From e853e22b46fd0d5fd2c03e82c781ccd67ae5e344 Mon Sep 17 00:00:00 2001 From: Patti Carroll Date: Mon, 11 May 2015 17:07:25 -0700 Subject: [PATCH 1/2] Add initial API for proposed model discretization project --- model_discretization_api.py | 1391 +++++++++++++++++++++++++++++++++++ 1 file changed, 1391 insertions(+) create mode 100644 model_discretization_api.py diff --git a/model_discretization_api.py b/model_discretization_api.py new file mode 100644 index 0000000..28d0bac --- /dev/null +++ b/model_discretization_api.py @@ -0,0 +1,1391 @@ + + + + + + + + + + + + astropy-api/model_discretization_api.py at model_discretization_api · adonath/astropy-api + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Skip to content +
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+ astropy-api/model_discretization_api.py +
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######################
# ConvolvedModel API #
######################
+
from astropy.modeling import ConvolvedModel
from astropy.modeling.models import Box2D, Lorentz1D, Gaussian2D
from astropy.convolution import Gaussian2DKernel, Gaussian1DKernel
+
# for simplicity we only support pixel coordinates and assume a fixed psf model.
# the convolved model should be initialized with a model and a kernel instance
# like:
source = Box2D(1, 0, 0, 1, 1)
psf = Gaussian2DKernel(1)
convolved_model = ConvolvedModel(source, psf)
+
# support of 1D models
source = Lorentz1D(1, 0, 0, 1, 1)
psf = Gaussian1DKernel(1)
convolved_model = ConvolvedModel(source, psf)
+
# should there be a Convolved1DModel and Convolved2DModel?
+
# later we can think about using any model as convolution kernels
# and even implement the analytical solution for the common Gaussian case
# or other cases where analytical solutions are known
source = Gaussian2D(1, 0, 0, 1, 1)
psf = Gaussian2D(1, 0, 0, 1, 1)
convolved_model = ConvolvedModel(source, psf)
+
# ConvolvedModel should inherit from FittableModel but overrides the evaluate method
# to perfom an additional numerical convolution
model_data = model(x, y)
+
# fitting works the same way as for FittableModel
# the parameters of the psf model are fixed during the fit.
+
+
# the convolution method can be set via string, to choose between the astropy.convolution
# methods
convolved_model = ConvolvedModel(source, psf, convolution='fft')
convolved_model = ConvolvedModel(source, psf, convolution='standard')
+
# or by passing a function that should be used. This is mainly nececessary, because
# the performance of the astropy convolution algorithms is rather weak...
convolved_model = ConvolvedModel(source, psf, convolution=scipy.signal.fftconvolve)
+
# recommendation would be to use scipy.signal.fftconvolve which is very fast
+
# additional keyword arguments can be passed to the convolution function
convolved_model = ConvolvedModel(source, psf, convolution='standard', boundary='none')
+
# Further notes:
# 1. Implementation of this class should be straight forward and not much effort
# 2. Testing could be set up using Gaussian models, where the analytical solution is
# known
# 3. Later one could think about assigning the corresponding fourier transforms to analytical
# models and use this for the convolution, which will probably have a better performance.
# Source model and PSF are evaluated analytically in Fourier space, mutliplied and transformed
# back to normal space.
# 4. As convolution is a linear operation the derivative of a convolution behaves like
# http://en.wikipedia.org/wiki/Convolution#Differentiation this relation can be used
# to implement `fit_deriv` methods for convolved models.
+
+
+
#########################
# Model integration API #
#########################
+
import numpy as np
+
# to avoid bias, when the scale of the model is similar to the size of the pixels,
# models have to be integrated over pixels, for this purpose models could define
# an integrate function, that takes upper and lower bounds of the integration
# (see also https://github.com/astropy/astropy/issues/1586)
model = Gaussian1D(1, 0, 1)
model.integrate(0, np.inf)
+
# it should also work with arrays of bounds of course
x_lo = np.arange(-10, 11) - 0.5
x_hi = np.arange(-10, 11) + 0.5
model.integrate(x_lo, x_hi)
+
# for 2d models it would be
y_lo = np.arange(-10, 11) - 0.5
y_hi = np.arange(-10, 11) + 0.5
model.integrate(x_lo, x_hi, y_lo, y_hi)
+
# whenever possible (e.g. polynomials) the integrate function would be implemented
# analytically, for all others a standard numerical integration routine would be used
# e.g. from scipy.integrate
+
# for convenience one could incorporate the functionality into the standard model API
model = Gaussian1D(1, 0, 1, eval_method='integrate')
model = Gaussian1D(1, 0, 1, eval_method='oversample')
model = Gaussian1D(1, 0, 1, eval_method='center')
+
# where the given evaluation method would be used when the model is called
# for evaluation. This would only work for models defined in pixel coordinates
x = np.arange(-10, 11)
model(x)
+
# models that are spatially confined to a certain region such as Gaussian2D, Disk2D,
# Delta2D, Box2D, ... should have the possibility to apply a different normalization,
# where the amplitude parameter corresponds to the integral of the model and not the
# peak value at maximum (see e.g.: https://gammapy.readthedocs.org/en/latest/api/gammapy.morphology.Shell2D.html#gammapy.morphology.Shell2D)
# This is very useful for modeling sources, because the amplitude parameter then
# corresponds to the total flux of the source...
model = Gaussian2D(1, 0, 0, 1, 1, normalization='peak')
model = Gaussian2D(1, 0, 0, 1, 1, normalization='integral')
+
# alternatively one could introduce new NormGaussian2D, NormBox2D, ... models, but that
# would probably be a lot of code duplication?
+
# all models that are 'normalisable' should have an `extent` attribute that specifies
# a rectangular region where the model is nonzero or has 99.99% containment (or a similar
# criterion). A reasonable value would choosen as default and would be given as multiples of the
# models size parameters. Model evaluation can later be limited to the region defined
# by `extent` for better performance
Gaussian2D.extent= dict(x=8 * width, y=8 * width)
Disk2D.extent = dict(x=radius, y=radius)
+
# models should have an attribute that defines a reasonable sample size for the model,
# warnings could be raised, when models are undersampled
Gaussian2D.sample_size = width / 5.
+
+
###############################
# Model Image Computation API #
###############################
+
# functionality is added to NDData via NDDataMixin classes
class SkyImage(NDData, NDSlicingMixin, NDWCSCutoutMixin) : pass
+
# a sky image object is created as following
sky_image = SkyImage(np.zeros(501, 10001), wcs=WCS())
+
# it has a coordinates attribute, that returns a SkyCoord object
# with every pixel containing the corresponding position
sky_image.coordinates
+
# one can make rectangular cutouts of the sky image using
cutout = sky_image.extract(position, source.extent)
cutout = sky_image.extract(position, source.extent, copy=True)
+
# which returns again a SkyImage object, but with modified WCS transform
# data can be copied optionally
+
# to render the model on a sky image a new function should be defined
source_image = render_model_to_sky(source, wcs=WCS())
+
# which would return again a (smaller) SkyImage object centered on the
# nearest pixel of the source position which can be added to sky_image
# with
+
sky_image.add(source_image)
+
# later `.add` could use any kind of resampling/reprojection
# for now we just assume that `sky_image` and `source_image`
# pixels are aligned (which should be checked...)
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+ + + + + + + + + + From 05184659329582d7da557bdf3da8589dd76f42f7 Mon Sep 17 00:00:00 2001 From: Patti Carroll Date: Tue, 12 May 2015 22:10:02 -0700 Subject: [PATCH 2/2] Add context, use case, and improvements --- model_discretization_api.py | 1534 ++++------------------------------- 1 file changed, 176 insertions(+), 1358 deletions(-) diff --git a/model_discretization_api.py b/model_discretization_api.py index 28d0bac..ed19b89 100644 --- a/model_discretization_api.py +++ b/model_discretization_api.py @@ -1,1391 +1,209 @@ +''' +A framework for efficient model image rasterization in astropy. +This is a GSoC 2015 project and is therefore on a relatively short time frame. +We focus first on developing a robust solution to a simple but common use case that +is extensible to future implementation of more complex models and solutions. +Use case: Generate a sky model image of discrete sources, e.g. something like +photutils.datasets.make_100gaussians_image(), but faster and convolving a source model +with an instrument PSF. - - - - - - - - - astropy-api/model_discretization_api.py at model_discretization_api · adonath/astropy-api - - - - - - - +The primary challenge- and motivation- is maximizing speed while maintainging precision. A +straightforward approach is to use oversampling within a bounded area around the +source containing the majority of its flux (e.g. 5-sigma) for discretization and integration. + +The key steps are: +1. Model generation + - Convolution of a source model with an instrument PSF model + - Fitting the convolved model to image data if required +2. Model discretization/Image rasterization + - Integration of the model over pixel areas + - Reprojection if required + +The pieces necessary are largely in existence. Relevant packages +include astropy.modeling, astropy.convolution, astropy.nddata, sherpa, galfit, reproject, +... others. + +Outlined here is a rough draft of the proposed API for community discussion. + +''' + +###################### +# ConvolvedModel API # +###################### + +from astropy.modeling import ConvolvedModel +from astropy.modeling.models import Box2D, Lorentz1D, Gaussian2D +from astropy.convolution import Gaussian2DKernel, Gaussian1DKernel + +# Initiate a ConvolvedModel instance, takes source model and convolution kernel +# like: +source = Box2D(1, 0, 0, 1, 1) +psf = Gaussian2DKernel(1) +convolved_model = ConvolvedModel(source, psf, mode='oversample', factor=10) + +# mode will be used both for convolution and later integration +# if a different mode is desired for convolution it should be passed in the psf + +# support of 1D models +source = Lorentz1D(1, 0, 0, 1, 1) +psf = Gaussian1DKernel(1) +convolved_model = ConvolvedModel(source, psf) + +# should there be a Convolved1DModel and Convolved2DModel? +# should this be an extension of the CompoundModel class? + +# later we can think about using any model as convolution kernels +# and even implement the analytical solution for the common Gaussian case +# or other cases where analytical solutions are known +source = Gaussian2D(1, 0, 0, 1, 1) +psf = Gaussian2D(1, 0, 0, 1, 1) +convolved_model = ConvolvedModel(source, psf) + + +# the convolution method can be set via string, to choose between the astropy.convolution +# methods +convolved_model = ConvolvedModel(source, psf, method='fft') +convolved_model = ConvolvedModel(source, psf, method='standard') + +# or by passing a function that should be used. This is mainly nececessary, because +# the performance of the astropy convolution algorithms is rather weak... +convolved_model = ConvolvedModel(source, psf, method=scipy.signal.fftconvolve) + +# recommendation would be to use scipy.signal.fftconvolve which is very fast + +# additional keyword arguments can be passed to the convolution function +convolved_model = ConvolvedModel(source, psf, method='standard', mode='oversample') + +# the convolved_model can be fit + +# Further notes: +# 1. Implementation of this class should be straight forward and not much effort +# 2. Testing could be set up using Gaussian models, where the analytical solution is +# known +# 3. Later one could think about assigning the corresponding fourier transforms to analytical +# models and use this for the convolution, which will probably have a better performance. +# Source model and PSF are evaluated analytically in Fourier space, mutliplied and transformed +# back to normal space. +# 4. As convolution is a linear operation the derivative of a convolution behaves like +# http://en.wikipedia.org/wiki/Convolution#Differentiation this relation can be used +# to implement `fit_deriv` methods for convolved models. + + +######################### +# Model integration API # +######################### + +import numpy as np + +# to avoid bias, when the scale of the model is similar to the size of the pixels, +# models have to be integrated over pixels, for this purpose models could define +# an integrate function, that takes upper and lower bounds of the integration +# (see also https://github.com/astropy/astropy/issues/1586) +model = Gaussian1D(1, 0, 1) +model.integrate(0, np.inf) - - - - - - - - +# it should also work with arrays of bounds of course +x_lo = np.arange(-10, 11) - 0.5 +x_hi = np.arange(-10, 11) + 0.5 +model.integrate((x_lo, x_hi)) - - - - +# for 2d models it would be +y_lo = np.arange(-10, 11) - 0.5 +y_hi = np.arange(-10, 11) + 0.5 +model.integrate((x_lo, x_hi, y_lo, y_hi)) - - - - - - - - +# whenever possible (e.g. polynomials) the integrate function would be implemented +# analytically, for all others a standard numerical integration routine would be used +# e.g. from scipy.integrate +# the integration mode can be passed to the integrate method if it is not already an +# attribute of model +model.integrate((x_lo, x_hi, y_lo, y_hi), mode='integrate') - - +# for convenience one could incorporate the functionality into the standard model API +# as is done for the convolution kernals +model = Gaussian1D(1, 0, 1, mode='center') +model = Gaussian1D(1, 0, 1, mode='linear_interp') +model = Gaussian1D(1, 0, 1, mode='integrate') +model = Gaussian1D(1, 0, 1, mode='oversample', factor=10) +# the given mode could also be used when the model is called for evaluation +x = np.arange(-10, 11) +y = np.arange(-10, 11) +model(np.meshgrid(x,y)) - - - - - - +# models that are spatially confined to a certain region such as Gaussian2D, Disk2D, +# Delta2D, Box2D, ... should have the possibility to apply a different normalization, +# where the amplitude parameter corresponds to the integral of the model and not the +# peak value at maximum (see e.g.: https://gammapy.readthedocs.org/en/latest/api/gammapy.morphology.Shell2D.html#gammapy.morphology.Shell2D) +# This is very useful for modeling sources, because the amplitude parameter then +# corresponds to the total flux of the source... +model = Gaussian2D(1, 0, 0, 1, 1, normalization='peak') +model = Gaussian2D(1, 0, 0, 1, 1, normalization='integral') +# alternatively one could introduce new NormGaussian2D, NormBox2D, ... models, but that +# would probably be a lot of code duplication? - +# all models that are 'normalisable' should have an `extent` attribute that specifies +# a rectangular region where the model is nonzero or has 99.99% containment (or a similar +# criterion). A reasonable value would be chosen as default and would be given as multiples +# model's width parameters. Model evaluation can later be limited to the region defined +# by `extent` for better performance +Gaussian2D.extent= dict(x=5 * x_stddev, y=5 * y_stddev) +Disk2D.extent = dict(x=R_0, y=R_0) - - - +# models should have an attribute that defines a reasonable sample size for the model, +# warnings could be raised, when models are undersampled. +Gaussian2D.sample_size = width / 5. - - - +############################### +# Model Image Computation API # +############################### +# functionality is added to NDData via NDDataMixin classes +class SkyImage(NDData, NDSlicingMixin, NDWCSCutoutMixin) : pass - - Skip to content -
- - - +# a sky image object is created as following +sky_image = SkyImage(np.zeros(501, 10001), wcs=WCS()) +# it has a coordinates attribute, that returns a SkyCoord object +# with every pixel containing the corresponding position +sky_image.coordinates - - - - - - - -
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- - /astropy-api - - - - - - - forked from astropy/astropy-api - -

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HTTPS clone URL

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You can clone with - HTTPS, SSH, or Subversion. - - - -

- - - - Clone in Desktop - - - - - - - Download ZIP - -
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- - - branch: - model_discreti… - - - -
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- astropy-api/model_discretization_api.py -
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- @adonath - - -
- Fixed a few typos -
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######################
# ConvolvedModel API #
######################
-
from astropy.modeling import ConvolvedModel
from astropy.modeling.models import Box2D, Lorentz1D, Gaussian2D
from astropy.convolution import Gaussian2DKernel, Gaussian1DKernel
-
# for simplicity we only support pixel coordinates and assume a fixed psf model.
# the convolved model should be initialized with a model and a kernel instance
# like:
source = Box2D(1, 0, 0, 1, 1)
psf = Gaussian2DKernel(1)
convolved_model = ConvolvedModel(source, psf)
-
# support of 1D models
source = Lorentz1D(1, 0, 0, 1, 1)
psf = Gaussian1DKernel(1)
convolved_model = ConvolvedModel(source, psf)
-
# should there be a Convolved1DModel and Convolved2DModel?
-
# later we can think about using any model as convolution kernels
# and even implement the analytical solution for the common Gaussian case
# or other cases where analytical solutions are known
source = Gaussian2D(1, 0, 0, 1, 1)
psf = Gaussian2D(1, 0, 0, 1, 1)
convolved_model = ConvolvedModel(source, psf)
-
# ConvolvedModel should inherit from FittableModel but overrides the evaluate method
# to perfom an additional numerical convolution
model_data = model(x, y)
-
# fitting works the same way as for FittableModel
# the parameters of the psf model are fixed during the fit.
-
-
# the convolution method can be set via string, to choose between the astropy.convolution
# methods
convolved_model = ConvolvedModel(source, psf, convolution='fft')
convolved_model = ConvolvedModel(source, psf, convolution='standard')
-
# or by passing a function that should be used. This is mainly nececessary, because
# the performance of the astropy convolution algorithms is rather weak...
convolved_model = ConvolvedModel(source, psf, convolution=scipy.signal.fftconvolve)
-
# recommendation would be to use scipy.signal.fftconvolve which is very fast
-
# additional keyword arguments can be passed to the convolution function
convolved_model = ConvolvedModel(source, psf, convolution='standard', boundary='none')
-
# Further notes:
# 1. Implementation of this class should be straight forward and not much effort
# 2. Testing could be set up using Gaussian models, where the analytical solution is
# known
# 3. Later one could think about assigning the corresponding fourier transforms to analytical
# models and use this for the convolution, which will probably have a better performance.
# Source model and PSF are evaluated analytically in Fourier space, mutliplied and transformed
# back to normal space.
# 4. As convolution is a linear operation the derivative of a convolution behaves like
# http://en.wikipedia.org/wiki/Convolution#Differentiation this relation can be used
# to implement `fit_deriv` methods for convolved models.
-
-
-
#########################
# Model integration API #
#########################
-
import numpy as np
-
# to avoid bias, when the scale of the model is similar to the size of the pixels,
# models have to be integrated over pixels, for this purpose models could define
# an integrate function, that takes upper and lower bounds of the integration
# (see also https://github.com/astropy/astropy/issues/1586)
model = Gaussian1D(1, 0, 1)
model.integrate(0, np.inf)
-
# it should also work with arrays of bounds of course
x_lo = np.arange(-10, 11) - 0.5
x_hi = np.arange(-10, 11) + 0.5
model.integrate(x_lo, x_hi)
-
# for 2d models it would be
y_lo = np.arange(-10, 11) - 0.5
y_hi = np.arange(-10, 11) + 0.5
model.integrate(x_lo, x_hi, y_lo, y_hi)
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# whenever possible (e.g. polynomials) the integrate function would be implemented
# analytically, for all others a standard numerical integration routine would be used
# e.g. from scipy.integrate
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# for convenience one could incorporate the functionality into the standard model API
model = Gaussian1D(1, 0, 1, eval_method='integrate')
model = Gaussian1D(1, 0, 1, eval_method='oversample')
model = Gaussian1D(1, 0, 1, eval_method='center')
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# where the given evaluation method would be used when the model is called
# for evaluation. This would only work for models defined in pixel coordinates
x = np.arange(-10, 11)
model(x)
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# models that are spatially confined to a certain region such as Gaussian2D, Disk2D,
# Delta2D, Box2D, ... should have the possibility to apply a different normalization,
# where the amplitude parameter corresponds to the integral of the model and not the
# peak value at maximum (see e.g.: https://gammapy.readthedocs.org/en/latest/api/gammapy.morphology.Shell2D.html#gammapy.morphology.Shell2D)
# This is very useful for modeling sources, because the amplitude parameter then
# corresponds to the total flux of the source...
model = Gaussian2D(1, 0, 0, 1, 1, normalization='peak')
model = Gaussian2D(1, 0, 0, 1, 1, normalization='integral')
-
# alternatively one could introduce new NormGaussian2D, NormBox2D, ... models, but that
# would probably be a lot of code duplication?
-
# all models that are 'normalisable' should have an `extent` attribute that specifies
# a rectangular region where the model is nonzero or has 99.99% containment (or a similar
# criterion). A reasonable value would choosen as default and would be given as multiples of the
# models size parameters. Model evaluation can later be limited to the region defined
# by `extent` for better performance
Gaussian2D.extent= dict(x=8 * width, y=8 * width)
Disk2D.extent = dict(x=radius, y=radius)
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# models should have an attribute that defines a reasonable sample size for the model,
# warnings could be raised, when models are undersampled
Gaussian2D.sample_size = width / 5.
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###############################
# Model Image Computation API #
###############################
-
# functionality is added to NDData via NDDataMixin classes
class SkyImage(NDData, NDSlicingMixin, NDWCSCutoutMixin) : pass
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# a sky image object is created as following
sky_image = SkyImage(np.zeros(501, 10001), wcs=WCS())
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# it has a coordinates attribute, that returns a SkyCoord object
# with every pixel containing the corresponding position
sky_image.coordinates
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# one can make rectangular cutouts of the sky image using
cutout = sky_image.extract(position, source.extent)
cutout = sky_image.extract(position, source.extent, copy=True)
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# which returns again a SkyImage object, but with modified WCS transform
# data can be copied optionally
-
# to render the model on a sky image a new function should be defined
source_image = render_model_to_sky(source, wcs=WCS())
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# which would return again a (smaller) SkyImage object centered on the
# nearest pixel of the source position which can be added to sky_image
# with
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sky_image.add(source_image)
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# later `.add` could use any kind of resampling/reprojection
# for now we just assume that `sky_image` and `source_image`
# pixels are aligned (which should be checked...)
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