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# Source code for astropy.convolution.utils

    # Licensed under a 3-clause BSD style license - see LICENSE.rst
    import numpy as np

    from astropy.modeling.core import Model, custom_model

    __all__ = ["discretize_model", "KernelSizeError"]

    class DiscretizationError(Exception):
        """
        Called when discretization of models goes wrong.
        """

    class KernelSizeError(Exception):
        """
        Called when size of kernels is even.
        """

    def has_even_axis(array):
        if isinstance(array, (list, tuple)):
            return not len(array) % 2
        else:
            return any(not axes_size % 2 for axes_size in array.shape)

    def raise_even_kernel_exception():
        raise KernelSizeError("Kernel size must be odd in all axes.")

    def add_kernel_arrays_1D(array_1, array_2):
        """
        Add two 1D kernel arrays of different size.

        The arrays are added with the centers lying upon each other.
        """
        if array_1.size > array_2.size:
            new_array = array_1.copy()
            center = array_1.size // 2
            slice_ = slice(center - array_2.size // 2, center + array_2.size // 2 + 1)
            new_array[slice_] += array_2
            return new_array
        elif array_2.size > array_1.size:
            new_array = array_2.copy()
            center = array_2.size // 2
            slice_ = slice(center - array_1.size // 2, center + array_1.size // 2 + 1)
            new_array[slice_] += array_1
            return new_array
        return array_2 + array_1

    def add_kernel_arrays_2D(array_1, array_2):
        """
        Add two 2D kernel arrays of different size.

        The arrays are added with the centers lying upon each other.
        """
        if array_1.size > array_2.size:
            new_array = array_1.copy()
            center = [axes_size // 2 for axes_size in array_1.shape]
            slice_x = slice(
                center[1] - array_2.shape[1] // 2, center[1] + array_2.shape[1] // 2 + 1
            )
            slice_y = slice(
                center[0] - array_2.shape[0] // 2, center[0] + array_2.shape[0] // 2 + 1
            )
            new_array[slice_y, slice_x] += array_2
            return new_array
        elif array_2.size > array_1.size:
            new_array = array_2.copy()
            center = [axes_size // 2 for axes_size in array_2.shape]
            slice_x = slice(
                center[1] - array_1.shape[1] // 2, center[1] + array_1.shape[1] // 2 + 1
            )
            slice_y = slice(
                center[0] - array_1.shape[0] // 2, center[0] + array_1.shape[0] // 2 + 1
            )
            new_array[slice_y, slice_x] += array_1
            return new_array
        return array_2 + array_1

    def discretize_model(model, x_range, y_range=None, mode="center", factor=10):
        """
        Function to evaluate analytical model functions on a grid.

        So far the function can only deal with pixel coordinates.

        Parameters
        ----------
        model : `~astropy.modeling.Model` or callable.
            Analytic model function to be discretized. Callables, which are not an
            instances of `~astropy.modeling.Model` are passed to
            `~astropy.modeling.custom_model` and then evaluated.
        x_range : tuple
            x range in which the model is evaluated. The difference between the
            upper an lower limit must be a whole number, so that the output array
            size is well defined.
        y_range : tuple, optional
            y range in which the model is evaluated. The difference between the
            upper an lower limit must be a whole number, so that the output array
            size is well defined. Necessary only for 2D models.
        mode : str, optional
            One of the following 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.
                    For 2D models interpolation is bilinear.
                * ``'oversample'``
                    Discretize model by taking the average
                    on an oversampled grid.
                * ``'integrate'``
                    Discretize model by integrating the model
                    over the bin using `scipy.integrate.quad`.
                    Very slow.
        factor : float or int
            Factor of oversampling. Default = 10.

        Returns
        -------
        array : `numpy.array`
            Model value array

        Notes
        -----
        The ``oversample`` mode allows to conserve the integral on a subpixel
        scale. Here is the example of a normalized Gaussian1D:

        .. plot::
            :include-source:

            import matplotlib.pyplot as plt
            import numpy as np
            from astropy.modeling.models import Gaussian1D
            from astropy.convolution.utils import discretize_model
            gauss_1D = Gaussian1D(1 / (0.5 * np.sqrt(2 * np.pi)), 0, 0.5)
            y_center = discretize_model(gauss_1D, (-2, 3), mode='center')
            y_corner = discretize_model(gauss_1D, (-2, 3), mode='linear_interp')
            y_oversample = discretize_model(gauss_1D, (-2, 3), mode='oversample')
            plt.plot(y_center, label='center sum = {0:3f}'.format(y_center.sum()))
            plt.plot(y_corner, label='linear_interp sum = {0:3f}'.format(y_corner.sum()))
            plt.plot(y_oversample, label='oversample sum = {0:3f}'.format(y_oversample.sum()))
            plt.xlabel('pixels')
            plt.ylabel('value')
            plt.legend()
            plt.show()

        """
        if not callable(model):
            raise TypeError("Model must be callable.")
        if not isinstance(model, Model):
            model = custom_model(model)()
        ndim = model.n_inputs
        if ndim > 2:
            raise ValueError("discretize_model only supports 1-d and 2-d models.")

        if not float(np.diff(x_range)).is_integer():
            raise ValueError(
                "The difference between the upper and lower limit of"
                " 'x_range' must be a whole number."
            )

        if y_range:
            if not float(np.diff(y_range)).is_integer():
                raise ValueError(
                    "The difference between the upper and lower limit of"
                    " 'y_range' must be a whole number."
                )

        if ndim == 2 and y_range is None:
            raise ValueError("y range not specified, but model is 2-d")
        if ndim == 1 and y_range is not None:
            raise ValueError("y range specified, but model is only 1-d.")
        if mode == "center":
            if ndim == 1:
                return discretize_center_1D(model, x_range)
            elif ndim == 2:
                return discretize_center_2D(model, x_range, y_range)
        elif mode == "linear_interp":
            if ndim == 1:
                return discretize_linear_1D(model, x_range)
            if ndim == 2:
                return discretize_bilinear_2D(model, x_range, y_range)
        elif mode == "oversample":
            if ndim == 1:
                return discretize_oversample_1D(model, x_range, factor)
            if ndim == 2:
                return discretize_oversample_2D(model, x_range, y_range, factor)
        elif mode == "integrate":
            if ndim == 1:
                return discretize_integrate_1D(model, x_range)
            if ndim == 2:
                return discretize_integrate_2D(model, x_range, y_range)
        else:
            raise DiscretizationError("Invalid mode.")

    def discretize_center_1D(model, x_range):
        """
        Discretize model by taking the value at the center of the bin.
        """
        x = np.arange(*x_range)
        return model(x)

    def discretize_center_2D(model, x_range, y_range):
        """
        Discretize model by taking the value at the center of the pixel.
        """
        x = np.arange(*x_range)
        y = np.arange(*y_range)
        x, y = np.meshgrid(x, y)
        return model(x, y)

    def discretize_linear_1D(model, x_range):
        """
        Discretize model by performing a linear interpolation.
        """
        # Evaluate model 0.5 pixel outside the boundaries
        x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
        values_intermediate_grid = model(x)
        return 0.5 * (values_intermediate_grid[1:] + values_intermediate_grid[:-1])

    def discretize_bilinear_2D(model, x_range, y_range):
        """
        Discretize model by performing a bilinear interpolation.
        """
        # Evaluate model 0.5 pixel outside the boundaries
        x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
        y = np.arange(y_range[0] - 0.5, y_range[1] + 0.5)
        x, y = np.meshgrid(x, y)
        values_intermediate_grid = model(x, y)

        # Mean in y direction
        values = 0.5 * (values_intermediate_grid[1:, :] + values_intermediate_grid[:-1, :])
        # Mean in x direction
        values = 0.5 * (values[:, 1:] + values[:, :-1])
        return values

    def discretize_oversample_1D(model, x_range, factor=10):
        """
        Discretize model by taking the average on an oversampled grid.
        """
        # Evaluate model on oversampled grid
        x = np.linspace(
            x_range[0] - 0.5 * (1 - 1 / factor),
            x_range[1] - 0.5 * (1 + 1 / factor),
            num=int((x_range[1] - x_range[0]) * factor),
        )

        values = model(x)

        # Reshape and compute mean
        values = np.reshape(values, (x.size // factor, factor))
        return values.mean(axis=1)

    def discretize_oversample_2D(model, x_range, y_range, factor=10):
        """
        Discretize model by taking the average on an oversampled grid.
        """
        # Evaluate model on oversampled grid
        x = np.linspace(
            x_range[0] - 0.5 * (1 - 1 / factor),
            x_range[1] - 0.5 * (1 + 1 / factor),
            num=int((x_range[1] - x_range[0]) * factor),
        )
        y = np.linspace(
            y_range[0] - 0.5 * (1 - 1 / factor),
            y_range[1] - 0.5 * (1 + 1 / factor),
            num=int((y_range[1] - y_range[0]) * factor),
        )

        x_grid, y_grid = np.meshgrid(x, y)
        values = model(x_grid, y_grid)

        # Reshape and compute mean
        shape = (y.size // factor, factor, x.size // factor, factor)
        values = np.reshape(values, shape)
        return values.mean(axis=3).mean(axis=1)

    def discretize_integrate_1D(model, x_range):
        """
        Discretize model by integrating numerically the model over the bin.
        """
        from scipy.integrate import quad

        # Set up grid
        x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
        values = np.array([])

        # Integrate over all bins
        for i in range(x.size - 1):
            values = np.append(values, quad(model, x[i], x[i + 1])[0])
        return values

    def discretize_integrate_2D(model, x_range, y_range):
        """
        Discretize model by integrating the model over the pixel.
        """
        from scipy.integrate import dblquad

        # Set up grid
        x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5)
        y = np.arange(y_range[0] - 0.5, y_range[1] + 0.5)
        values = np.empty((y.size - 1, x.size - 1))

        # Integrate over all pixels
        for i in range(x.size - 1):
            for j in range(y.size - 1):
                values[j, i] = dblquad(
                    func=lambda y, x: model(x, y),
                    a=x[i],
                    b=x[i + 1],
                    gfun=lambda x: y[j],
                    hfun=lambda x: y[j + 1],
                )[0]
        return values