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.
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:
- I. A full-sky Jones formalism
- II. Calibration and direction-dependent effects
- III. Addressing direction-dependent effects in 21cm WSRT observations of 3C147
- IV. A generalized tensor formalism
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) |
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, coords, l_grid, m_grid, …) |
Computes Direction Dependent Effects (E) by sampling complex values in beam at the coordinates coords . |
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 . |
-
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:
\[V_{pq} = G_{p} \left( B_{pq} + \sum_{s} A_{ps} X_{pqs} A_{qs}^H \right) G_{q}^H\]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_index :
numpy.ndarray
Time index used to look up the antenna Jones index for a particular baseline. shape
(row,)
.- antenna1 :
numpy.ndarray
Antenna 1 index used to look up the antenna Jones for a particular baseline. with shape
(row,)
.- antenna2 :
numpy.ndarray
Antenna 2 index used to look up the antenna Jones for a particular baseline. with shape
(row,)
.- dde1_jones :
numpy.ndarray
, optional \(A_{ps}\) Direction-Dependent Jones terms for the first antenna. shape
(source,time,ant,chan,corr_1,corr_2)
- source_coh :
numpy.ndarray
, optional \(X_{pqs}\) Direction-Dependent Coherency matrix for the baseline. with shape
(source,row,chan,corr_1,corr_2)
- dde2_jones :
numpy.ndarray
, optional \(A_{qs}\) Direction-Dependent Jones terms for the second antenna. shape
(source,time,ant,chan,corr_1,corr_2)
- die1_jones :
numpy.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_vis :
numpy.ndarray
, optional \(B_{pq}\) base visibilities, added to source coherency summation before multiplication with die1_jones and die2_jones.
- die2_jones :
numpy.ndarray
, optional \(G_{ps}\) Direction-Independent Jones terms for the second antenna of the baseline. with shape
(time,ant,chan,corr_1,corr_2)
Returns: - visibilities :
numpy.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
andant
(antenna) dimensions. - Each
row
is associated with a pair of antenna Jones matrices at a particular timestep via thetime_index
,antenna1
andantenna2
inputs. - The
row
dimension must be an increasing partial order in time.
-
africanus.rime.
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: - lm :
numpy.ndarray
LM coordinates of shape
(source, 2)
with L and M components in the last dimension.- uvw :
numpy.ndarray
UVW coordinates of shape
(row, 3)
with U, V and W components in the last dimension.- frequency :
numpy.ndarray
frequencies of shape
(chan,)
Returns: - complex_phase :
numpy.ndarray
complex of shape
(source, row, chan)
Notes
Corresponds to the complex exponential of the Van Cittert-Zernike Theorem.
MeqTrees uses a positive sign convention and so any UVW coordinates must be inverted in order for their phase delay terms (and therefore visibilities) to agree.
- lm :
-
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: - times :
numpy.ndarray
Array of Mean Julian Date times in seconds with shape
(time,)
,- antenna_positions :
numpy.ndarray
Antenna positions of shape
(ant, 3)
in metres in the ITRF frame.- field_centre :
numpy.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 onpython-casacore
. This backend should be used by default.test
creates parallactic angles by multiplying thetimes
andantenna_position
arrays. It exist solely for testing.
Returns: - parallactic_angles :
numpy.ndarray
Parallactic angles of shape
(time,ant)
- times :
-
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_angles :
numpy.ndarray
floating point parallactic angles. Of shape
(pa0, pa1, ..., pan)
.- feed_type : {‘linear’, ‘circular’}
The type of feed
Returns: - feed_matrix :
numpy.ndarray
Feed rotation matrix of shape
(pa0, pa1,...,pan,2,2)
- parallactic_angles :
-
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 theparallactic_angles
- Adding
pointing_errors
- Scaling by
antenna_scaling
Parameters: - lm :
numpy.ndarray
LM coordinates of shape
(src,2)
in radians offset from the phase centre.- parallactic_angles :
numpy.ndarray
parallactic angles of shape
(time, antenna)
in radians.- pointing_errors :
numpy.ndarray
LM pointing errors for each antenna at each timestep in radians. Has shape
(time, antenna, 2)
- antenna_scaling :
numpy.ndarray
antenna scaling factor for each channel and each antenna. Has shape
(antenna, chan)
- frequency :
numpy.ndarray
frequencies for each channel. Has shape
(chan,)
- dtype :
numpy.dtype
, optional Numpy dtype of result array. Should be float32 or float64. Defaults to float64
Returns: - coords :
numpy.ndarray
coordinates of shape
(3, src, time, antenna, chan)
where each coordinate component represents l, m and frequency, respectively.
- Rotating
-
africanus.rime.
beam_cube_dde
(beam, coords, l_grid, m_grid, freq_grid, spline_order=1, mode=u'nearest')[source]¶ Computes Direction Dependent Effects (E) by sampling complex values in
beam
at the coordinatescoords
.Both real and imaginary beam values are sampled at the given coordinates and normalised to form a mean of circular quantities.
l_grid
,m_grid
andfreq_grid
can be obtained frombeam_grids()
.Parameters: - beam :
numpy.ndarray
complex beam cube of shape
(beam_lw, beam_mh, beam_nud, corr_1, corr_2)
wherebeam_lw
is the grid width of the l dimension,beam_mh
is the grid height of the m dimension andbeam_nud
is the grid depth of the frequency dimension. Eithercorr_1
or bothcorr_1
andcorr_2
may be present, representing 1, 2 or 2x2 correlations respectively.- coords :
numpy.ndarray
beam cube coordinates of shape
(coords, dim_1, ..., dim_n)
wherecoord
always has size 3 and refers to (l,m,frequency).- l_grid :
numpy.ndarray
Monotonically increasing or decreasing grid values for the l axis, with shape
(beam_lw,)
. If decreasing, the- m_grid :
numpy.ndarray
Monotonically increasing or decreasing grid values for the m axis, with shape
(beam_mh,)
- freq_grid :
numpy.ndarray
Monotonically increasing grid values for the frequency axis, with shape
(beam_nud,)
- spline_order : int
Spline order to use in
scipy.ndimage.interpolation.map_coordinates()
. Defaults to 1 (‘linear’)- mode : str
Border mode to use in
scipy.ndimage.interpolation.map_coordinates()
Defaults to ‘nearest’
Returns: - ddes :
numpy.ndarray
Sampled complex beam values at the specified coordinates with shape
(dim_1, ..., dim_n, corr_1, corr_2)
- beam :
-
africanus.rime.
zernike_dde
(coords, coeffs, noll_index)[source]¶ Computes Direction Dependent Effects by evaluating Zernicke Polynomials defined by coefficients
coeffs
and noll indexesnoll_index
at the specified coordinatescoords
.Decomposition of a voxel beam cube into Zernicke polynomial coefficients can be achieved through the use of the eidos package.
Parameters: - coords :
numpy.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.- coeffs :
numpy.ndarray
complex Zernicke polynomial coefficients. Has shape
(ant, chan, corr_1, ..., corr_n, poly)
wherepoly
is the number of polynomial coefficients andcorr_1, ..., corr_n
are a variable number of correlation dimensions.- noll_index :
numpy.ndarray
Noll index associated with each polynomial coefficient. Has shape
(ant, chan, corr_1, ..., corr_n, poly)
.
Returns: - dde :
numpy.ndarray
complex values with shape
(source, time, ant, chan, corr_1, ..., corr_n)
- coords :
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 . |
-
africanus.rime.cuda.
predict_vis
(time_index, antenna1, antenna2, dde1_jones, source_coh, dde2_jones, die1_jones, base_vis, die2_jones)[source]¶ Multiply Jones terms together to form model visibilities according to the following formula:
\[V_{pq} = G_{p} \left( B_{pq} + \sum_{s} A_{ps} X_{pqs} A_{qs}^H \right) G_{q}^H\]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_index :
cupy.ndarray
Time index used to look up the antenna Jones index for a particular baseline. shape
(row,)
.- antenna1 :
cupy.ndarray
Antenna 1 index used to look up the antenna Jones for a particular baseline. with shape
(row,)
.- antenna2 :
cupy.ndarray
Antenna 2 index used to look up the antenna Jones for a particular baseline. with shape
(row,)
.- dde1_jones :
cupy.ndarray
, optional \(A_{ps}\) Direction-Dependent Jones terms for the first antenna. shape
(source,time,ant,chan,corr_1,corr_2)
- source_coh :
cupy.ndarray
, optional \(X_{pqs}\) Direction-Dependent Coherency matrix for the baseline. with shape
(source,row,chan,corr_1,corr_2)
- dde2_jones :
cupy.ndarray
, optional \(A_{qs}\) Direction-Dependent Jones terms for the second antenna. shape
(source,time,ant,chan,corr_1,corr_2)
- die1_jones :
cupy.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_vis :
cupy.ndarray
, optional \(B_{pq}\) base visibilities, added to source coherency summation before multiplication with die1_jones and die2_jones.
- die2_jones :
cupy.ndarray
, optional \(G_{ps}\) Direction-Independent Jones terms for the second antenna of the baseline. with shape
(time,ant,chan,corr_1,corr_2)
Returns: - visibilities :
cupy.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
andant
(antenna) dimensions. - Each
row
is associated with a pair of antenna Jones matrices at a particular timestep via thetime_index
,antenna1
andantenna2
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: - lm :
cupy.ndarray
LM coordinates of shape
(source, 2)
with L and M components in the last dimension.- uvw :
cupy.ndarray
UVW coordinates of shape
(row, 3)
with U, V and W components in the last dimension.- frequency :
cupy.ndarray
frequencies of shape
(chan,)
Returns: - complex_phase :
cupy.ndarray
complex of shape
(source, row, chan)
Notes
Corresponds to the complex exponential of the Van Cittert-Zernike Theorem.
MeqTrees uses a positive sign convention and so any UVW coordinates must be inverted in order for their phase delay terms (and therefore visibilities) to agree.
- lm :
-
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_angles :
cupy.ndarray
floating point parallactic angles. Of shape
(pa0, pa1, ..., pan)
.- feed_type : {‘linear’, ‘circular’}
The type of feed
Returns: - feed_matrix :
cupy.ndarray
Feed rotation matrix of shape
(pa0, pa1,...,pan,2,2)
- parallactic_angles :
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) |
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, coords, l_grid, m_grid, …) |
Computes Direction Dependent Effects (E) by sampling complex values in beam at the coordinates coords . |
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 . |
-
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)[source]¶ Multiply Jones terms together to form model visibilities according to the following formula:
\[V_{pq} = G_{p} \left( B_{pq} + \sum_{s} A_{ps} X_{pqs} A_{qs}^H \right) G_{q}^H\]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_index :
dask.array.Array
Time index used to look up the antenna Jones index for a particular baseline. shape
(row,)
.- antenna1 :
dask.array.Array
Antenna 1 index used to look up the antenna Jones for a particular baseline. with shape
(row,)
.- antenna2 :
dask.array.Array
Antenna 2 index used to look up the antenna Jones for a particular baseline. with shape
(row,)
.- dde1_jones :
dask.array.Array
, optional \(A_{ps}\) Direction-Dependent Jones terms for the first antenna. shape
(source,time,ant,chan,corr_1,corr_2)
- source_coh :
dask.array.Array
, optional \(X_{pqs}\) Direction-Dependent Coherency matrix for the baseline. with shape
(source,row,chan,corr_1,corr_2)
- dde2_jones :
dask.array.Array
, optional \(A_{qs}\) Direction-Dependent Jones terms for the second antenna. shape
(source,time,ant,chan,corr_1,corr_2)
- die1_jones :
dask.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_vis :
dask.array.Array
, optional \(B_{pq}\) base visibilities, added to source coherency summation before multiplication with die1_jones and die2_jones.
- die2_jones :
dask.array.Array
, optional \(G_{ps}\) Direction-Independent Jones terms for the second antenna of the baseline. with shape
(time,ant,chan,corr_1,corr_2)
Returns: - visibilities :
dask.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
andant
(antenna) dimensions.Each
row
is associated with a pair of antenna Jones matrices at a particular timestep via thetime_index
,antenna1
andantenna2
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 eachrow
can contain any antenna, random access must be preserved along this dimension.The chunks in the
row
andtime
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]
indexing10
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
andtime
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:
The number chunks in
row
andtime
must match although the individual chunk sizes need not.Unique timesteps should not be split across row chunks.
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)
Use
aggregate_chunks()
to aggregate multiplerow
andtime
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)[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: - lm :
dask.array.Array
LM coordinates of shape
(source, 2)
with L and M components in the last dimension.- uvw :
dask.array.Array
UVW coordinates of shape
(row, 3)
with U, V and W components in the last dimension.- frequency :
dask.array.Array
frequencies of shape
(chan,)
Returns: - complex_phase :
dask.array.Array
complex of shape
(source, row, chan)
Notes
Corresponds to the complex exponential of the Van Cittert-Zernike Theorem.
MeqTrees uses a positive sign convention and so any UVW coordinates must be inverted in order for their phase delay terms (and therefore visibilities) to agree.
- lm :
-
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: - times :
dask.array.Array
Array of Mean Julian Date times in seconds with shape
(time,)
,- antenna_positions :
dask.array.Array
Antenna positions of shape
(ant, 3)
in metres in the ITRF frame.- field_centre :
dask.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 onpython-casacore
. This backend should be used by default.test
creates parallactic angles by multiplying thetimes
andantenna_position
arrays. It exist solely for testing.
Returns: - parallactic_angles :
dask.array.Array
Parallactic angles of shape
(time,ant)
- times :
-
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_angles :
numpy.ndarray
floating point parallactic angles. Of shape
(pa0, pa1, ..., pan)
.- feed_type : {‘linear’, ‘circular’}
The type of feed
Returns: - feed_matrix :
numpy.ndarray
Feed rotation matrix of shape
(pa0, pa1,...,pan,2,2)
- parallactic_angles :
-
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 theparallactic_angles
- Adding
pointing_errors
- Scaling by
antenna_scaling
Parameters: - lm :
dask.array.Array
LM coordinates of shape
(src,2)
in radians offset from the phase centre.- parallactic_angles :
dask.array.Array
parallactic angles of shape
(time, antenna)
in radians.- pointing_errors :
dask.array.Array
LM pointing errors for each antenna at each timestep in radians. Has shape
(time, antenna, 2)
- antenna_scaling :
dask.array.Array
antenna scaling factor for each channel and each antenna. Has shape
(antenna, chan)
- frequency :
dask.array.Array
frequencies for each channel. Has shape
(chan,)
- dtype :
numpy.dtype
, optional Numpy dtype of result array. Should be float32 or float64. Defaults to float64
Returns: - coords :
dask.array.Array
coordinates of shape
(3, src, time, antenna, chan)
where each coordinate component represents l, m and frequency, respectively.
- Rotating
-
africanus.rime.dask.
beam_cube_dde
(beam, coords, l_grid, m_grid, freq_grid, spline_order=1, mode='nearest')[source]¶ Computes Direction Dependent Effects (E) by sampling complex values in
beam
at the coordinatescoords
.Both real and imaginary beam values are sampled at the given coordinates and normalised to form a mean of circular quantities.
l_grid
,m_grid
andfreq_grid
can be obtained frombeam_grids()
.Parameters: - beam :
dask.array.Array
complex beam cube of shape
(beam_lw, beam_mh, beam_nud, corr_1, corr_2)
wherebeam_lw
is the grid width of the l dimension,beam_mh
is the grid height of the m dimension andbeam_nud
is the grid depth of the frequency dimension. Eithercorr_1
or bothcorr_1
andcorr_2
may be present, representing 1, 2 or 2x2 correlations respectively.- coords :
dask.array.Array
beam cube coordinates of shape
(coords, dim_1, ..., dim_n)
wherecoord
always has size 3 and refers to (l,m,frequency).- l_grid :
dask.array.Array
Monotonically increasing or decreasing grid values for the l axis, with shape
(beam_lw,)
. If decreasing, the- m_grid :
dask.array.Array
Monotonically increasing or decreasing grid values for the m axis, with shape
(beam_mh,)
- freq_grid :
dask.array.Array
Monotonically increasing grid values for the frequency axis, with shape
(beam_nud,)
- spline_order : int
Spline order to use in
scipy.ndimage.interpolation.map_coordinates()
. Defaults to 1 (‘linear’)- mode : str
Border mode to use in
scipy.ndimage.interpolation.map_coordinates()
Defaults to ‘nearest’
Returns: - ddes :
dask.array.Array
Sampled complex beam values at the specified coordinates with shape
(dim_1, ..., dim_n, corr_1, corr_2)
- beam :
-
africanus.rime.dask.
zernike_dde
(coords, coeffs, noll_index)[source]¶ Computes Direction Dependent Effects by evaluating Zernicke Polynomials defined by coefficients
coeffs
and noll indexesnoll_index
at the specified coordinatescoords
.Decomposition of a voxel beam cube into Zernicke polynomial coefficients can be achieved through the use of the eidos package.
Parameters: - coords :
dask.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.- coeffs :
dask.array.Array
complex Zernicke polynomial coefficients. Has shape
(ant, chan, corr_1, ..., corr_n, poly)
wherepoly
is the number of polynomial coefficients andcorr_1, ..., corr_n
are a variable number of correlation dimensions.- noll_index :
dask.array.Array
Noll index associated with each polynomial coefficient. Has shape
(ant, chan, corr_1, ..., corr_n, poly)
.
Returns: - dde :
dask.array.Array
complex values with shape
(source, time, ant, chan, corr_1, ..., corr_n)
- coords :