Source code for photutils.isophote.sample

# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
This module provides a class to sample data along an elliptical path.
"""

import copy

import numpy as np

from .geometry import EllipseGeometry
from .integrator import INTEGRATORS

__all__ = ['EllipseSample']


[docs]class EllipseSample: """ Class to sample image data along an elliptical path. The image intensities along the elliptical path can be extracted using a selection of integration algorithms. The ``geometry`` attribute describes the geometry of the elliptical path. Parameters ---------- image : 2D `~numpy.ndarray` The input image. sma : float The semimajor axis length in pixels. x0, y0 : float, optional The (x, y) coordinate of the ellipse center. astep : float, optional The step value for growing/shrinking the semimajor axis. It can be expressed either in pixels (when ``linear_growth=True``) or as a relative value (when ``linear_growth=False``). The default is 0.1. eps : float, optional The ellipticity of the ellipse. The default is 0.2. pa : float, optional The position angle of ellipse in relation to the positive x axis of the image array (rotating towards the positive y axis). The default is 0. sclip : float, optional The sigma-clip sigma value. The default is 3.0. nclip : int, optional The number of sigma-clip iterations. Set to zero to skip sigma-clipping. The default is 0. linear_growth : bool, optional The semimajor axis growing/shrinking mode. The default is `False`. integrmode : {'bilinear', 'nearest_neighbor', 'mean', 'median'}, optional The area integration mode. The default is 'bilinear'. geometry : `~photutils.isophote.EllipseGeometry` instance or `None` The geometry that describes the ellipse. This can be used in lieu of the explicit specification of parameters ``sma``, ``x0``, ``y0``, ``eps``, etc. In any case, the `~photutils.isophote.EllipseGeometry` instance becomes an attribute of the `~photutils.isophote.EllipseSample` object. The default is `None`. Attributes ---------- values : 2D `~numpy.ndarray` The sampled values as a 2D array, where the rows contain the angles, radii, and extracted intensity values, respectively. mean : float The mean intensity along the elliptical path. geometry : `~photutils.isophote.EllipseGeometry` instance The geometry of the elliptical path. gradient : float The local radial intensity gradient. gradient_error : float The error associated with the local radial intensity gradient. gradient_relative_error : float The relative error associated with the local radial intensity gradient. sector_area : float The average area of the sectors along the elliptical path from which the sample values were integrated. total_points : int The total number of sample values that would cover the entire elliptical path. actual_points : int The actual number of sample values that were taken from the image. It can be smaller than ``total_points`` when the ellipse encompasses regions outside the image, or when sigma-clipping removed some of the points. """ def __init__(self, image, sma, x0=None, y0=None, astep=0.1, eps=0.2, position_angle=0., sclip=3., nclip=0, linear_growth=False, integrmode='bilinear', geometry=None): self.image = image self.integrmode = integrmode if geometry: # when the geometry is inherited from somewhere else, # its sma attribute must be replaced by the value # explicitly passed to the constructor. self.geometry = copy.deepcopy(geometry) self.geometry.sma = sma else: # if no center was specified, assume it's roughly # coincident with the image center _x0 = x0 _y0 = y0 if not _x0 or not _y0: _x0 = image.shape[1] / 2 _y0 = image.shape[0] / 2 self.geometry = EllipseGeometry(_x0, _y0, sma, eps, position_angle, astep, linear_growth) # sigma-clip parameters self.sclip = sclip self.nclip = nclip # extracted values associated with this sample. self.values = None self.mean = None self.gradient = None self.gradient_error = None self.gradient_relative_error = None self.sector_area = None # total_points reports the total number of pairs angle-radius that # were attempted. actual_points reports the actual number of sampled # pairs angle-radius that resulted in valid values. self.total_points = 0 self.actual_points = 0
[docs] def extract(self): """ Extract sample data by scanning an elliptical path over the image array. Returns ------- result : 2D `~numpy.ndarray` The rows of the array contain the angles, radii, and extracted intensity values, respectively. """ # the sample values themselves are kept cached to prevent # multiple calls to the integrator code. if self.values is not None: return self.values else: s = self._extract() self.values = s return s
def _extract(self, phi_min=0.05): # Here the actual sampling takes place. This is called only once # during the life of an EllipseSample instance, because it's an # expensive calculation. This method should not be called from # external code. # If one wants to force it to re-run, then do: # # sample.values = None # # before calling sample.extract() # individual extracted sample points will be stored in here angles = [] radii = [] intensities = [] sector_areas = [] # reset counters self.total_points = 0 self.actual_points = 0 # build integrator integrator = INTEGRATORS[self.integrmode](self.image, self.geometry, angles, radii, intensities) # initialize walk along elliptical path radius = self.geometry.initial_polar_radius phi = self.geometry.initial_polar_angle # In case of an area integrator, ask the integrator to deliver a # hint of how much area the sectors will have. In case of too # small areas, tests showed that the area integrators (mean, # median) won't perform properly. In that case, we override the # caller's selection and use the bilinear integrator regardless. if integrator.is_area(): integrator.integrate(radius, phi) area = integrator.get_sector_area() # this integration that just took place messes up with the # storage arrays and the constructors. We have to build a new # integrator instance from scratch, even if it is the same # kind as originally selected by the caller. angles = [] radii = [] intensities = [] if area < 1.0: integrator = INTEGRATORS['bilinear']( self.image, self.geometry, angles, radii, intensities) else: integrator = INTEGRATORS[self.integrmode](self.image, self.geometry, angles, radii, intensities) # walk along elliptical path, integrating at specified # places defined by polar vector. Need to go a bit beyond # full circle to ensure full coverage. while phi <= np.pi*2. + phi_min: # do the integration at phi-radius position, and append # results to the angles, radii, and intensities lists. integrator.integrate(radius, phi) # store sector area locally sector_areas.append(integrator.get_sector_area()) # update total number of points self.total_points += 1 # update angle and radius to be used to define # next polar vector along the elliptical path phistep_ = integrator.get_polar_angle_step() phi += min(phistep_, 0.5) radius = self.geometry.radius(phi) # average sector area is calculated after the integrator had # the opportunity to step over the entire elliptical path. self.sector_area = np.mean(np.array(sector_areas)) # apply sigma-clipping. angles, radii, intensities = self._sigma_clip(angles, radii, intensities) # actual number of sampled points, after sigma-clip removed outliers. self.actual_points = len(angles) # pack results in 2-d array result = np.array([np.array(angles), np.array(radii), np.array(intensities)]) return result def _sigma_clip(self, angles, radii, intensities): if self.nclip > 0: for i in range(self.nclip): # do not use list.copy()! must be python2-compliant. angles, radii, intensities = self._iter_sigma_clip( angles[:], radii[:], intensities[:]) return np.array(angles), np.array(radii), np.array(intensities) def _iter_sigma_clip(self, angles, radii, intensities): # Can't use scipy or astropy tools because they use masked arrays. # Also, they operate on a single array, and we need to operate on # three arrays simultaneously. We need something that physically # removes the clipped points from the arrays, since that is what # the remaining of the `ellipse` code expects. r_angles = [] r_radii = [] r_intensities = [] values = np.array(intensities) mean = np.mean(values) sig = np.std(values) lower = mean - self.sclip * sig upper = mean + self.sclip * sig count = 0 for k in range(len(intensities)): if intensities[k] >= lower and intensities[k] < upper: r_angles.append(angles[k]) r_radii.append(radii[k]) r_intensities.append(intensities[k]) count += 1 return r_angles, r_radii, r_intensities
[docs] def update(self, fixed_parameters=None): """ Update this `~photutils.isophote.EllipseSample` instance. This method calls the :meth:`~photutils.isophote.EllipseSample.extract` method to get the values that match the current ``geometry`` attribute, and then computes the the mean intensity, local gradient, and other associated quantities. """ if fixed_parameters is None: fixed_parameters = np.array([False, False, False, False]) self.geometry.fix = fixed_parameters step = self.geometry.astep # Update the mean value first, using extraction from main sample. s = self.extract() self.mean = np.mean(s[2]) # Get sample with same geometry but at a different distance from # center. Estimate gradient from there. gradient, gradient_error = self._get_gradient(step) # Check for meaningful gradient. If no meaningful gradient, try # another sample, this time using larger radius. Meaningful # gradient means something shallower, but still close to within # a factor 3 from previous gradient estimate. If no previous # estimate is available, guess it by adding the error to the # current gradient. previous_gradient = self.gradient if not previous_gradient: previous_gradient = gradient + gradient_error # solution adopted before 08/12/2019 # previous_gradient = -0.05 # good enough, based on usage if gradient >= (previous_gradient / 3.): # gradient is negative! gradient, gradient_error = self._get_gradient(2 * step) # If still no meaningful gradient can be measured, try with # previous one, slightly shallower. A factor 0.8 is not too far # from what is expected from geometrical sampling steps of 10-20% # and a deVaucouleurs law or an exponential disk (at least at its # inner parts, r <~ 5 req). Gradient error is meaningless in this # case. if gradient >= (previous_gradient / 3.): gradient = previous_gradient * 0.8 gradient_error = None self.gradient = gradient self.gradient_error = gradient_error if gradient_error and gradient < 0.: self.gradient_relative_error = gradient_error / np.abs(gradient) else: self.gradient_relative_error = None
def _get_gradient(self, step): gradient_sma = (1. + step) * self.geometry.sma gradient_sample = EllipseSample( self.image, gradient_sma, x0=self.geometry.x0, y0=self.geometry.y0, astep=self.geometry.astep, sclip=self.sclip, nclip=self.nclip, eps=self.geometry.eps, position_angle=self.geometry.pa, linear_growth=self.geometry.linear_growth, integrmode=self.integrmode) sg = gradient_sample.extract() mean_g = np.mean(sg[2]) gradient = (mean_g - self.mean) / self.geometry.sma / step s = self.extract() sigma = np.std(s[2]) sigma_g = np.std(sg[2]) gradient_error = (np.sqrt(sigma**2 / len(s[2]) + sigma_g**2 / len(sg[2])) / self.geometry.sma / step) return gradient, gradient_error
[docs] def coordinates(self): """ Return the (x, y) coordinates associated with each sampled point. Returns ------- x, y : 1D `~numpy.ndarray` The x and y coordinate arrays. """ angles = self.values[0] radii = self.values[1] x = np.zeros(len(angles)) y = np.zeros(len(angles)) for i in range(len(x)): x[i] = (radii[i] * np.cos(angles[i] + self.geometry.pa) + self.geometry.x0) y[i] = (radii[i] * np.sin(angles[i] + self.geometry.pa) + self.geometry.y0) return x, y
class CentralEllipseSample(EllipseSample): """ An `~photutils.isophote.EllipseSample` subclass designed to handle the special case of the central pixel in the galaxy image. """ def update(self, fixed_parameters): """ Update this `~photutils.isophote.EllipseSample` instance with the intensity integrated at the (x0, y0) center position using bilinear integration. The local gradient is set to `None`. 'fixed_parameters' is ignored in this subclass. """ s = self.extract() self.mean = s[2][0] self.gradient = None self.gradient_error = None self.gradient_relative_error = None def _extract(self): angles = [] radii = [] intensities = [] integrator = INTEGRATORS['bilinear'](self.image, self.geometry, angles, radii, intensities) integrator.integrate(0.0, 0.0) self.total_points = 1 self.actual_points = 1 return np.array([np.array(angles), np.array(radii), np.array(intensities)])