"""Source Extraction Helpers.
These are used in conjunction with image.ImageData.
"""
import logging
from collections.abc import MutableMapping
import numpy as np
from numba import guvectorize, float64, float32, int32
from sourcefinder.deconv import (
deconv,
covariance_matrix,
cov_p_to_cov_S,
cov_S_to_cov_r,
)
from sourcefinder.utility import coordinates
from sourcefinder.utility.uncertain import Uncertain
from . import measure
from . import utils
from .config import Conf, ImgConf
from .gaussian import gaussian
np.seterr(divide="raise", over="raise", invalid="raise")
try:
import ndimage
except ImportError:
from scipy import ndimage
[docs]
logger = logging.getLogger(__name__)
# This is used as a dummy value, -BIGNUM values will be always be masked.
# As such, it should be larger than the expected range of real values,
# since we will get negative values representing real data after
# background subtraction, etc.
[docs]
sigma_to_ax = np.sqrt(2.0 * np.log(2.0))
[docs]
class Island(object):
"""The source extraction process forms islands, which it then fits.
Each island needs to know its position in the image (ie, x, y pixel
value at one corner), the threshold above which it is detected
(analysis_threshold by default, but will increase if the island is
the result of deblending), and a data array.
The island should provide a means of deblending: splitting itself
apart and returning multiple sub-islands, if necessary.
Parameters
----------
data : ndarray
A 2D array representing the rectangular patch of the observational
image encompassing the island. Values as small as -BIGNUM denote
pixels outside the island, they will typically be in the corners of
the patch.
rms : MaskedArray
A 2D masked array representing the patch of the rms noise map,
corresponding to the same pixel positions as `data`. The values are
interpolated from a grid of standard deviations of the background
noise across the image.
chunk : tuple of slices
Defines the corners of the patch encompassing the island as a
tuple of slices.
detection_map : MaskedArray
A 2D masked array corresponding to the same patch of the sky as
`data`, but applied to the detection threshold map. Typically a
higher threshold than the analysis threshold map.
beam : tuple of floats
The clean beam parameters as the semi-major and semi-minor axes
in pixel coordinates and the position angle in radians.
image_conf : config.ImgConf
Holds the configuration parameters for observational image processing.
analysis_threshold : float, default: None
The analysis threshold, when multiplied with the local rms noise,
segments the observational image - with the mean background
subtracted - into islands. Only applied in the deblending process,
then it will be set to 1.0.
rms_orig : MaskedArray, default: None
The original rms noise of the island.
flux_orig : float, default: None
The original flux value of the island.
subthrrange : ndarray, default: None
The subthreshold range for deblending.
"""
def __init__(
self,
data,
rms,
chunk,
detection_map,
beam,
image_conf,
analysis_threshold=None,
rms_orig=None,
flux_orig=None,
subthrrange=None,
):
[docs]
self.image_conf = image_conf
# deblend_nthresh is the number of subthresholds used when deblending.
[docs]
self.deblend_nthresh = self.image_conf.deblend_nthresh
# If we deblend too far, we hit the recursion limit. And it's slow.
if self.deblend_nthresh > 300:
logger.warning("Limiting to 300 deblending subtresholds")
self.deblend_nthresh = 300
else:
logger.debug("Using %d subthresholds", self.deblend_nthresh)
# Deblended components of this island must contain at least
# deblend_mincont times the total flux of the original to be regarded
# as significant.
[docs]
self.deblend_mincont = self.image_conf.deblend_mincont
# The structuring element defines connectivity between pixels.
[docs]
self.structuring_element = self.image_conf.structuring_element
# NB we have set all unused data to -(lots) before passing it to
# Island().
mask = np.where(data > -BIGNUM / 10.0, 0, 1)
[docs]
self.data = np.ma.array(data, mask=mask)
if analysis_threshold is None:
self.analysis_threshold = self.image_conf.analysis_thr
else:
self.analysis_threshold = analysis_threshold
[docs]
self.detection_map = detection_map
[docs]
self.max_pos = ndimage.maximum_position(self.data.filled(fill_value=0))
[docs]
self.position = (self.chunk[0].start, self.chunk[1].start)
if not isinstance(rms_orig, np.ndarray):
self.rms_orig = self.rms
else:
self.rms_orig = rms_orig
# The idea here is to retain the flux of the original, unblended
# island. That flux is used as a criterion for deblending.
if not isinstance(flux_orig, float):
self.flux_orig = self.data.sum()
else:
self.flux_orig = flux_orig
if isinstance(subthrrange, np.ndarray):
self.subthrrange = subthrrange
else:
self.subthrrange = utils.generate_subthresholds(
self.data.min(), self.data.max(), self.deblend_nthresh
)
[docs]
def deblend(self, niter=0):
"""Decompose the island into subislands.
Parameters
----------
niter : int, default: 0
A value of niter corresponds to a subthreshold level. There will be
self.deblend_nthresh subthresholds in total, evenly spaced
logarithmically, between the lowest and highest pixel value, but not
include these limits. niter==0 corresponds to the lowest
subthreshold, i.e. to the subthreshold just above self.data.min().
Returns
-------
numpy.ndarray
A decomposed numpy array of all the subislands.
Notes
-----
This function iterates up through subthresholds, looking for the island
to split into two or more separate islands. If splitting occurs, the
function starts again with the new subislands.
"""
logger.debug("Deblending source")
for level in self.subthrrange[niter:]:
# The idea is to retain the parent island when no significant
# subislands are found and jump to the next subthreshold
# using niter.
# Deblending is started at a level higher than the lowest
# pixel value in the island.
# Deblending at the level of the lowest pixel value will
# likely not yield anything, because the island was formed at
# threshold just below that.
# So that is why we use niter+1 (>=1) instead of niter (>=0).
if level > self.data.max():
# level is above the highest pixel value...
# Return the current island.
break
clipped_data = np.where(
self.data.filled(fill_value=0) >= level, 1, 0
)
labels, number = ndimage.label(
clipped_data, self.structuring_element
)
# If we have more than one island, then we need to make subislands.
if number > 1:
subislands = []
label = 0
for chunk in ndimage.find_objects(labels):
label += 1
newdata = np.where(
labels == label,
self.data.filled(fill_value=-BIGNUM),
-BIGNUM,
)
# NB: In class Island(object), rms * analysis_threshold
# is taken as the threshold for the bottom of the island.
# Everything below that level is masked.
# For subislands, this product should be equal to level
# and flat, i.e., horizontal.
# We can achieve this by setting rms=level*ones and
# analysis_threshold=1.
island = Island(
newdata[chunk],
np.ones(self.data[chunk].shape) * level,
(
slice(
self.chunk[0].start + chunk[0].start,
self.chunk[0].start + chunk[0].stop,
),
slice(
self.chunk[1].start + chunk[1].start,
self.chunk[1].start + chunk[1].stop,
),
),
self.detection_map[chunk],
self.beam,
self.image_conf,
analysis_threshold=1,
rms_orig=self.rms_orig[
chunk[0].start : chunk[0].stop,
chunk[1].start : chunk[1].stop,
],
flux_orig=self.flux_orig,
subthrrange=self.subthrrange,
)
subislands.append(island)
# This line should filter out any subisland with insufficient
# flux, in about the same way as SExtractor.
# Sufficient means: the flux of the branch above the
# subthreshold (=level) must exceed some user given fraction
# of the composite object, i.e., the original island.
subislands = [
isl
for isl in subislands
if (isl.data - level * np.ma.ones_like(isl.data)).sum()
> self.deblend_mincont * self.flux_orig
]
# Discard subislands below detection threshold
subislands = [
isl
for isl in subislands
if (isl.data - isl.detection_map).max() >= 0
]
numbersignifsub = len(subislands)
# Proceed with the previous island, but make sure the next
# subthreshold is higher than the present one.
# Or we would end up in an infinite loop...
if numbersignifsub > 1:
if niter + 1 < self.deblend_nthresh:
# Apparently, the map command always results in
# nested lists.
return list(
utils.flatten(
[
island.deblend(niter=niter + 1)
for island in subislands
]
)
)
else:
return subislands
elif numbersignifsub == 1 and niter + 1 < self.deblend_nthresh:
return Island.deblend(self, niter=niter + 1)
else:
# In this case we have numbersignifsub == 0 or
# (1 and reached the highest subthreshold level).
# Pull out of deblending loop, return current island.
break
# We've not found any subislands: just return this island.
return self
[docs]
def threshold(self):
"""Threshold for island segmentation.
It is expressed as the rms noise at the position of the
island's pixel with the highest spectral brightness times the
analysis threshold.
"""
return self.noise() * self.analysis_threshold
[docs]
def noise(self):
"""Noise at position of the island pixel with the highest
spectral brightness.
"""
return self.rms[self.max_pos]
[docs]
def sig(self):
"""Source significance expressed as the maximum
signal-to-noise across the island.
"""
return (self.data / self.rms_orig).max()
[docs]
def fit(
self, fudge_max_pix_factor, beamsize, correlation_lengths, fixed=None
):
"""Fit.
Measure the source, i.e. compute its Gaussian parameters and the
corresponding errors.
Parameters
----------
fudge_max_pix_factor : float
Factor to correct for the underestimation of the peak spectral
brightness, since that peak will in general be positioned some
small angular distance from the center of the pixel with the highest
spectral brightness.
beamsize : float
The size of the clean beam, in square pixels.
correlation_lengths : tuple
2 floats describing over which distance (in pixels) noise should be
considered correlated, along both principal axes of the Gaussian
profile of the restoring beam. This has to be taken into account
when errors on source parameters are derived.
fixed : dict, default: None
Parameters & their values to be kept frozen (ie, not fitted).
Returns
-------
tuple
A tuple containing the measurement as a Paramset instance and a
Gaussian island and a Gaussian residual, both as regular ndarrays.
In those ndarrays masked (unfitted) regions have been filled with
0-values, typically in the corners of the rectangular area
encompassing the island.
"""
try:
measurement, gauss_island, gauss_residual = (
source_profile_and_errors(
self.data,
self.threshold(),
self.rms,
self.noise(),
self.beam,
fudge_max_pix_factor,
beamsize,
correlation_lengths,
self.image_conf,
fixed=fixed,
)
)
except ValueError:
# Fitting failed
logger.error(
"Moments & Gaussian fitting failed at %s"
% (str(self.position))
)
return None
measurement["xbar"] += self.position[0]
measurement["ybar"] += self.position[1]
measurement.sig = self.sig()
return measurement, gauss_island, gauss_residual
[docs]
class ParamSet(MutableMapping):
"""All the source fitting methods should go to produce a
ParamSet, which gives all the information necessary to make a
Detection.
Parameters
----------
image_conf : config.ImgConf
Holds the configuration parameters for observational image processing.
"""
def __init__(self, image_conf: ImgConf | None = None):
[docs]
self.image_conf = image_conf if image_conf is not None else ImgConf()
[docs]
self.clean_bias = self.image_conf.clean_bias
[docs]
self.clean_bias_error = self.image_conf.clean_bias_error
[docs]
self.frac_flux_cal_error = self.image_conf.frac_flux_cal_error
[docs]
self.alpha_maj1 = self.image_conf.alpha_maj1
[docs]
self.alpha_maj2 = self.image_conf.alpha_maj2
[docs]
self.alpha_min1 = self.image_conf.alpha_min1
[docs]
self.alpha_min2 = self.image_conf.alpha_min2
[docs]
self.alpha_brightness1 = self.image_conf.alpha_brightness1
[docs]
self.alpha_brightness2 = self.image_conf.alpha_brightness2
[docs]
self.measurements = {
"peak": Uncertain(),
"flux": Uncertain(),
"xbar": Uncertain(),
"ybar": Uncertain(),
"semimajor": Uncertain(),
"semiminor": Uncertain(),
"theta": Uncertain(),
"semimaj_deconv": Uncertain(),
"semimin_deconv": Uncertain(),
"theta_deconv": Uncertain(),
}
# This parameter gives the number of components that could not be
# deconvolved, IERR from deconf.f.
# These flags are used to indicate where the values stored in this
# parameterset have come from: we set them to True if & when moments
# and/or Gaussian fitting succeeds.
# Gaussian fits are preferably performed with bounds for better
# stability, but to establish those bounds in a meaningful manner
# moments estimation is required, i.e. self.moments = True.
[docs]
self.bounds: dict[str, tuple[float, float, bool]] = {}
# It is instructive to keep a record of the minimal cross-section of
# the island, i.e. is its minimal width large enough for at least a
# proper moments computation? Set thin_detection to True as default.
# Will be set to False before the start of a source measurement if the
# island is wide enough.
[docs]
self.thin_detection = True
# More metadata about the fit: only valid for Gaussian fits:
[docs]
self.reduced_chisq = None
def __getitem__(self, item):
return self.measurements[item]
def __setitem__(self, item, value):
if item in self.measurements:
if isinstance(value, Uncertain):
self.measurements[item] = value
else:
self.measurements[item].value = value
else:
raise AttributeError("Invalid parameter")
def __delitem__(self, key):
del self.measurements[key]
def __iter__(self):
return iter(self.measurements)
def __len__(self):
return len(self.measurements)
[docs]
def keys(self):
return list(self.measurements.keys())
[docs]
def compute_bounds(self, data_shape):
"""Calculate bounds for 'safer' Gauss fitting.
Here, 'safer' means a smaller chance on runaway solutions. The
bounds are largely based on moments estimation, so it only
makes sense to impose bounds if moments estimation was
successful.
Parameters
----------
data_shape : tuple of (int32, int32) or (int64, int64)
Shape of the rectangular area (slice) encompassing the island used
for the fit. This shape is used to set bounds for the position of
the source in the fitting process, i.e. the position is bounded to
be within this shape.
Returns
-------
dict of (float, float, bool) tuples
Bounds for a maximum of six Gaussian fit parameters, less if "fixed"
is not None. Each 3-tuple has lower_bound (float), upper_bound
(float) and boolean elements. If the boolean is True, a bound will
be loosened when the fit becomes unfeasible. See the documentation
on scipy.optimize.Bounds for details.
"""
if hasattr(self["peak"], "value"):
self.bounds["peak"] = (
0.5 * self["peak"].value,
1.5 * self["peak"].value,
False,
)
else:
self.bounds["peak"] = (
0.5 * self["peak"],
1.5 * self["peak"],
False,
)
# Accommodate for negative heights. The "bounds" argument in
# scipy.optimize.least-squares demands that the lower bound is
# smaller than the upper bound and with the (0.5, 1.5) fractions
# this does not work out well for negative heights. Background:
# only to be expected in images from visibilities from polarization
# products other than Stokes I.
if self.bounds["peak"][0] > self.bounds["peak"][1]:
true_upper = self.bounds["peak"][0]
true_lower = self.bounds["peak"][1]
self.bounds["peak"] = (true_lower, true_upper, False)
if hasattr(self["semimajor"], "value"):
self.bounds["semimajor"] = (
0.5 * self["semimajor"].value,
1.5 * self["semimajor"].value,
False,
)
else:
self.bounds["semimajor"] = (
0.5 * self["semimajor"],
1.5 * self["semimajor"],
False,
)
if hasattr(self["semiminor"], "value"):
self.bounds["semiminor"] = (
0.5 * self["semiminor"].value,
1.5 * self["semiminor"].value,
False,
)
else:
self.bounds["semiminor"] = (
0.5 * self["semiminor"],
1.5 * self["semiminor"],
False,
)
self.bounds["xbar"] = (0.0, data_shape[0], False)
self.bounds["ybar"] = (0.0, data_shape[1], False)
# The upper bound for theta is a bit odd, one would expect
# np.pi/2 here, but that will yield imperfect fits in
# cases where the axes are aligned with the coordinate axes,
# which, in turn, breaks the AxesSwapGaussTest.testFitHeight
# and AxesSwapGaussTest.testFitSize unit tests. Thus, some
# margin needs to be applied.
# keep_feasibly is True here to accommodate for a fitting process
# where the margin is exceeded.
self.bounds["theta"] = (-np.pi / 2, np.pi, True)
return self
[docs]
def calculate_errors(self, noise, correlation_lengths, threshold):
"""Calculate 1-sigma error bars for the source parameters.
This method uses the Condon formulae if the object is based on a
Gaussian fit, or error bars from moments if it's based on moments.
Parameters
----------
noise : float
The noise level at the position of the island pixel with the
highest spectral brightness.
correlation_lengths : tuple of floats
Tuple describing over which distance (in pixels) noise should be
considered correlated, along both principal axes of the Gaussian
profile of the restoring beam.
threshold : float
The threshold for island segmentation expressed as the rms noise at
the position of the island's pixel with the highest spectral
brightness times the analysis threshold.
Returns
-------
An updated ParamSet instance
"""
if self.gaussian:
return self._condon_formulae(noise, correlation_lengths)
else:
# If thin_detection == True, _error_bars_from_moments probably
# gives a better estimate of the true errors than errors from
# Gaussian fits, i.e. from _condon_formulae, since they are
# generally larger. _error_bars_from_moments could still be
# underestimating the true errors in case of thin detections.
if not threshold:
threshold = 0
return self._error_bars_from_moments(
noise, correlation_lengths, threshold
)
[docs]
def _error_bars_from_moments(self, noise, correlation_lengths, threshold):
"""Provide 1-sigma error bars for source parameters derived from
moments
Parameters
----------
noise : float
The noise level at the position of the island pixel with the
highest spectral brightness.
correlation_lengths : tuple of floats
Tuple describing over which distance (in pixels) noise should be
considered correlated, along both principal axes of the Gaussian
profile of the restoring beam.
threshold : float
The threshold for island segmentation expressed as the rms noise at
the position of the island's pixel with the highest spectral
brightness times the analysis threshold.
Returns
-------
ParamSet
The updated ParamSet instance with calculated errors.
"""
# The formulae below should give some reasonable estimate of the
# errors from moments, should always be higher than the errors from
# Gauss fitting.
peak = self["peak"].value
flux = self["flux"].value
smaj = self["semimajor"].value
smin = self["semiminor"].value
theta = self["theta"].value
# There is no point in proceeding with processing an image if any
# detected peak spectral brightness is below zero since that implies
# that part of detectionthresholdmap is below zero.
if peak < 0:
raise ValueError(
(
f"Peak from moments = {peak:.2e}, something is "
"possibly wrong with detectionthresholdmap, "
"since a negative peak from moments analysis "
"should not occur."
)
)
clean_bias_error = self.clean_bias_error
frac_flux_cal_error = self.frac_flux_cal_error
theta_B, theta_b = correlation_lengths
# This is eq. 2.81 from Spreeuw's thesis.
rho_sq = (
16.0 * smaj * smin / (np.log(2.0) * theta_B * theta_b * noise**2)
) * ((peak - threshold) / (np.log(peak) - np.log(threshold))) ** 2
rho = np.sqrt(rho_sq)
denom = np.sqrt(2.0 * np.log(2.0)) * rho
# Again, like above for the Condon formulae, we set the
# positional variances to twice the theoretical values.
error_par_major = 2.0 * smaj / denom
error_par_minor = 2.0 * smin / denom
# When these errors are converted to RA and Dec,
# calibration uncertainties will have to be added,
# like in formulae 27 of the NVSS paper.
errorx = np.sqrt(
(error_par_major * np.sin(theta)) ** 2
+ (error_par_minor * np.cos(theta)) ** 2
)
errory = np.sqrt(
(error_par_major * np.cos(theta)) ** 2
+ (error_par_minor * np.sin(theta)) ** 2
)
# Note that we report errors in HWHM axes instead of FWHM axes
# so the errors are half the errors of formula 29 of the NVSS paper.
errorsmaj = np.sqrt(2) * smaj / rho
errorsmin = np.sqrt(2) * smin / rho
if smaj > smin:
errortheta = 2.0 * (smaj * smin / (smaj**2 - smin**2)) / rho
else:
errortheta = np.pi / 2.0
if errortheta > np.pi / 2.0:
errortheta = np.pi / 2.0
# Basically, this is equation 37 of the NVSS paper, with the middle
# term of the rhs of that equation heuristically replaced by
# noise**2 since the threshold is not expected to affect the error
# on peak brightnesses from tweaked moments, while it is part of the
# expression for rho_sq above.
errorpeaksq = (
(frac_flux_cal_error * peak) ** 2 + clean_bias_error**2 + noise**2
)
errorpeak = np.sqrt(errorpeaksq)
help1 = (errorsmaj / smaj) ** 2
help2 = (errorsmin / smin) ** 2
help3 = theta_B * theta_b / (4.0 * smaj * smin)
errorflux = flux * np.sqrt(
errorpeaksq / peak**2 + help3 * (help1 + help2)
)
self["peak"].error = errorpeak
self["flux"].error = errorflux
self["xbar"].error = errorx
self["ybar"].error = errory
self["semimajor"].error = errorsmaj
self["semiminor"].error = errorsmin
self["theta"].error = errortheta
return self
[docs]
def deconvolve_from_clean_beam(self, beam):
"""Deconvolve from the clean beam.
Parameters
----------
beam : tuple of floats
The clean beam parameters as the semi-major and semi-minor axes
in pixel coordinates and the position angle in radians.
Returns
-------
ParamSet
The updated ParamSet instance with deconvolved Gaussian shape
parameters, i.e. the semi-major and semi-minor axes and the position
angle.
"""
# If the fitted axes are larger than the clean beam
# (=restoring beam) axes, the axes and position angle
# can be deconvolved from it.
fmaj = 2.0 * self["semimajor"].value
fmajerror = 2.0 * self["semimajor"].error
fmin = 2.0 * self["semiminor"].value
fminerror = 2.0 * self["semiminor"].error
fpa = np.degrees(self["theta"].value)
fpaerror = np.degrees(self["theta"].error)
cmaj = 2.0 * beam[0]
cmin = 2.0 * beam[1]
cpa = np.degrees(beam[2])
rmaj, rmin, rpa, ierr = deconv(fmaj, fmin, fpa, cmaj, cmin, cpa)
if rpa > 90:
rpa = -np.mod(-rpa, 180.0)
# This parameter gives the number of components that could not be
# deconvolved, IERR from DECONV.FOR.
self.deconv_imposs = ierr
# Now, figure out the error bars.
# Start with the case that all elliptical components can be deconvolved.
if ierr == 0:
# Need to convert half axes to widths first.
# Will use underscore _ to denote widths instead of half axes.
meas_ = (
self["semimajor"].value / sigma_to_ax,
self["semiminor"].value / sigma_to_ax,
self["theta"].value,
)
beam_ = (
beam[0] / sigma_to_ax,
beam[1] / sigma_to_ax,
beam[2],
)
C_p_ = np.zeros((3, 3), dtype=np.float64)
C_p_[0, 0] = (self["semimajor"].error / sigma_to_ax) ** 2
C_p_[1, 1] = (self["semiminor"].error / sigma_to_ax) ** 2
C_p_[2, 2] = self["theta"].error ** 2
C_s_ = cov_p_to_cov_S(C_p_, meas_[0], meas_[1], meas_[2])
Sigma_meas_ = covariance_matrix(*meas_)
Sigma_beam_ = covariance_matrix(*beam_)
Sigma_dec_ = Sigma_meas_ - Sigma_beam_
S_dec_ = np.array(
[Sigma_dec_[0, 0], Sigma_dec_[1, 1], Sigma_dec_[0, 1]]
)
r_vec_, C_r_, ok = cov_S_to_cov_r(S_dec_, C_s_)
if ok:
# Convert back to HWHM axes instead of sigma axes.
self["semimaj_deconv"].value = r_vec_[0] * sigma_to_ax
self["semimin_deconv"].value = r_vec_[1] * sigma_to_ax
self["theta_deconv"].value = np.rad2deg(r_vec_[2])
if self["theta_deconv"].value > 90:
self["theta_deconv"].value = -np.mod(
-self["theta_deconv"].value, 180.0
)
# Check that we find the same deconvolved components as
# returned by the deconv function.
if not (
np.isclose(self["semimaj_deconv"].value * 2.0, rmaj)
and np.isclose(self["semimin_deconv"].value * 2.0, rmin)
and np.isclose(self["theta_deconv"].value, rpa)
):
raise RuntimeError(
"Deconvolved parameters from covariance "
"matrices do not match those from deconv."
)
# Now the errors.
self["semimaj_deconv"].error = (
np.sqrt(C_r_[0, 0]) * sigma_to_ax
)
self["semimin_deconv"].error = (
np.sqrt(C_r_[1, 1]) * sigma_to_ax
)
self["theta_deconv"].error = min(
np.rad2deg(np.sqrt(C_r_[2, 2])), 90.0
)
else:
# In this case at least one of the elliptical components could not be
# deconvolved. This makes any kind of error analysis on the remaining
# components dubious. Therefore, we set all three error bars to NaN.
self["semimaj_deconv"].error = np.nan
self["semimin_deconv"].error = np.nan
self["theta_deconv"].error = np.nan
dec_components = (rmaj / 2.0, rmin / 2.0, rpa)
(
self["semimaj_deconv"].value,
self["semimin_deconv"].value,
self["theta_deconv"].value,
) = [dc if dc != 0 else np.nan for dc in dec_components]
return self
[docs]
def source_profile_and_errors(
data,
threshold,
rms,
noise,
beam,
fudge_max_pix_factor,
beamsize,
correlation_lengths,
image_conf,
fixed=None,
):
"""Return a number of measurable properties with errorbars.
Given an island of pixels it will return a number of measurable
properties including errorbars. It will also compute residuals
from Gauss fitting and export these to a residual map.
In addition to handling the initial parameter estimation, and any fits
which fail to converge, this function runs the goodness-of-fit
calculations -
see :func:`sourcefinder.measuring.goodness_of_fit` for details.
Parameters
----------
data : np.ndarray
Array of pixel values, can be a masked array, which is necessary for
proper Gauss fitting, because the pixels below the threshold in the
corners and along the edges should not be included in the fitting
process.
threshold : float
Threshold used for selecting pixels for the source (ie, building an
island). Typically, this will be the analysis threshold (float) times
the noise level (float) at the position of the island's pixel with the
highest spectral brightness.
rms : MaskedArray
A 2D masked array representing the patch of the rms noise map,
corresponding to the same pixel positions as `data`. The values are
interpolated from a grid of standard deviations of the background
noise across the image.
noise : float
Noise level at the position of the island pixel with the highest
spectral brightness.
beam : tuple
Beam parameters (semimaj, semimin, theta), i.e. the semi-major and
semi-minor axes in pixel coordinates and the position angle in radians.
fudge_max_pix_factor : float
Correct for the underestimation of the peak when taking the maximum
pixel value.
beamsize : float
The FWHM size of the clean beam in square pixels.
correlation_lengths : tuple
Two floats describing the distance along the semimajor and
semiminor axes of the clean beam beyond which noise is assumed
uncorrelated. Some background: Aperture synthesis imaging yields
noise that is partially correlated over the entire image. This has a
considerable effect on error estimates. We approximate this by
considering all noise within the correlation length completely
correlated and beyond that completely uncorrelated.
image_conf : config.ImgConf
Holds the configuration parameters for observational image processing.
fixed : dict, default: None
Parameters (and their values) to hold fixed while fitting. Passed on
to measuring.fitgaussian().
Returns
-------
tuple
A populated ParamSet, a Gaussian islands np.ndarray and a residuals
np.ndarray. The Gaussian islands are reconstructions using the derived
Gaussian parameters and the residuals are the difference between the
data and those reconstructions, i.e. the reconstructions are subtracted
from the data. Both the Gaussian islands and residuals are regular
ndarrays, where masked (unfitted) regions have been filled with
0-values. The Gaussian islands and residuals arrays have nonzero values
for the pixel posiions of the corresponding island, i.e. for the
corresponding contiguous region of the observational image (with mean
background subtracted), which was segmented at the level of the analysis
threshold.
"""
if fixed is None:
fixed = {}
param = ParamSet(image_conf)
if threshold is None:
moments_threshold = 0
else:
moments_threshold = threshold
# We can always find the maximum pixel value and derive the barycenter
# position. The other three Gaussian parameters we can copy from the clean
# beam.
peak = data.max()
# Are we fitting a -ve or +ve Gaussian?
if peak <= 0:
peak = data.min()
# The peak is always underestimated when you take the highest (or lowest)
# pixel.
peak *= fudge_max_pix_factor
total = data.sum()
x, y = np.indices(data.shape)
xbar = float((x * data).sum() / total)
ybar = float((y * data).sum() / total)
param.update(
{
"peak": peak,
"flux": np.pi * peak * beam[0] * beam[1] / beamsize,
"xbar": xbar,
"ybar": ybar,
"semimajor": beam[0],
"semiminor": beam[1],
"theta": beam[2],
}
)
if fixed:
param.update(fixed)
# data_as_ones is constructed to help determine if the island has enough
# width for Gauss fitting.
try:
if data.mask.shape == data.data.shape:
data_as_ones = np.where(~data.mask == 1, 1, 0)
else:
data_as_ones = np.where(data.data > moments_threshold, 1, 0)
except AttributeError:
data_as_ones = np.where(data > moments_threshold, 1, 0)
max_along_x = np.sum(data_as_ones, axis=0).max()
max_along_y = np.sum(data_as_ones, axis=1).max()
minimum_width = min(max_along_x, max_along_y)
if minimum_width > 2:
# We can realistically compute moments and perform Gaussian fits if
# the island has a thickness of more than 2 in both dimensions.
param.thin_detection = False
if not fixed:
# Moments can only be computed if no parameters are fixed.
try:
param.update(
measure.moments(
data,
fudge_max_pix_factor,
beam,
beamsize,
moments_threshold,
)
)
if moments_threshold:
# A complete moments computation is only possible if we have
# imposed a non-zero threshold (and no parameters are
# fixed).
param.moments = True
param.compute_bounds(data.shape)
except ValueError:
logger.warning("Moments computations failed, use defaults.")
try:
gaussian_soln = measure.fitgaussian(
data, param, fixed=fixed, bounds=param.bounds
)
param.update(gaussian_soln)
param.gaussian = True
logger.debug("Gaussian fitting was successful.")
except ValueError:
logger.warning("Gaussian fitting failed.")
else:
logger.debug(
"Unable to estimate gaussian parameters from moments."
" Proceeding with defaults %s"
"",
str(param),
)
param["flux"] = (
np.pi
* param["peak"]
* param["semimajor"]
* param["semiminor"]
/ beamsize
)
param.calculate_errors(noise, correlation_lengths, threshold)
param.deconvolve_from_clean_beam(beam)
# Calculate residuals
# NB this works even if Gaussian fitting fails, we generate the model from
# the moments parameters.
gauss_arg = (
param["peak"].value,
param["xbar"].value,
param["ybar"].value,
param["semimajor"].value,
param["semiminor"].value,
param["theta"].value,
)
try:
gauss_island_masked = np.ma.array(
gaussian(*gauss_arg)(*np.indices(data.shape)), mask=data.mask
)
gauss_resid_masked = data - gauss_island_masked
gauss_island_filled = gauss_island_masked.filled(fill_value=0.0)
gauss_resid_filled = gauss_resid_masked.filled(fill_value=0.0)
except AttributeError:
gauss_island_masked = gaussian(*gauss_arg)(*np.indices(data.shape))
gauss_resid_masked = data - gauss_island_masked
gauss_island_filled = gauss_island_masked
gauss_resid_filled = gauss_resid_masked
param.chisq, param.reduced_chisq = measure.goodness_of_fit(
gauss_resid_masked, rms, correlation_lengths
)
return param, gauss_island_filled, gauss_resid_filled
[docs]
class Detection(object):
"""Propagate a measurement in pixel space to celestial coordinates.
A source measurement is primarily done in pixel space, this includes the
parameters peak spectral brightness, position and (Gaussian) shape, but
also derived quanities such as flux density, signal-to-noise ratio and
(reduced) chi-squared of the Gaussian model.
On top of that, the Gaussian shape parameters have to be deconvolved from
the clean beam, if the source is resolved. This adds up to a total of ten
source parameters that have to be supplemented with their 1-sigma error
bars:
1) peak spectral brightness
2) integrated flux density
3) x-coordinate in pixel space
4) y-coordinate in pixel space
5) semi-major axis in pixel space
6) semi-minor axis in pixel space
7) position angle in radians
8) deconvolved semi-major axis in pixel space
9) deconvolved semi-minor axis in pixel space
10) deconvolved position angle in radians
Quantities 3 through 10 all have to be converted to celestial coordinates.
Parameters
----------
paramset : a ParamSet instance
The measurement of the source, reflected by Gaussian model
parameters supplemented with some auxiliary quantities.
imagedata : an image.ImageData instance
The actual pixel data from the input image are not used here,
we simply need the wcs attribute that is needed to convert to celestial
coordinates.
chunk : tuple of slices, default: None
The rectangular region of the image encompassing the source pixels
above the analysis threshold.
eps_ra : float, default: 0
The calibration error in right ascension in degrees following equation
27a of the NVSS paper (Condon et al. 1998, AJ, 115, 1693).
eps_dec : float, default: 0
The calibration error in declination in degrees following equation
27b of the NVSS paper (Condon et al. 1998, AJ, 115, 1693).
Attributes
----------
peak : Uncertain instance
The peak spectral brightness of the source in the units used in
the image, typically Jy/beam.
flux : Uncertain instance
The integrated flux density of the source, typically in Jy.
x : Uncertain instance
The x-coordinate of the source in pixel space.
y : Uncertain instance
The y-coordinate of the source in pixel space.
smaj : Uncertain instance
The semi-major axis of the source in units of pixels.
smin : Uncertain instance
The semi-minor axis of the source in units of pixels.
theta : Uncertain instance
The position angle of the major axis in radians, measured from the
positive y-axis towards the negative x-axis.
dc_imposs : int
The number of elliptical axes that could not be deconvolved,
minimum = 0, maximum = 2
smaj_dc : Uncertain instance
The deconvolved semi-major axis of the source in units of pixels.
smin_dc : Uncertain instance
The deconvolved semi-minor axis of the source in units of pixels.
theta_dc : Uncertain instance
The deconvolved position angle of the source in degrees.
error_radius : float or None
A pessimistic estimate of the 1-sigma positional uncertainty, in
arcseconds.
gaussian : bool
Indicates whether the measurement is based on a Gaussian fit.
chisq : float
The chi-squared value of the Gaussian model relative to the data.
Can be a Gaussian model derived from a fit or from moments.
reduced_chisq : float
The reduced chi-squared value of the Gaussian model relative to the
data. Can be a Gaussian model derived from a fit or from moments.
sig : float
The significance of a detection is defined as the maximum
signal-to-noise ratio across the island. Often this will be the ratio
of the maximum pixel value within the source island divided by the
noise at that position.
imagedata : an image.ImageData instance
This instance contains the observational image data, as well as the
objects that describe how that data should be perceived, e.g. the
resolving beam and the WCS information.
chunk : tuple of slices or None, default: None
The rectangular region of the image encompassing the source pixels
above the analysis threshold.
eps_ra : float, default: 0
Extra positional uncertainty (degrees) from calibration errors along
right ascension, following equation 27a from the NVSS paper.
eps_dec : float, default: 0
Extra positional uncertainty (degrees) from calibration errors along
declination, following equation 27b from the NVSS paper.
"""
def __init__(self, paramset, imagedata, chunk=None):
[docs]
self.eps_ra = paramset.image_conf.eps_ra
[docs]
self.eps_dec = paramset.image_conf.eps_dec
[docs]
self.imagedata = imagedata
# self.wcs = imagedata.wcs
[docs]
self.peak = paramset["peak"]
[docs]
self.flux = paramset["flux"]
[docs]
self.x = paramset["xbar"]
[docs]
self.y = paramset["ybar"]
[docs]
self.smaj = paramset["semimajor"]
[docs]
self.smin = paramset["semiminor"]
[docs]
self.theta = paramset["theta"]
# This parameter gives the number of components that could not
# be deconvolved, IERR from deconf.f.
[docs]
self.dc_imposs = paramset.deconv_imposs
[docs]
self.smaj_dc = paramset["semimaj_deconv"]
[docs]
self.smin_dc = paramset["semimin_deconv"]
[docs]
self.theta_dc = paramset["theta_deconv"]
[docs]
self.error_radius = None
[docs]
self.gaussian = paramset.gaussian
[docs]
self.chisq = paramset.chisq
[docs]
self.reduced_chisq = paramset.reduced_chisq
[docs]
self.sig = paramset.sig
try:
self._physical_coordinates()
except RuntimeError:
logger.warning(
"Physical coordinates failed at %f, %f" % (self.x, self.y)
)
raise
def __getstate__(self):
return {
"imagedata": self.imagedata,
"chunk": (
self.chunk[0].start,
self.chunk[0].stop,
self.chunk[1].start,
self.chunk[1].stop,
),
"peak": self.peak,
"flux": self.flux,
"x": self.x,
"y": self.y,
"smaj": self.smaj,
"smin": self.smin,
"theta": self.theta,
"sig": self.sig,
"error_radius": self.error_radius,
"gaussian": self.gaussian,
}
def __setstate__(self, attrdict):
self.imagedata = attrdict["imagedata"]
self.chunk = (
slice(attrdict["chunk"][0], attrdict["chunk"][1]),
slice(attrdict["chunk"][2], attrdict["chunk"][3]),
)
self.peak = attrdict["peak"]
self.flux = attrdict["flux"]
self.x = attrdict["x"]
self.y = attrdict["y"]
self.smaj = attrdict["smaj"]
self.smin = attrdict["smin"]
self.theta = attrdict["theta"]
self.sig = attrdict["sig"]
self.error_radius = attrdict["error_radius"]
self.gaussian = attrdict["gaussian"]
try:
self._physical_coordinates()
except RuntimeError as e:
logger.warning(
"Physical coordinates failed at %f, %f" % (self.x, self.y)
)
raise
def __getattr__(self, attrname):
# Backwards compatibility for "errquantity" attributes
if attrname[:3] == "err":
return self.__getattribute__(attrname[3:]).error
else:
raise AttributeError(attrname)
def __str__(self):
return "(%.2f, %.2f) +/- (%.2f, %.2f): %g +/- %g" % (
self.ra.value,
self.dec.value,
self.ra.error * 3600,
self.dec.error * 3600,
self.peak.value,
self.peak.error,
)
def __repr__(self):
return str(self)
[docs]
def _physical_coordinates(self):
"""Convert the pixel parameters for this object into something
physical.
"""
# First, the RA & dec.
self.ra, self.dec = [
Uncertain(x)
for x in self.imagedata.wcs.p2s([self.x.value, self.y.value])
]
if np.isnan(self.dec.value) or abs(self.dec) > 90.0:
raise ValueError("object falls outside the sky")
# First, determine local north.
help1 = np.cos(np.radians(self.ra.value))
help2 = np.sin(np.radians(self.ra.value))
help3 = np.cos(np.radians(self.dec.value))
help4 = np.sin(np.radians(self.dec.value))
center_position = np.array([help3 * help1, help3 * help2, help4])
# The length of this vector is chosen such that it touches
# the tangent plane at center position.
# The cross product of the local north vector and the local east
# vector will always be aligned with the center_position vector.
if center_position[2] != 0:
local_north_position = np.array(
[0.0, 0.0, 1.0 / center_position[2]]
)
else:
# If we are right on the equator (ie dec=0) the division above
# will blow up: as a workaround, we use something Really Big
# instead.
local_north_position = np.array([0.0, 0.0, 99e99])
# Next, determine the orientation of the y-axis wrt local north
# by incrementing y by a small amount and converting that
# to celestial coordinates. That small increment is conveniently
# chosen to be an increment of 1 pixel.
endy_ra, endy_dec = self.imagedata.wcs.p2s(
[self.x.value, self.y.value + 1.0]
)
help5 = np.cos(np.radians(endy_ra))
help6 = np.sin(np.radians(endy_ra))
help7 = np.cos(np.radians(endy_dec))
help8 = np.sin(np.radians(endy_dec))
endy_position = np.array([help7 * help5, help7 * help6, help8])
# Extend the length of endy_position to make it touch the plane
# tangent at center_position.
endy_position /= np.dot(center_position, endy_position)
diff1 = endy_position - center_position
diff2 = local_north_position - center_position
cross_prod = np.cross(diff2, diff1)
length_cross_sq = np.dot(cross_prod, cross_prod)
normalization = np.dot(diff1, diff1) * np.dot(diff2, diff2)
# The length of the cross product equals the product of the lengths of
# the vectors times the sine of their angle.
# This is the angle between the y-axis and local north,
# measured eastwards.
# yoffset_angle = np.degrees(
# np.arcsin(np.sqrt(length_cross_sq/normalization)))
# The formula above is commented out because the angle computed
# in this way will always be 0<=yoffset_angle<=90.
# We'll use the dotproduct instead.
arg_for_arccos = np.dot(diff1, diff2) / np.sqrt(normalization)
if np.abs(arg_for_arccos) > 1.000001:
raise ValueError("arccos argument outside valid domain by >1e-6")
arg_for_arccos = min(1.0, max(-1.0, arg_for_arccos))
yoffs_rad = np.arccos(arg_for_arccos)
# The multiplication with -sign_cor makes sure that the angle
# is measured eastwards (increasing RA), not westwards.
sign_cor = np.dot(cross_prod, center_position) / np.sqrt(
length_cross_sq
)
yoffs_rad *= -sign_cor
yoffset_angle = np.degrees(yoffs_rad)
# Now that we have the BPA, we can also compute the position errors
# properly, by projecting the errors in pixel coordinates (x and y)
# on local north and local east.
errorx_proj = np.sqrt(
(self.x.error * np.cos(yoffs_rad)) ** 2
+ (self.y.error * np.sin(yoffs_rad)) ** 2
)
errory_proj = np.sqrt(
(self.x.error * np.sin(yoffs_rad)) ** 2
+ (self.y.error * np.cos(yoffs_rad)) ** 2
)
# Now we have to sort out which combination of errorx_proj and
# errory_proj gives the largest errors in RA and Dec.
try:
end_ra1, end_dec1 = self.imagedata.wcs.p2s(
[self.x.value + errorx_proj, self.y.value]
)
end_ra2, end_dec2 = self.imagedata.wcs.p2s(
[self.x.value, self.y.value + errory_proj]
)
# Here we include the position calibration errors
self.ra.error = self.eps_ra + max(
np.fabs(self.ra.value - end_ra1),
np.fabs(self.ra.value - end_ra2),
)
self.dec.error = self.eps_dec + max(
np.fabs(self.dec.value - end_dec1),
np.fabs(self.dec.value - end_dec2),
)
except RuntimeError:
# We get a runtime error from wcs.p2s if the errors place the
# limits outside the image.
# In which case we set the RA / DEC uncertainties to infinity
self.ra.error = float("inf")
self.dec.error = float("inf")
# Estimate an absolute angular error on our central position.
self.error_radius = utils.get_error_radius(
self.imagedata.wcs,
self.x.value,
self.x.error,
self.y.value,
self.y.error,
)
# Now we can compute the BPA, east from local north.
# That these angles can simply be added is not completely trivial.
# First, the Gaussian in gaussian.py must be such that theta is
# measured from the positive y-axis in the direction of negative x.
# Secondly, x and y are defined such that the direction
# positive y-->negative x-->negative y-->positive x is the same
# direction (counterclockwise) as (local) north-->east-->south-->west.
# If these two conditions are matched, the formula below is valid.
# Of course, the formula is also valid if theta is measured
# from the positive y-axis towards positive x
# and both of these directions are equal (clockwise).
self.theta_celes = Uncertain(
(np.degrees(self.theta.value) + yoffset_angle) % 180,
np.degrees(self.theta.error),
)
if not np.isnan(self.theta_dc.value):
self.theta_dc_celes = Uncertain(
(self.theta_dc.value + yoffset_angle) % 180,
np.degrees(self.theta_dc.error),
)
else:
self.theta_dc_celes = Uncertain(np.nan, np.nan)
# Next, the axes.
# Note that the signs of np.sin and np.cos in the
# four expressions below are arbitrary.
self.end_smaj_x = (
self.x.value - np.sin(self.theta.value) * self.smaj.value
)
self.start_smaj_x = (
self.x.value + np.sin(self.theta.value) * self.smaj.value
)
self.end_smaj_y = (
self.y.value + np.cos(self.theta.value) * self.smaj.value
)
self.start_smaj_y = (
self.y.value - np.cos(self.theta.value) * self.smaj.value
)
self.end_smin_x = (
self.x.value + np.cos(self.theta.value) * self.smin.value
)
self.start_smin_x = (
self.x.value - np.cos(self.theta.value) * self.smin.value
)
self.end_smin_y = (
self.y.value + np.sin(self.theta.value) * self.smin.value
)
self.start_smin_y = (
self.y.value - np.sin(self.theta.value) * self.smin.value
)
def pixel_to_spatial(x, y):
try:
return self.imagedata.wcs.p2s([x, y])
except RuntimeError:
logger.debug("pixel_to_spatial failed at %f, %f" % (x, y))
return np.nan, np.nan
end_smaj_ra, end_smaj_dec = pixel_to_spatial(
self.end_smaj_x, self.end_smaj_y
)
end_smin_ra, end_smin_dec = pixel_to_spatial(
self.end_smin_x, self.end_smin_y
)
smaj_asec = coordinates.angsep(
self.ra.value, self.dec.value, end_smaj_ra, end_smaj_dec
)
scaling_smaj = smaj_asec / self.smaj.value
errsmaj_asec = scaling_smaj * self.smaj.error
self.smaj_asec = Uncertain(smaj_asec, errsmaj_asec)
smin_asec = coordinates.angsep(
self.ra.value, self.dec.value, end_smin_ra, end_smin_dec
)
scaling_smin = smin_asec / self.smin.value
errsmin_asec = scaling_smin * self.smin.error
self.smin_asec = Uncertain(smin_asec, errsmin_asec)
[docs]
def distance_from(self, x, y):
"""Distance from the center."""
return ((self.x - x) ** 2 + (self.y - y) ** 2) ** 0.5
[docs]
def serialize(self, conf=Conf, every_parm=False):
"""Return source properties suitable for database storage.
We manually add ew_sys_err, ns_sys_err as defined in conf.image.
Parameters
----------
conf : Conf, default: Conf
Configuration object for customizing the parameters to be included.
every_parm : bool, default: False
If True, return every parameter from conf.export.source_params, if
False, return only the parameters from
conf.export.source_params_file.
Returns
-------
list
A list with all entries from either conf.export.source_params or
conf.export.source_params_file.
"""
def _get_param(param_name):
"""
Retrieve the value or error of a specified parameter.
Parameters
----------
param_name : str
The name of the parameter to retrieve. If the parameter name
ends with '_err', the method returns the 1-sigma error bar of
the measured parameter.
Returns
-------
float
The value of the parameter or its associated error.
Notes
-----
Some quantities, such as "error_radius", have no associated
error.
Raises
------
KeyError
If "param_name" or param_name[:-4] is not an attribute of the
Detection instance. In the latter case, we will have
param_name.endswith("_err").
AttributeError
If the param_name ends with '_err' and its base, i.e.
param_name[:-4], is an attribute of the Detection instance,
but has no "error" attribute.
"""
# Handle special case of ns_sys_err and ew_sys_err
if param_name == "ns_sys_err":
return conf.image.ew_sys_err
if param_name == "ew_sys_err":
return conf.image.ew_sys_err
# Return the 1-sigma error bar of the measured parameter
if param_name.endswith("_err"):
base_name = param_name[:-4]
try:
return getattr(self, base_name).error
except KeyError as e:
raise KeyError(f"Unknown parameter '{param_name}'") from e
except AttributeError as e:
raise AttributeError(
f"Parameter '{base_name}' has no associated error value"
) from e
# Return the measured parameter.
try:
param_val = getattr(self, param_name)
if hasattr(param_val, "value"):
return param_val.value
return param_val
except KeyError as e:
raise KeyError(f"Unknown parameter '{param_name}'") from e
result = [
_get_param(name)
for name in (
conf.export.source_params
if every_parm
else conf.export.source_params_file
)
]
return result
@guvectorize(
[(float64[:], float64[:], float32[:], float32[:], float32[:], float32[:])],
"(n), (n), (n), (l), (m) -> (m)",
nopython=True,
target="parallel",
)
[docs]
def first_part_of_celestial_coordinates(
ra_dec,
endy_ra_dec,
xbar_ybar_error,
xbar_ybar_smaj_smin_theta,
dummy,
return_values,
): # pragma: no cover
"""First part of celestial coordinates.
Similar to func:`extract.Detection._physical_coordinates`, but vectorized and
mainly the first part, until we need another call to wcs.all_pix2world,
based on the output from this part.
What we have learned from moments_enhanced is that measuring the islands
can be done very rapidly, by vectorizing the measurements rather than
parallellizing, although one can do both by using the guvectorize
decorator from Numba. Contrary to vectorizing moments, vectorizing
the transformation to celestial coordinates is harder, since it involves
wcs.wcs_pix2world from Astropy, which Numba cannot compile. The way out
of this is to use wcs.all_pix2world from Astropy, which is a fast
vectorized function, but this has to be done outside the routine compiled
by Numba, i.e. this routine. We will be needing a number of calls to
wcs.all_pix2world to traverse all the steps from
extract.Detection._physical_coordinates.
Parameters
----------
ra_dec : np.ndarray
Array of floats of length 2, containing the right ascension (degrees)
and the declination (degrees) corresponding to [xbar, ybar] of the
source.
endy_ra_dec : np.ndarray
Array of floats of length 2, containing the right ascension (degrees)
and the declination (degrees) corresponding to [xbar, ybar + 1] of the
source.
xbar_ybar_error : np.ndarray
Array of floats of length 2, with the errors on the barycentric
positions, in pixel coordinates, in both dimensions.
xbar_ybar_smaj_smin_theta : np.ndarray
Array of floats of length 5, with the barycentric positions, the
semi-major and semi-minor axes, all in pixel coordinates and the
position angles, in radians.
dummy : np.ndarray
Same shape as return_values, to accommodate for a missing feature in the
guvectorize decorator, i.e. this is a trick to pass on information about
the shape of the output array.
return_values : np.ndarray
Strictly speaking nothing is returned, because of the guvectorize
decorator, but return_values is filled with xerror_proj, yerror_proj,
yoffset_angle, end_smaj_x, start_smaj_x, end_smaj_y, start_smaj_y,
end_smin_x, start_smin_x, end_smin_y and start_smin_y.
Returns
-------
None
This method does not return anything. The results are stored in the
return_values array.
"""
ra, dec = ra_dec
if np.isnan(dec) or abs(dec) > 90.0:
raise ValueError("object falls outside the sky")
# First, determine local north.
help1 = np.cos(np.radians(ra))
help2 = np.sin(np.radians(ra))
help3 = np.cos(np.radians(dec))
help4 = np.sin(np.radians(dec))
center_position = np.array([help3 * help1, help3 * help2, help4])
# The length of this vector is chosen such that it touches
# the tangent plane at center position.
# The cross product of the local north vector and the local east
# vector will always be aligned with the center_position vector.
if center_position[2] != 0:
local_north_position = np.array([0.0, 0.0, 1.0 / center_position[2]])
else:
# If we are right on the equator (ie dec=0) the division above
# will blow up: as a workaround, we use a large number instead.
# instead.
local_north_position = np.array([0.0, 0.0, 99e99])
endy_ra, endy_dec = endy_ra_dec
help5 = np.cos(np.radians(endy_ra))
help6 = np.sin(np.radians(endy_ra))
help7 = np.cos(np.radians(endy_dec))
help8 = np.sin(np.radians(endy_dec))
endy_position = np.array([help7 * help5, help7 * help6, help8])
# Extend the length of endy_position to make it touch the plane
# tangent at center_position.
endy_position /= np.dot(center_position, endy_position)
diff1 = endy_position - center_position
diff2 = local_north_position - center_position
cross_prod = np.cross(diff2, diff1)
length_cross_sq = np.dot(cross_prod, cross_prod)
normalization = np.dot(diff1, diff1) * np.dot(diff2, diff2)
# The length of the cross product equals the product of the lengths of
# the vectors times the sine of their angle.
# This is the angle between the y-axis and local north,
# measured eastwards.
# yoffset_angle = np.degrees(
# np.arcsin(np.sqrt(length_cross_sq/normalization)))
# The formula above is commented out because the angle computed
# in this way will always be 0<=yoffset_angle<=90.
# We'll use the dotproduct instead.
arg_for_arccos = np.dot(diff1, diff2) / np.sqrt(normalization)
if np.abs(arg_for_arccos) > 1.000001:
raise ValueError("arccos argument outside valid domain by >1e-6")
arg_for_arccos = min(1.0, max(-1.0, arg_for_arccos))
yoffs_rad = np.arccos(arg_for_arccos)
# The multiplication with -sign_cor makes sure that the angle
# is measured eastwards (increasing RA), not westwards.
sign_cor = np.dot(cross_prod, center_position) / np.sqrt(length_cross_sq)
yoffs_rad *= -sign_cor
yoffset_angle = np.degrees(yoffs_rad)
# Now that we have the BPA, we can also compute the position errors
# properly, by projecting the errors in pixel coordinates (x and y)
# on local north and local east.
xbar_error, ybar_error = xbar_ybar_error
errorx_proj = np.sqrt(
(xbar_error * np.cos(yoffs_rad)) ** 2
+ (ybar_error * np.sin(yoffs_rad)) ** 2
)
errory_proj = np.sqrt(
(xbar_error * np.sin(yoffs_rad)) ** 2
+ (ybar_error * np.cos(yoffs_rad)) ** 2
)
# Next, the axes.
# Note that the signs of np.sin and np.cos in the
# four expressions below are arbitrary.
xbar, ybar, smaj, smin, theta = xbar_ybar_smaj_smin_theta
end_smaj_x = xbar - np.sin(theta) * smaj
start_smaj_x = xbar + np.sin(theta) * smaj
end_smaj_y = ybar + np.cos(theta) * smaj
start_smaj_y = ybar - np.cos(theta) * smaj
end_smin_x = xbar + np.cos(theta) * smin
start_smin_x = xbar - np.cos(theta) * smin
end_smin_y = ybar + np.sin(theta) * smin
start_smin_y = ybar - np.sin(theta) * smin
return_values[:] = np.array(
[
errorx_proj,
errory_proj,
yoffset_angle,
end_smaj_x,
start_smaj_x,
end_smaj_y,
start_smaj_y,
end_smin_x,
start_smin_x,
end_smin_y,
start_smin_y,
]
)
@guvectorize(
[
(
float32[:, :],
float32[:, :],
int32[:],
int32[:, :],
int32[:],
int32[:],
float32[:],
float32[:],
int32[:],
int32[:],
int32[:],
)
],
"(n, m), (n, m), (l), (n, m), (), (), (k) -> (k), (k), (k), ()",
target="parallel",
)
[docs]
def insert_sources_and_noise(
some_image,
noise_map,
inds,
labelled_data,
label,
npix,
source,
noise,
xpos,
ypos,
min_width,
): # pragma: no cover
"""Insert sources and noise.
We want to copy the relevant source and noise data into input arrays for
measuring.moments_enhanced. Simultaneously calculate the minimum width of
each island; when determining source properties this is an important
integer, i.e. with sufficient width all six Gaussian parameters can be
calculated in a robust manner.
Parameters
----------
some_image : np.ndarray
The 2D ndarray with all the pixel values, typically
image.ImageData().data_bgsubbed.data.
noise_map : np.ndarray
The 2D ndarray with all the noise values, i.e. an estimate of the
standard deviation of the background pixels, from an interpolation
across the background grid, centered on subimages. Typically
image.ImageData().rmsmap.data.
inds : np.ndarray
A ndarray of four indices indicating the slice encompassing an island.
Such a slice would typically be a pick from a list of slices from a call
to scipy.ndimage.find_objects. Since we are attempting vectorized
processing here, the slice should have been replaced by its four
coordinates through a call to image.ImageData.slices_to_indices.
labelled_data : np.ndarray
A ndarray with the same shape as some_image, with labelled islands with
integer values and zeroes for all background pixels.
label : int
The label (integer value) indicates the island we are processing since
the pixel positions of the island are determined by
labelled_data==label.
npix : int
Number of pixels comprising the island we are processing. The island
pixel positions are determined by labelled_data==label.
source : np.ndarray
1D ndarray of float32 pixel values of the island with label = label.
Length= maxpix, the number of pixels in the largest possible island,
indicating that there will be a number of unassigned values for the
highest indices, for some islands.
noise : np.ndarray
1D ndarray of float32 rms noise values - local estimates of the standard
deviation of the background noise - of the island with label = label.
Length= maxpix, the number of pixels in the largest possible island,
indicating that there will be a number of unassigned values for the
highest indices, for some islands.
xpos : np.ndarray
1D ndarray of integers indicating the row indices of the pixels of the
island with label = label, relative to the position of pixel [0, 0] of
the rectangular slice encompassing the island. Must have same order as
pixel values in island. Length = maxpix, the number of pixels in the
largest possible island, indicating that there will be a number of
unassigned values for the highest indices.
ypos : np.ndarray
1D ndarray of integers indicating the column indices of the pixels of
the island with label = label, relative to the position of pixel [0, 0]
of the rectangular slice encompassing the island. Must have same order
as pixel values in island. Length = maxpix, the number of pixels in the
largest possible island, indicating that there will be a number of
unassigned values for the highest indices.
min_width : int
int32 indicating the minimum width of the island, in order to assess
whether the island has sufficient width to determine Gaussian
parameters. Calculated from the maximum widths of the island over x
and y and subsequently taking the minimum of those two maximum widths.
Returns
-------
None
No return values, because of the use of the guvectorize decorator:
'guvectorize() functions don’t return their result value: they take it
as an array argument, which must be filled in by the function'. In this
case source, noise, xpos, ypos and min_width will be filled with values.
"""
image_chunk = some_image[inds[0] : inds[1], inds[2] : inds[3]]
labelled_data_chunk = labelled_data[inds[0] : inds[1], inds[2] : inds[3]]
noise_chunk = noise_map[inds[0] : inds[1], inds[2] : inds[3]]
segmented_island = np.where(labelled_data_chunk == label[0], 1, 0)
max_along_x = np.sum(segmented_island, axis=0).max()
max_along_y = np.sum(segmented_island, axis=1).max()
min_width[0] = min(max_along_x, max_along_y)
# pos = "positions", i.e. the row and column indices of the island pixels.
pos = segmented_island.nonzero()
for i in range(npix[0]):
index = pos[0][i], pos[1][i]
source[i] = image_chunk[index]
noise[i] = noise_chunk[index]
xpos[i], ypos[i] = index
[docs]
def source_measurements_vectorised(
num_islands,
npixs,
maxposs,
maxis,
data_bgsubbeddata,
rmsdata,
analysisthresholddata,
indices,
labelled_data,
labels,
wcs,
fudge_max_pix_factor,
beam,
beamsize,
correlation_lengths,
conf,
):
"""Source measurements (vectorised).
From islands of pixels above the analysis threshold with peaks above the
detection threshold source parameters are extracted, including error bars.
These quantities are transformed to celestial coordinates in a vectorized
way, making it suitable for tens of thousands of sources per image. Per
island one can extract a maximum of 10 quantities: peak spectral brightness,
flux density, i.e. the spectral brightness integrated over the source,
position in the sky along both axes and the source shape parameters:
semi-major and semi-minor axes and the position angle of the major axis,
measured east from local north. The latter three quantities can be
deconvolved from the clean beam if the source is resolved. That gives a
total of 20 numbers, 10 measurements and their error bars. 8 of these have
to be transformed to celestial coordinates, which adds another 16 numbers.
This function is a duplicate of code elsewhere, in particular of
'measuring.moments' and 'extract.Detection._physical_coordinates' but with
a data layout suitable for vectorisation.
Parameters
----------
num_islands : int
Number of islands detected.
npixs : np.ndarray
1D int32 array of length num_islands representing the number of pixels
comprising every island.
maxposs : np.ndarray
2D int32 array of shape (num_islands, 2) with the peak positions per
island.
maxis : np.ndarray
1D float32 array of length num_islands with the peak pixel values
corresponding to the maxposs positions.
data_bgsubbeddata : np.ndarray
2D float32 array representing the image. These are the data of
image.ImageData().data_bgsubbed, i.e. ImageData().data_bgsubbed.data,
without the mask, since we assume that any mask has already been
properly propagated in selecting the islands pixels. The interpolated
mean background has been subtracted from the image data.
rmsdata : np.ndarray
2D float32 or float64 array, same shape as the image (data_bgsubbeddata).
rms is jargon in image processing, it refers to "Root mean square", but
is taken as the standard deviation of the background noise. The standard
deviation of the background noise is determined after kappa, sigma
clipping subimages of appropriate size and interpolating this across the
image while including masks. This is image.ImageData().rmsmap.data, i.e.
without the mask, since we assume that any mask has already been
properly propagated in selecting the islands pixels.
analysisthresholddata : np.ndarray
2D float32 or float64 array, same shape as data_bgsubbeddata. These are
the data of the analysisthresholdmap, i.e. analysisthresholdmap.data,
without the mask, since we assume that any mask has already been properly
propagated in the process of selecting the island pixels.
indices : np.ndarray
2D int32 array of shape (num_islands, 4) representing positions of the
corners of the "chunks", i.e. slices encompassing every island, relative
to upper left corner of the image, i.e. relative to array element [0,0]
of data_bgsubbeddata.
labelled_data : np.ndarray
2D int32 array of shape data_bgsubbeddata.shape, representing all
unmasked island pixels above the analysis threshold, with labels
(integers) > 0. All background or masked pixels from
image.ImageData().data_bgsubbed should have value (label) = 0.
labels : np.ndarray
1D int32 or int64 array representing the labels in labelled_data
corresponding to islands in data_bgsubbeddata that have peak values above
the local detection threshold. Thus, it is a subset of np.unique(
labelled_data) because the 'insignificant' islands have been filtered
out, i.e. the islands above the analysis threshold with peak values below
the (local) detection threshold. Also, labels does not contain the zero
label corresponding to background or masked pixels in
ImageData.data_bgsubbed.
wcs : utility.coordinates.wcs
A utility.coordinates.wcs instance, filled with appropriate values from
the image header, issued e.g. through accessors.fitsimage.FitSImage. With
numbers representing the center of the image and the width of the pixels
in celestial coordinates plus the type of projection used, we can
transform from pixel coordinates to celestial coordinates.
fudge_max_pix_factor : float
Correction for the underestimate of the true peak when the maximum pixel
method is used. It is a statistical correction, so on average correct
over a large ensemble of unresolved sources, when a circular restoring
beam is appropriate.
beam : tuple
Three floats describing the restoring beam in terms of its
semi-major and semi-minor axes (in pixels) and the position angle of the
semi-major axis, east from local north, in radians.
beamsize : float
Area of the restoring beam, in square pixels.
correlation_lengths : tuple
Two floats describing over which distance (in pixels) noise
should be considered correlated, along both principal axes of the
Gaussian profile of the restoring beam.
conf : config.Conf instance
Configuration options for source finding. This includes settings
related to image processing (e.g., background and rms
noise estimation, thresholds) as well as export options (e.g., source
parameters and output maps).
Returns
-------
moments_of_sources : np.ndarray
3D float32 array, with a row index corresponding to each island, i.e.
num_islands rows, a 0 and 1 column index corresponding to values and
their error bars, respectively and a third index [0...9] which
represents the measurements of the sources, i.e. peak spectral
brightness, in Jy/beam and the integrated spectral brightness a.k.a.
flux density in Jy. All the other numbers in moments_of_sources are in
pixel coordinates. These are position on the sky, along both image axes,
semi-major and semi-minor axis of the Gaussian profile of the source and
the position angle of the major axis (in radians) measured from the
positive y-axis towards the positive x-axis.
These three Gaussian profile parameters can be deconvolved from the
clean beam if the source is resolved. This adds up to ten quantities and
corresponding error bars for each island. Note that the deconvolved
position angle is in degrees, not in radians.
sky_barycenters : np.ndarray
(num_islands, 2) array of floats: each row has an entry for right
ascension (degrees, float64) and declination (degrees, float64).
chunk_positions : np.ndarray
(num_islands, 2) array of integers denoting the indices that correspond
to the upper left corners of the islands. They are used in this module
and returned to the calling module. However, their return is only useful
if the user requires a residual map.
ra_errors : np.ndarray
1D float64 array of uncertainties (degrees) corresponding to the first
column in sky_barycenters.
dec_errors : np.ndarray
1D float64 array of uncertainties (degrees) corresponding to the second
column in sky_barycenters.
error_radii : np.ndarray
1D float64 array representing an absolute error bar (arcseconds) on the
position of every source. This is an important quantity to associate an
observation of a source with its previous observations.
smaj_asec : np.ndarray
1D float64 array representing the convolved semi-major axes - i.e. not
deconvolved from the restoring beam - transformed from pixel coordinates
to celestial coordinates, in arcseconds.
errsmaj_asec : np.ndarray
1D float64 array representing the 1-sigma error bars of the convolved
semi-major axes, in arcseconds.
smin_asec : np.ndarray
1D float64 array representing the convolved semi-minor axes - i.e. not
deconvolved from the restoring beam - transformed from pixel coordinates
to celestial coordinates, in arcseconds.
errsmin_asec : np.ndarray
1D float64 array representing the 1-sigma error bars of the convolved
semi-minor axes, in arcseconds.
theta_celes_values : np.ndarray
1D float32 array representing the position angles of the semi-major axes
of the convolved Gaussian profiles, i.e. not yet deconvolved from the
restoring beam, in degrees.
theta_celes_errors : np.ndarray
1D float32 array representing the 1-sigma error bars of the position
angles of the semi-major axes of the convolved Gaussian profiles, in
degrees.
theta_dc_celes_values : np.ndarray
1D float32 array representing the position angles of the semi-major axes
of the deconvolved Gaussian profiles, i.e. deconvolved from the
restoring beam, in degrees.
theta_dc_celes_errors : np.ndarray
1D float32 array representing the 1-sigma error bars of the position
angles of the semi-major axes of the deconvolved Gaussian profiles, in
degrees.
Gaussian_islands_map : np.ndarray
2D float32 array with the same shape as data_bgsubbed from the
image.ImageData class instantiation. The derived Gaussian parameters
have been used to reconstruct Gaussian profiles at the pixel positions
of the islands and zero outside those islands. This array can be saved
e.g. as a FITS image for inspection of the source processing.
Gaussian_residuals_map : np.ndarray
Similar to Gaussian_islands_map, but as residuals, i.e. the Gaussian
islands have been subtracted from the image data at the pixel positions
of the islands - and zero outside the islands. This array can be saved
e.g. as a FITS image for inspection of the source processing.
sig : np.ndarray
1D float32 array indicating the significances of the detections. Often
this will be the ratio of the peak spectral brightness of the source
island divided by the noise at the position of that peak. But for
extended sources, the noise can perhaps decrease away from the position
of the peak spectral brightness more steeply than the source spectral
brightness and the maximum signal-to-noise ratio can be found at a
different position.
chisq : np.ndarray
1D float32 array representing chi-squared statistics reflecting an
indication of the goodness-of-fit, equivalent to chisq as calculated in
measuring.goodness_of_fit.
reduced_chisq : np.ndarray
1D float32 array representing reduced chi-squared statistics reflecting
an indication of the goodness-of-fit, equivalent to reduced_chisq as
calculated in measuring.goodness_of_fit.
"""
# This is the conditional route to the fastest algorithm for source
# measurements, with no forced_beam and deblending options and no Gauss
# fitting, so a slightly coarser way of measuring sources. The difference
# in accuracy wrt Gaussian fits can be noticeable when performing astrometry
# at very high signal-to-noise ratios.
# Make 2D input data suitable for moments_enhanced with guvectorize
# decorator, Each row will contain the pixel values of a flattened source.
# First, determine the correct dimensions for the input
# The number of rows will be num_labels = number of islands
# (sources).
# The number of columns will be max_pixels = the maximum number
# of pixels an island can have.
# We will also be needing auxiliary arrays.
# Two of those will be index arrays, xpositions and ypositions.
# These arrays will have shape (num_labels, max_pixels).
# I.e. these are 2D arrays of integers, indicating the relative
# positions of the source pixel relative to the top left corner of the slice
# encompassing the island.
# Later we will be needing another 2D array of floats with a number
# of quantities related to sky position.
try:
max_pixels = npixs.max()
except ValueError:
# In this case, npixs is an empty ndarray, i.e. there are no islands,
# no sources have been detected.
max_pixels = 0
sources = np.empty((num_islands, max_pixels), dtype=np.float32)
noises = np.empty_like(sources)
# xpositions and ypositions are relative to the upper left corner of
# the chunk.
xpositions = np.empty((num_islands, max_pixels), dtype=np.int32)
ypositions = np.empty((num_islands, max_pixels), dtype=np.int32)
# It makes sense to calculate the minimum width of each island of pixels
# upfront such that we are not trying to estimate any Gaussian parameters,
# either through moments estimation or through fitting, when the island has
# a width of less than 3 pixels along any axis. For these "thin" detections
# we can still determine the peak spectral brightness and position, but the
# other four Gaussian parameters, i.e. the flux density, the axes and the
# position angle will have to be derived with the help of the clean beam
# parameters, i.e. by assuming the source is unresolved.
minimum_widths = np.empty(num_islands, dtype=np.int32)
insert_sources_and_noise(
data_bgsubbeddata.astype(np.float32, copy=False),
rmsdata.astype(np.float32, copy=False),
indices,
labelled_data,
labels.astype(np.int32, copy=False),
npixs,
sources,
noises,
xpositions,
ypositions,
minimum_widths,
)
# Make sure we get a single precision array of floats, which
# measuring.moments_enhanced expects.
thresholds = analysisthresholddata[maxposs[:, 0], maxposs[:, 1]].astype(
np.float32, copy=False
)
local_noise_levels = rmsdata[maxposs[:, 0], maxposs[:, 1]].astype(
np.float32, copy=False
)
# In order to convert to celestial coordinates, at a later stage, we
# need to keep a record of the positions of the upper left corners
# of the chunks. moments_enhanced starts by calculating xbar and
# ybar as if those upper left corners have indices [0, 0] in the
# image. We can add the indices of the chunks as arguments of
# moments_enhanced to correct for that.
chunk_positions = np.empty((num_islands, 2), dtype=np.int32)
chunk_positions[:, 0] = indices[:, 0]
chunk_positions[:, 1] = indices[:, 2]
# The result will be put in an array 'moments_of_sources' containing
# ten quantities and their uncertainties: peak spectral brightness,
# flux density, xbar, ybar, semi-major axis, semi-minor axis,
# elliptical position angle and the deconvolved equivalents of the latter
# three quantities. The second column of this array will contain
# the uncertainties on these quantities, i.e. the 1-sigma error bars.
moments_of_sources = np.empty((num_islands, 2, 10), dtype=np.float32)
dummy = np.empty_like(moments_of_sources)
# sig is to be filled with the significances of each detection, i.e. the
# maximum signal-to-noise ratio across all island pixels, for each island.
sig = np.empty(num_islands, dtype=np.float32)
chisq = np.empty_like(sig)
reduced_chisq = np.empty_like(sig)
Gaussian_islands = np.zeros_like(data_bgsubbeddata)
Gaussian_residuals = np.zeros_like(Gaussian_islands)
# This is a workaround for an unresolved issue:
# https://github.com/numba/numba/issues/6690
# https://numpy.org/neps/nep-0020-gufunc-signature-enhancement.html
# The output shape can apparently not be set as fixed numbers.
# So we will add a dummy array with shape corresponding
# to the output array (moments_of_sources), as (useless) input
# array. In this way Numba can infer the shape of the output array.
with np.errstate(invalid="ignore"):
# Context manager added to fix issue #165.
measure.moments_enhanced(
sources,
noises,
chunk_positions,
xpositions,
ypositions,
minimum_widths,
npixs,
thresholds,
local_noise_levels,
maxposs,
maxis,
fudge_max_pix_factor,
np.array(beam),
beamsize,
conf.image.force_beam,
np.array(correlation_lengths),
conf.image.clean_bias_error,
conf.image.frac_flux_cal_error,
Gaussian_islands,
Gaussian_residuals,
dummy,
moments_of_sources,
sig,
chisq,
reduced_chisq,
)
barycentric_pixel_positions = moments_of_sources[:, 0, 2:4]
# Convert the barycentric positions to celestial_coordinates.
sky_barycenters = wcs.all_p2s(barycentric_pixel_positions)
# We need to determine the orientation of the y-axis wrt local north
# by incrementing y by a small amount and converting that
# to celestial coordinates. That small increment is conveniently
# chosen to be an increment of 1 pixel.
endy_barycentric_positions = barycentric_pixel_positions.copy()
endy_barycentric_positions[:, 1] += 1
endy_sky_coordinates = wcs.all_p2s(endy_barycentric_positions)
input_for_second_part = np.empty((num_islands, 11), dtype=np.float32)
# Unfortunately, the use of the guvectorize decorator again
# requires a dummy input with the same shape as the output,
# such that Numba can infer the shape of the output array.
dummy = np.empty_like(input_for_second_part)
first_part_of_celestial_coordinates(
sky_barycenters,
endy_sky_coordinates,
moments_of_sources[:, 1, 2:4],
moments_of_sources[:, 0, 2:7],
dummy,
input_for_second_part,
)
# Derive an absolute angular error on position, as
# utils.get_error_radius does, but less involved.
# Simply derive the angle between the celestial positions
# corresponding to [xbar, ybar] and [xbar + errorx,
# ybar + errory], that should suffice.
error_radii = np.empty(num_islands, dtype=np.float64)
try:
# Compute sky positions corresponding to [x_bar + x_error,
# y_bar + y_error]
pix_offset = (
moments_of_sources[:, 0, 2:4] + moments_of_sources[:, 1, 2:4]
)
sky_offset = wcs.all_p2s(pix_offset)
coordinates.angsep_vectorized(sky_barycenters, sky_offset, error_radii)
except RuntimeError:
# Mimic error handling from utils.get_error_radius.
# The downside is that all error radii will be infinite
# also when only the calculation of the error radius for a
# single source gives a RuntimeError.
error_radii.fill(float("inf"))
# Now we have to sort out which combination of errorx_proj and
# errory_proj gives the largest errors in RA and Dec.
try:
# Derive end_ra1, end_dec1, end_ra2, end_dec2 as in
# extract.Detection._physical_coordinates.
# We need to add errorx_proj to xbar and zero to ybar.
# So we need to extract the first column from
# input_for_second_part and append a column with zeros
# in order to perform the addition.
helper1 = input_for_second_part[:, :1]
errorx_proj_and_zeros = np.hstack(
(helper1, np.zeros((helper1.shape[0], 1), dtype=helper1.dtype))
)
pix_x_plus_errorx_proj = (
moments_of_sources[:, 0, 2:4] + errorx_proj_and_zeros
)
end_ra1_end_dec1 = wcs.all_p2s(pix_x_plus_errorx_proj)
# Now we need to add errory_proj to ybar and zero to xbar.
# So we need to extract the second column from
# input_for_second_part and prepend a column with zeros
# in order to perform the addition.
helper2 = input_for_second_part[:, 1:2]
zeros_and_errory_proj = np.hstack(
(np.zeros((helper2.shape[0], 1), dtype=helper2.dtype), helper2)
)
pix_y_plus_errory_proj = (
moments_of_sources[:, 0, 2:4] + zeros_and_errory_proj
)
end_ra2_end_dec2 = wcs.all_p2s(pix_y_plus_errory_proj)
# Here we include the position calibration errors
ra_errors = conf.image.eps_ra + np.maximum(
np.fabs(sky_barycenters[:, :1] - end_ra1_end_dec1[:, :1]),
np.fabs(sky_barycenters[:, :1] - end_ra2_end_dec2[:, :1]),
)
dec_errors = conf.image.eps_dec + np.maximum(
np.fabs(sky_barycenters[:, 1:2] - end_ra1_end_dec1[:, 1:2]),
np.fabs(sky_barycenters[:, 1:2] - end_ra2_end_dec2[:, 1:2]),
)
except RuntimeError:
# We get a runtime error from wcs.all_p2s if the errors place the
# limits outside the image.
# In which case we set the RA / DEC uncertainties to infinity.
# The downside of this vectorized approach is that the position
# errors for all the sources will be set to infinity.
ra_errors = np.empty(num_islands).fill(np.inf)
dec_errors = np.empty(num_islands).fill(np.inf)
theta_celes_values = (
np.degrees(moments_of_sources[:, 0, 6:7])
+ input_for_second_part[:, 2:3]
) % 180
theta_celes_errors = np.degrees(moments_of_sources[:, 1, 6:7])
# This should also work for any nan value of theta_dc.
theta_dc_celes_values = (
np.degrees(moments_of_sources[:, 0, 9:10])
+ input_for_second_part[:, 2:3]
) % 180
theta_dc_celes_errors = np.degrees(moments_of_sources[:, 1, 9:10])
try:
end_smaj_ra_dec = wcs.all_p2s(input_for_second_part[:, [3, 5]])
end_smin_ra_dec = wcs.all_p2s(input_for_second_part[:, [7, 9]])
except RuntimeError:
# Here we are again facing a downside of the vectorized
# approach: if the FWHM ends of any source give a problem
# wrt to pixel to sky conversion, all sky coordinates have to
# be set to nans.
logger.debug("pixel_to_spatial failed")
end_smaj_ra_dec = np.empty((num_islands, 2)).fill(np.nan)
end_smin_ra_dec = np.empty((num_islands, 2)).fill(np.nan)
smaj_asec = np.empty(num_islands, dtype=np.float64)
coordinates.angsep_vectorized(sky_barycenters, end_smaj_ra_dec, smaj_asec)
scaling_smaj = smaj_asec / moments_of_sources[:, 0, 4]
errsmaj_asec = scaling_smaj * moments_of_sources[:, 1, 4]
smin_asec = np.empty(num_islands, dtype=np.float64)
coordinates.angsep_vectorized(sky_barycenters, end_smin_ra_dec, smin_asec)
scaling_smin = smin_asec / moments_of_sources[:, 0, 5]
errsmin_asec = scaling_smin * moments_of_sources[:, 1, 5]
return (
moments_of_sources,
sky_barycenters,
ra_errors,
dec_errors,
error_radii,
smaj_asec,
errsmaj_asec,
smin_asec,
errsmin_asec,
theta_celes_values,
theta_celes_errors,
theta_dc_celes_values,
theta_dc_celes_errors,
Gaussian_islands,
Gaussian_residuals,
sig,
chisq,
reduced_chisq,
)