# Licensed under a 3-clause BSD style license - see LICENSE.rst
import numpy as np
from astropy.modeling.core import Model, custom_model
__all__ = [
"discretize_model",
"KernelError",
"KernelSizeError",
"KernelArithmeticError",
]
[docs]
class KernelError(Exception):
"""
Base error class for kernel errors.
"""
[docs]
class KernelSizeError(KernelError):
"""
Called when size of kernels is even.
"""
[docs]
class KernelArithmeticError(KernelError):
"""Called when doing invalid arithmetic with a kernel."""
def has_even_axis(array):
if isinstance(array, (list, tuple)):
return not len(array) % 2
return any(not axes_size % 2 for axes_size in array.shape)
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
if 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
if 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
[docs]
def discretize_model(model, x_range, y_range=None, mode="center", factor=10):
"""
Evaluate an analytical model function on a pixel grid.
Parameters
----------
model : `~astropy.modeling.Model` or callable.
Analytical model function to be discretized. A callable that is
not a `~astropy.modeling.Model` instance is converted to a model
using `~astropy.modeling.custom_model`.
x_range : 2-tuple
Lower and upper bounds of x pixel values at which the model is
evaluated. The upper bound is non-inclusive. A ``x_range`` of
``(0, 3)`` means the model will be evaluated at x pixels 0, 1,
and 2. The difference between the upper and lower bound must be
a whole number so that the output array size is well defined.
y_range : 2-tuple or `None`, optional
Lower and upper bounds of y pixel values at which the model is
evaluated. The upper bound is non-inclusive. A ``y_range`` of
``(0, 3)`` means the model will be evaluated at y pixels of 0,
1, and 2. The difference between the upper and lower bound must
be a whole number so that the output array size is well defined.
``y_range`` is necessary only for 2D models.
mode : {'center', 'linear_interp', 'oversample', 'integrate'}, optional
One of the following modes:
* ``'center'`` (default)
Discretize model by taking the value at the center of
the pixel bins.
* ``'linear_interp'``
Discretize model by linearly interpolating between the
values at the edges (1D) or corners (2D) of the pixel
bins. For 2D models, the interpolation is bilinear.
* ``'oversample'``
Discretize model by taking the average of model values
in the pixel bins on an oversampled grid. Use the
``factor`` keyword to set the integer oversampling
factor.
* ``'integrate'``
Discretize model by integrating the model over the pixel
bins using `scipy.integrate.quad`. This mode conserves
the model integral on a subpixel scale, but is very
slow.
factor : int, optional
The integer oversampling factor used when ``mode='oversample'``.
Ignored otherwise.
Returns
-------
array : `numpy.ndarray`
The discretized model array.
Examples
--------
In this example, we define a
`~astropy.modeling.functional_models.Gaussian1D` model that has been
normalized so that it sums to 1.0. We then discretize this model
using the ``'center'``, ``'linear_interp'``, and ``'oversample'``
(with ``factor=10``) modes.
.. plot::
:show-source-link:
import matplotlib.pyplot as plt
import numpy as np
from astropy.convolution.utils import discretize_model
from astropy.modeling.models import Gaussian1D
gauss_1D = Gaussian1D(1 / (0.5 * np.sqrt(2 * np.pi)), 0, 0.5)
x_range = (-2, 3)
x = np.arange(*x_range)
y_center = discretize_model(gauss_1D, x_range, mode='center')
y_edge = discretize_model(gauss_1D, x_range, mode='linear_interp')
y_oversample = discretize_model(gauss_1D, x_range, mode='oversample')
fig, ax = plt.subplots(figsize=(8, 6))
label = f'center (sum={y_center.sum():.3f})'
ax.plot(x, y_center, '.-', label=label)
label = f'linear_interp (sum={y_edge.sum():.3f})'
ax.plot(x, y_edge, '.-', label=label)
label = f'oversample (sum={y_oversample.sum():.3f})'
ax.plot(x, y_oversample, '.-', label=label)
ax.set_xlabel('x')
ax.set_ylabel('Value')
plt.legend()
"""
if not callable(model):
raise TypeError("Model must be callable.")
if not isinstance(model, Model):
model = custom_model(model)()
ndim = model.n_inputs
if ndim > 2:
raise ValueError("discretize_model supports only 1D and 2D models.")
dxrange = np.diff(x_range)[0]
if dxrange != int(dxrange):
raise ValueError(
"The difference between the upper and lower limit of"
" 'x_range' must be a whole number."
)
if y_range:
dyrange = np.diff(y_range)[0]
if dyrange != int(dyrange):
raise ValueError(
"The difference between the upper and lower limit of"
" 'y_range' must be a whole number."
)
if factor != int(factor):
raise ValueError("factor must have an integer value")
factor = int(factor)
if ndim == 2 and y_range is None:
raise ValueError("y_range must be specified for a 2D model")
if ndim == 1 and y_range is not None:
raise ValueError("y_range should not be input for a 1D model")
if mode == "center":
if ndim == 1:
return discretize_center_1D(model, x_range)
if 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 ValueError("Invalid mode for discretize_model.")
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
return 0.5 * (values[:, 1:] + values[:, :-1])
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.linspace(
x_range[0] - 0.5 * (1 - 1 / factor),
x_range[1] - 0.5 * (1 + 1 / factor),
num=int((x_range[1] - x_range[0]) * factor),
)
values = model(x)
# Reshape and compute mean
values = np.reshape(values, (x.size // factor, factor))
return values.mean(axis=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.linspace(
x_range[0] - 0.5 * (1 - 1 / factor),
x_range[1] - 0.5 * (1 + 1 / factor),
num=int((x_range[1] - x_range[0]) * factor),
)
y = np.linspace(
y_range[0] - 0.5 * (1 - 1 / factor),
y_range[1] - 0.5 * (1 + 1 / factor),
num=int((y_range[1] - y_range[0]) * 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)
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(
func=lambda y, x: model(x, y),
a=x[i],
b=x[i + 1],
gfun=lambda x: y[j],
hfun=lambda x: y[j + 1],
)[0]
return values
