testbed/astropy__astropy/astropy/convolution/kernels.py

# Licensed under a 3-clause BSD style license - see LICENSE.rst

import math

import numpy as np

from .core import Kernel1D, Kernel2D, Kernel
from .utils import has_even_axis, raise_even_kernel_exception
from astropy.modeling import models
from astropy.modeling.core import Fittable1DModel, Fittable2DModel
from astropy.utils.decorators import deprecated_renamed_argument

__all__ = ['Gaussian1DKernel', 'Gaussian2DKernel', 'CustomKernel',
           'Box1DKernel', 'Box2DKernel', 'Tophat2DKernel',
           'Trapezoid1DKernel', 'MexicanHat1DKernel', 'MexicanHat2DKernel',
           'AiryDisk2DKernel', 'Moffat2DKernel', 'Model1DKernel',
           'Model2DKernel', 'TrapezoidDisk2DKernel', 'Ring2DKernel']


def _round_up_to_odd_integer(value):
    i = math.ceil(value)
    if i % 2 == 0:
        return i + 1
    else:
        return i


class Gaussian1DKernel(Kernel1D):
    """
    1D Gaussian filter kernel.

    The Gaussian filter is a filter with great smoothing properties. It is
    isotropic and does not produce artifacts.

    Parameters
    ----------
    stddev : number
        Standard deviation of the Gaussian kernel.
    x_size : odd int, optional
        Size of the kernel array. Default = 8 * stddev
    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. Very slow.
    factor : number, optional
        Factor of oversampling. Default factor = 10. If the factor
        is too large, evaluation can be very slow.


    See Also
    --------
    Box1DKernel, Trapezoid1DKernel, MexicanHat1DKernel


    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Gaussian1DKernel
        gauss_1D_kernel = Gaussian1DKernel(10)
        plt.plot(gauss_1D_kernel, drawstyle='steps')
        plt.xlabel('x [pixels]')
        plt.ylabel('value')
        plt.show()
    """
    _separable = True
    _is_bool = False

    def __init__(self, stddev, **kwargs):
        self._model = models.Gaussian1D(1. / (np.sqrt(2 * np.pi) * stddev),
                                        0, stddev)
        self._default_size = _round_up_to_odd_integer(8 * stddev)
        super().__init__(**kwargs)
        self._truncation = np.abs(1. - self._array.sum())


class Gaussian2DKernel(Kernel2D):
    """
    2D Gaussian filter kernel.

    The Gaussian filter is a filter with great smoothing properties. It is
    isotropic and does not produce artifacts.

    Parameters
    ----------
    x_stddev : float
        Standard deviation of the Gaussian in x before rotating by theta.
    y_stddev : float
        Standard deviation of the Gaussian in y before rotating by theta.
    theta : float
        Rotation angle in radians. The rotation angle increases
        counterclockwise.
    x_size : odd int, optional
        Size in x direction of the kernel array. Default = 8 * stddev.
    y_size : odd int, optional
        Size in y direction of the kernel array. Default = 8 * stddev.
    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.


    See Also
    --------
    Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel,
    TrapezoidDisk2DKernel, AiryDisk2DKernel, Moffat2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Gaussian2DKernel
        gaussian_2D_kernel = Gaussian2DKernel(10)
        plt.imshow(gaussian_2D_kernel, interpolation='none', origin='lower')
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()

    """
    _separable = True
    _is_bool = False

    @deprecated_renamed_argument('stddev', 'x_stddev', '3.0')
    def __init__(self, x_stddev, y_stddev=None, theta=0.0, **kwargs):
        if y_stddev is None:
            y_stddev = x_stddev
        self._model = models.Gaussian2D(1. / (2 * np.pi * x_stddev * y_stddev),
                                        0, 0, x_stddev=x_stddev,
                                        y_stddev=y_stddev, theta=theta)
        self._default_size = _round_up_to_odd_integer(
            8 * np.max([x_stddev, y_stddev]))
        super().__init__(**kwargs)
        self._truncation = np.abs(1. - self._array.sum())


class Box1DKernel(Kernel1D):
    """
    1D Box filter kernel.

    The Box filter or running mean is a smoothing filter. It is not isotropic
    and can produce artifacts, when applied repeatedly to the same data.

    By default the Box kernel uses the ``linear_interp`` discretization mode,
    which allows non-shifting, even-sized kernels.  This is achieved by
    weighting the edge pixels with 1/2. E.g a Box kernel with an effective
    smoothing of 4 pixel would have the following array: [0.5, 1, 1, 1, 0.5].


    Parameters
    ----------
    width : number
        Width of the filter kernel.
    mode : str, optional
        One of the following discretization modes:
            * 'center'
                Discretize model by taking the value
                at the center of the bin.
            * 'linear_interp' (default)
                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.

    See Also
    --------
    Gaussian1DKernel, Trapezoid1DKernel, MexicanHat1DKernel


    Examples
    --------
    Kernel response function:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Box1DKernel
        box_1D_kernel = Box1DKernel(9)
        plt.plot(box_1D_kernel, drawstyle='steps')
        plt.xlim(-1, 9)
        plt.xlabel('x [pixels]')
        plt.ylabel('value')
        plt.show()

    """
    _separable = True
    _is_bool = True

    def __init__(self, width, **kwargs):
        self._model = models.Box1D(1. / width, 0, width)
        self._default_size = _round_up_to_odd_integer(width)
        kwargs['mode'] = 'linear_interp'
        super().__init__(**kwargs)
        self._truncation = 0
        self.normalize()


class Box2DKernel(Kernel2D):
    """
    2D Box filter kernel.

    The Box filter or running mean is a smoothing filter. It is not isotropic
    and can produce artifact, when applied repeatedly to the same data.

    By default the Box kernel uses the ``linear_interp`` discretization mode,
    which allows non-shifting, even-sized kernels.  This is achieved by
    weighting the edge pixels with 1/2.


    Parameters
    ----------
    width : number
        Width of the filter kernel.
    mode : str, optional
        One of the following discretization modes:
            * 'center'
                Discretize model by taking the value
                at the center of the bin.
            * 'linear_interp' (default)
                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.


    See Also
    --------
    Gaussian2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel,
    TrapezoidDisk2DKernel, AiryDisk2DKernel, Moffat2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Box2DKernel
        box_2D_kernel = Box2DKernel(9)
        plt.imshow(box_2D_kernel, interpolation='none', origin='lower',
                   vmin=0.0, vmax=0.015)
        plt.xlim(-1, 9)
        plt.ylim(-1, 9)
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()
    """
    _separable = True
    _is_bool = True

    def __init__(self, width, **kwargs):
        self._model = models.Box2D(1. / width ** 2, 0, 0, width, width)
        self._default_size = _round_up_to_odd_integer(width)
        kwargs['mode'] = 'linear_interp'
        super().__init__(**kwargs)
        self._truncation = 0
        self.normalize()


class Tophat2DKernel(Kernel2D):
    """
    2D Tophat filter kernel.

    The Tophat filter is an isotropic smoothing filter. It can produce
    artifacts when applied repeatedly on the same data.

    Parameters
    ----------
    radius : int
        Radius 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 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.


    See Also
    --------
    Gaussian2DKernel, Box2DKernel, MexicanHat2DKernel, Ring2DKernel,
    TrapezoidDisk2DKernel, AiryDisk2DKernel, Moffat2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Tophat2DKernel
        tophat_2D_kernel = Tophat2DKernel(40)
        plt.imshow(tophat_2D_kernel, interpolation='none', origin='lower')
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()

    """
    def __init__(self, radius, **kwargs):
        self._model = models.Disk2D(1. / (np.pi * radius ** 2), 0, 0, radius)
        self._default_size = _round_up_to_odd_integer(2 * radius)
        super().__init__(**kwargs)
        self._truncation = 0


class Ring2DKernel(Kernel2D):
    """
    2D Ring filter kernel.

    The Ring filter kernel is the difference between two Tophat kernels of
    different width. This kernel is useful for, e.g., background estimation.

    Parameters
    ----------
    radius_in : number
        Inner radius of the ring kernel.
    width : number
        Width of the ring 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 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.

    See Also
    --------
    Gaussian2DKernel, Box2DKernel, Tophat2DKernel, MexicanHat2DKernel,
    Ring2DKernel, AiryDisk2DKernel, Moffat2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Ring2DKernel
        ring_2D_kernel = Ring2DKernel(9, 8)
        plt.imshow(ring_2D_kernel, interpolation='none', origin='lower')
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()
    """
    def __init__(self, radius_in, width, **kwargs):
        radius_out = radius_in + width
        self._model = models.Ring2D(1. / (np.pi * (radius_out ** 2 - radius_in ** 2)),
                                    0, 0, radius_in, width)
        self._default_size = _round_up_to_odd_integer(2 * radius_out)
        super().__init__(**kwargs)
        self._truncation = 0


class Trapezoid1DKernel(Kernel1D):
    """
    1D trapezoid kernel.

    Parameters
    ----------
    width : number
        Width of the filter kernel, defined as the width of the constant part,
        before it begins to slope down.
    slope : number
        Slope of the filter kernel's tails
    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.

    See Also
    --------
    Box1DKernel, Gaussian1DKernel, MexicanHat1DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Trapezoid1DKernel
        trapezoid_1D_kernel = Trapezoid1DKernel(17, slope=0.2)
        plt.plot(trapezoid_1D_kernel, drawstyle='steps')
        plt.xlabel('x [pixels]')
        plt.ylabel('amplitude')
        plt.xlim(-1, 28)
        plt.show()
    """
    _is_bool = False

    def __init__(self, width, slope=1., **kwargs):
        self._model = models.Trapezoid1D(1, 0, width, slope)
        self._default_size = _round_up_to_odd_integer(width + 2. / slope)
        super().__init__(**kwargs)
        self._truncation = 0
        self.normalize()


class TrapezoidDisk2DKernel(Kernel2D):
    """
    2D trapezoid kernel.

    Parameters
    ----------
    radius : number
        Width of the filter kernel, defined as the width of the constant part,
        before it begins to slope down.
    slope : number
        Slope of the filter kernel's tails
    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.

    See Also
    --------
    Gaussian2DKernel, Box2DKernel, Tophat2DKernel, MexicanHat2DKernel,
    Ring2DKernel, AiryDisk2DKernel, Moffat2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import TrapezoidDisk2DKernel
        trapezoid_2D_kernel = TrapezoidDisk2DKernel(20, slope=0.2)
        plt.imshow(trapezoid_2D_kernel, interpolation='none', origin='lower')
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()

    """
    _is_bool = False

    def __init__(self, radius, slope=1., **kwargs):
        self._model = models.TrapezoidDisk2D(1, 0, 0, radius, slope)
        self._default_size = _round_up_to_odd_integer(2 * radius + 2. / slope)
        super().__init__(**kwargs)
        self._truncation = 0
        self.normalize()


class MexicanHat1DKernel(Kernel1D):
    """
    1D Mexican hat filter kernel.

    The Mexican Hat, or inverted Gaussian-Laplace filter, is a
    bandpass filter. It smooths the data and removes slowly varying
    or constant structures (e.g. Background). It is useful for peak or
    multi-scale detection.

    This kernel is derived from a normalized Gaussian function, by
    computing the second derivative. This results in an amplitude
    at the kernels center of 1. / (sqrt(2 * pi) * width ** 3). The
    normalization is the same as for `scipy.ndimage.gaussian_laplace`,
    except for a minus sign.

    Parameters
    ----------
    width : number
        Width of the filter kernel, defined as the standard deviation
        of the Gaussian function from which it is derived.
    x_size : odd int, optional
        Size in x 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 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.


    See Also
    --------
    Box1DKernel, Gaussian1DKernel, Trapezoid1DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import MexicanHat1DKernel
        mexicanhat_1D_kernel = MexicanHat1DKernel(10)
        plt.plot(mexicanhat_1D_kernel, drawstyle='steps')
        plt.xlabel('x [pixels]')
        plt.ylabel('value')
        plt.show()

    """
    _is_bool = True

    def __init__(self, width, **kwargs):
        amplitude = 1.0 / (np.sqrt(2 * np.pi) * width ** 3)
        self._model = models.MexicanHat1D(amplitude, 0, width)
        self._default_size = _round_up_to_odd_integer(8 * width)
        super().__init__(**kwargs)
        self._truncation = np.abs(self._array.sum() / self._array.size)


class MexicanHat2DKernel(Kernel2D):
    """
    2D Mexican hat filter kernel.

    The Mexican Hat, or inverted Gaussian-Laplace filter, is a
    bandpass filter. It smooths the data and removes slowly varying
    or constant structures (e.g. Background). It is useful for peak or
    multi-scale detection.

    This kernel is derived from a normalized Gaussian function, by
    computing the second derivative. This results in an amplitude
    at the kernels center of 1. / (pi * width ** 4). The normalization
    is the same as for `scipy.ndimage.gaussian_laplace`, except
    for a minus sign.

    Parameters
    ----------
    width : number
        Width of the filter kernel, defined as the standard deviation
        of the Gaussian function from which it is derived.
    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.


    See Also
    --------
    Gaussian2DKernel, Box2DKernel, Tophat2DKernel, Ring2DKernel,
    TrapezoidDisk2DKernel, AiryDisk2DKernel, Moffat2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import MexicanHat2DKernel
        mexicanhat_2D_kernel = MexicanHat2DKernel(10)
        plt.imshow(mexicanhat_2D_kernel, interpolation='none', origin='lower')
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()
    """
    _is_bool = False

    def __init__(self, width, **kwargs):
        amplitude = 1.0 / (np.pi * width ** 4)
        self._model = models.MexicanHat2D(amplitude, 0, 0, width)
        self._default_size = _round_up_to_odd_integer(8 * width)
        super().__init__(**kwargs)
        self._truncation = np.abs(self._array.sum() / self._array.size)


class AiryDisk2DKernel(Kernel2D):
    """
    2D Airy disk kernel.

    This kernel models the diffraction pattern of a circular aperture. This
    kernel is normalized to a peak value of 1.

    Parameters
    ----------
    radius : float
        The radius of the Airy disk kernel (radius of the first zero).
    x_size : odd int, optional
        Size in x direction of the kernel array. Default = 8 * radius.
    y_size : odd int, optional
        Size in y direction of the kernel array. Default = 8 * radius.
    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.

    See Also
    --------
    Gaussian2DKernel, Box2DKernel, Tophat2DKernel, MexicanHat2DKernel,
    Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel, Moffat2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import AiryDisk2DKernel
        airydisk_2D_kernel = AiryDisk2DKernel(10)
        plt.imshow(airydisk_2D_kernel, interpolation='none', origin='lower')
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()
    """
    _is_bool = False

    def __init__(self, radius, **kwargs):
        self._model = models.AiryDisk2D(1, 0, 0, radius)
        self._default_size = _round_up_to_odd_integer(8 * radius)
        super().__init__(**kwargs)
        self.normalize()
        self._truncation = None


class Moffat2DKernel(Kernel2D):
    """
    2D Moffat kernel.

    This kernel is a typical model for a seeing limited PSF.

    Parameters
    ----------
    gamma : float
        Core width of the Moffat model.
    alpha : float
        Power index of the Moffat model.
    x_size : odd int, optional
        Size in x direction of the kernel array. Default = 8 * radius.
    y_size : odd int, optional
        Size in y direction of the kernel array. Default = 8 * radius.
    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.

    See Also
    --------
    Gaussian2DKernel, Box2DKernel, Tophat2DKernel, MexicanHat2DKernel,
    Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel

    Examples
    --------
    Kernel response:

     .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from astropy.convolution import Moffat2DKernel
        moffat_2D_kernel = Moffat2DKernel(3, 2)
        plt.imshow(moffat_2D_kernel, interpolation='none', origin='lower')
        plt.xlabel('x [pixels]')
        plt.ylabel('y [pixels]')
        plt.colorbar()
        plt.show()
    """
    _is_bool = False

    def __init__(self, gamma, alpha, **kwargs):
        # Compute amplitude, from
        # https://en.wikipedia.org/wiki/Moffat_distribution
        amplitude = (alpha - 1.0) / (np.pi * gamma * gamma)
        self._model = models.Moffat2D(amplitude, 0, 0, gamma, alpha)
        self._default_size = _round_up_to_odd_integer(4.0 * self._model.fwhm)
        super().__init__(**kwargs)
        self.normalize()
        self._truncation = None


class Model1DKernel(Kernel1D):
    """
    Create kernel from 1D model.

    The model has to be centered on x = 0.

    Parameters
    ----------
    model : `~astropy.modeling.Fittable1DModel`
        Kernel response function model
    x_size : odd int, optional
        Size in x 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 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.

    Raises
    ------
    TypeError
        If model is not an instance of `~astropy.modeling.Fittable1DModel`

    See also
    --------
    Model2DKernel : Create kernel from `~astropy.modeling.Fittable2DModel`
    CustomKernel : Create kernel from list or array

    Examples
    --------
    Define a Gaussian1D model:

        >>> from astropy.modeling.models import Gaussian1D
        >>> from astropy.convolution.kernels import Model1DKernel
        >>> gauss = Gaussian1D(1, 0, 2)

    And create a custom one dimensional kernel from it:

        >>> gauss_kernel = Model1DKernel(gauss, x_size=9)

    This kernel can now be used like a usual Astropy kernel.
    """
    _separable = False
    _is_bool = False

    def __init__(self, model, **kwargs):
        if isinstance(model, Fittable1DModel):
            self._model = model
        else:
            raise TypeError("Must be Fittable1DModel")
        super().__init__(**kwargs)


class Model2DKernel(Kernel2D):
    """
    Create kernel from 2D model.

    The model has to be centered on x = 0 and y = 0.

    Parameters
    ----------
    model : `~astropy.modeling.Fittable2DModel`
        Kernel response function model
    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.

    Raises
    ------
    TypeError
        If model is not an instance of `~astropy.modeling.Fittable2DModel`

    See also
    --------
    Model1DKernel : Create kernel from `~astropy.modeling.Fittable1DModel`
    CustomKernel : Create kernel from list or array

    Examples
    --------
    Define a Gaussian2D model:

        >>> from astropy.modeling.models import Gaussian2D
        >>> from astropy.convolution.kernels import Model2DKernel
        >>> gauss = Gaussian2D(1, 0, 0, 2, 2)

    And create a custom two dimensional kernel from it:

        >>> gauss_kernel = Model2DKernel(gauss, x_size=9)

    This kernel can now be used like a usual astropy kernel.

    """
    _is_bool = False
    _separable = False

    def __init__(self, model, **kwargs):
        self._separable = False
        if isinstance(model, Fittable2DModel):
            self._model = model
        else:
            raise TypeError("Must be Fittable2DModel")
        super().__init__(**kwargs)


class PSFKernel(Kernel2D):
    """
    Initialize filter kernel from astropy PSF instance.
    """
    _separable = False

    def __init__(self):
        raise NotImplementedError('Not yet implemented')


class CustomKernel(Kernel):
    """
    Create filter kernel from list or array.

    Parameters
    ----------
    array : list or array
        Filter kernel array. Size must be odd.

    Raises
    ------
    TypeError
        If array is not a list or array.
    KernelSizeError
        If array size is even.

    See also
    --------
    Model2DKernel, Model1DKernel

    Examples
    --------
    Define one dimensional array:

        >>> from astropy.convolution.kernels import CustomKernel
        >>> import numpy as np
        >>> array = np.array([1, 2, 3, 2, 1])
        >>> kernel = CustomKernel(array)
        >>> kernel.dimension
        1

    Define two dimensional array:

        >>> array = np.array([[1, 1, 1], [1, 2, 1], [1, 1, 1]])
        >>> kernel = CustomKernel(array)
        >>> kernel.dimension
        2
    """
    def __init__(self, array):
        self.array = array
        super().__init__(self._array)

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

    @array.setter
    def array(self, array):
        """
        Filter kernel array setter
        """
        if isinstance(array, np.ndarray):
            self._array = array.astype(np.float64)
        elif isinstance(array, list):
            self._array = np.array(array, dtype=np.float64)
        else:
            raise TypeError("Must be list or array.")

        # Check if array is odd in all axes
        if has_even_axis(self):
            raise_even_kernel_exception()

        # Check if array is bool
        ones = self._array == 1.
        zeros = self._array == 0
        self._is_bool = bool(np.all(np.logical_or(ones, zeros)))

        self._truncation = 0.0