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# Source code for astropy.stats.spatial

    # Licensed under a 3-clause BSD style license - see LICENSE.rst
    """
    This module implements functions and classes for spatial statistics.
    """

    import math

    import numpy as np

    __all__ = ["RipleysKEstimator"]

    class RipleysKEstimator:
        """
        Estimators for Ripley's K function for two-dimensional spatial data.
        See [1]_, [2]_, [3]_, [4]_, [5]_ for detailed mathematical and
        practical aspects of those estimators.

        Parameters
        ----------
        area : float
            Area of study from which the points where observed.
        x_max, y_max : float, float, optional
            Maximum rectangular coordinates of the area of study.
            Required if ``mode == 'translation'`` or ``mode == ohser``.
        x_min, y_min : float, float, optional
            Minimum rectangular coordinates of the area of study.
            Required if ``mode == 'variable-width'`` or ``mode == ohser``.

        Examples
        --------
        >>> import numpy as np
        >>> from matplotlib import pyplot as plt # doctest: +SKIP
        >>> from astropy.stats import RipleysKEstimator
        >>> z = np.random.uniform(low=5, high=10, size=(100, 2))
        >>> Kest = RipleysKEstimator(area=25, x_max=10, y_max=10,
        ... x_min=5, y_min=5)
        >>> r = np.linspace(0, 2.5, 100)
        >>> plt.plot(r, Kest.poisson(r)) # doctest: +SKIP
        >>> plt.plot(r, Kest(data=z, radii=r, mode='none')) # doctest: +SKIP
        >>> plt.plot(r, Kest(data=z, radii=r, mode='translation')) # doctest: +SKIP
        >>> plt.plot(r, Kest(data=z, radii=r, mode='ohser')) # doctest: +SKIP
        >>> plt.plot(r, Kest(data=z, radii=r, mode='var-width')) # doctest: +SKIP
        >>> plt.plot(r, Kest(data=z, radii=r, mode='ripley')) # doctest: +SKIP

        References
        ----------
        .. [1] Peebles, P.J.E. *The large scale structure of the universe*.
           <https://ui.adsabs.harvard.edu/abs/1980lssu.book.....P>
        .. [2] Spatial descriptive statistics.
           <https://en.wikipedia.org/wiki/Spatial_descriptive_statistics>
        .. [3] Package spatstat.
           <https://cran.r-project.org/web/packages/spatstat/spatstat.pdf>
        .. [4] Cressie, N.A.C. (1991). Statistics for Spatial Data,
           Wiley, New York.
        .. [5] Stoyan, D., Stoyan, H. (1992). Fractals, Random Shapes and
           Point Fields, Akademie Verlag GmbH, Chichester.
        """

        def __init__(self, area, x_max=None, y_max=None, x_min=None, y_min=None):
            self.area = area
            self.x_max = x_max
            self.y_max = y_max
            self.x_min = x_min
            self.y_min = y_min

        @property
        def area(self):
            return self._area

        @area.setter
        def area(self, value):
            if isinstance(value, (float, int)) and value > 0:
                self._area = value
            else:
                raise ValueError(f"area is expected to be a positive number. Got {value}.")

        @property
        def y_max(self):
            return self._y_max

        @y_max.setter
        def y_max(self, value):
            if value is None or isinstance(value, (float, int)):
                self._y_max = value
            else:
                raise ValueError(
                    f"y_max is expected to be a real number or None. Got {value}."
                )

        @property
        def x_max(self):
            return self._x_max

        @x_max.setter
        def x_max(self, value):
            if value is None or isinstance(value, (float, int)):
                self._x_max = value
            else:
                raise ValueError(
                    f"x_max is expected to be a real number or None. Got {value}."
                )

        @property
        def y_min(self):
            return self._y_min

        @y_min.setter
        def y_min(self, value):
            if value is None or isinstance(value, (float, int)):
                self._y_min = value
            else:
                raise ValueError(f"y_min is expected to be a real number. Got {value}.")

        @property
        def x_min(self):
            return self._x_min

        @x_min.setter
        def x_min(self, value):
            if value is None or isinstance(value, (float, int)):
                self._x_min = value
            else:
                raise ValueError(f"x_min is expected to be a real number. Got {value}.")

        def __call__(self, data, radii, mode="none"):
            return self.evaluate(data=data, radii=radii, mode=mode)

        def _pairwise_diffs(self, data):
            npts = len(data)
            diff = np.zeros(shape=(npts * (npts - 1) // 2, 2), dtype=np.double)
            k = 0
            for i in range(npts - 1):
                size = npts - i - 1
                diff[k : k + size] = abs(data[i] - data[i + 1 :])
                k += size

            return diff

        def poisson(self, radii):
            """
            Evaluates the Ripley K function for the homogeneous Poisson process,
            also known as Complete State of Randomness (CSR).

            Parameters
            ----------
            radii : 1D array
                Set of distances in which Ripley's K function will be evaluated.

            Returns
            -------
            output : 1D array
                Ripley's K function evaluated at ``radii``.
            """

            return np.pi * radii * radii

        def Lfunction(self, data, radii, mode="none"):
            """
            Evaluates the L function at ``radii``. For parameter description
            see ``evaluate`` method.
            """

            return np.sqrt(self.evaluate(data, radii, mode=mode) / np.pi)

        def Hfunction(self, data, radii, mode="none"):
            """
            Evaluates the H function at ``radii``. For parameter description
            see ``evaluate`` method.
            """

            return self.Lfunction(data, radii, mode=mode) - radii

        def evaluate(self, data, radii, mode="none"):
            """
            Evaluates the Ripley K estimator for a given set of values ``radii``.

            Parameters
            ----------
            data : 2D array
                Set of observed points in as a n by 2 array which will be used to
                estimate Ripley's K function.
            radii : 1D array
                Set of distances in which Ripley's K estimator will be evaluated.
                Usually, it's common to consider max(radii) < (area/2)**0.5.
            mode : str
                Keyword which indicates the method for edge effects correction.
                Available methods are 'none', 'translation', 'ohser', 'var-width',
                and 'ripley'.

                * 'none'
                    this method does not take into account any edge effects
                    whatsoever.
                * 'translation'
                    computes the intersection of rectangular areas centered at
                    the given points provided the upper bounds of the
                    dimensions of the rectangular area of study. It assumes that
                    all the points lie in a bounded rectangular region satisfying
                    x_min < x_i < x_max; y_min < y_i < y_max. A detailed
                    description of this method can be found on ref [4].
                * 'ohser'
                    this method uses the isotropized set covariance function of
                    the window of study as a weight to correct for
                    edge-effects. A detailed description of this method can be
                    found on ref [4].
                * 'var-width'
                    this method considers the distance of each observed point to
                    the nearest boundary of the study window as a factor to
                    account for edge-effects. See [3] for a brief description of
                    this method.
                * 'ripley'
                    this method is known as Ripley's edge-corrected estimator.
                    The weight for edge-correction is a function of the
                    proportions of circumferences centered at each data point
                    which crosses another data point of interest. See [3] for
                    a detailed description of this method.

            Returns
            -------
            ripley : 1D array
                Ripley's K function estimator evaluated at ``radii``.
            """

            data = np.asarray(data)

            if not data.shape[1] == 2:
                raise ValueError(
                    "data must be an n by 2 array, where n is the "
                    "number of observed points."
                )

            npts = len(data)
            ripley = np.zeros(len(radii))

            if mode == "none":
                diff = self._pairwise_diffs(data)
                distances = np.hypot(diff[:, 0], diff[:, 1])
                for r in range(len(radii)):
                    ripley[r] = (distances < radii[r]).sum()

                ripley = self.area * 2.0 * ripley / (npts * (npts - 1))
            # eq. 15.11 Stoyan book page 283
            elif mode == "translation":
                diff = self._pairwise_diffs(data)
                distances = np.hypot(diff[:, 0], diff[:, 1])
                intersec_area = ((self.x_max - self.x_min) - diff[:, 0]) * (
                    (self.y_max - self.y_min) - diff[:, 1]
                )

                for r in range(len(radii)):
                    dist_indicator = distances < radii[r]
                    ripley[r] = ((1 / intersec_area) * dist_indicator).sum()

                ripley = (self.area**2 / (npts * (npts - 1))) * 2 * ripley
            # Stoyan book page 123 and eq 15.13
            elif mode == "ohser":
                diff = self._pairwise_diffs(data)
                distances = np.hypot(diff[:, 0], diff[:, 1])
                a = self.area
                b = max(
                    (self.y_max - self.y_min) / (self.x_max - self.x_min),
                    (self.x_max - self.x_min) / (self.y_max - self.y_min),
                )
                x = distances / math.sqrt(a / b)
                u = np.sqrt((x * x - 1) * (x > 1))
                v = np.sqrt((x * x - b**2) * (x < math.sqrt(b**2 + 1)) * (x > b))
                c1 = np.pi - 2 * x * (1 + 1 / b) + x * x / b
                c2 = 2 * np.arcsin((1 / x) * (x > 1)) - 1 / b - 2 * (x - u)
                c3 = (
                    2
                    * np.arcsin(
                        ((b - u * v) / (x * x)) * (x > b) * (x < math.sqrt(b**2 + 1))
                    )
                    + 2 * u
                    + 2 * v / b
                    - b
                    - (1 + x * x) / b
                )

                cov_func = (a / np.pi) * (
                    c1 * (x >= 0) * (x <= 1)
                    + c2 * (x > 1) * (x <= b)
                    + c3 * (b < x) * (x < math.sqrt(b**2 + 1))
                )

                for r in range(len(radii)):
                    dist_indicator = distances < radii[r]
                    ripley[r] = ((1 / cov_func) * dist_indicator).sum()

                ripley = (self.area**2 / (npts * (npts - 1))) * 2 * ripley
            # Cressie book eq 8.2.20 page 616
            elif mode == "var-width":
                lt_dist = np.minimum(
                    np.minimum(self.x_max - data[:, 0], self.y_max - data[:, 1]),
                    np.minimum(data[:, 0] - self.x_min, data[:, 1] - self.y_min),
                )

                for r in range(len(radii)):
                    for i in range(npts):
                        for j in range(npts):
                            if i != j:
                                diff = abs(data[i] - data[j])
                                dist = math.sqrt((diff * diff).sum())
                                if dist < radii[r] < lt_dist[i]:
                                    ripley[r] = ripley[r] + 1
                    lt_dist_sum = (lt_dist > radii[r]).sum()
                    if not lt_dist_sum == 0:
                        ripley[r] = ripley[r] / lt_dist_sum

                ripley = self.area * ripley / npts
            # Cressie book eq 8.4.22 page 640
            elif mode == "ripley":
                hor_dist = np.zeros(shape=(npts * (npts - 1)) // 2, dtype=np.double)
                ver_dist = np.zeros(shape=(npts * (npts - 1)) // 2, dtype=np.double)

                for k in range(npts - 1):
                    min_hor_dist = min(self.x_max - data[k][0], data[k][0] - self.x_min)
                    min_ver_dist = min(self.y_max - data[k][1], data[k][1] - self.y_min)
                    start = (k * (2 * (npts - 1) - (k - 1))) // 2
                    end = ((k + 1) * (2 * (npts - 1) - k)) // 2
                    hor_dist[start:end] = min_hor_dist * np.ones(npts - 1 - k)
                    ver_dist[start:end] = min_ver_dist * np.ones(npts - 1 - k)

                diff = self._pairwise_diffs(data)
                dist = np.hypot(diff[:, 0], diff[:, 1])
                dist_ind = dist <= np.hypot(hor_dist, ver_dist)

                w1 = (
                    1
                    - (
                        np.arccos(np.minimum(ver_dist, dist) / dist)
                        + np.arccos(np.minimum(hor_dist, dist) / dist)
                    )
                    / np.pi
                )
                w2 = (
                    3 / 4
                    - 0.5
                    * (
                        np.arccos(ver_dist / dist * ~dist_ind)
                        + np.arccos(hor_dist / dist * ~dist_ind)
                    )
                    / np.pi
                )

                weight = dist_ind * w1 + ~dist_ind * w2

                for r in range(len(radii)):
                    ripley[r] = ((dist < radii[r]) / weight).sum()

                ripley = self.area * 2.0 * ripley / (npts * (npts - 1))
            else:
                raise ValueError(f"mode {mode} is not implemented.")

            return ripley