# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
This module provides a class to fit ellipses.
"""
import math
import numpy as np
from astropy import log
from photutils.isophote.harmonics import (first_and_second_harmonic_function,
fit_first_and_second_harmonics)
from photutils.isophote.isophote import CentralPixel, Isophote
from photutils.isophote.sample import EllipseSample
__all__ = ['EllipseFitter']
__doctest_skip__ = ['EllipseFitter.fit']
PI2 = np.pi / 2
MAX_EPS = 0.95
MIN_EPS = 0.05
DEFAULT_CONVERGENCE = 0.05
DEFAULT_MINIT = 10
DEFAULT_MAXIT = 50
DEFAULT_FFLAG = 0.7
DEFAULT_MAXGERR = 0.5
[docs]
class EllipseFitter:
"""
Class to fit ellipses.
Parameters
----------
sample : `~photutils.isophote.EllipseSample` instance
The sample data to be fitted.
"""
def __init__(self, sample):
self._sample = sample
[docs]
def fit(self, conver=DEFAULT_CONVERGENCE, minit=DEFAULT_MINIT,
maxit=DEFAULT_MAXIT, fflag=DEFAULT_FFLAG, maxgerr=DEFAULT_MAXGERR,
going_inwards=False):
"""
Fit an elliptical isophote.
Parameters
----------
conver : float, optional
The main convergence criterion. Iterations stop when the
largest harmonic amplitude becomes smaller (in absolute
value) than ``conver`` times the harmonic fit rms. The
default is 0.05.
minit : int, optional
The minimum number of iterations to perform. A minimum of 10
(the default) iterations guarantees that, on average, 2
iterations will be available for fitting each independent
parameter (the four harmonic amplitudes and the intensity
level). For the first isophote, the minimum number of
iterations is 2 * ``minit`` to ensure that, even departing
from not-so-good initial values, the algorithm has a better
chance to converge to a sensible solution.
maxit : int, optional
The maximum number of iterations to perform. The default is
50.
fflag : float, optional
The acceptable fraction of flagged data points in the
sample. If the actual fraction of valid data points is
smaller than this, the iterations will stop and the current
`~photutils.isophote.Isophote` will be returned. Flagged
data points are points that either lie outside the image
frame, are masked, or were rejected by sigma-clipping. The
default is 0.7.
maxgerr : float, optional
The maximum acceptable relative error in the local radial
intensity gradient. This is the main control for preventing
ellipses to grow to regions of too low signal-to-noise
ratio. It specifies the maximum acceptable relative error
in the local radial intensity gradient. `Busko (1996; ASPC
101, 139)
<https://ui.adsabs.harvard.edu/abs/1996ASPC..101..139B/abstract>`_
showed that the fitting precision relates to that relative
error. The usual behavior of the gradient relative error is
to increase with semimajor axis, being larger in outer,
fainter regions of a galaxy image. In the current
implementation, the ``maxgerr`` criterion is triggered only
when two consecutive isophotes exceed the value specified by
the parameter. This prevents premature stopping caused by
contamination such as stars and HII regions.
A number of actions may happen when the gradient error
exceeds ``maxgerr`` (or becomes non-significant and is set
to `None`). If the maximum semimajor axis specified by
``maxsma`` is set to `None`, semimajor axis growth is
stopped and the algorithm proceeds inwards to the galaxy
center. If ``maxsma`` is set to some finite value, and this
value is larger than the current semimajor axis length, the
algorithm enters non-iterative mode and proceeds outwards
until reaching ``maxsma``. The default is 0.5.
going_inwards : bool, optional
Parameter to define the sense of SMA growth. When fitting
just one isophote, this parameter is used only by the code
that defines the details of how elliptical arc segments
("sectors") are extracted from the image, when using area
extraction modes (see the ``integrmode`` parameter in the
`~photutils.isophote.EllipseSample` class). The default is
`False`.
Returns
-------
result : `~photutils.isophote.Isophote` instance
The fitted isophote, which also contains fit status
information.
Examples
--------
>>> from photutils.isophote import EllipseSample, EllipseFitter
>>> sample = EllipseSample(data, sma=10.0)
>>> fitter = EllipseFitter(sample)
>>> isophote = fitter.fit()
"""
sample = self._sample
# this flag signals that limiting gradient error (`maxgerr`)
# wasn't exceeded yet.
lexceed = False
# here we keep track of the sample that caused the minimum harmonic
# amplitude(in absolute value). This will eventually be used to
# build the resulting Isophote in cases where iterations run to
# the maximum allowed (maxit), or the maximum number of flagged
# data points (fflag) is reached.
minimum_amplitude_value = np.inf
minimum_amplitude_sample = None
# these must be passed throughout the execution chain.
fixed_parameters = self._sample.geometry.fix
for i in range(maxit):
# Force the sample to compute its gradient and associated values.
sample.update(fixed_parameters)
# The extract() method returns sampled values as a 2-d numpy array
# with the following structure:
# values[0] = 1-d array with angles
# values[1] = 1-d array with radii
# values[2] = 1-d array with intensity
values = sample.extract()
# We have to check for a zero-length condition here, and bail out
# in case it is detected. The scipy fitter won't raise an exception
# for zero-length input arrays, but just prints an "INFO" message.
# This may result in an infinite loop.
if len(values[2]) < 1:
s = str(sample.geometry.sma)
log.warning('Too small sample to warrant a fit. SMA is ' + s)
sample.geometry.fix = fixed_parameters
return Isophote(sample, i + 1, False, 3)
# Fit harmonic coefficients. Failure in fitting is
# a fatal error; terminate immediately with sample
# marked as invalid.
try:
coeffs = fit_first_and_second_harmonics(values[0], values[2])
coeffs = coeffs[0]
except Exception as e:
log.warning(e)
sample.geometry.fix = fixed_parameters
return Isophote(sample, i + 1, False, 3)
# Mask out coefficients that control fixed ellipse parameters.
free_coeffs = np.ma.masked_array(coeffs[1:], mask=fixed_parameters)
# Largest non-masked harmonic in absolute value drives the
# correction.
largest_harmonic_index = np.argmax(np.abs(free_coeffs))
largest_harmonic = free_coeffs[largest_harmonic_index]
# see if the amplitude decreased; if yes, keep the
# corresponding sample for eventual later use.
if abs(largest_harmonic) < minimum_amplitude_value:
minimum_amplitude_value = abs(largest_harmonic)
minimum_amplitude_sample = sample
# check if converged
model = first_and_second_harmonic_function(values[0], coeffs)
residual = values[2] - model
if ((conver * sample.sector_area * np.std(residual))
> np.abs(largest_harmonic)):
# Got a valid solution. But before returning, ensure
# that a minimum of iterations has run.
if i >= minit - 1:
sample.update(fixed_parameters)
return Isophote(sample, i + 1, True, 0)
# it may not have converged yet, but the sample contains too
# many invalid data points: return.
if sample.actual_points < (sample.total_points * fflag):
# when too many data points were flagged, return the
# best fit sample instead of the current one.
minimum_amplitude_sample.update(fixed_parameters)
return Isophote(minimum_amplitude_sample, i + 1, True, 1)
# pick appropriate corrector code.
corrector = _CORRECTORS[largest_harmonic_index]
# generate *NEW* EllipseSample instance with corrected
# parameter. Note that this instance is still devoid of other
# information besides its geometry. It needs to be explicitly
# updated for computations to proceed. We have to build a new
# EllipseSample instance every time because of the lazy
# extraction process used by EllipseSample code. To minimize
# the number of calls to the area integrators, we pay a
# (hopefully smaller) price here, by having multiple calls to
# the EllipseSample constructor.
sample = corrector.correct(sample, largest_harmonic)
sample.update(fixed_parameters)
# see if any abnormal (or unusual) conditions warrant
# the change to non-iterative mode, or go-inwards mode.
proceed, lexceed = self._check_conditions(
sample, maxgerr, going_inwards, lexceed)
if not proceed:
sample.update(fixed_parameters)
return Isophote(sample, i + 1, True, -1)
# Got to the maximum number of iterations. Return with
# code 2, and handle it as a valid isophote. Use the
# best fit sample instead of the current one.
minimum_amplitude_sample.update(fixed_parameters)
return Isophote(minimum_amplitude_sample, maxit, True, 2)
@staticmethod
def _check_conditions(sample, maxgerr, going_inwards, lexceed):
proceed = True
# If center wandered more than allowed, put it back
# in place and signal the end of iterative mode.
# if wander:
# if abs(dx) > WANDER(al)) or abs(dy) > WANDER(al):
# sample.geometry.x0 -= dx
# sample.geometry.y0 -= dy
# STOP(al) = ST_NONITERATE
# proceed = False
# check if an acceptable gradient value could be computed.
if sample.gradient_error and sample.gradient_relative_error:
if not going_inwards and (
sample.gradient_relative_error > maxgerr
or sample.gradient >= 0.0):
if lexceed:
proceed = False
else:
lexceed = True
else:
proceed = False
# check if ellipse geometry diverged.
if abs(sample.geometry.eps > MAX_EPS):
proceed = False
if (sample.geometry.x0 < 1.0
or sample.geometry.x0 > sample.image.shape[1]
or sample.geometry.y0 < 1.0
or sample.geometry.y0 > sample.image.shape[0]):
proceed = False
# See if eps == 0 (round isophote) was crossed.
# If so, fix it but still proceed
if sample.geometry.eps < 0.0:
sample.geometry.eps = min(-sample.geometry.eps, MAX_EPS)
if sample.geometry.pa < PI2:
sample.geometry.pa += PI2
else:
sample.geometry.pa -= PI2
# If ellipse is an exact circle, computations will diverge.
# Make it slightly flat, but still proceed
if sample.geometry.eps == 0.0:
sample.geometry.eps = MIN_EPS
return proceed, lexceed
class _ParameterCorrector:
def correct(self, sample, harmonic):
raise NotImplementedError
class _PositionCorrector(_ParameterCorrector):
@staticmethod
def finalize_correction(dx, dy, sample):
new_x0 = sample.geometry.x0 + dx
new_y0 = sample.geometry.y0 + dy
return EllipseSample(sample.image, sample.geometry.sma, x0=new_x0,
y0=new_y0, astep=sample.geometry.astep,
sclip=sample.sclip, nclip=sample.nclip,
eps=sample.geometry.eps,
position_angle=sample.geometry.pa,
linear_growth=sample.geometry.linear_growth,
integrmode=sample.integrmode)
class _PositionCorrector0(_PositionCorrector):
def correct(self, sample, harmonic):
aux = -harmonic * (1.0 - sample.geometry.eps) / sample.gradient
dx = -aux * math.sin(sample.geometry.pa)
dy = aux * math.cos(sample.geometry.pa)
return self.finalize_correction(dx, dy, sample)
class _PositionCorrector1(_PositionCorrector):
def correct(self, sample, harmonic):
aux = -harmonic / sample.gradient
dx = aux * math.cos(sample.geometry.pa)
dy = aux * math.sin(sample.geometry.pa)
return self.finalize_correction(dx, dy, sample)
class _AngleCorrector(_ParameterCorrector):
def correct(self, sample, harmonic):
eps = sample.geometry.eps
sma = sample.geometry.sma
gradient = sample.gradient
correction = (harmonic * 2.0 * (1.0 - eps) / sma / gradient
/ ((1.0 - eps)**2 - 1.0))
# '% np.pi' to make angle lie between 0 and np.pi radians
new_pa = (sample.geometry.pa + correction) % np.pi
return EllipseSample(sample.image, sample.geometry.sma,
x0=sample.geometry.x0, y0=sample.geometry.y0,
astep=sample.geometry.astep, sclip=sample.sclip,
nclip=sample.nclip, eps=sample.geometry.eps,
position_angle=new_pa,
linear_growth=sample.geometry.linear_growth,
integrmode=sample.integrmode)
class _EllipticityCorrector(_ParameterCorrector):
def correct(self, sample, harmonic):
eps = sample.geometry.eps
sma = sample.geometry.sma
gradient = sample.gradient
correction = harmonic * 2.0 * (1.0 - eps) / sma / gradient
new_eps = min((sample.geometry.eps - correction), MAX_EPS)
return EllipseSample(sample.image, sample.geometry.sma,
x0=sample.geometry.x0, y0=sample.geometry.y0,
astep=sample.geometry.astep, sclip=sample.sclip,
nclip=sample.nclip, eps=new_eps,
position_angle=sample.geometry.pa,
linear_growth=sample.geometry.linear_growth,
integrmode=sample.integrmode)
# instances of corrector code live here:
_CORRECTORS = [_PositionCorrector0(), _PositionCorrector1(),
_AngleCorrector(), _EllipticityCorrector()]
class CentralEllipseFitter(EllipseFitter):
"""
A special Fitter class to handle the case of the central pixel in
the galaxy image.
"""
def fit(self, conver=DEFAULT_CONVERGENCE, minit=DEFAULT_MINIT,
maxit=DEFAULT_MAXIT, fflag=DEFAULT_FFLAG, maxgerr=DEFAULT_MAXGERR,
going_inwards=False):
"""
Perform just a simple 1-pixel extraction at the current (x0, y0)
position using bilinear interpolation.
The input parameters are ignored, but included simple to match
the calling signature of the parent class.
Returns
-------
result : `~photutils.isophote.CentralEllipsePixel` instance
The central pixel value. For convenience, the
`~photutils.isophote.CentralEllipsePixel` class inherits
from the `~photutils.isophote.Isophote` class, although it's
not really a true isophote but just a single intensity value
at the central position. Thus, most of its attributes are
hardcoded to `None` or other default value when appropriate.
"""
# default values
fixed_parameters = np.array([False, False, False, False])
self._sample.update(fixed_parameters)
return CentralPixel(self._sample)