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 linearXX,XY,YX,YY
and circularRR, 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
canoutput
can be arbitrarily nested or ordered lists, but the appropriate inputs must be present to produce the requested outputs.The elements of
input
andoutput
may be strings or integers representing stokes parameters or correlations. See the Notes for a full list.Parameters: - input :
numpy.ndarray
Complex or floating point input data of shape
(dim_1, ..., dim_n, icorr_1, ..., icorr_m)
- input_schema : list of str or int
A schema describing the
icorr_1, ..., icorr_m
dimension ofinput
. Must have the same shape as the last dimensions ofinput
.- output_schema : list of str or int
A schema describing the
ocorr_1, ..., ocorr_n
dimension of the return value.
Returns: - result :
numpy.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 inoutput
.
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 }}
- input :
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 linearXX,XY,YX,YY
and circularRR, 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
canoutput
can be arbitrarily nested or ordered lists, but the appropriate inputs must be present to produce the requested outputs.The elements of
input
andoutput
may be strings or integers representing stokes parameters or correlations. See the Notes for a full list.Parameters: - input :
cupy.ndarray
Complex or floating point input data of shape
(dim_1, ..., dim_n, icorr_1, ..., icorr_m)
- input_schema : list of str or int
A schema describing the
icorr_1, ..., icorr_m
dimension ofinput
. Must have the same shape as the last dimensions ofinput
.- output_schema : list of str or int
A schema describing the
ocorr_1, ..., ocorr_n
dimension of the return value.
Returns: - result :
cupy.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 inoutput
.
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 }}
- input :
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 linearXX,XY,YX,YY
and circularRR, 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
canoutput
can be arbitrarily nested or ordered lists, but the appropriate inputs must be present to produce the requested outputs.The elements of
input
andoutput
may be strings or integers representing stokes parameters or correlations. See the Notes for a full list.Parameters: - input :
dask.array.Array
Complex or floating point input data of shape
(dim_1, ..., dim_n, icorr_1, ..., icorr_m)
- input_schema : list of str or int
A schema describing the
icorr_1, ..., icorr_m
dimension ofinput
. Must have the same shape as the last dimensions ofinput
.- output_schema : list of str or int
A schema describing the
ocorr_1, ..., ocorr_n
dimension of the return value.
Returns: - result :
dask.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 inoutput
.
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 }}
- input :
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) & = & \sum_{i=0} \alpha_{i} (\lambda / \lambda_0 - 1)^i \, \textrm{where} \, \alpha_0 = I(\lambda_0) \\ \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: - stokes :
numpy.ndarray
Stokes parameters of shape
(source,)
or(source, pol)
. If apol
dimension is present, then it must also be present onspi
.- spi :
numpy.ndarray
Spectral index of shape
(source, spi-comps)
or(source, spi-comps, pol)
.- ref_freq :
numpy.ndarray
Reference frequencies of shape
(source,)
- frequencies :
numpy.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_model :
numpy.ndarray
Spectral Model of shape
(source, chan)
or(source, chan, pol)
.
- stokes :
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) & = & \sum_{i=0} \alpha_{i} (\lambda / \lambda_0 - 1)^i \, \textrm{where} \, \alpha_0 = I(\lambda_0) \\ \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: - stokes :
dask.array.Array
Stokes parameters of shape
(source,)
or(source, pol)
. If apol
dimension is present, then it must also be present onspi
.- spi :
dask.array.Array
Spectral index of shape
(source, spi-comps)
or(source, spi-comps, pol)
.- ref_freq :
dask.array.Array
Reference frequencies of shape
(source,)
- frequencies :
dask.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_model :
dask.array.Array
Spectral Model of shape
(source, chan)
or(source, chan, pol)
.
- stokes :
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
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, tol=1e-06, maxiter=100, dtype=<type 'numpy.float64'>)[source]¶ Computes the spectral indices and the intensity at the reference frequency of a spectral index model:
\[I(\nu) = I(\nu_0) \left( \frac{\nu}{\nu_0} \right) ^ \alpha\]Parameters: - data :
numpy.ndarray
array of shape
(comps, chan)
The noisy data as a function of frequency.- weights :
numpy.ndarray
array of shape
(chan,)
Inverse of variance on each frequency axis.- freqs :
numpy.ndarray
frequencies of shape
(chan,)
- freq0 : float
Reference frequency
- alphai :
numpy.ndarray
, optional array of shape
(comps,)
Initial guess for the alphas. Defaults to -0.7.- I0i :
numpy.ndarray
, optional array of shape
(comps,)
Initial guess for the intensities at the reference frequency. Defaults to 1.0.- tol : float, optional
Solver absolute tolerance (optional). Defaults to 1e-6.
- maxiter : int, optional
Solver maximum iterations (optional). Defaults to 100.
- dtype : np.dtype, optional
Datatype of result. Should be either np.float32 or np.float64. Defaults to np.float64.
Returns: - out :
numpy.ndarray
array of shape
(4, comps)
The fitted components arranged as [alphas, alphavars, I0s, I0vars]
- data :
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, tol=1e-06, maxiter=100, dtype=<type 'numpy.float64'>)[source]¶ Computes the spectral indices and the intensity at the reference frequency of a spectral index model:
\[I(\nu) = I(\nu_0) \left( \frac{\nu}{\nu_0} \right) ^ \alpha\]Parameters: - data :
dask.array.Array
array of shape
(comps, chan)
The noisy data as a function of frequency.- weights :
dask.array.Array
array of shape
(chan,)
Inverse of variance on each frequency axis.- freqs :
dask.array.Array
frequencies of shape
(chan,)
- freq0 : float
Reference frequency
- alphai :
dask.array.Array
, optional array of shape
(comps,)
Initial guess for the alphas. Defaults to -0.7.- I0i :
dask.array.Array
, optional array of shape
(comps,)
Initial guess for the intensities at the reference frequency. Defaults to 1.0.- tol : float, optional
Solver absolute tolerance (optional). Defaults to 1e-6.
- maxiter : int, optional
Solver maximum iterations (optional). Defaults to 100.
- dtype : np.dtype, optional
Datatype of result. Should be either np.float32 or np.float64. Defaults to np.float64.
Returns: - out :
dask.array.Array
array of shape
(4, comps)
The fitted components arranged as [alphas, alphavars, I0s, I0vars]
- data :
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: - uvw :
numpy.ndarray
UVW coordinates of shape
(row, 3)
- frequency :
numpy.ndarray
frequencies of shape
(chan,)
- shape_param :
numpy.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_shape :
numpy.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: - uvw :
dask.array.Array
UVW coordinates of shape
(row, 3)
- frequency :
dask.array.Array
frequencies of shape
(chan,)
- shape_param :
dask.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_shape :
dask.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: - filename : str 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
See also
-
africanus.model.wsclean.
spectra
(I, coeffs, log_poly, 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: - I :
numpy.ndarray
flux density in Janskys at the reference frequency of shape
(source,)
- coeffs :
numpy.ndarray
Polynomial coefficients for each source of shape
(source, comp)
- log_poly :
numpy.ndarray
or bool boolean array of shape
(source, )
indicating whether logarithmic (True) or ordinary (False) polynomials should be used.- ref_freq :
numpy.ndarray
Source reference frequencies of shape
(source,)
- frequency :
numpy.ndarray
frequencies of shape
(chan,)
Returns: - spectral_model :
numpy.ndarray
Spectral Model of shape
(source, chan)
See also
- I :
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: - I :
dask.array.Array
flux density in Janskys at the reference frequency of shape
(source,)
- coeffs :
dask.array.Array
Polynomial coefficients for each source of shape
(source, comp)
- log_poly :
dask.array.Array
or bool boolean array of shape
(source, )
indicating whether logarithmic (True) or ordinary (False) polynomials should be used.- ref_freq :
dask.array.Array
Source reference frequencies of shape
(source,)
- frequency :
dask.array.Array
frequencies of shape
(chan,)
Returns: - spectral_model :
dask.array.Array
Spectral Model of shape
(source, chan)
See also
- I :