/usr/lib/python3/dist-packages/photutils/psf/models.py is in python3-photutils 0.4-1.
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"""
Models for doing PSF/PRF fitting photometry on image data.
"""
from __future__ import division
import warnings
import copy
import numpy as np
from astropy.modeling import models, Parameter, Fittable2DModel
from astropy.utils.exceptions import AstropyWarning
__all__ = ['FittableImageModel', 'NonNormalizable',
'IntegratedGaussianPRF', 'PRFAdapter',
'prepare_psf_model', 'get_grouped_psf_model']
class NonNormalizable(AstropyWarning):
"""
Used to indicate that a :py:class:`FittableImageModel` model is
non-normalizable.
"""
pass
class FittableImageModel(Fittable2DModel):
"""
A fittable 2D model of an image allowing for image intensity scaling
and image translations.
This class takes 2D image data and computes the
values of the model at arbitrary locations (including at intra-pixel,
fractional positions) within this image using spline interpolation
provided by :py:class:`~scipy.interpolate.RectBivariateSpline`.
The fittable model provided by this class has three model parameters:
an image intensity scaling factor (`flux`) which is applied to
(normalized) image, and two positional parameters (`x_0` and `y_0`)
indicating the location of a feature in the coordinate grid on which
the model is to be evaluated.
If this class is initialized with `flux` (intensity scaling factor)
set to `None`, then `flux` is going to be estimated as ``sum(data)``.
Parameters
----------
data : numpy.ndarray
Array containing 2D image.
origin : tuple, None, optional
A reference point in the input image ``data`` array. When origin is
`None`, origin will be set at the middle of the image array.
If `origin` represents the location of a feature (e.g., the position
of an intensity peak) in the input ``data``, then model parameters
`x_0` and `y_0` show the location of this peak in an another target
image to which this model was fitted. Fundamentally, it is the
coordinate in the model's image data that should map to
coordinate (`x_0`, `y_0`) of the output coordinate system on which the
model is evaluated.
Alternatively, when `origin` is set to ``(0,0)``, then model parameters
`x_0` and `y_0` are shifts by which model's image should be translated
in order to match a target image.
normalize : bool, optional
Indicates whether or not the model should be build on normalized
input image data. If true, then the normalization constant (*N*) is
computed so that
.. math::
N \\cdot C \\cdot \\Sigma_{i,j}D_{i,j} = 1,
where *N* is the normalization constant, *C* is correction factor
given by the parameter ``normalization_correction``, and
:math:`D_{i,j}` are the elements of the input image ``data`` array.
normalization_correction : float, optional
A strictly positive number that represents correction that needs to
be applied to model's data normalization (see *C* in the equation
in the comments to ``normalize`` for more details).
A possible application for this parameter is to account for aperture
correction. Assuming model's data represent a PSF to be fitted to
some target star, we set ``normalization_correction`` to the aperture
correction that needs to be applied to the model. That is,
``normalization_correction`` in this case should be set to the
ratio between the total flux of the PSF (including flux outside model's
data) to the flux of model's data.
Then, best fitted value of the `flux` model
parameter will represent an aperture-corrected flux of the target star.
fill_value : float, optional
The value to be returned by the `evaluate` or
``astropy.modeling.Model.__call__`` methods
when evaluation is performed outside the definition domain of the
model.
ikwargs : dict, optional
Additional optional keyword arguments to be passed directly to the
`compute_interpolator` method. See `compute_interpolator` for more
details.
"""
flux = Parameter(description='Intensity scaling factor for image data.',
default=1.0)
x_0 = Parameter(description='X-position of a feature in the image in '
'the output coordinate grid on which the model is '
'evaluated.', default=0.0)
y_0 = Parameter(description='Y-position of a feature in the image in '
'the output coordinate grid on which the model is '
'evaluated.', default=0.0)
def __init__(self, data, flux=flux.default,
x_0=x_0.default, y_0=y_0.default,
normalize=False, normalization_correction=1.0,
origin=None, oversampling=1, fill_value=0.0, ikwargs={}):
self._fill_value = fill_value
self._img_norm = None
self._normalization_status = 0 if normalize else 2
self._store_interpolator_kwargs(ikwargs)
self._set_oversampling(oversampling)
if normalization_correction <= 0:
raise ValueError("'normalization_correction' must be strictly "
"positive.")
self._normalization_correction = normalization_correction
self._data = np.array(data, copy=True, dtype=np.float64)
if not np.all(np.isfinite(self._data)):
raise ValueError("All elements of input 'data' must be finite.")
# set input image related parameters:
self._ny, self._nx = self._data.shape
self._shape = self._data.shape
if self._data.size < 1:
raise ValueError("Image data array cannot be zero-sized.")
# set the origin of the coordinate system in image's pixel grid:
self.origin = origin
if flux is None:
if self._img_norm is None:
self._img_norm = self._compute_raw_image_norm(self._data)
flux = self._img_norm
self._compute_normalization(normalize)
super(FittableImageModel, self).__init__(flux, x_0, y_0)
# initialize interpolator:
self.compute_interpolator(ikwargs)
def _compute_raw_image_norm(self, data):
"""
Helper function that computes the uncorrected inverse normalization
factor of input image data. This quantity is computed as the
*sum of all pixel values*.
.. note::
This function is intended to be overriden in a subclass if one
desires to change the way the normalization factor is computed.
"""
return np.sum(self._data, dtype=np.float64)
def _compute_normalization(self, normalize):
"""
Helper function that computes (corrected) normalization factor
of the original image data. This quantity is computed as the
inverse "raw image norm" (or total "flux" of model's image)
corrected by the ``normalization_correction``:
.. math::
N = 1/(\\Phi * C),
where :math:`\\Phi` is the "total flux" of model's image as
computed by `_compute_raw_image_norm` and *C* is the
normalization correction factor. :math:`\\Phi` is computed only
once if it has not been previously computed. Otherwise, the
existing (stored) value of :math:`\\Phi` is not modified as
:py:class:`FittableImageModel` does not allow image data to be
modified after the object is created.
.. note::
Normally, this function should not be called by the
end-user. It is intended to be overriden in a subclass if
one desires to change the way the normalization factor is
computed.
"""
self._normalization_constant = 1.0 / self._normalization_correction
if normalize:
# compute normalization constant so that
# N*C*sum(data) = 1:
if self._img_norm is None:
self._img_norm = self._compute_raw_image_norm(self._data)
if self._img_norm != 0.0 and np.isfinite(self._img_norm):
self._normalization_constant /= self._img_norm
self._normalization_status = 0
else:
self._normalization_constant = 1.0
self._normalization_status = 1
warnings.warn("Overflow encountered while computing "
"normalization constant. Normalization "
"constant will be set to 1.", NonNormalizable)
else:
self._normalization_status = 2
@property
def oversampling(self):
"""
The factor by which the stored image is oversampled. I.e., an input
to this model is multipled by this factor to yield the index into the
stored image.
"""
return self._oversampling
def _set_oversampling(self, value):
"""
This is a private method because it's used in the initializer but the
``oversampling``
"""
try:
value = float(value)
except ValueError:
raise ValueError('Oversampling factor must be a scalar')
if value <= 0:
raise ValueError('Oversampling factor must be greater than 0')
self._oversampling = value
@property
def data(self):
""" Get original image data. """
return self._data
@property
def normalized_data(self):
""" Get normalized and/or intensity-corrected image data. """
return (self._normalization_constant * self._data)
@property
def normalization_constant(self):
""" Get normalization constant. """
return self._normalization_constant
@property
def normalization_status(self):
"""
Get normalization status. Possible status values are:
- 0: **Performed**. Model has been successfuly normalized at
user's request.
- 1: **Failed**. Attempt to normalize has failed.
- 2: **NotRequested**. User did not request model to be normalized.
"""
return self._normalization_status
@property
def normalization_correction(self):
"""
Set/Get flux correction factor.
.. note::
When setting correction factor, model's flux will be adjusted
accordingly such that if this model was a good fit to some target
image before, then it will remain a good fit after correction
factor change.
"""
return self._normalization_correction
@normalization_correction.setter
def normalization_correction(self, normalization_correction):
old_cf = self._normalization_correction
self._normalization_correction = normalization_correction
self._compute_normalization(normalize=self._normalization_status != 2)
# adjust model's flux so that if this model was a good fit to some
# target image, then it will remain a good fit after correction factor
# change:
self.flux *= normalization_correction / old_cf
@property
def shape(self):
"""A tuple of dimensions of the data array in numpy style (ny, nx)."""
return self._shape
@property
def nx(self):
"""Number of columns in the data array."""
return self._nx
@property
def ny(self):
"""Number of rows in the data array."""
return self._ny
@property
def origin(self):
"""
A tuple of ``x`` and ``y`` coordinates of the origin of the coordinate
system in terms of pixels of model's image.
When setting the coordinate system origin, a tuple of two `int` or
`float` may be used. If origin is set to `None`, the origin of the
coordinate system will be set to the middle of the data array
(``(npix-1)/2.0``).
.. warning::
Modifying `origin` will not adjust (modify) model's parameters
`x_0` and `y_0`.
"""
return (self._x_origin, self._y_origin)
@origin.setter
def origin(self, origin):
if origin is None:
self._x_origin = (self._nx - 1) / 2.0
self._y_origin = (self._ny - 1) / 2.0
elif hasattr(origin, '__iter__') and len(origin) == 2:
self._x_origin, self._y_origin = origin
else:
raise TypeError("Parameter 'origin' must be either None or an "
"iterable with two elements.")
@property
def x_origin(self):
"""X-coordinate of the origin of the coordinate system."""
return self._x_origin
@property
def y_origin(self):
"""Y-coordinate of the origin of the coordinate system."""
return self._y_origin
@property
def fill_value(self):
"""Fill value to be returned for coordinates outside of the domain of
definition of the interpolator. If ``fill_value`` is `None`, then
values outside of the domain of definition are the ones returned
by the interpolator.
"""
return self._fill_value
@fill_value.setter
def fill_value(self, fill_value):
self._fill_value = fill_value
def _store_interpolator_kwargs(self, ikwargs):
"""
This function should be called in a subclass whenever model's
interpolator is (re-)computed.
"""
self._interpolator_kwargs = copy.deepcopy(ikwargs)
@property
def interpolator_kwargs(self):
"""
Get current interpolator's arguments used when interpolator was
created.
"""
return self._interpolator_kwargs
def compute_interpolator(self, ikwargs={}):
"""
Compute/define the interpolating spline. This function can be overriden
in a subclass to define custom interpolators.
Parameters
----------
ikwargs : dict, optional
Additional optional keyword arguments. Possible values are:
- **degree** : int, tuple, optional
Degree of the interpolating spline. A tuple can be used to
provide different degrees for the X- and Y-axes.
Default value is degree=3.
- **s** : float, optional
Non-negative smoothing factor. Default value s=0 corresponds to
interpolation.
See :py:class:`~scipy.interpolate.RectBivariateSpline` for more
details.
Notes
-----
* When subclassing :py:class:`FittableImageModel` for the
purpose of overriding :py:func:`compute_interpolator`,
the :py:func:`evaluate` may need to overriden as well depending
on the behavior of the new interpolator. In addition, for
improved future compatibility, make sure
that the overriding method stores keyword arguments ``ikwargs``
by calling ``_store_interpolator_kwargs`` method.
* Use caution when modifying interpolator's degree or smoothness in
a computationally intensive part of the code as it may decrease
code performance due to the need to recompute interpolator.
"""
from scipy.interpolate import RectBivariateSpline
if 'degree' in ikwargs:
degree = ikwargs['degree']
if hasattr(degree, '__iter__') and len(degree) == 2:
degx = int(degree[0])
degy = int(degree[1])
else:
degx = int(degree)
degy = int(degree)
if degx < 0 or degy < 0:
raise ValueError("Interpolator degree must be a non-negative "
"integer")
else:
degx = 3
degy = 3
if 's' in ikwargs:
smoothness = ikwargs['s']
else:
smoothness = 0
x = np.arange(self._nx, dtype=np.float)
y = np.arange(self._ny, dtype=np.float)
self.interpolator = RectBivariateSpline(
x, y, self._data.T, kx=degx, ky=degx, s=smoothness
)
self._store_interpolator_kwargs(ikwargs)
def evaluate(self, x, y, flux, x_0, y_0):
"""
Evaluate the model on some input variables and provided model
parameters.
"""
xi = self._oversampling * (np.asarray(x) - x_0) + self._x_origin
yi = self._oversampling * (np.asarray(y) - y_0) + self._y_origin
f = flux * self._normalization_constant
evaluated_model = f * self.interpolator.ev(xi, yi)
if self._fill_value is not None:
# find indices of pixels that are outside the input pixel grid and
# set these pixels to the 'fill_value':
invalid = (((xi < 0) | (xi > self._nx - 1)) |
((yi < 0) | (yi > self._ny - 1)))
evaluated_model[invalid] = self._fill_value
return evaluated_model
class IntegratedGaussianPRF(Fittable2DModel):
r"""
Circular Gaussian model integrated over pixels. Because it is
integrated, this model is considered a PRF, *not* a PSF (see
:ref:`psf-terminology` for more about the terminology used here.)
This model is a Gaussian *integrated* over an area of ``1`` (in
units of the model input coordinates, e.g. 1 pixel). This is in
contrast to the apparently similar
`astropy.modeling.functional_models.Gaussian2D`, which is the value
of a 2D Gaussian *at* the input coordinates, with no integration.
So this model is equivalent to assuming the PSF is Gaussian at a
*sub-pixel* level.
Parameters
----------
sigma : float
Width of the Gaussian PSF.
flux : float (default 1)
Total integrated flux over the entire PSF
x_0 : float (default 0)
Position of the peak in x direction.
y_0 : float (default 0)
Position of the peak in y direction.
Notes
-----
This model is evaluated according to the following formula:
.. math::
f(x, y) =
\frac{F}{4}
\left[
{\rm erf} \left(\frac{x - x_0 + 0.5}
{\sqrt{2} \sigma} \right) -
{\rm erf} \left(\frac{x - x_0 - 0.5}
{\sqrt{2} \sigma} \right)
\right]
\left[
{\rm erf} \left(\frac{y - y_0 + 0.5}
{\sqrt{2} \sigma} \right) -
{\rm erf} \left(\frac{y - y_0 - 0.5}
{\sqrt{2} \sigma} \right)
\right]
where ``erf`` denotes the error function and ``F`` the total
integrated flux.
"""
flux = Parameter(default=1)
x_0 = Parameter(default=0)
y_0 = Parameter(default=0)
sigma = Parameter(default=1, fixed=True)
_erf = None
fit_deriv = None
@property
def bounding_box(self):
halfwidth = 4 * self.sigma
return ((int(self.y_0 - halfwidth), int(self.y_0 + halfwidth)),
(int(self.x_0 - halfwidth), int(self.x_0 + halfwidth)))
def __init__(self, sigma=sigma.default,
x_0=x_0.default, y_0=y_0.default, flux=flux.default,
**kwargs):
if self._erf is None:
from scipy.special import erf
self.__class__._erf = erf
super(IntegratedGaussianPRF, self).__init__(n_models=1, sigma=sigma,
x_0=x_0, y_0=y_0,
flux=flux, **kwargs)
def evaluate(self, x, y, flux, x_0, y_0, sigma):
"""Model function Gaussian PSF model."""
return (flux / 4 *
((self._erf((x - x_0 + 0.5) / (np.sqrt(2) * sigma)) -
self._erf((x - x_0 - 0.5) / (np.sqrt(2) * sigma))) *
(self._erf((y - y_0 + 0.5) / (np.sqrt(2) * sigma)) -
self._erf((y - y_0 - 0.5) / (np.sqrt(2) * sigma)))))
class PRFAdapter(Fittable2DModel):
"""
A model that adapts a supplied PSF model to act as a PRF. It
integrates the PSF model over pixel "boxes". A critical built-in
assumption is that the PSF model scale and location parameters are
in *pixel* units.
Parameters
----------
psfmodel : a 2D model
The model to assume as representative of the PSF
renormalize_psf : bool
If True, the model will be integrated from -inf to inf and
re-scaled so that the total integrates to 1. Note that this
renormalization only occurs *once*, so if the total flux of
``psfmodel`` depends on position, this will *not* be correct.
xname : str or None
The name of the ``psfmodel`` parameter that corresponds to the
x-axis center of the PSF. If None, the model will be assumed to
be centered at x=0.
yname : str or None
The name of the ``psfmodel`` parameter that corresponds to the
y-axis center of the PSF. If None, the model will be assumed to
be centered at y=0.
fluxname : str or None
The name of the ``psfmodel`` parameter that corresponds to the
total flux of the star. If None, a scaling factor will be
applied by the ``PRFAdapter`` instead of modifying the
``psfmodel``.
Notes
-----
This current implementation of this class (using numerical
integration for each pixel) is extremely slow, and only suited for
experimentation over relatively few small regions.
"""
flux = Parameter(default=1)
x_0 = Parameter(default=0)
y_0 = Parameter(default=0)
def __init__(self, psfmodel, renormalize_psf=True, flux=flux.default,
x_0=x_0.default, y_0=y_0.default, xname=None, yname=None,
fluxname=None, **kwargs):
self.psfmodel = psfmodel.copy()
if renormalize_psf:
from scipy.integrate import dblquad
self._psf_scale_factor = 1. / dblquad(self.psfmodel,
-np.inf, np.inf,
lambda x: -np.inf,
lambda x: np.inf)[0]
else:
self._psf_scale_factor = 1
self.xname = xname
self.yname = yname
self.fluxname = fluxname
# these can be used to adjust the integration behavior. Might be
# used in the future to expose how the integration happens
self._dblquadkwargs = {}
super(PRFAdapter, self).__init__(n_models=1, x_0=x_0, y_0=y_0,
flux=flux, **kwargs)
def evaluate(self, x, y, flux, x_0, y_0):
"""The evaluation function for PRFAdapter."""
if self.xname is None:
dx = x - x_0
else:
dx = x
setattr(self.psfmodel, self.xname, x_0)
if self.xname is None:
dy = y - y_0
else:
dy = y
setattr(self.psfmodel, self.yname, y_0)
if self.fluxname is None:
return (flux * self._psf_scale_factor *
self._integrated_psfmodel(dx, dy))
else:
setattr(self.psfmodel, self.yname, flux * self._psf_scale_factor)
return self._integrated_psfmodel(dx, dy)
def _integrated_psfmodel(self, dx, dy):
from scipy.integrate import dblquad
# infer type/shape from the PSF model. Seems wasteful, but the
# integration step is a *lot* more expensive so its just peanuts
out = np.empty_like(self.psfmodel(dx, dy))
outravel = out.ravel()
for i, (xi, yi) in enumerate(zip(dx.ravel(), dy.ravel())):
outravel[i] = dblquad(self.psfmodel,
xi-0.5, xi+0.5,
lambda x: yi-0.5, lambda x: yi+0.5,
**self._dblquadkwargs)[0]
return out
def prepare_psf_model(psfmodel, xname=None, yname=None, fluxname=None,
renormalize_psf=True):
"""
Convert a 2D PSF model to one suitable for use with
`BasicPSFPhotometry` or its subclasses.
The resulting model may be a composite model, but should have only
the x, y, and flux related parameters un-fixed.
Parameters
----------
psfmodel : a 2D model
The model to assume as representative of the PSF.
xname : str or None
The name of the ``psfmodel`` parameter that corresponds to the
x-axis center of the PSF. If None, the model will be assumed to
be centered at x=0, and a new parameter will be added for the
offset.
yname : str or None
The name of the ``psfmodel`` parameter that corresponds to the
y-axis center of the PSF. If None, the model will be assumed to
be centered at x=0, and a new parameter will be added for the
offset.
fluxname : str or None
The name of the ``psfmodel`` parameter that corresponds to the
total flux of the star. If None, a scaling factor will be added
to the model.
renormalize_psf : bool
If True, the model will be integrated from -inf to inf and
re-scaled so that the total integrates to 1. Note that this
renormalization only occurs *once*, so if the total flux of
``psfmodel`` depends on position, this will *not* be correct.
Returns
-------
outmod : a model
A new model ready to be passed into `BasicPSFPhotometry` or its
subclasses.
"""
if xname is None:
xinmod = models.Shift(0, name='x_offset')
xname = 'offset_0'
else:
xinmod = models.Identity(1)
xname = xname + '_2'
xinmod.fittable = True
if yname is None:
yinmod = models.Shift(0, name='y_offset')
yname = 'offset_1'
else:
yinmod = models.Identity(1)
yname = yname + '_2'
yinmod.fittable = True
outmod = (xinmod & yinmod) | psfmodel
if fluxname is None:
outmod = outmod * models.Const2D(1, name='flux_scaling')
fluxname = 'amplitude_3'
else:
fluxname = fluxname + '_2'
if renormalize_psf:
# we do the import here because other machinery works w/o scipy
from scipy import integrate
integrand = integrate.dblquad(psfmodel, -np.inf, np.inf,
lambda x: -np.inf, lambda x: np.inf)[0]
normmod = models.Const2D(1./integrand, name='renormalize_scaling')
outmod = outmod * normmod
# final setup of the output model - fix all the non-offset/scale
# parameters
for pnm in outmod.param_names:
outmod.fixed[pnm] = pnm not in (xname, yname, fluxname)
# and set the names so that BasicPSFPhotometry knows what to do
outmod.xname = xname
outmod.yname = yname
outmod.fluxname = fluxname
# now some convenience aliases if reasonable
outmod.psfmodel = outmod[2]
if 'x_0' not in outmod.param_names and 'y_0' not in outmod.param_names:
outmod.x_0 = getattr(outmod, xname)
outmod.y_0 = getattr(outmod, yname)
if 'flux' not in outmod.param_names:
outmod.flux = getattr(outmod, fluxname)
return outmod
def get_grouped_psf_model(template_psf_model, star_group, pars_to_set):
"""
Construct a joint PSF model which consists of a sum of PSF's templated on
a specific model, but whose parameters are given by a table of objects.
Parameters
----------
template_psf_model : `astropy.modeling.Fittable2DModel` instance
The model to use for *individual* objects. Must have parameters named
``x_0``, ``y_0``, and ``flux``.
star_group : `~astropy.table.Table`
Table of stars for which the compound PSF will be constructed. It
must have columns named ``x_0``, ``y_0``, and ``flux_0``.
Returns
-------
group_psf
An `astropy.modeling` ``CompoundModel`` instance which is a sum of the
given PSF models.
"""
group_psf = None
for star in star_group:
psf_to_add = template_psf_model.copy()
for param_tab_name, param_name in pars_to_set.items():
setattr(psf_to_add, param_name, star[param_tab_name])
if group_psf is None:
# this is the first one only
group_psf = psf_to_add
else:
group_psf += psf_to_add
return group_psf
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