astropy:docs

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 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 if self._array.sum() == 0: self._normalization = np.inf else: 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.isinf(self._normalization): warnings.warn('Kernel cannot be normalized because the ' 'normalization factor is infinite.', AstropyUserWarning) return 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': np.divide(self._array, self._array.max(), self.array) 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

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