancements (GH#103) and dask channel chunking fix (GH#104).
Directly jit DFT functions (GH#100, GH#101)
Spectral Models (GH#86)
Fix radec sign conversion in wsclean sky model (GH#96)
Full Time and Channel Averaging Implementation (GH#80, GH#97, GH#98)
Support integer seconds in wsclean ra and dec columns (GH#91, GH#93)
Fix ratio computation in Gaussian Shape (GH#89, GH#90)

0.1.4 (2019-03-11)¶

Support complete and complete-cuda to support non-GPU installs (GH#87)
Gaussian Shape Parameter Implementation (GH#82, GH#83)
WSClean Spectral Model (GH#81)
Compare predict versus MeqTrees (GH#79)
Time and channel averaging (GH#75)
cupy implementation of predict_vis (GH#73)
Introduce transpose in second antenna term of predict (GH#72)
cupy implementation of feed_rotation (GH#67)
cupy implementation of stokes_convert kernel (GH#65)
Add a basic RIME example (GH#64)
requires_optional accepts ImportError’s for a better debugging experience (GH#62, GH#63)
Added fit_component_spi function (GH#61)
cupy implementation of the phase_delay kernel (GH#59)
Correct phase_delay argument ordering (GH#57)
Support dask for radec_to_lmn and lmn_to_radec. Also add support for radec_to_lm and lm_to_radec (GH#56)
Added test for dft to test if image space covariance is symmetric(GH#55)
Correct Parallactic Angle Computation (GH#49)
Enhance visibility predict (GH#50)
Fix Kaiser Bessel filter and taper (GH#48)
Stokes/Correlation conversion (GH#41)
Fix gridding examples (GH#43)
Add simple dask gridder example (GH#42)
Implement Kaiser Bessel filter (GH#38)
Implement W-stacking gridder/degridder (GH#38)
Use 2D filters by default (GH#37)
Fixed bug in im_to_vis. Added more tests for im_to_vis. Removed division by $n$ since it is trivial to reinstate after the fact. (GH#34)
Move numba implementations out of API functions. (GH#33)
Zernike Polynomial Direction Dependent Effects (GH#18, GH#30)
Added division by $n$ to DFT. Fixed dask chunking issue. Updated test_vis_to_im_dask (GH#29).
Implement RIME visibility predict (GH#24, GH#25)
Direct Fourier Transform (GH#19)
Parallactic Angle computation (GH#15)
Implement Feed Rotation term (GH#14)
Swap gridding correlation dimensions (GH#13)
Implement Direction Dependent Effect beam cubes (GH#12)
Implement Brightness Matrix Calculation (GH#9)
Implement RIME Phase Delay term (GH#8)
Support user supplied grids (GH#7)
Add dask wrappers to the gridder and degridder (GH#4)
Add weights to gridder/degridder and remove PSF function (GH#2)

0.1.2 (2018-03-28)¶

First release on PyPI.