def test_gaussian_sum_moments():
"""Check analytical against numerical solution.
"""
# We define three components with different flux, position and size
F_1, F_2, F_3 = 100, 200, 300
sigma_1, sigma_2, sigma_3 = 15, 10, 5
x_1, x_2, x_3 = 100, 120, 70
y_1, y_2, y_3 = 100, 90, 120
# Convert into non-normalized amplitude for astropy model
def A(F, sigma):
return F * 1 / (2 * np.pi * sigma ** 2)
# Define and evaluate models
f_1 = Gaussian2D(A(F_1, sigma_1), x_1, y_1, sigma_1, sigma_1)
f_2 = Gaussian2D(A(F_2, sigma_2), x_2, y_2, sigma_2, sigma_2)
f_3 = Gaussian2D(A(F_3, sigma_3), x_3, y_3, sigma_3, sigma_3)
F_1_image = discretize_model(f_1, (0, 200), (0, 200))
F_2_image = discretize_model(f_2, (0, 200), (0, 200))
F_3_image = discretize_model(f_3, (0, 200), (0, 200))
moments_num = measure_image_moments(F_1_image + F_2_image + F_3_image)
# Compute analytical values
cov_matrix = np.zeros((12, 12))
F = [F_1, F_2, F_3]
sigma = [sigma_1, sigma_2, sigma_3]
x = [x_1, x_2, x_3]
y = [y_1, y_2, y_3]
moments_ana, uncertainties = gaussian_sum_moments(F, sigma, x, y, cov_matrix)
assert_allclose(moments_ana, moments_num, 1e-6)
assert_allclose(uncertainties, 0)
def _make_gaussian_sources_image(self, table_bgstars, nsigma=6):
"the one from photutils was too slow"
image = np.zeros(self.image_shape_pix)
for i in range(self.nstars_in_image):
amplitude = table_bgstars['flux'][i] / (
2. * np.pi * table_bgstars['x_stddev'][i] *
table_bgstars['y_stddev'][i])
x_mean = table_bgstars['x_mean'][i]
y_mean = table_bgstars['y_mean'][i]
x_stddev = table_bgstars['x_stddev'][i]
y_stddev = table_bgstars['y_stddev'][i]
gmodel = Gaussian2D(amplitude=amplitude,
x_mean=0,
y_mean=0,
x_stddev=x_stddev,
y_stddev=y_stddev,
theta=table_bgstars['theta'][i])
x_range = self._get_range(mean_val=x_mean,
sigma=x_stddev,
nsigma=nsigma,
axis='x')
y_range = self._get_range(mean_val=y_mean,
sigma=y_stddev,
nsigma=nsigma,
axis='y')
dmodel = discretize_model(model=gmodel,
x_range=tuple(x_range - x_mean),
y_range=tuple(y_range - y_mean),
mode='oversample',
factor=self.psf_oversample)
image[int(x_range[0]):int(x_range[1]),
int(y_range[0]):int(y_range[1])] += dmodel.T
return image
def exp_kern(alpha, size, norm=True, mode='center', factor=10):
"""
Generate 2D, radially symmetric exponential kernel The kernels are
discretized using astropy.convolution.discretize_model.
Parameters
----------
alpha : float
The scale length of the exponential.
size : odd int
Number of pixel in x & y directions.
norm_array : bool, optional
If True, normalize the kern array.
mode : str, optional
One of the following discretization modes:
'center', 'oversample', 'linear_interp',
or 'integrate'. See astropy docs for details.
factor : float or int
Factor of oversampling.
Returns
-------
kern : 2D ndarray
The convolution kernel.
"""
assert size % 2 != 0, 'ERROR: size must be odd'
x_range = (-(int(size) - 1) // 2, (int(size) - 1) // 2 + 1)
model = lambda x, y: np.exp(-np.sqrt(x**2 + y**2) / alpha)
kern = discretize_model(model, x_range, x_range, mode=mode, factor=factor)
if norm:
kern /= kern.sum()
return kern
def _discretized_psfmodel(self, dx, dy):
minx = np.min(dx)
miny = np.min(dy)
maxx = np.max(dx) + 0.5
maxy = np.max(dy) + 0.5
out = discretize_model(self.psfmodel, (minx, maxx), (miny, maxy), self.discretizemode, **self._discretize_modelkwargs)
return out
def test_gaussian_sum_moments():
"""Check analytical against numerical solution.
"""
binsz = 0.02
# We define three components with different flux, position and size in pixel coordinates
F_1, F_2, F_3 = 100, 200, 300
sigma_1, sigma_2, sigma_3 = 15, 10, 5
x_1, x_2, x_3 = 100, 120, 70
y_1, y_2, y_3 = 100, 90, 120
# Convert into non-normalized amplitude for astropy model
def A(F, sigma):
return F * 1 / (2 * np.pi * sigma**2)
# Define and evaluate models
f_1 = Gaussian2D(A(F_1, sigma_1), x_1, y_1, sigma_1, sigma_1)
f_2 = Gaussian2D(A(F_2, sigma_2), x_2, y_2, sigma_2, sigma_2)
f_3 = Gaussian2D(A(F_3, sigma_3), x_3, y_3, sigma_3, sigma_3)
F_1_image = discretize_model(f_1, (0, 201), (0, 201))
F_2_image = discretize_model(f_2, (0, 201), (0, 201))
F_3_image = discretize_model(f_3, (0, 201), (0, 201))
image = WcsNDMap.create(npix=(201, 201), binsz=binsz)
image.data = F_1_image + F_2_image + F_3_image
moments_num = measure_image_moments(image)
# Right now the flux doesn't have a unit
moments_num = [moments_num[0]] + [_.value for _ in moments_num[1:]]
# Compute analytical values
cov_matrix = np.zeros((12, 12))
F = [F_1, F_2, F_3]
sigma = np.array([sigma_1, sigma_2, sigma_3]) * binsz
x, y = image.geom.wcs.wcs_pix2world([x_1, x_2, x_3], [y_1, y_2, y_3], 0)
x = np.where(x > 180, x - 360, x)
moments_ana, uncertainties = gaussian_sum_moments(F,
sigma,
x,
y,
cov_matrix,
shift=0)
assert_allclose(moments_ana, moments_num, 1e-6)
assert_allclose(uncertainties, 0)
def test_gaussian_sum_moments():
"""Check analytical against numerical solution.
"""
# We define three components with different flux, position and size in pixel coordinates
F_1, F_2, F_3 = 100, 200, 300
sigma_1, sigma_2, sigma_3 = 15, 10, 5
x_1, x_2, x_3 = 100, 120, 70
y_1, y_2, y_3 = 100, 90, 120
# Convert into non-normalized amplitude for astropy model
def A(F, sigma):
return F * 1 / (2 * np.pi * sigma**2)
# Define and evaluate models
f_1 = Gaussian2D(A(F_1, sigma_1), x_1, y_1, sigma_1, sigma_1)
f_2 = Gaussian2D(A(F_2, sigma_2), x_2, y_2, sigma_2, sigma_2)
f_3 = Gaussian2D(A(F_3, sigma_3), x_3, y_3, sigma_3, sigma_3)
F_1_image = discretize_model(f_1, (0, 201), (0, 201))
F_2_image = discretize_model(f_2, (0, 201), (0, 201))
F_3_image = discretize_model(f_3, (0, 201), (0, 201))
image = set_header(fits.ImageHDU(F_1_image + F_2_image + F_3_image))
moments_num = measure_image_moments(image)
wcs = WCS(image.header)
# Compute analytical values
cov_matrix = np.zeros((12, 12))
F = [F_1, F_2, F_3]
sigma = np.array([sigma_1, sigma_2, sigma_3]) * BINSZ
origin = 0 # convention for gammapy
x, y = wcs.wcs_pix2world([x_1, x_2, x_3], [y_1, y_2, y_3], origin)
# Fix longitude range, is there a wcs option for this?
x = np.where(x > 180, x - 360, x)
moments_ana, uncertainties = gaussian_sum_moments(F,
sigma,
x,
y,
cov_matrix,
shift=0)
assert_allclose(moments_ana, moments_num, 1e-6)
assert_allclose(uncertainties, 0)
def gauss_kern(width, size, width_type='fwhm', norm_array=False, mode='center',
factor=10):
"""
Generate a 2D radially symmetric Gaussian kernel for sextractor,
The kernels are discretized using `astropy.convolution.discretize_model`.
Parameters
----------
width : float
The width of the Gaussian.
size : odd int
Number of pixel in x & y directions.
width_type : string, optional
The width type given ('fwhm' or 'sigma').
norm_array : bool, optional
If True, normalize the kern array.
mode : str, optional
One of the following discretization modes:
'center', 'oversample', 'linear_interp',
or 'integrate'. See astropy docs for details.
factor : float or int
Factor of oversampling.
Returns
-------
kern : 2D ndarray, if (return_fn=False)
The convolution kernel.
kern, fn, comment : ndarray, string, string (if return_fn=True)
The kernel, file name, and the comment
for the file.
Notes
-----
i) The kernel will be normalized by sextractor by
default, and the non-normalized files are a bit
cleaner due to less leading zeros.
"""
assert size%2!=0, 'ERROR: size must be odd'
from astropy.convolution import discretize_model
convert = 2.0*np.sqrt(2*np.log(2))
if width_type=='fwhm':
sigma = width/convert
fwhm = width
elif width_type=='sigma':
sigma = width
fwhm = width*convert
x_range = (-(int(size) - 1) // 2, (int(size) - 1) // 2 + 1)
model = lambda x, y: np.exp(-(x**2 + y**2)/(2*sigma**2))
kern = discretize_model(model, x_range, x_range, mode=mode, factor=factor)
if norm_array:
kern /= kern.sum()
return kern
def test_gaussian_sum_moments():
"""Check analytical against numerical solution.
"""
binsz = 0.02
# We define three components with different flux, position and size in pixel coordinates
F_1, F_2, F_3 = 100, 200, 300
sigma_1, sigma_2, sigma_3 = 15, 10, 5
x_1, x_2, x_3 = 100, 120, 70
y_1, y_2, y_3 = 100, 90, 120
# Convert into non-normalized amplitude for astropy model
def A(F, sigma):
return F * 1 / (2 * np.pi * sigma ** 2)
# Define and evaluate models
f_1 = Gaussian2D(A(F_1, sigma_1), x_1, y_1, sigma_1, sigma_1)
f_2 = Gaussian2D(A(F_2, sigma_2), x_2, y_2, sigma_2, sigma_2)
f_3 = Gaussian2D(A(F_3, sigma_3), x_3, y_3, sigma_3, sigma_3)
F_1_image = discretize_model(f_1, (0, 201), (0, 201))
F_2_image = discretize_model(f_2, (0, 201), (0, 201))
F_3_image = discretize_model(f_3, (0, 201), (0, 201))
image = WcsNDMap.create(npix=(201, 201), binsz=binsz)
image.data = F_1_image + F_2_image + F_3_image
moments_num = measure_image_moments(image)
# Right now the flux doesn't have a unit
moments_num = [moments_num[0]] + [_.value for _ in moments_num[1:]]
# Compute analytical values
cov_matrix = np.zeros((12, 12))
F = [F_1, F_2, F_3]
sigma = np.array([sigma_1, sigma_2, sigma_3]) * binsz
x, y = image.geom.wcs.wcs_pix2world([x_1, x_2, x_3], [y_1, y_2, y_3], 0)
x = np.where(x > 180, x - 360, x)
moments_ana, uncertainties = gaussian_sum_moments(
F, sigma, x, y, cov_matrix, shift=0
)
assert_allclose(moments_ana, moments_num, 1e-6)
assert_allclose(uncertainties, 0)
def test_gaussian_sum_moments():
"""Check analytical against numerical solution.
"""
# We define three components with different flux, position and size in pixel coordinates
F_1, F_2, F_3 = 100, 200, 300
sigma_1, sigma_2, sigma_3 = 15, 10, 5
x_1, x_2, x_3 = 100, 120, 70
y_1, y_2, y_3 = 100, 90, 120
# Convert into non-normalized amplitude for astropy model
def A(F, sigma):
return F * 1 / (2 * np.pi * sigma ** 2)
# Define and evaluate models
f_1 = Gaussian2D(A(F_1, sigma_1), x_1, y_1, sigma_1, sigma_1)
f_2 = Gaussian2D(A(F_2, sigma_2), x_2, y_2, sigma_2, sigma_2)
f_3 = Gaussian2D(A(F_3, sigma_3), x_3, y_3, sigma_3, sigma_3)
F_1_image = discretize_model(f_1, (0, 201), (0, 201))
F_2_image = discretize_model(f_2, (0, 201), (0, 201))
F_3_image = discretize_model(f_3, (0, 201), (0, 201))
image = set_header(fits.ImageHDU(F_1_image + F_2_image + F_3_image))
moments_num = measure_image_moments(image)
wcs = WCS(image.header)
# Compute analytical values
cov_matrix = np.zeros((12, 12))
F = [F_1, F_2, F_3]
sigma = np.array([sigma_1, sigma_2, sigma_3]) * BINSZ
origin = 0 # convention for gammapy
x, y = wcs.wcs_pix2world([x_1, x_2, x_3], [y_1, y_2, y_3], origin)
# Fix longitude range, is there a wcs option for this?
x = np.where(x > 180, x - 360, x)
moments_ana, uncertainties = gaussian_sum_moments(F, sigma, x, y, cov_matrix, shift=0)
assert_allclose(moments_ana, moments_num, 1e-6)
assert_allclose(uncertainties, 0)
def exp_kern(alpha, size, norm_array=False, mode='center', factor=10):
"""
Generate 2D, radially symmetric exponential kernal for sextractor.
The kernels are discretized using `astropy.convolution.discretize_model`.
Parameters
----------
alpha : float
The scale length of the exponential.
size : odd int
Number of pixel in x & y directions.
norm_array : bool, optional
If True, normalize the kern array.
mode : str, optional
One of the following discretization modes:
'center', 'oversample', 'linear_interp',
or 'integrate'. See astropy docs for details.
factor : float or int
Factor of oversampling.
Returns
-------
kern : 2D ndarray, if (return_fn=False)
The convolution kernel.
kern, fn, comment : ndarray, string, string (if return_fn=True)
The kernel, file name, and the comment
for the file.
Notes
-----
The kernel will be normalized by sextractor by
default, and the non-normalized files are a bit
cleaner due to less leading zeros.
"""
assert size%2!=0, 'ERROR: size must be odd'
from astropy.convolution import discretize_model
x_range = (-(int(size) - 1) // 2, (int(size) - 1) // 2 + 1)
model = lambda x, y: np.exp(-np.sqrt(x**2 + y**2)/alpha)
kern = discretize_model(model, x_range, x_range, mode=mode, factor=factor)
if norm_array:
kern /= kern.sum()
return kern
def pixellated(self, size=21, offsets=(0.0, 0.0)):
"""
Calculates a pixellated version of the PSF.
The pixel values are calculated using 10x oversampling, i.e. by
evaluating the continuous PSF model at a 10 x 10 grid of positions
within each pixel and averaging the results.
Parameters
----------
size : int, optional
Size of the pixellated PSF to calculate, the returned image
will have `size` x `size` pixels. Default value 21.
offset : tuple of floats, optional
y and x axis offsets of the centre of the PSF from the centre
of the returned image, in pixels.
Returns
-------
pixellated : numpy.array
Pixellated PSF image with `size` by `size` pixels. The PSF
is normalised to an integral of 1 however the sum of the
pixellated PSF will be somewhat less due to truncation of the
PSF wings by the edge of the image.
"""
size = int(size)
if size <= 0:
raise ValueError("`size` must be > 0, got {}!".format(size))
# Update PSF centre coordinates
self.x_0 = offsets[0]
self.y_0 = offsets[1]
xrange = (-(size - 1) / 2, (size + 1) / 2)
yrange = (-(size - 1) / 2, (size + 1) / 2)
return discretize_model(self,
xrange,
yrange,
mode='oversample',
factor=10)
def make_gaussian_source_image(self, image, amplitude, x_mean, y_mean,
x_stddev, y_stddev, theta, nsigma):
gmodel = Gaussian2D(amplitude=amplitude,
x_mean=0,
y_mean=0,
x_stddev=x_stddev,
y_stddev=y_stddev,
theta=theta)
x_range = self._get_range(mean_val=x_mean,
sigma=x_stddev,
nsigma=nsigma,
axis='x')
y_range = self._get_range(mean_val=y_mean,
sigma=y_stddev,
nsigma=nsigma,
axis='y')
dmodel = discretize_model(model=gmodel,
x_range=tuple(x_range - x_mean),
y_range=tuple(y_range - y_mean),
mode='oversample',
factor=self.psf_oversample)
image[int(x_range[0]):int(x_range[1]),
int(y_range[0]):int(y_range[1])] += dmodel.T
return image
def make_model_sources_image(shape, model, source_table, oversample=1):
"""
Make an image containing sources generated from a user-specified
model.
Parameters
----------
shape : 2-tuple of int
The shape of the output 2D image.
model : 2D astropy.modeling.models object
The model to be used for rendering the sources.
source_table : `~astropy.table.Table`
Table of parameters for the sources. Each row of the table
corresponds to a source whose model parameters are defined by
the column names, which must match the model parameter names.
Column names that do not match model parameters will be ignored.
Model parameters not defined in the table will be set to the
``model`` default value.
oversample : float, optional
The sampling factor used to discretize the models on a pixel
grid. If the value is 1.0 (the default), then the models will
be discretized by taking the value at the center of the pixel
bin. Note that this method will not preserve the total flux of
very small sources. Otherwise, the models will be discretized
by taking the average over an oversampled grid. The pixels will
be oversampled by the ``oversample`` factor.
Returns
-------
image : 2D `~numpy.ndarray`
Image containing model sources.
See Also
--------
make_random_models_table, make_gaussian_sources_image
Examples
--------
.. plot::
:include-source:
from collections import OrderedDict
from astropy.modeling.models import Moffat2D
from photutils.datasets import (make_random_models_table,
make_model_sources_image)
model = Moffat2D()
n_sources = 10
shape = (100, 100)
param_ranges = [('amplitude', [100, 200]),
('x_0', [0, shape[1]]),
('y_0', [0, shape[0]]),
('gamma', [5, 10]),
('alpha', [1, 2])]
param_ranges = OrderedDict(param_ranges)
sources = make_random_models_table(n_sources, param_ranges,
random_state=12345)
data = make_model_sources_image(shape, model, sources)
plt.imshow(data)
"""
image = np.zeros(shape, dtype=np.float64)
y, x = np.indices(shape)
params_to_set = []
for param in source_table.colnames:
if param in model.param_names:
params_to_set.append(param)
# Save the initial parameter values so we can set them back when
# done with the loop. It's best not to copy a model, because some
# models (e.g. PSF models) may have substantial amounts of data in
# them.
init_params = {param: getattr(model, param) for param in params_to_set}
try:
for i, source in enumerate(source_table):
for param in params_to_set:
setattr(model, param, source[param])
if oversample == 1:
image += model(x, y)
else:
image += discretize_model(model, (0, shape[1]),
(0, shape[0]), mode='oversample',
factor=oversample)
finally:
for param, value in init_params.items():
setattr(model, param, value)
return image
def make_gaussian_sources(image_shape, source_table, oversample=1):
"""
Make an image containing 2D Gaussian sources.
Parameters
----------
image_shape : 2-tuple of int
Shape of the output 2D image.
source_table : `astropy.table.Table`
Table of parameters for the Gaussian sources. Each row of the
table corresponds to a Gaussian source whose parameters are
defined by the column names. The column names must include
``flux`` or ``amplitude``, ``x_mean``, ``y_mean``, ``x_stddev``,
``y_stddev``, and ``theta`` (see
`~astropy.modeling.functional_models.Gaussian2D` for a
description of most of these parameter names). If both ``flux``
and ``amplitude`` are present, then ``amplitude`` will be
ignored.
oversample : float, optional
The sampling factor used to discretize the
`~astropy.modeling.functional_models.Gaussian2D` models on a
pixel grid.
If the value is 1.0 (the default), then the models will be
discretized by taking the value at the center of the pixel bin.
Note that this method will not preserve the total flux of very
small sources.
Otherwise, the models will be discretized by taking the average
over an oversampled grid. The pixels will be oversampled by the
``oversample`` factor.
Returns
-------
image : `numpy.ndarray`
Image containing 2D Gaussian sources.
See Also
--------
make_random_gaussians, make_noise_image, make_poisson_noise
Examples
--------
.. plot::
:include-source:
# make a table of Gaussian sources
from astropy.table import Table
table = Table()
table['amplitude'] = [50, 70, 150, 210]
table['x_mean'] = [160, 25, 150, 90]
table['y_mean'] = [70, 40, 25, 60]
table['x_stddev'] = [15.2, 5.1, 3., 8.1]
table['y_stddev'] = [2.6, 2.5, 3., 4.7]
table['theta'] = np.array([145., 20., 0., 60.]) * np.pi / 180.
# make an image of the sources without noise, with Gaussian
# noise, and with Poisson noise
from photutils.datasets import make_gaussian_sources
from photutils.datasets import make_noise_image
shape = (100, 200)
image1 = make_gaussian_sources(shape, table)
image2 = image1 + make_noise_image(shape, type='gaussian', mean=0.,
stddev=5.)
image3 = image1 + make_noise_image(shape, type='poisson', mean=5.)
# plot the images
import matplotlib.pyplot as plt
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
ax1.imshow(image1, origin='lower', interpolation='nearest')
ax2.imshow(image2, origin='lower', interpolation='nearest')
ax3.imshow(image3, origin='lower', interpolation='nearest')
"""
image = np.zeros(image_shape, dtype=np.float64)
y, x = np.indices(image_shape)
if 'flux' in source_table.colnames:
amplitude = source_table['flux'] / (
2. * np.pi * source_table['x_stddev'] * source_table['y_stddev'])
elif 'amplitude' in source_table.colnames:
amplitude = source_table['amplitude']
else:
raise ValueError('either "amplitude" or "flux" must be columns in '
'the input source_table')
for i, source in enumerate(source_table):
model = Gaussian2D(amplitude=amplitude[i],
x_mean=source['x_mean'],
y_mean=source['y_mean'],
x_stddev=source['x_stddev'],
y_stddev=source['y_stddev'],
theta=source['theta'])
if oversample == 1:
image += model(x, y)
else:
image += discretize_model(model, (0, image_shape[1]),
(0, image_shape[0]),
mode='oversample',
factor=oversample)
return image
def make_gaussian_sources(image_shape, source_table, oversample=1):
"""
Make an image containing 2D Gaussian sources.
Parameters
----------
image_shape : 2-tuple of int
Shape of the output 2D image.
source_table : `astropy.table.Table`
Table of parameters for the Gaussian sources. Each row of the
table corresponds to a Gaussian source whose parameters are
defined by the column names. The column names must include
``flux`` or ``amplitude``, ``x_mean``, ``y_mean``, ``x_stddev``,
``y_stddev``, and ``theta`` (see
`~astropy.modeling.functional_models.Gaussian2D` for a
description of most of these parameter names). If both ``flux``
and ``amplitude`` are present, then ``amplitude`` will be
ignored.
oversample : float, optional
The sampling factor used to discretize the
`~astropy.modeling.functional_models.Gaussian2D` models on a
pixel grid.
If the value is 1.0 (the default), then the models will be
discretized by taking the value at the center of the pixel bin.
Note that this method will not preserve the total flux of very
small sources.
Otherwise, the models will be discretized by taking the average
over an oversampled grid. The pixels will be oversampled by the
``oversample`` factor.
Returns
-------
image : `numpy.ndarray`
Image containing 2D Gaussian sources.
See Also
--------
make_random_gaussians, make_noise_image, make_poisson_noise
Examples
--------
.. plot::
:include-source:
# make a table of Gaussian sources
from astropy.table import Table
table = Table()
table['amplitude'] = [50, 70, 150, 210]
table['x_mean'] = [160, 25, 150, 90]
table['y_mean'] = [70, 40, 25, 60]
table['x_stddev'] = [15.2, 5.1, 3., 8.1]
table['y_stddev'] = [2.6, 2.5, 3., 4.7]
table['theta'] = np.array([145., 20., 0., 60.]) * np.pi / 180.
# make an image of the sources without noise, with Gaussian
# noise, and with Poisson noise
from photutils.datasets import make_gaussian_sources
from photutils.datasets import make_noise_image
shape = (100, 200)
image1 = make_gaussian_sources(shape, table)
image2 = image1 + make_noise_image(shape, type='gaussian', mean=0.,
stddev=5.)
image3 = image1 + make_noise_image(shape, type='poisson', mean=5.)
# plot the images
import matplotlib.pyplot as plt
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
ax1.imshow(image1, origin='lower', interpolation='nearest')
ax2.imshow(image2, origin='lower', interpolation='nearest')
ax3.imshow(image3, origin='lower', interpolation='nearest')
"""
image = np.zeros(image_shape, dtype=np.float64)
y, x = np.indices(image_shape)
if 'flux' in source_table.colnames:
amplitude = source_table['flux'] / (2. * np.pi *
source_table['x_stddev'] *
source_table['y_stddev'])
elif 'amplitude' in source_table.colnames:
amplitude = source_table['amplitude']
else:
raise ValueError('either "amplitude" or "flux" must be columns in '
'the input source_table')
for i, source in enumerate(source_table):
model = Gaussian2D(amplitude=amplitude[i], x_mean=source['x_mean'],
y_mean=source['y_mean'],
x_stddev=source['x_stddev'],
y_stddev=source['y_stddev'], theta=source['theta'])
if oversample == 1:
image += model(x, y)
else:
image += discretize_model(model, (0, image_shape[1]),
(0, image_shape[0]), mode='oversample',
factor=oversample)
return image
def make_gaussian_sources(image_shape, source_table, oversample=1, unit=None,
hdu=False, wcs=False, wcsheader=None):
"""
Make an image containing 2D Gaussian sources.
Parameters
----------
image_shape : 2-tuple of int
Shape of the output 2D image.
source_table : `~astropy.table.Table`
Table of parameters for the Gaussian sources. Each row of the
table corresponds to a Gaussian source whose parameters are
defined by the column names. The column names must include
``flux`` or ``amplitude``, ``x_mean``, ``y_mean``, ``x_stddev``,
``y_stddev``, and ``theta`` (see
`~astropy.modeling.functional_models.Gaussian2D` for a
description of most of these parameter names). If both ``flux``
and ``amplitude`` are present, then ``amplitude`` will be
ignored.
oversample : float, optional
The sampling factor used to discretize the
`~astropy.modeling.functional_models.Gaussian2D` models on a
pixel grid.
If the value is 1.0 (the default), then the models will be
discretized by taking the value at the center of the pixel bin.
Note that this method will not preserve the total flux of very
small sources.
Otherwise, the models will be discretized by taking the average
over an oversampled grid. The pixels will be oversampled by the
``oversample`` factor.
unit : `~astropy.units.UnitBase` instance, str, optional
An object that represents the unit desired for the output image.
Must be an `~astropy.units.UnitBase` object or a string
parseable by the `~astropy.units` package.
hdu : bool, optional
If `True` returns ``image`` as an `~astropy.io.fits.ImageHDU`
object. To include WCS information in the header, use the
``wcs`` and ``wcsheader`` inputs. Otherwise the header will be
minimal. Default is `False`.
wcs : bool, optional
If `True` and ``hdu=True``, then a simple WCS will be included
in the returned `~astropy.io.fits.ImageHDU` header. Default is
`False`.
wcsheader : dict or `None`, optional
If ``hdu`` and ``wcs`` are `True`, this dictionary is passed to
`~astropy.wcs.WCS` to generate the returned
`~astropy.io.fits.ImageHDU` header.
Returns
-------
image : `~numpy.ndarray` or `~astropy.units.Quantity` or `~astropy.io.fits.ImageHDU`
Image or `~astropy.io.fits.ImageHDU` containing 2D Gaussian
sources.
See Also
--------
make_random_gaussians, make_noise_image, make_poisson_noise
Examples
--------
.. plot::
:include-source:
# make a table of Gaussian sources
from astropy.table import Table
table = Table()
table['amplitude'] = [50, 70, 150, 210]
table['x_mean'] = [160, 25, 150, 90]
table['y_mean'] = [70, 40, 25, 60]
table['x_stddev'] = [15.2, 5.1, 3., 8.1]
table['y_stddev'] = [2.6, 2.5, 3., 4.7]
table['theta'] = np.array([145., 20., 0., 60.]) * np.pi / 180.
# make an image of the sources without noise, with Gaussian
# noise, and with Poisson noise
from photutils.datasets import make_gaussian_sources
from photutils.datasets import make_noise_image
shape = (100, 200)
image1 = make_gaussian_sources(shape, table)
image2 = image1 + make_noise_image(shape, type='gaussian', mean=5.,
stddev=5.)
image3 = image1 + make_noise_image(shape, type='poisson', mean=5.)
# plot the images
import matplotlib.pyplot as plt
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
ax1.imshow(image1, origin='lower', interpolation='nearest')
ax2.imshow(image2, origin='lower', interpolation='nearest')
ax3.imshow(image3, origin='lower', interpolation='nearest')
"""
image = np.zeros(image_shape, dtype=np.float64)
y, x = np.indices(image_shape)
if 'flux' in source_table.colnames:
amplitude = source_table['flux'] / (2. * np.pi *
source_table['x_stddev'] *
source_table['y_stddev'])
elif 'amplitude' in source_table.colnames:
amplitude = source_table['amplitude']
else:
raise ValueError('either "amplitude" or "flux" must be columns in '
'the input source_table')
for i, source in enumerate(source_table):
model = Gaussian2D(amplitude=amplitude[i], x_mean=source['x_mean'],
y_mean=source['y_mean'],
x_stddev=source['x_stddev'],
y_stddev=source['y_stddev'], theta=source['theta'])
if oversample == 1:
image += model(x, y)
else:
image += discretize_model(model, (0, image_shape[1]),
(0, image_shape[0]), mode='oversample',
factor=oversample)
if unit is not None:
image = u.Quantity(image, unit=unit)
if wcs and not hdu:
raise ValueError("wcs header only works with hdu output, use keyword "
"'hdu=True'")
if hdu is True:
from astropy.io import fits
if wcs:
from astropy.wcs import WCS
if wcsheader is None:
# Go with the simplest valid header
header = WCS({'CTYPE1': 'RA---TAN',
'CTYPE2': 'DEC--TAN',
'CRPIX1': int(image_shape[1] / 2),
'CRPIX2': int(image_shape[0] / 2)}, ).to_header()
else:
header = WCS(wcsheader)
else:
header = None
image = fits.ImageHDU(image, header=header)
return image
def make_model_sources_image(shape, model, source_table, oversample=1):
"""
Make an image containing sources generated from a user-specified
model.
Parameters
----------
shape : 2-tuple of int
The shape of the output 2D image.
model : 2D astropy.modeling.models object
The model to be used for rendering the sources.
source_table : `~astropy.table.Table`
Table of parameters for the sources. Each row of the table
corresponds to a source whose model parameters are defined by
the column names, which must match the model parameter names.
Column names that do not match model parameters will be ignored.
Model parameters not defined in the table will be set to the
``model`` default value.
oversample : float, optional
The sampling factor used to discretize the models on a pixel
grid. If the value is 1.0 (the default), then the models will
be discretized by taking the value at the center of the pixel
bin. Note that this method will not preserve the total flux of
very small sources. Otherwise, the models will be discretized
by taking the average over an oversampled grid. The pixels will
be oversampled by the ``oversample`` factor.
Returns
-------
image : 2D `~numpy.ndarray`
Image containing model sources.
See Also
--------
make_random_models_table, make_gaussian_sources_image
Examples
--------
.. plot::
:include-source:
from collections import OrderedDict
from astropy.modeling.models import Moffat2D
from photutils.datasets import (make_random_models_table,
make_model_sources_image)
model = Moffat2D()
n_sources = 10
shape = (100, 100)
param_ranges = [('amplitude', [100, 200]),
('x_0', [0, shape[1]]),
('y_0', [0, shape[0]]),
('gamma', [5, 10]),
('alpha', [1, 2])]
param_ranges = OrderedDict(param_ranges)
sources = make_random_models_table(n_sources, param_ranges,
random_state=12345)
data = make_model_sources_image(shape, model, sources)
plt.imshow(data)
"""
image = np.zeros(shape, dtype=np.float64)
y, x = np.indices(shape)
params_to_set = []
for param in source_table.colnames:
if param in model.param_names:
params_to_set.append(param)
# Save the initial parameter values so we can set them back when
# done with the loop. It's best not to copy a model, because some
# models (e.g. PSF models) may have substantial amounts of data in
# them.
init_params = {param: getattr(model, param) for param in params_to_set}
try:
for i, source in enumerate(source_table):
for param in params_to_set:
setattr(model, param, source[param])
if oversample == 1:
image += model(x, y)
else:
image += discretize_model(model, (0, shape[1]), (0, shape[0]),
mode='oversample',
factor=oversample)
finally:
for param, value in init_params.items():
setattr(model, param, value)
return image
def make_gaussian_sources(image_shape,
source_table,
oversample=1,
unit=None,
hdu=False,
wcs=False,
wcsheader=None):
"""
Make an image containing 2D Gaussian sources.
Parameters
----------
image_shape : 2-tuple of int
Shape of the output 2D image.
source_table : `~astropy.table.Table`
Table of parameters for the Gaussian sources. Each row of the
table corresponds to a Gaussian source whose parameters are
defined by the column names. The column names must include
``flux`` or ``amplitude``, ``x_mean``, ``y_mean``, ``x_stddev``,
``y_stddev``, and ``theta`` (see
`~astropy.modeling.functional_models.Gaussian2D` for a
description of most of these parameter names). If both ``flux``
and ``amplitude`` are present, then ``amplitude`` will be
ignored.
oversample : float, optional
The sampling factor used to discretize the
`~astropy.modeling.functional_models.Gaussian2D` models on a
pixel grid.
If the value is 1.0 (the default), then the models will be
discretized by taking the value at the center of the pixel bin.
Note that this method will not preserve the total flux of very
small sources.
Otherwise, the models will be discretized by taking the average
over an oversampled grid. The pixels will be oversampled by the
``oversample`` factor.
unit : `~astropy.units.UnitBase` instance, str, optional
An object that represents the unit desired for the output image.
Must be an `~astropy.units.UnitBase` object or a string
parseable by the `~astropy.units` package.
hdu : bool, optional
If `True` returns ``image`` as an `~astropy.io.fits.ImageHDU`
object. To include WCS information in the header, use the
``wcs`` and ``wcsheader`` inputs. Otherwise the header will be
minimal. Default is `False`.
wcs : bool, optional
If `True` and ``hdu=True``, then a simple WCS will be included
in the returned `~astropy.io.fits.ImageHDU` header. Default is
`False`.
wcsheader : dict or `None`, optional
If ``hdu`` and ``wcs`` are `True`, this dictionary is passed to
`~astropy.wcs.WCS` to generate the returned
`~astropy.io.fits.ImageHDU` header.
Returns
-------
image : `~numpy.ndarray` or `~astropy.units.Quantity` or `~astropy.io.fits.ImageHDU`
Image or `~astropy.io.fits.ImageHDU` containing 2D Gaussian
sources.
See Also
--------
make_random_gaussians, make_noise_image, make_poisson_noise
Examples
--------
.. plot::
:include-source:
# make a table of Gaussian sources
from astropy.table import Table
table = Table()
table['amplitude'] = [50, 70, 150, 210]
table['x_mean'] = [160, 25, 150, 90]
table['y_mean'] = [70, 40, 25, 60]
table['x_stddev'] = [15.2, 5.1, 3., 8.1]
table['y_stddev'] = [2.6, 2.5, 3., 4.7]
table['theta'] = np.array([145., 20., 0., 60.]) * np.pi / 180.
# make an image of the sources without noise, with Gaussian
# noise, and with Poisson noise
from photutils.datasets import make_gaussian_sources
from photutils.datasets import make_noise_image
shape = (100, 200)
image1 = make_gaussian_sources(shape, table)
image2 = image1 + make_noise_image(shape, type='gaussian', mean=5.,
stddev=5.)
image3 = image1 + make_noise_image(shape, type='poisson', mean=5.)
# plot the images
import matplotlib.pyplot as plt
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
ax1.imshow(image1, origin='lower', interpolation='nearest')
ax2.imshow(image2, origin='lower', interpolation='nearest')
ax3.imshow(image3, origin='lower', interpolation='nearest')
"""
image = np.zeros(image_shape, dtype=np.float64)
y, x = np.indices(image_shape)
if 'flux' in source_table.colnames:
amplitude = source_table['flux'] / (
2. * np.pi * source_table['x_stddev'] * source_table['y_stddev'])
elif 'amplitude' in source_table.colnames:
amplitude = source_table['amplitude']
else:
raise ValueError('either "amplitude" or "flux" must be columns in '
'the input source_table')
for i, source in enumerate(source_table):
model = Gaussian2D(amplitude=amplitude[i],
x_mean=source['x_mean'],
y_mean=source['y_mean'],
x_stddev=source['x_stddev'],
y_stddev=source['y_stddev'],
theta=source['theta'])
if oversample == 1:
image += model(x, y)
else:
image += discretize_model(model, (0, image_shape[1]),
(0, image_shape[0]),
mode='oversample',
factor=oversample)
if unit is not None:
image = u.Quantity(image, unit=unit)
if wcs and not hdu:
raise ValueError("wcs header only works with hdu output, use keyword "
"'hdu=True'")
if hdu is True:
from astropy.io import fits
if wcs:
from astropy.wcs import WCS
if wcsheader is None:
# Go with the simplest valid header
header = WCS(
{
'CTYPE1': 'RA---TAN',
'CTYPE2': 'DEC--TAN',
'CRPIX1': int(image_shape[1] / 2),
'CRPIX2': int(image_shape[0] / 2)
}, ).to_header()
else:
header = WCS(wcsheader)
else:
header = None
image = fits.ImageHDU(image, header=header)
return image
def make_model_sources(image_shape, model, source_table, oversample=1,
unit=None, hdu=False, wcs=False, wcsheader=None):
"""
Make an image containing sources generated from a user-specified flux model.
Parameters
----------
image_shape : 2-tuple of int or `~numpy.ndarray`
If a 2-tuple, shape of the output 2D image. If an array, these sources
will be *added* to that array.
model : 2D astropy.modeling.models object
The model to be used for rendering the sources.
source_table : `~astropy.table.Table`
Table of parameters for the sources. The column names must
match the model parameter names. Column names that do not match
model parameters will be ignored. Any model parameter that is
*not* in the table will be left at whatever value it has for
``model``.
oversample : float, optional
The sampling factor used to discretize the models on a
pixel grid.
If the value is 1.0 (the default), then the models will be
discretized by taking the value at the center of the pixel bin.
Note that this method will not preserve the total flux of very
small sources.
Otherwise, the models will be discretized by taking the average
over an oversampled grid. The pixels will be oversampled by the
``oversample`` factor.
unit : `~astropy.units.UnitBase` instance, str, optional
An object that represents the unit desired for the output image.
Must be an `~astropy.units.UnitBase` object or a string
parseable by the `~astropy.units` package.
hdu : bool, optional
If `True` returns ``image`` as an `~astropy.io.fits.ImageHDU`
object. To include WCS information in the header, use the
``wcs`` and ``wcsheader`` inputs. Otherwise the header will be
minimal. Default is `False`.
wcs : bool, optional
If `True` and ``hdu=True``, then a simple WCS will be included
in the returned `~astropy.io.fits.ImageHDU` header. Default is
`False`.
wcsheader : dict or `None`, optional
If ``hdu`` and ``wcs`` are `True`, this dictionary is passed to
`~astropy.wcs.WCS` to generate the returned
`~astropy.io.fits.ImageHDU` header.
Returns
-------
image : `~numpy.ndarray` or `~astropy.units.Quantity` or `~astropy.io.fits.ImageHDU`
Image or `~astropy.io.fits.ImageHDU` containing 2D Gaussian
sources.
"""
image = np.zeros(image_shape, dtype=np.float64)
y, x = np.indices(image_shape)
params_to_set = []
for colnm in source_table.colnames:
if colnm in model.param_names:
params_to_set.append(colnm)
# use this to store the *initial* values so we can set them back when done
# with the loop. Best not to copy a model, because some PSF models may have
# substantial amounts of data in them
init_params = {pnm: getattr(model, pnm) for pnm in params_to_set}
try:
for i, source in enumerate(source_table):
for paramnm in params_to_set:
setattr(model, paramnm, source[paramnm])
if oversample == 1:
image += model(x, y)
else:
image += discretize_model(model, (0, image_shape[1]),
(0, image_shape[0]), mode='oversample',
factor=oversample)
finally:
for pnm, val in init_params.items():
setattr(model, paramnm, val)
if unit is not None:
image = u.Quantity(image, unit=unit)
if wcs and not hdu:
raise ValueError("wcs header only works with hdu output, use keyword "
"'hdu=True'")
if hdu is True:
from astropy.io import fits
if wcs:
from astropy.wcs import WCS
if wcsheader is None:
# Go with the simplest valid header
header = WCS({'CTYPE1': 'RA---TAN',
'CTYPE2': 'DEC--TAN',
'CRPIX1': int(image_shape[1] / 2),
'CRPIX2': int(image_shape[0] / 2)}, ).to_header()
else:
header = WCS(wcsheader)
else:
header = None
image = fits.ImageHDU(image, header=header)
return image