"""
Source Extraction Helpers.
These are used in conjunction with image.ImageData.
"""
import logging
import math
# DictMixin may need to be replaced using collections.MutableMapping;
# see http://docs.python.org/library/userdict.html#UserDict.DictMixin
from UserDict import DictMixin
import numpy
try:
import ndimage
except ImportError:
from scipy import ndimage
from tkp.sourcefinder.deconv import deconv
from ..utility import coordinates
from ..utility.uncertain import Uncertain
from .gaussian import gaussian
from . import fitting
from . import utils
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.
BIGNUM = 99999.0
[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.
"""
def __init__(self, data, rms, chunk, analysis_threshold, detection_map,
beam, deblend_nthresh, deblend_mincont, structuring_element,
rms_orig=None, flux_orig=None, subthrrange=None
):
# deblend_nthresh is the number of subthresholds used when deblending.
self.deblend_nthresh = deblend_nthresh
# If we deblend too far, we hit the recursion limit. And it's slow.
if self.deblend_nthresh > 300:
logger.warn("Limiting to 300 deblending subtresholds")
self.deblend_nthresh = 300
else:
logger.debug("Using %d subthresholds", 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.
self.deblend_mincont = deblend_mincont
# The structuring element defines connectivity between pixels.
self.structuring_element = structuring_element
# NB we have set all unused data to -(lots) before passing it to
# Island().
mask = numpy.where(data > -BIGNUM / 10.0, 0, 1)
self.data = numpy.ma.array(data, mask=mask)
self.rms = rms
self.chunk = chunk
self.analysis_threshold = analysis_threshold
self.detection_map = detection_map
self.beam = beam
self.max_pos = ndimage.maximum_position(self.data.filled(fill_value=0))
self.position = (self.chunk[0].start, self.chunk[1].start)
if not isinstance(rms_orig, numpy.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, numpy.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):
"""Return a decomposed numpy array of all the subislands.
Iterate up through subthresholds, looking for our island
splitting into two. If it does, start again, with two or more
separate islands.
"""
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 = numpy.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 = numpy.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],
(numpy.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)
),
1,
self.detection_map[chunk],
self.beam,
self.deblend_nthresh,
self.deblend_mincont,
self.structuring_element,
self.rms_orig[chunk[0].start:chunk[0].stop, chunk[1].start:chunk[1].stop],
self.flux_orig,
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 = filter(
lambda isl: (isl.data-numpy.ma.array(
numpy.ones(isl.data.shape)*level,
mask=isl.data.mask)).sum() > self.deblend_mincont *
self.flux_orig, subislands)
# Discard subislands below detection threshold
subislands = filter(
lambda isl: (isl.data - isl.detection_map).max() >= 0,
subislands)
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(map(
lambda island: island.deblend(niter=niter+1),
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"""
return self.noise() * self.analysis_threshold
[docs] def noise(self):
"""Noise at maximum position"""
return self.rms[self.max_pos]
[docs] def sig(self):
"""Deviation"""
return (self.data/ self.rms_orig).max()
[docs] def fit(self, fixed=None):
"""Fit the position"""
try:
measurement, gauss_residual = source_profile_and_errors(
self.data, self.threshold(), self.noise(), self.beam, 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_residual
[docs]class ParamSet(DictMixin):
"""
All the source fitting methods should go to produce a ParamSet, which
gives all the information necessary to make a Detection.
"""
def __init__(self, clean_bias=0.0, clean_bias_error=0.0,
frac_flux_cal_error=0.0, alpha_maj1=2.5, alpha_min1=0.5,
alpha_maj2=0.5, alpha_min2=2.5, alpha_maj3=1.5, alpha_min3=1.5):
self.clean_bias = clean_bias
self.clean_bias_error = clean_bias_error
self.frac_flux_cal_error = frac_flux_cal_error
self.alpha_maj1 = alpha_maj1
self.alpha_min1 = alpha_min1
self.alpha_maj2 = alpha_maj2
self.alpha_min2 = alpha_min2
self.alpha_maj3 = alpha_maj3
self.alpha_min3 = alpha_min3
self.values = {
'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.
self.deconv_imposs = 2
# 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.
self.moments = False
self.gaussian = False
##More metadata about the fit: only valid for Gaussian fits:
self.chisq = None
self.reduced_chisq = None
def __getitem__(self, item):
return self.values[item]
def __setitem__(self, item, value):
if item in self.values:
if isinstance(value, Uncertain):
self.values[item] = value
else:
self.values[item].value = value
elif item[:3] == 'err' and item[3:] in self.values:
self.values[item[3:]].error = value
else:
raise AttributeError("Invalid parameter")
[docs] def keys(self):
""" """
return self.values.keys()
[docs] def calculate_errors(self, noise, beam, threshold):
"""Calculate positional errors
Uses _condon_formulae() if this object is based on a Gaussian fit,
_error_bars_from_moments() if it's based on moments.
"""
if self.gaussian:
return self._condon_formulae(noise, beam)
elif self.moments:
if not threshold:
threshold = 0
return self._error_bars_from_moments(noise, beam, threshold)
else:
return False
def _condon_formulae(self, noise, beam):
"""Returns the errors on parameters from Gaussian fits according to
the Condon (PASP 109, 166 (1997)) formulae.
These formulae are not perfect, but we'll use them for the
time being. (See Refregier and Brown (astro-ph/9803279v1) for
a more rigorous approach.) It also returns the corrected peak.
The peak is corrected for the overestimate due to the local
noise gradient.
"""
peak = self['peak'].value
flux = self['flux'].value
smaj = self['semimajor'].value
smin = self['semiminor'].value
theta = self['theta'].value
theta_B, theta_b = utils.calculate_correlation_lengths(
beam[0], beam[1])
rho_sq1 = ((smaj*smin/(theta_B*theta_b)) *
(1.+(theta_B/(2.*smaj))**2)**self.alpha_maj1 *
(1.+(theta_b/(2.*smin))**2)**self.alpha_min1 *
(peak/noise)**2)
rho_sq2 = ((smaj*smin/(theta_B*theta_b)) *
(1.+(theta_B/(2.*smaj))**2)**self.alpha_maj2 *
(1.+(theta_b/(2.*smin))**2)**self.alpha_min2 *
(peak/noise)**2)
rho_sq3 = ((smaj*smin/(theta_B*theta_b)) *
(1.+(theta_B/(2.*smaj))**2)**self.alpha_maj3 *
(1.+(theta_b/(2.*smin))**2)**self.alpha_min3 *
(peak/noise)**2)
rho1 = numpy.sqrt(rho_sq1)
rho2 = numpy.sqrt(rho_sq2)
rho3 = numpy.sqrt(rho_sq3)
denom1 = numpy.sqrt(2.*numpy.log(2.)) * rho1
denom2 = numpy.sqrt(2.*numpy.log(2.)) * rho2
# Here you get the errors parallel to the fitted semi-major and
# semi-minor axes as taken from the NVSS paper (Condon et al. 1998,
# AJ, 115, 1693), formula 25.
# Those variances are twice the theoreticals, so the errors in
# position are sqrt(2) as large as one would get from formula 21
# of the Condon (1997) paper.
error_par_major = 2.*smaj/denom1
error_par_minor = 2.*smin/denom2
# 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 = numpy.sqrt((error_par_major * numpy.sin(theta))**2 +
(error_par_minor * numpy.cos(theta))**2)
errory = numpy.sqrt((error_par_major * numpy.cos(theta))**2 +
(error_par_minor * numpy.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 = numpy.sqrt(2) * smaj / rho1
errorsmin = numpy.sqrt(2) * smin / rho2
if smaj > smin:
errortheta = 2.0 * (smaj*smin/(smaj**2-smin**2))/rho2
else:
errortheta = numpy.pi
if errortheta > numpy.pi:
errortheta = numpy.pi
peak += -noise**2/peak + self.clean_bias
errorpeaksq = ((self.frac_flux_cal_error * peak)**2 +
self.clean_bias_error**2 +
2. * peak**2 / rho_sq3)
errorpeak = numpy.sqrt(errorpeaksq)
help1 = (errorsmaj/smaj)**2
help2 = (errorsmin/smin)**2
help3 = theta_B * theta_b / (4. * smaj * smin)
errorflux = numpy.abs(flux)*numpy.sqrt(errorpeaksq/peak**2+help3*(help1+help2))
self['peak'] = Uncertain(peak, 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
def _error_bars_from_moments(self, noise, beam, threshold):
"""Provide reasonable error estimates from the moments"""
# 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
# This analysis is only possible if the peak flux is >= 0. This
# follows from the definition of eq. 2.81 in Spreeuw's thesis. In that
# situation, we set all errors to be infinite
if peak < 0:
self['peak'].error = float('inf')
self['flux'].error = float('inf')
self['semimajor'].error = float('inf')
self['semiminor'].error = float('inf')
self['theta'].error = float('inf')
return self
clean_bias_error = self.clean_bias_error
frac_flux_cal_error = self.frac_flux_cal_error
theta_B, theta_b = utils.calculate_correlation_lengths(
beam[0], beam[1])
# This is eq. 2.81 from Spreeuw's thesis.
rho_sq = ((16. * smaj * smin /
(numpy.log(2.) * theta_B * theta_b*noise**2))
* ((peak - threshold) /
(numpy.log(peak) - numpy.log(threshold)))**2)
rho = numpy.sqrt(rho_sq)
denom = numpy.sqrt(2.*numpy.log(2.))*rho
# Again, like above for the Condon formulae, we set the
# positional variances to twice the theoretical values.
error_par_major = 2. * smaj / denom
error_par_minor = 2. * 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 = numpy.sqrt((error_par_major * numpy.sin(theta))**2
+ (error_par_minor * numpy.cos(theta))**2)
errory = numpy.sqrt((error_par_major * numpy.cos(theta))**2
+ (error_par_minor * numpy.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 = numpy.sqrt(2) * smaj / rho
errorsmin = numpy.sqrt(2) * smin / rho
if smaj > smin:
errortheta = 2.0 * (smaj * smin / (smaj**2 -smin**2)) / rho
else:
errortheta = numpy.pi
if errortheta > numpy.pi:
errortheta = numpy.pi
# The peak from "moments" is just the value of the maximum pixel
# times a correction, fudge_max_pix, for the fact that the
# centre of the Gaussian is not at the centre of the pixel.
# This correction is performed in fitting.py. The maximum pixel
# method introduces a peak dependent error corresponding to the last
# term in the expression below for errorpeaksq.
# To this, we add, in quadrature, the errors corresponding
# to the first and last term of the rhs of equation 37 of the
# NVSS paper. The middle term in that equation 37 is heuristically
# replaced by noise**2 since the threshold should not affect
# the error from the (corrected) maximum pixel method,
# while it is part of the expression for rho_sq above.
errorpeaksq = ((frac_flux_cal_error*peak)**2 +
clean_bias_error**2+noise**2 +
utils.maximum_pixel_method_variance(
beam[0], beam[1], beam[2])*peak**2)
errorpeak = numpy.sqrt(errorpeaksq)
help1 = (errorsmaj/smaj)**2
help2 = (errorsmin/smin)**2
help3 = theta_B*theta_b/(4.*smaj*smin)
errorflux = flux*numpy.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 with the clean beam"""
# If the fitted axes are smaller than the clean beam
# (=restoring beam) axes, the axes and position angle
# can be deconvolved from it.
fmaj = 2.*self['semimajor'].value
fmajerror = 2.*self['semimajor'].error
fmin = 2.*self['semiminor'].value
fminerror = 2.*self['semiminor'].error
fpa = numpy.degrees(self['theta'].value)
fpaerror = numpy.degrees(self['theta'].error)
cmaj = 2.*beam[0]
cmin = 2.*beam[1]
cpa = numpy.degrees(beam[2])
rmaj, rmin, rpa, ierr = deconv(fmaj, fmin, fpa, cmaj, cmin, cpa)
# This parameter gives the number of components that could not be
# deconvolved, IERR from deconf.f.
self.deconv_imposs = ierr
# Now, figure out the error bars.
if rmaj > 0:
# In this case the deconvolved position angle is defined.
# For convenience we reset rpa to the interval [-90, 90].
if rpa > 90:
rpa = -numpy.mod(-rpa, 180.)
self['theta_deconv'].value = rpa
# In the general case, where the restoring beam is elliptic,
# calculating the error bars of the deconvolved position angle
# is more complicated than in the NVSS case, where a circular
# restoring beam was used.
# In the NVSS case the error bars of the deconvolved angle are
# equal to the fitted angle.
rmaj1, rmin1, rpa1, ierr1 = deconv(
fmaj, fmin, fpa+fpaerror, cmaj, cmin, cpa)
if ierr1 < 2:
if rpa1 > 90:
rpa1 = -numpy.mod(-rpa1, 180.)
rpaerror1 = numpy.abs(rpa1-rpa)
# An angle error can never be more than 90 degrees.
if rpaerror1 > 90.:
rpaerror1 = numpy.mod(-rpaerror1, 180.)
else:
rpaerror1 = numpy.nan
rmaj2, rmin2, rpa2, ierr2 = deconv(
fmaj, fmin, fpa-fpaerror, cmaj, cmin, cpa)
if ierr2 < 2:
if rpa2 > 90:
rpa2 = -numpy.mod(-rpa2, 180.)
rpaerror2 = numpy.abs(rpa2 - rpa)
# An angle error can never be more than 90 degrees.
if rpaerror2 > 90.:
rpaerror2 = numpy.mod(-rpaerror2, 180.)
else:
rpaerror2 = numpy.nan
if numpy.isnan(rpaerror1) or numpy.isnan(rpaerror2):
self['theta_deconv'].error = numpy.nansum(
[rpaerror1, rpaerror2])
else:
self['theta_deconv'].error = numpy.mean(
[rpaerror1, rpaerror2])
self['semimaj_deconv'].value = rmaj / 2.
rmaj3, rmin3, rpa3, ierr3 = deconv(
fmaj + fmajerror, fmin, fpa, cmaj, cmin, cpa)
# If rmaj>0, then rmaj3 should also be > 0,
# if I am not mistaken, see the formulas at
# the end of ch.2 of Spreeuw's Ph.D. thesis.
if fmaj-fmajerror > fmin:
rmaj4, rmin4, rpa4, ierr4 = deconv(
fmaj-fmajerror, fmin, fpa, cmaj, cmin, cpa)
if rmaj4 > 0:
self['semimaj_deconv'].error = numpy.mean(
[numpy.abs(rmaj3-rmaj), numpy.abs(rmaj - rmaj4)])
else:
self['semimaj_deconv'].error = numpy.abs(rmaj3 - rmaj)
else:
rmin4, rmaj4, rpa4, ierr4 = deconv(
fmin, fmaj - fmajerror, fpa, cmaj, cmin, cpa)
if rmaj4>0:
self['semimaj_deconv'].error = numpy.mean(
[numpy.abs(rmaj3-rmaj), numpy.abs(rmaj - rmaj4)])
else:
self['semimaj_deconv'].error = numpy.abs(rmaj3 - rmaj)
if rmin > 0:
self['semimin_deconv'].value = rmin / 2.
if fmin + fminerror < fmaj:
rmaj5, rmin5, rpa5, ierr5 = deconv(
fmaj, fmin+fminerror, fpa, cmaj, cmin, cpa)
else:
rmin5, rmaj5, rpa5, ierr5 = deconv(
fmin+fminerror, fmaj, fpa, cmaj, cmin, cpa)
# If rmin > 0, then rmin5 should also be > 0,
# if I am not mistaken, see the formulas at
# the end of ch.2 of Spreeuw's Ph.D. thesis.
rmaj6, rmin6, rpa6, ierr6 = deconv(
fmaj, fmin-fminerror, fpa, cmaj, cmin, cpa)
if rmin6 > 0:
self['semimin_deconv'].error = numpy.mean(
[numpy.abs(rmin6-rmin), numpy.abs(rmin5 - rmin)])
else:
self['semimin_deconv'].error = numpy.abs(rmin5 - rmin)
else:
self['semimin_deconv'] = Uncertain(
numpy.nan, numpy.nan)
else:
self['semimaj_deconv'] = Uncertain(numpy.nan, numpy.nan)
self['semimin_deconv'] = Uncertain(numpy.nan, numpy.nan)
self['theta_deconv'] = Uncertain(numpy.nan, numpy.nan)
return self
[docs]def source_profile_and_errors(data, threshold, noise,
beam, 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:`tkp.sourcefinder.fitting.goodness_of_fit` for details.
Args:
data (numpy.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)
noise (float): Noise level in data
beam (tuple): beam parameters (semimaj,semimin,theta)
Kwargs:
fixed (dict): Parameters (and their values) to hold fixed while fitting.
Passed on to fitting.fitgaussian().
Returns:
tuple: a populated ParamSet, and a residuals map.
Note the residuals map is a regular ndarray, where masked (unfitted)
regions have been filled with 0-values.
"""
if fixed is None:
fixed = {}
param = ParamSet()
if threshold is None:
moments_threshold=0
else:
moments_threshold = threshold
try:
param.update(fitting.moments(data, beam, moments_threshold))
param.moments = True
except ValueError:
# If this happens, we have two choices:
# 1) Bomb out and tell the user to fit something sensible instead;
# 2) Make up our own estimate (all 1s or something) to give the
# gaussian fitter a starting point.
param.update({
"peak": 1,
"flux": 1,
"xbar": data.shape[0]/2.0,
"ybar": data.shape[1]/2.0,
"semimajor": 1,
"semiminor": 1,
"theta": 0
})
logger.debug("Unable to estimate gaussian parameters."
" Proceeding with defaults %s""",
str(param))
ranges = data.nonzero()
xmin = min(ranges[0])
xmax = max(ranges[0])
ymin = min(ranges[1])
ymax = max(ranges[1])
if (numpy.fabs(xmax-xmin) > 2) and (numpy.fabs(ymax-ymin) > 2):
# Now we can do Gauss fitting if the island or subisland has a
# thickness of more than 2 in both dimensions.
try:
gaussian_soln = fitting.fitgaussian(data, param, fixed=fixed)
param.update(gaussian_soln)
param.gaussian = True
logger.debug('Gauss fitting was successful.')
except ValueError:
logger.warn('Gauss fitting failed.')
if fixed and not param.gaussian:
# moments can't handle fixed params
raise ValueError("fit failed with given fixed parameters")
beamsize = utils.calculate_beamsize(beam[0], beam[1])
param["flux"] = (numpy.pi * param["peak"] * param["semimajor"] *
param["semiminor"] / beamsize)
param.calculate_errors(noise, beam, threshold)
param.deconvolve_from_clean_beam(beam)
# Calculate residuals
# NB this works even if Gaussian fitting fails, we generate the model from
# the moments-fit parameters.
gauss_arg = (param["peak"].value,
param["xbar"].value,
param["ybar"].value,
param["semimajor"].value,
param["semiminor"].value,
param["theta"].value)
gauss_resid_masked = -(gaussian(*gauss_arg)(*numpy.indices(data.shape)) - data)
param.chisq, param.reduced_chisq = fitting.goodness_of_fit(
gauss_resid_masked, noise, beam)
gauss_resid_filled = gauss_resid_masked.filled(fill_value=0.)
return param, gauss_resid_filled
[docs]class Detection(object):
"""The result of a measurement at a given position in a given image."""
def __init__(self, paramset, imagedata, chunk=None, eps_ra=0, eps_dec=0):
self.eps_ra = eps_ra
self.eps_dec = eps_dec
self.imagedata = imagedata
##self.wcs = imagedata.wcs
self.chunk = chunk
self.peak = paramset['peak']
self.flux = paramset['flux']
self.x = paramset['xbar']
self.y = paramset['ybar']
self.smaj = paramset['semimajor']
self.smin = paramset['semiminor']
self.theta = paramset['theta']
# This parameter gives the number of components that could not
# be deconvolved, IERR from deconf.f.
self.dc_imposs = paramset.deconv_imposs
self.smaj_dc = paramset['semimaj_deconv']
self.smin_dc = paramset['semimin_deconv']
self.theta_dc = paramset['theta_deconv']
self.error_radius = None
self.gaussian = paramset.gaussian
self.chisq = paramset.chisq
self.reduced_chisq = paramset.reduced_chisq
self.sig = paramset.sig
try:
self._physical_coordinates()
except RuntimeError:
logger.warn("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, e:
logger.warn("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)
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 numpy.isnan(self.dec.value) or abs(self.dec) > 90.0:
raise ValueError("object falls outside the sky")
# First, determine local north.
help1 = numpy.cos(numpy.radians(self.ra.value))
help2 = numpy.sin(numpy.radians(self.ra.value))
help3 = numpy.cos(numpy.radians(self.dec.value))
help4 = numpy.sin(numpy.radians(self.dec.value))
center_position = numpy.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 = numpy.array([0., 0., 1./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 = numpy.array([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.])
help5 = numpy.cos(numpy.radians(endy_ra))
help6 = numpy.sin(numpy.radians(endy_ra))
help7 = numpy.cos(numpy.radians(endy_dec))
help8 = numpy.sin(numpy.radians(endy_dec))
endy_position = numpy.array([help7*help5, help7*help6, help8])
# Extend the length of endy_position to make it touch the plane
# tangent at center_position.
endy_position /= numpy.dot(center_position, endy_position)
diff1 = endy_position-center_position
diff2 = local_north_position-center_position
cross_prod = numpy.cross(diff2, diff1)
length_cross_sq = numpy.dot(cross_prod, cross_prod)
normalization = numpy.dot(diff1, diff1) * numpy.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 = numpy.degrees(
# numpy.arcsin(numpy.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.
yoffs_rad = (numpy.arccos(numpy.dot(diff1, diff2) /
numpy.sqrt(normalization)))
# The multiplication with -sign_cor makes sure that the angle
# is measured eastwards (increasing RA), not westwards.
sign_cor = (numpy.dot(cross_prod, center_position) /
numpy.sqrt(length_cross_sq))
yoffs_rad *= -sign_cor
yoffset_angle = numpy.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 = numpy.sqrt(
(self.x.error*numpy.cos(yoffs_rad))**2 +
(self.y.error*numpy.sin(yoffs_rad))**2)
errory_proj = numpy.sqrt(
(self.x.error*numpy.sin(yoffs_rad))**2 +
(self.y.error*numpy.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(
numpy.fabs(self.ra.value - end_ra1),
numpy.fabs(self.ra.value - end_ra2))
self.dec.error = self.eps_dec + max(
numpy.fabs(self.dec.value - end_dec1),
numpy.fabs(self.dec.value - end_dec2))
except RuntimeError:
#We get a runtime error from wcs.p2s if the errors place the
#limits outside of 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(
(numpy.degrees(self.theta.value) + yoffset_angle) % 180,
numpy.degrees(self.theta.error))
self.theta_dc_celes = Uncertain(
(self.theta_dc.value + yoffset_angle) % 180,
numpy.degrees(self.theta_dc.error))
# Next, the axes.
# Note that the signs of numpy.sin and numpy.cos in the
# four expressions below are arbitrary.
self.end_smaj_x = (self.x.value - numpy.sin(self.theta.value) *
self.smaj.value)
self.start_smaj_x = (self.x.value + numpy.sin(self.theta.value) *
self.smaj.value)
self.end_smaj_y = (self.y.value + numpy.cos(self.theta.value) *
self.smaj.value)
self.start_smaj_y = (self.y.value - numpy.cos(self.theta.value) *
self.smaj.value)
self.end_smin_x = (self.x.value + numpy.cos(self.theta.value) *
self.smin.value)
self.start_smin_x = (self.x.value - numpy.cos(self.theta.value) *
self.smin.value)
self.end_smin_y = (self.y.value + numpy.sin(self.theta.value) *
self.smin.value)
self.start_smin_y = (self.y.value - numpy.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 numpy.nan, numpy.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 center"""
return ((self.x - x)**2 + (self.y - y)**2)**0.5
[docs] def serialize(self, ew_sys_err, ns_sys_err):
"""
Return source properties suitable for database storage.
We manually add ew_sys_err, ns_sys_err
returns: a list of tuples containing all relevant fields
"""
return [
self.ra.value,
self.dec.value,
self.ra.error,
self.dec.error,
self.peak.value,
self.peak.error,
self.flux.value,
self.flux.error,
self.sig,
self.smaj_asec.value,
self.smin_asec.value,
self.theta_celes.value,
ew_sys_err,
ns_sys_err,
self.error_radius,
self.gaussian,
self.chisq,
self.reduced_chisq
]
