text: from numbers import Number
  from typing import Dict
  
  import numpy as np
  
  from phi import math
  from phi.math import Tensor, Shape, spatial, EMPTY_SHAPE, GLOBAL_AXIS_ORDER
  from phi.math._tensors import variable_attributes, copy_with
  
  
  class Geometry:
      """
      Abstract base class for N-dimensional shapes.
  
      Main implementing classes:
  
      * Sphere
      * box family: box (generator), Box, Cuboid, BaseBox
  
      All geometry objects support batching.
      Thereby any parameter defining the geometry can be varied along arbitrary batch dims.
      All batch dimensions are listed in Geometry.shape.
      """
  
      @property
      def center(self) -> Tensor:
          """
          Center location in single channel dimension, ordered according to GLOBAL_AXIS_ORDER
          """
          raise NotImplementedError(self)
  
      @property
      def shape(self) -> Shape:
          """
          Specifies the number of copies of the geometry as batch and spatial dimensions.
          """
          raise NotImplementedError()
  
      @property
      def volume(self) -> Tensor:
          """
          Volume of the geometry as `phi.math.Tensor`.
          The result retains all batch dimensions while collection dimensions are summed over.
          """
          raise NotImplementedError()
  
      def unstack(self, dimension: str) -> tuple:
          """
          Unstacks this Geometry along the given dimension.
          The shapes of the returned geometries are reduced by `dimension`.
  
          Args:
              dimension: dimension along which to unstack
  
          Returns:
              geometries: tuple of length equal to `geometry.shape.get_size(dimension)`
  
          """
          raise NotImplementedError()
  
      @property
      def spatial_rank(self) -> int:
          """ Number of spatial dimensions of the geometry, 1 = 1D, 2 = 2D, 3 = 3D, etc. """
          return self.shape.spatial.rank
  
      def lies_inside(self, location: Tensor) -> Tensor:
          """
          Tests whether the given location lies inside or outside of the geometry. Locations on the surface count as inside.
  
          Args:
            location: float tensor of shape (batch_size, ..., rank)
            location: Tensor:
  
          Returns:
            bool tensor of shape (*location.shape[:-1], 1).
  
          """
          raise NotImplementedError(self.__class__)
  
      def approximate_signed_distance(self, location: Tensor) -> Tensor:
          """
          Computes the approximate distance from location to the surface of the geometry.
          Locations outside return positive values, inside negative values and zero exactly at the boundary.
  
          The exact distance metric used depends on the geometry.
          The approximation holds close to the surface and the distance grows to infinity as the location is moved infinitely far from the geometry.
          The distance metric is differentiable and its gradients are bounded at every point in space.
  
          Args:
            location: float tensor of shape (batch_size, ..., rank)
            location: Tensor:
  
          Returns:
            float tensor of shape (*location.shape[:-1], 1).
  
          """
          raise NotImplementedError(self.__class__)
  
      def approximate_fraction_inside(self, other_geometry: 'Geometry', balance: Tensor or Number = 0.5) -> Tensor:
          """
          Computes the approximate overlap between the geometry and a small other geometry.
          Returns 1.0 if `other_geometry` is fully enclosed in this geometry and 0.0 if there is no overlap.
          Close to the surface of this geometry, the fraction filled is differentiable w.r.t. the location and size of `other_geometry`.
  
          To call this method on batches of geometries of same shape, pass a batched Geometry instance.
          The result tensor will match the batch shape of `other_geometry`.
  
          The result may only be accurate in special cases.
          The given geometries may be approximated as spheres or boxes using `bounding_radius()` and `bounding_half_extent()`.
  
          The default implementation of this method approximates other_geometry as a Sphere and computes the fraction using `approximate_signed_distance()`.
  
          Args:
              other_geometry: `Geometry` or geometry batch for which to compute the overlap with `self`.
              balance: Mid-level between 0 and 1, default 0.5.
                  This value is returned when exactly half of `other_geometry` lies inside `self`.
                  `0.5 < balance <= 1` makes `self` seem larger while `0 <= balance < 0.5`makes `self` seem smaller.
  
          Returns:
            fraction of cell volume lying inside the geometry. float tensor of shape (other_geometry.batch_shape, 1).
  
          """
          assert isinstance(other_geometry, Geometry)
          radius = other_geometry.bounding_radius()
          location = other_geometry.center
          distance = self.approximate_signed_distance(location)
          inside_fraction = balance - distance / radius
          inside_fraction = math.clip(inside_fraction, 0, 1)
          return inside_fraction
  
      def push(self, positions: Tensor, outward: bool = True, shift_amount: float = 0) -> Tensor:
          """
          Shifts positions either into or out of geometry.
  
          Args:
              positions: Tensor holding positions to shift
              outward: Flag for indicating inward (False) or outward (True) shift
              shift_amount: Minimum distance between positions and box boundaries after shifting
  
          Returns:
              Tensor holding shifted positions
          """
          raise NotImplementedError(self.__class__)
  
      def bounding_radius(self) -> Tensor:
          """
          Returns the radius of a Sphere object that fully encloses this geometry.
          The sphere is centered at the center of this geometry.
  
          :return: radius of type float
  
          Args:
  
          Returns:
  
          """
          raise NotImplementedError(self.__class__)
  
      def bounding_half_extent(self) -> Tensor:
          """
          The bounding half-extent sets a limit on the outer-most point for each coordinate axis.
          Each component is non-negative.
  
          Let the bounding half-extent have value `e` in dimension `d` (`extent[...,d] = e`).
          Then, no point of the geometry lies further away from its center point than `e` along `d` (in both axis directions).
  
          :return: float vector
  
          Args:
  
          Returns:
  
          """
          raise NotImplementedError(self.__class__)
  
      def shifted(self, delta: Tensor) -> 'Geometry':
          """
          Returns a translated version of this geometry.
  
          Args:
            delta: direction vector
            delta: Tensor:
  
          Returns:
            Geometry: shifted geometry
  
          """
          raise NotImplementedError(self.__class__)
  
      def rotated(self, angle) -> 'Geometry':
          """
          Returns a rotated version of this geometry.
          The geometry is rotated about its center point.
  
          Args:
            angle: scalar (2d) or vector (3D+) representing delta angle
  
          Returns:
            Geometry: rotated geometry
  
          """
          raise NotImplementedError(self.__class__)
  
      def __invert__(self):
          return _InvertedGeometry(self)
  
      def __eq__(self, other):
          """
          Slow equality check.
          Unlike `==`, this method compares all tensor elements to check whether they are equal.
          Use `==` for a faster check which only checks whether the referenced tensors are the same.
  
          See Also:
              `shallow_equals()`
          """
          if self is other:
              return True
          if not isinstance(other, type(self)):
              return False
          if self.shape != other.shape:
              return False
          c1 = {a: getattr(self, a) for a in variable_attributes(self)}
          c2 = {a: getattr(other, a) for a in variable_attributes(self)}
          for c in c1.keys():
              if c1[c] is not c2[c] and math.any(c1[c] != c2[c]):
                  return False
          return True
  
      def shallow_equals(self, other):
          """
          Quick equality check.
          May return `False` even if `other == self`.
          However, if `True` is returned, the geometries are guaranteed to be equal.
  
          The `shallow_equals()` check does not compare all tensor elements but merely checks whether the same tensors are referenced.
          """
          if self is other:
              return True
          if not isinstance(other, type(self)):
              return False
          if self.shape != other.shape:
              return False
          c1 = {a: getattr(self, a) for a in variable_attributes(self)}
          c2 = {a: getattr(other, a) for a in variable_attributes(self)}
          for c in c1.keys():
              if c1[c] is not c2[c]:
                  return False
          return True
  
      def __ne__(self, other):
          return not self == other
  
      def __hash__(self):
          raise NotImplementedError(self.__class__)
  
      def __repr__(self):
          return f"{self.__class__.__name__}{self.shape}"
  
      def __getitem__(self, item: dict):
          assert isinstance(item, dict), "Index must be dict of type {dim: slice/int}."
          item = {dim: sel for dim, sel in item.items() if dim != 'vector'}
          attrs = {a: getattr(self, a)[item] for a in variable_attributes(self)}
          return copy_with(self, **attrs)
  
  
  class _InvertedGeometry(Geometry):
  
      def __init__(self, geometry):
          self.geometry = geometry
  
      @property
      def center(self):
          raise NotImplementedError()
  
      @property
      def shape(self):
          return self.geometry.shape
  
      def lies_inside(self, location: Tensor) -> Tensor:
          return ~self.geometry.lies_inside(location)
  
      def approximate_signed_distance(self, location: Tensor) -> Tensor:
          return -self.geometry.approximate_signed_distance(location)
  
      def approximate_fraction_inside(self, other_geometry: Geometry) -> Tensor:
          return 1 - self.geometry.approximate_fraction_inside(other_geometry)
  
      def push(self, positions: Tensor, outward: bool = True, shift_amount: float = 0) -> Tensor:
          return self.geometry.push(positions, outward=not outward, shift_amount=shift_amount)
  
      def bounding_radius(self) -> Tensor:
          raise NotImplementedError()
  
      def bounding_half_extent(self) -> Tensor:
          raise NotImplementedError()
  
      def shifted(self, delta: Tensor) -> Geometry:
          return _InvertedGeometry(self.geometry.shifted(delta))
  
      def rotated(self, angle) -> Geometry:
          return _InvertedGeometry(self.geometry.rotated(angle))
  
      def unstack(self, dimension):
          return [_InvertedGeometry(g) for g in self.geometry.unstack(dimension)]
  
      def __eq__(self, other):
          return isinstance(other, _InvertedGeometry) and self.geometry == other.geometry
  
      def __hash__(self):
          return -hash(self.geometry)
  
  
  class _NoGeometry(Geometry):
  
      @property
      def shape(self):
          return EMPTY_SHAPE
  
      @property
      def center(self):
          return 0
  
      def bounding_radius(self):
          return 0
  
      def bounding_half_extent(self):
          return 0
  
      def approximate_signed_distance(self, location):
          return math.zeros(location.shape.non_channel) + np.inf
  
      def lies_inside(self, location):
          return math.zeros(location.shape.non_channel, dtype=math.DType(bool))
  
      def approximate_fraction_inside(self, other_geometry):
          return math.zeros(other_geometry.shape)
  
      def shifted(self, delta):
          return self
  
      def rotated(self, angle):
          return self
  
      def unstack(self, dimension):
          raise AssertionError('empty geometry cannot be unstacked')
  
      def __eq__(self, other):
          return isinstance(other, _NoGeometry)
  
      def __hash__(self):
          return 1
  
  
  NO_GEOMETRY = _NoGeometry()
  
  
  class Point(Geometry):
  
      def __init__(self, location: math.Tensor):
          self._location = location
  
      @property
      def center(self) -> Tensor:
          return self._location
  
      @property
      def shape(self) -> Shape:
          return self._location.shape.without('vector')
  
      def unstack(self, dimension: str) -> tuple:
          return tuple(Point(loc) for loc in self._location.unstack(dimension))
  
      def lies_inside(self, location: Tensor) -> Tensor:
          return math.wrap(False)
  
      def approximate_signed_distance(self, location: Tensor) -> Tensor:
          return math.vec_abs(location - self._location)
  
      def push(self, positions: Tensor, outward: bool = True, shift_amount: float = 0) -> Tensor:
          return positions
  
      def bounding_radius(self) -> Tensor:
          return math.zeros()
  
      def bounding_half_extent(self) -> Tensor:
          return math.zeros()
  
      def shifted(self, delta: Tensor) -> 'Geometry':
          return Point(self._location + delta)
  
      def rotated(self, angle) -> 'Geometry':
          return self
  
      def __hash__(self):
          return hash(self._location)
  
      def _characteristics_(self) -> Dict[str, math.Tensor]:
          return {'location': self._location}
  
  
  def assert_same_rank(rank1, rank2, error_message):
      rank1_, rank2_ = _rank(rank1), _rank(rank2)
      if rank1_ is not None and rank2_ is not None:
          assert rank1_ == rank2_, 'Ranks do not match: %s and %s. %s' % (rank1_, rank2_, error_message)
  
  
  def _rank(rank):
      if rank is None:
          return None
      elif isinstance(rank, int):
          pass
      elif isinstance(rank, Geometry):
          rank = rank.spatial_rank
      elif isinstance(rank, Shape):
          rank = rank.spatial.rank
      elif isinstance(rank, Tensor):
          rank = rank.shape.spatial_rank
      else:
          raise NotImplementedError(f"{type(rank)} now allowed. Allowed are (int, Geometry, Shape, Tensor).")
      return None if rank == 0 else rank
  
  
  def _fill_spatial_with_singleton(shape: Shape):
      if shape.spatial.rank == shape.get_size('vector'):
          return shape
      else:
          assert shape.spatial.rank == 0, shape
          names = [GLOBAL_AXIS_ORDER.axis_name(i, shape.get_size('vector')) for i in range(shape.get_size('vector'))]
          return shape & spatial(**{n: 1 for n in names})
  