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# 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

    from .utils import (
        KernelArithmeticError,
        add_kernel_arrays_1D,
        add_kernel_arrays_2D,
        discretize_model,
    )

    MAX_NORMALIZATION = 100

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

    class Kernel:
        """
        Convolution kernel base class.

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

        _separable = False
        _is_bool = True
        _model = None

        # numpy should not try to do any arithmetic
        __array_ufunc__ = 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]

        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 __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, dtype=None, copy=None):
            """
            Array representation of the kernel.
            """
            return self._array

    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)

    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)

    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.
        operation : {'add', 'sub', 'mul'}
            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)
            elif operation == "sub":
                new_array = add_kernel_arrays_1D(kernel.array, -value.array)
            elif operation == "mul":
                raise KernelArithmeticError(
                    "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)
            elif operation == "sub":
                new_array = add_kernel_arrays_2D(kernel.array, -value.array)
            elif operation == "mul":
                raise KernelArithmeticError(
                    "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, Kernel2D)) and np.isscalar(value):
            if operation != "mul":
                raise KernelArithmeticError("Kernel operation not supported.")
            new_kernel = copy.copy(kernel)
            new_kernel._array *= value
        else:
            raise KernelArithmeticError("Kernel operation not supported.")
        return new_kernel