# Source code for astropy.convolution.core

```# 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 `FittableModel`, 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.
"""

import copy
import warnings

import numpy as np

from astropy.utils.exceptions import AstropyUserWarning

MAX_NORMALIZATION = 100

__all__ = ["Kernel", "Kernel1D", "Kernel2D", "kernel_arithmetics"]

[docs]
class Kernel:
"""
Convolution kernel base class.

Parameters
----------
array : ndarray
Kernel array.
"""

_separable = False
_is_bool = True
_model = None

def __init__(self, array):
self._array = np.asanyarray(array)

@property
def truncation(self):
"""
Absolute deviation of the sum of the kernel array values from
one.
"""
return np.abs(1.0 - self._array.sum())

@property
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
def model(self):
"""
Kernel response model.
"""
return self._model

@property
def dimension(self):
"""
Kernel dimension.
"""
return self.array.ndim

@property
def center(self):
"""
Index of the kernel center.
"""
return [axes_size // 2 for axes_size in self._array.shape]

[docs]
def normalize(self, mode="integral"):
"""
Normalize the filter kernel.

Parameters
----------
mode : {'integral', 'peak'}
One of the following modes:
* 'integral' (default)
Kernel is normalized such that its integral = 1.
* 'peak'
Kernel is normalized such that its peak = 1.
"""
if mode == "integral":
normalization = self._array.sum()
elif mode == "peak":
normalization = self._array.max()
else:
raise ValueError("invalid mode, must be 'integral' or 'peak'")

# Warn the user for kernels that sum to zero
if normalization == 0:
warnings.warn(
"The kernel cannot be normalized because it sums to zero.",
AstropyUserWarning,
)
else:
np.divide(self._array, normalization, self._array)

self._kernel_sum = self._array.sum()

@property
def shape(self):
"""
Shape of the kernel array.
"""
return self._array.shape

@property
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
def array(self):
"""
Filter kernel array.
"""
return self._array

"""
"""

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

def __array_wrap__(self, array, context=None):
"""
Wrapper for multiplication with numpy arrays.
"""
if type(context) == np.ufunc:
return NotImplemented
else:
return array

[docs]
class Kernel1D(Kernel):
"""
Base class for 1D filter kernels.

Parameters
----------
model : `~astropy.modeling.FittableModel`
Model to be evaluated.
x_size : int or None, optional
Size of the kernel array. Default = ⌊8*width+1⌋.
Only used if ``array`` is None.
array : ndarray or None, optional
Kernel array.
width : number
Width of the filter kernel.
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 self._model:
if array is not None:
# Reject "array" keyword for kernel models, to avoid them not being
# populated as expected.
raise TypeError("Array argument not allowed for kernel models.")

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 None:
raise TypeError("Must specify either array or model.")

super().__init__(array)

[docs]
class Kernel2D(Kernel):
"""
Base class for 2D filter kernels.

Parameters
----------
model : `~astropy.modeling.FittableModel`
Model to be evaluated.
x_size : int, optional
Size in x direction of the kernel array. Default = ⌊8*width + 1⌋.
Only used if ``array`` is None.
y_size : int, optional
Size in y direction of the kernel array. Default = ⌊8*width + 1⌋.
Only used if ``array`` is None,
array : ndarray or None, optional
Kernel array. Default is None.
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.
width : number
Width of the filter kernel.
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 self._model:
if array is not None:
# Reject "array" keyword for kernel models, to avoid them not being
# populated as expected.
raise TypeError("Array argument not allowed for kernel models.")
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 y_size != int(y_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 None:
raise TypeError("Must specify either array or model.")

super().__init__(array)

[docs]
def kernel_arithmetics(kernel, value, operation):
"""
Add, subtract or multiply two kernels.

Parameters
----------
kernel : `astropy.convolution.Kernel`
Kernel instance.
value : `astropy.convolution.Kernel`, float, or int
Value to operate with.
One of the following operations:
* '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 == "sub":
if operation == "mul":
raise Exception(
"Kernel operation not supported. Maybe you want "
)
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 == "sub":
if operation == "mul":
raise Exception(
"Kernel operation not supported. Maybe you want "
)
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, Kernel2D)) and np.isscalar(value):
if operation == "mul":
new_kernel = copy.copy(kernel)
new_kernel._array *= value
else:
raise Exception("Kernel operation not supported.")
else:
raise Exception("Kernel operation not supported.")
return new_kernel

```