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# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import numpy as np
from ..modeling.core import FittableModel, custom_model
from ..extern.six.moves import range
__all__ = ['discretize_model']
class DiscretizationError(Exception):
"""
Called when discretization of models goes wrong.
"""
class KernelSizeError(Exception):
"""
Called when size of kernels is even.
"""
def add_kernel_arrays_1D(array_1, array_2):
"""
Add two 1D kernel arrays of different size.
The arrays are added with the centers lying upon each other.
"""
if array_1.size > array_2.size:
new_array = array_1.copy()
center = array_1.size // 2
slice_ = slice(center - array_2.size // 2,
center + array_2.size // 2 + 1)
new_array[slice_] += array_2
return new_array
elif array_2.size > array_1.size:
new_array = array_2.copy()
center = array_2.size // 2
slice_ = slice(center - array_1.size // 2,
center + array_1.size // 2 + 1)
new_array[slice_] += array_1
return new_array
return array_2 + array_1
def add_kernel_arrays_2D(array_1, array_2):
"""
Add two 2D kernel arrays of different size.
The arrays are added with the centers lying upon each other.
"""
if array_1.size > array_2.size:
new_array = array_1.copy()
center = [axes_size // 2 for axes_size in array_1.shape]
slice_x = slice(center[1] - array_2.shape[1] // 2,
center[1] + array_2.shape[1] // 2 + 1)
slice_y = slice(center[0] - array_2.shape[0] // 2,
center[0] + array_2.shape[0] // 2 + 1)
new_array[slice_y, slice_x] += array_2
return new_array
elif array_2.size > array_1.size:
new_array = array_2.copy()
center = [axes_size // 2 for axes_size in array_2.shape]
slice_x = slice(center[1] - array_1.shape[1] // 2,
center[1] + array_1.shape[1] // 2 + 1)
slice_y = slice(center[0] - array_1.shape[0] // 2,
center[0] + array_1.shape[0] // 2 + 1)
new_array[slice_y, slice_x] += array_1
return new_array
return array_2 + array_1
def discretize_model(model, x_range, y_range=None, mode='center', factor=10):
"""
Function to evaluate analytical model functions on a grid.
So far the function can only deal with pixel coordinates.
Parameters
----------
model : `~astropy.modeling.FittableModel` or callable.
Analytic model function to be discretized. Callables, which are not an
instances of `~astropy.modeling.FittableModel` are passed to
`~astropy.modeling.custom_model` and then evaluated.
x_range : tuple
x range in which the model is evaluated. The difference between the
upper an lower limit must be a whole number, so that the output array
size is well defined.
y_range : tuple, optional
y range in which the model is evaluated. The difference between the
upper an lower limit must be a whole number, so that the output array
size is well defined. Necessary only for 2D models.
mode : str, optional
One of the following modes:
* ``'center'`` (default)
Discretize model by taking the value
at the center of the bin.
* ``'linear_interp'``
Discretize model by linearly interpolating
between the values at the corners of the bin.
For 2D models interpolation is bilinear.
* ``'oversample'``
Discretize model by taking the average
on an oversampled grid.
* ``'integrate'``
Discretize model by integrating the model
over the bin using `scipy.integrate.quad`.
Very slow.
factor : float or int
Factor of oversampling. Default = 10.
Returns
-------
array : `numpy.array`
Model value array
Notes
-----
The ``oversample`` mode allows to conserve the integral on a subpixel
scale. Here is the example of a normalized Gaussian1D:
.. plot::
:include-source:
import matplotlib.pyplot as plt
import numpy as np
from astropy.modeling.models import Gaussian1D
from astropy.convolution.utils import discretize_model
gauss_1D = Gaussian1D(1 / (0.5 * np.sqrt(2 * np.pi)), 0, 0.5)
y_center = discretize_model(gauss_1D, (-2, 3), mode='center')
y_corner = discretize_model(gauss_1D, (-2, 3), mode='linear_interp')
y_oversample = discretize_model(gauss_1D, (-2, 3), mode='oversample')
plt.plot(y_center, label='center sum = {0:3f}'.format(y_center.sum()))
plt.plot(y_corner, label='linear_interp sum = {0:3f}'.format(y_corner.sum()))
plt.plot(y_oversample, label='oversample sum = {0:3f}'.format(y_oversample.sum()))
plt.xlabel('pixels')
plt.ylabel('value')
plt.legend()
plt.show()
"""
if not callable(model):
raise TypeError('Model must be callable.')
if not isinstance(model, FittableModel):
model = custom_model(model)()
ndim = model.n_inputs
if ndim > 2:
raise ValueError('discretize_model only supports 1-d and 2-d models.')
if not float(np.diff(x_range)).is_integer():
raise ValueError("The difference between the upper an lower limit of"
" 'x_range' must be a whole number.")
if y_range:
if not float(np.diff(y_range)).is_integer():
raise ValueError("The difference between the upper an lower limit of"
" 'y_range' must be a whole number.")
if ndim == 2 and y_range is None:
raise ValueError("y range not specified, but model is 2-d")
if ndim == 1 and y_range is not None:
raise ValueError("y range specified, but model is only 1-d.")
if mode == "center":
if ndim == 1:
return discretize_center_1D(model, x_range)
elif ndim == 2:
return discretize_center_2D(model, x_range, y_range)
elif mode == "linear_interp":
if ndim == 1:
return discretize_linear_1D(model, x_range)
if ndim == 2:
return discretize_bilinear_2D(model, x_range, y_range)
elif mode == "oversample":
if ndim == 1:
return discretize_oversample_1D(model, x_range, factor)
if ndim == 2:
return discretize_oversample_2D(model, x_range, y_range, factor)
elif mode == "integrate":
if ndim == 1:
return discretize_integrate_1D(model, x_range)
if ndim == 2:
return discretize_integrate_2D(model, x_range, y_range)
else:
raise DiscretizationError('Invalid mode.')
def discretize_center_1D(model, x_range):
"""
Discretize model by taking the value at the center of the bin.
"""
x = np.arange(*x_range)
return model(x)
def discretize_center_2D(model, x_range, y_range):
"""
Discretize model by taking the value at the center of the pixel.
"""
x = np.arange(*x_range)
y = np.arange(*y_range)
x, y = np.meshgrid(x, y)
return model(x, y)
def discretize_linear_1D(model, x_range):
"""
Discretize model by performing a linear interpolation.
"""
# Evaluate model 0.5 pixel outside the boundaries
x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
values_intermediate_grid = model(x)
return 0.5 * (values_intermediate_grid[1:] + values_intermediate_grid[:-1])
def discretize_bilinear_2D(model, x_range, y_range):
"""
Discretize model by performing a bilinear interpolation.
"""
# Evaluate model 0.5 pixel outside the boundaries
x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
y = np.arange(y_range[0] - 0.5, y_range[1] + 0.5)
x, y = np.meshgrid(x, y)
values_intermediate_grid = model(x, y)
# Mean in y direction
values = 0.5 * (values_intermediate_grid[1:, :]
+ values_intermediate_grid[:-1, :])
# Mean in x direction
values = 0.5 * (values[:, 1:]
+ values[:, :-1])
return values
def discretize_oversample_1D(model, x_range, factor=10):
"""
Discretize model by taking the average on an oversampled grid.
"""
# Evaluate model on oversampled grid
x = np.arange(x_range[0] - 0.5 * (1 - 1 / factor),
x_range[1] + 0.5 * (1 + 1 / factor), 1. / factor)
values = model(x)
# Reshape and compute mean
values = np.reshape(values, (x.size // factor, factor))
return values.mean(axis=1)[:-1]
def discretize_oversample_2D(model, x_range, y_range, factor=10):
"""
Discretize model by taking the average on an oversampled grid.
"""
# Evaluate model on oversampled grid
x = np.arange(x_range[0] - 0.5 * (1 - 1 / factor),
x_range[1] + 0.5 * (1 + 1 / factor), 1. / factor)
y = np.arange(y_range[0] - 0.5 * (1 - 1 / factor),
y_range[1] + 0.5 * (1 + 1 / factor), 1. / factor)
x_grid, y_grid = np.meshgrid(x, y)
values = model(x_grid, y_grid)
# Reshape and compute mean
shape = (y.size // factor, factor, x.size // factor, factor)
values = np.reshape(values, shape)
return values.mean(axis=3).mean(axis=1)[:-1, :-1]
def discretize_integrate_1D(model, x_range):
"""
Discretize model by integrating numerically the model over the bin.
"""
from scipy.integrate import quad
# Set up grid
x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
values = np.array([])
# Integrate over all bins
for i in range(x.size - 1):
values = np.append(values, quad(model, x[i], x[i + 1])[0])
return values
def discretize_integrate_2D(model, x_range, y_range):
"""
Discretize model by integrating the model over the pixel.
"""
from scipy.integrate import dblquad
# Set up grid
x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
y = np.arange(y_range[0] - 0.5, y_range[1] + 0.5)
values = np.empty((y.size - 1, x.size - 1))
# Integrate over all pixels
for i in range(x.size - 1):
for j in range(y.size - 1):
values[j, i] = dblquad(model, x[i], x[i + 1],
lambda x: y[j], lambda x: y[j + 1])[0]
return values
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