# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
This module contains the convolution and filter functionalities of astropy.
A few conceptual notes:
A filter kernel is mainly characterized by its response function. In the 1D
case we speak of "impulse response function", in the 2D case we call it
"point spread function". This response function is given for every kernel
by an astropy ParametricModel, which is evaluated on a grid to obtain a filter
array, which can then be applied to binned data.
The model is centered on the array and should have an amplitude such that the array
integrates to one per default.
Currently only symmetric 2D kernels are supported.
"""
from __future__ import division
import warnings
import copy
import numpy as np
from ..utils.exceptions import AstropyUserWarning
from .utils import (discretize_model, add_kernel_arrays_1D,
add_kernel_arrays_2D)
MAX_NORMALIZATION = 100
[docs]class Kernel(object):
"""
Convolution kernel base class.
Parameters
----------
array : ndarray
Kernel array.
"""
_separable = False
_is_bool = True
_model = None
def __init__(self, array):
self._array = array
self._normalization = 1. / self._array.sum()
@property
[docs] def truncation(self):
"""
Deviation from the normalization to one.
"""
return self._truncation
@property
[docs] def is_bool(self):
"""
Indicates if kernel is bool.
If the kernel is bool the multiplication in the convolution could
be omitted, to increase the performance.
"""
return self._is_bool
@property
[docs] def model(self):
"""
Kernel response model.
"""
return self._model
@property
[docs] def dimension(self):
"""
Kernel dimension.
"""
return self.array.ndim
@property
[docs] def center(self):
"""
Index of the kernel center.
"""
return [axes_size // 2 for axes_size in self._array.shape]
@property
[docs] def normalization(self):
"""
Kernel normalization factor
"""
return self._normalization
[docs] def normalize(self, mode='integral'):
"""
Force normalization of filter kernel.
Parameters
----------
mode : str
One of the following modes:
* 'integral' (default)
Kernel normalized such that its integral = 1.
* 'peak'
Kernel normalized such that its peak = 1.
"""
# There are kernel that sum to zero and
# the user should be warned in this case
if np.abs(self._normalization) > MAX_NORMALIZATION:
warnings.warn("Normalization factor of kernel is "
"exceptionally large > {0}.".format(MAX_NORMALIZATION),
AstropyUserWarning)
if mode == 'integral':
self._array *= self._normalization
if mode == 'peak':
self._array /= self._array.max()
self._normalization = 1. / self._array.sum()
@property
[docs] def shape(self):
"""
Shape of the kernel array.
"""
return self._array.shape
@property
[docs] def separable(self):
"""
Indicates if the filter kernel is separable.
A 2D filter is separable, when its filter array can be written as the
outer product of two 1D arrays.
If a filter kernel is separable, higher dimension convolutions will be
performed by applying the 1D filter array consecutively on every dimension.
This is significantly faster, than using a filter array with the same
dimension.
"""
return self._separable
@property
[docs] def array(self):
"""
Filter kernel array.
"""
return self._array
def __add__(self, kernel):
"""
Add two filter kernels.
"""
return kernel_arithmetics(self, kernel, 'add')
def __sub__(self, kernel):
"""
Subtract two filter kernels.
"""
return kernel_arithmetics(self, kernel, 'sub')
def __mul__(self, value):
"""
Multiply kernel with number or convolve two kernels.
"""
return kernel_arithmetics(self, value, "mul")
def __rmul__(self, value):
"""
Multiply kernel with number or convolve two kernels.
"""
return kernel_arithmetics(self, value, "mul")
def __array__(self):
"""
Array representation of the kernel.
"""
return self._array
[docs]class Kernel1D(Kernel):
"""
Base class for 1D filter kernels.
Parameters
----------
width : number
Width of the filter kernel.
x_size : odd int, optional
Size of the kernel array. Default = 8 * width.
mode : str, optional
One of the following discretization 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.
* 'oversample'
Discretize model by taking the average
on an oversampled grid.
* 'integrate'
Discretize model by integrating the
model over the bin.
factor : number, optional
Factor of oversampling. Default factor = 10.
"""
def __init__(self, model=None, x_size=None, array=None, **kwargs):
# Initialize from model
if array is None:
if x_size is None:
x_size = self._default_size
elif x_size != int(x_size):
raise TypeError("x_size should be an integer")
# Set ranges where to evaluate the model
if x_size % 2 == 0: # even kernel
x_range = (-(int(x_size)) // 2 + 0.5, (int(x_size)) // 2 + 0.5)
else: # odd kernel
x_range = (-(int(x_size) - 1) // 2, (int(x_size) - 1) // 2 + 1)
array = discretize_model(self._model, x_range, **kwargs)
# Initialize from array
elif array is not None:
self._model = None
else:
raise TypeError("Must specify either array or model.")
super(Kernel1D, self).__init__(array)
[docs]class Kernel2D(Kernel):
"""
Base class for 2D filter kernels.
Parameters
----------
width : number
Width of the filter kernel.
x_size : odd int, optional
Size in x direction of the kernel array. Default = 8 * width.
y_size : odd int, optional
Size in y direction of the kernel array. Default = 8 * width.
mode : str, optional
One of the following discretization modes:
* 'center' (default)
Discretize model by taking the value
at the center of the bin.
* 'linear_interp'
Discretize model by performing a bilinear interpolation
between the values at the corners of the bin.
* 'oversample'
Discretize model by taking the average
on an oversampled grid.
* 'integrate'
Discretize model by integrating the
model over the bin.
factor : number, optional
Factor of oversampling. Default factor = 10.
"""
def __init__(self, model=None, x_size=None, y_size=None, array=None, **kwargs):
# Initialize from model
if array is None:
if x_size is None:
x_size = self._default_size
elif x_size != int(x_size):
raise TypeError("x_size should be an integer")
if y_size is None:
y_size = x_size
elif x_size != int(x_size):
raise TypeError("y_size should be an integer")
# Set ranges where to evaluate the model
if x_size % 2 == 0: # even kernel
x_range = (-(int(x_size)) // 2 + 0.5, (int(x_size)) // 2 + 0.5)
else: # odd kernel
x_range = (-(int(x_size) - 1) // 2, (int(x_size) - 1) // 2 + 1)
if y_size % 2 == 0: # even kernel
y_range = (-(int(y_size)) // 2 + 0.5, (int(y_size)) // 2 + 0.5)
else: # odd kernel
y_range = (-(int(y_size) - 1) // 2, (int(y_size) - 1) // 2 + 1)
array = discretize_model(self._model, x_range, y_range, **kwargs)
# Initialize from array
elif array is not None:
self._model = None
else:
raise TypeError("Must specify either array or model.")
super(Kernel2D, self).__init__(array)
[docs]def kernel_arithmetics(kernel, value, operation):
"""
Add, subtract or multiply two kernels.
Parameters
----------
kernel : astropy.convolution.kernel
Kernel instance
values : kernel, float or int
Value to operate with
operation : str
One of the following operations:
* 'add'
Add two kernels
* 'sub'
Subtract two kernels
* 'mul'
Multiply kernel with number or convolve two kernels.
"""
# 1D kernels
if isinstance(kernel, Kernel1D) and isinstance(value, Kernel1D):
if operation == "add":
new_array = add_kernel_arrays_1D(kernel.array, value.array)
if operation == "sub":
new_array = add_kernel_arrays_1D(kernel.array, -value.array)
if operation == "mul":
raise Exception("Kernel operation not supported. Maybe you want to"
"use convolve(kernel1, kernel2) instead.")
new_kernel = Kernel1D(array=new_array)
new_kernel._separable = kernel._separable and value._separable
new_kernel._is_bool = kernel._is_bool or value._is_bool
# 2D kernels
elif isinstance(kernel, Kernel2D) and isinstance(value, Kernel2D):
if operation == "add":
new_array = add_kernel_arrays_2D(kernel.array, value.array)
if operation == "sub":
new_array = add_kernel_arrays_2D(kernel.array, -value.array)
if operation == "mul":
raise Exception("Kernel operation not supported. Maybe you want to"
"use convolve(kernel1, kernel2) instead.")
new_kernel = Kernel2D(array=new_array)
new_kernel._separable = kernel._separable and value._separable
new_kernel._is_bool = kernel._is_bool or value._is_bool
# kernel and number
elif ((isinstance(kernel, Kernel1D) or isinstance(kernel, Kernel2D))
and isinstance(value, (int, float))):
if operation == "mul":
new_kernel = copy.copy(kernel)
new_kernel._array *= value
new_kernel._normalization /= value
else:
raise Exception("Kernel operation not supported.")
else:
raise Exception("Operations between 1D and 2D kernels are not supported.")
return new_kernel