435 行
15 KiB
Cython
435 行
15 KiB
Cython
"""
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Template for intervaltree
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WARNING: DO NOT edit .pxi FILE directly, .pxi is generated from .pxi.in
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"""
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from pandas._libs.algos import is_monotonic
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ctypedef fused int_scalar_t:
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int64_t
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float64_t
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ctypedef fused uint_scalar_t:
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uint64_t
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float64_t
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ctypedef fused scalar_t:
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int_scalar_t
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uint_scalar_t
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# ----------------------------------------------------------------------
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# IntervalTree
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# ----------------------------------------------------------------------
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cdef class IntervalTree(IntervalMixin):
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"""A centered interval tree
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Based off the algorithm described on Wikipedia:
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https://en.wikipedia.org/wiki/Interval_tree
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we are emulating the IndexEngine interface
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"""
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cdef readonly:
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ndarray left, right
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IntervalNode root
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object dtype
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str closed
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object _is_overlapping, _left_sorter, _right_sorter
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Py_ssize_t _na_count
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def __init__(self, left, right, closed='right', leaf_size=100):
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"""
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Parameters
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----------
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left, right : np.ndarray[ndim=1]
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Left and right bounds for each interval. Assumed to contain no
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NaNs.
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closed : {'left', 'right', 'both', 'neither'}, optional
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Whether the intervals are closed on the left-side, right-side, both
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or neither. Defaults to 'right'.
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leaf_size : int, optional
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Parameter that controls when the tree switches from creating nodes
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to brute-force search. Tune this parameter to optimize query
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performance.
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"""
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if closed not in ['left', 'right', 'both', 'neither']:
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raise ValueError("invalid option for 'closed': %s" % closed)
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left = np.asarray(left)
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right = np.asarray(right)
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self.dtype = np.result_type(left, right)
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self.left = np.asarray(left, dtype=self.dtype)
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self.right = np.asarray(right, dtype=self.dtype)
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indices = np.arange(len(left), dtype='int64')
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self.closed = closed
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# GH 23352: ensure no nan in nodes
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mask = ~np.isnan(self.left)
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self._na_count = len(mask) - mask.sum()
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self.left = self.left[mask]
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self.right = self.right[mask]
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indices = indices[mask]
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node_cls = NODE_CLASSES[str(self.dtype), closed]
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self.root = node_cls(self.left, self.right, indices, leaf_size)
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@property
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def left_sorter(self) -> np.ndarray:
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"""How to sort the left labels; this is used for binary search
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"""
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if self._left_sorter is None:
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self._left_sorter = np.argsort(self.left)
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return self._left_sorter
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@property
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def right_sorter(self) -> np.ndarray:
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"""How to sort the right labels
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"""
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if self._right_sorter is None:
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self._right_sorter = np.argsort(self.right)
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return self._right_sorter
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@property
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def is_overlapping(self) -> bool:
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"""
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Determine if the IntervalTree contains overlapping intervals.
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Cached as self._is_overlapping.
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"""
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if self._is_overlapping is not None:
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return self._is_overlapping
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# <= when both sides closed since endpoints can overlap
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op = le if self.closed == 'both' else lt
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# overlap if start of current interval < end of previous interval
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# (current and previous in terms of sorted order by left/start side)
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current = self.left[self.left_sorter[1:]]
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previous = self.right[self.left_sorter[:-1]]
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self._is_overlapping = bool(op(current, previous).any())
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return self._is_overlapping
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@property
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def is_monotonic_increasing(self) -> bool:
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"""
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Return True if the IntervalTree is monotonic increasing (only equal or
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increasing values), else False
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"""
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if self._na_count > 0:
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return False
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values = [self.right, self.left]
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sort_order = np.lexsort(values)
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return is_monotonic(sort_order, False)[0]
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def get_indexer(self, scalar_t[:] target) -> np.ndarray:
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"""Return the positions corresponding to unique intervals that overlap
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with the given array of scalar targets.
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"""
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# TODO: write get_indexer_intervals
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cdef:
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Py_ssize_t old_len
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Py_ssize_t i
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Int64Vector result
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result = Int64Vector()
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old_len = 0
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for i in range(len(target)):
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try:
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self.root.query(result, target[i])
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except OverflowError:
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# overflow -> no match, which is already handled below
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pass
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if result.data.n == old_len:
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result.append(-1)
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elif result.data.n > old_len + 1:
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raise KeyError(
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'indexer does not intersect a unique set of intervals')
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old_len = result.data.n
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return result.to_array().astype('intp')
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def get_indexer_non_unique(self, scalar_t[:] target):
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"""Return the positions corresponding to intervals that overlap with
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the given array of scalar targets. Non-unique positions are repeated.
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"""
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cdef:
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Py_ssize_t old_len
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Py_ssize_t i
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Int64Vector result, missing
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result = Int64Vector()
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missing = Int64Vector()
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old_len = 0
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for i in range(len(target)):
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try:
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self.root.query(result, target[i])
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except OverflowError:
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# overflow -> no match, which is already handled below
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pass
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if result.data.n == old_len:
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result.append(-1)
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missing.append(i)
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old_len = result.data.n
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return (result.to_array().astype('intp'),
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missing.to_array().astype('intp'))
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def __repr__(self) -> str:
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return ('<IntervalTree[{dtype},{closed}]: '
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'{n_elements} elements>'.format(
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dtype=self.dtype, closed=self.closed,
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n_elements=self.root.n_elements))
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# compat with IndexEngine interface
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def clear_mapping(self) -> None:
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pass
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cdef take(ndarray source, ndarray indices):
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"""Take the given positions from a 1D ndarray
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"""
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return PyArray_Take(source, indices, 0)
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cdef sort_values_and_indices(all_values, all_indices, subset):
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indices = take(all_indices, subset)
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values = take(all_values, subset)
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sorter = PyArray_ArgSort(values, 0, NPY_QUICKSORT)
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sorted_values = take(values, sorter)
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sorted_indices = take(indices, sorter)
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return sorted_values, sorted_indices
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# ----------------------------------------------------------------------
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# Nodes
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# ----------------------------------------------------------------------
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@cython.internal
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cdef class IntervalNode:
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cdef readonly:
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int64_t n_elements, n_center, leaf_size
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bint is_leaf_node
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def __repr__(self) -> str:
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if self.is_leaf_node:
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return (
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f"<{type(self).__name__}: {self.n_elements} elements (terminal)>"
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)
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else:
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n_left = self.left_node.n_elements
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n_right = self.right_node.n_elements
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n_center = self.n_elements - n_left - n_right
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return (
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f"<{type(self).__name__}: "
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f"pivot {self.pivot}, {self.n_elements} elements "
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f"({n_left} left, {n_right} right, {n_center} overlapping)>"
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)
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def counts(self):
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"""
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Inspect counts on this node
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useful for debugging purposes
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"""
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if self.is_leaf_node:
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return self.n_elements
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else:
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m = len(self.center_left_values)
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l = self.left_node.counts()
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r = self.right_node.counts()
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return (m, (l, r))
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# we need specialized nodes and leaves to optimize for different dtype and
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# closed values
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{{py:
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nodes = []
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for dtype in ['float64', 'int64', 'uint64']:
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for closed, cmp_left, cmp_right in [
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('left', '<=', '<'),
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('right', '<', '<='),
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('both', '<=', '<='),
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('neither', '<', '<')]:
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cmp_left_converse = '<' if cmp_left == '<=' else '<='
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cmp_right_converse = '<' if cmp_right == '<=' else '<='
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if dtype.startswith('int'):
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fused_prefix = 'int_'
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elif dtype.startswith('uint'):
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fused_prefix = 'uint_'
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elif dtype.startswith('float'):
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fused_prefix = ''
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nodes.append((dtype, dtype.title(),
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closed, closed.title(),
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cmp_left,
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cmp_right,
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cmp_left_converse,
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cmp_right_converse,
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fused_prefix))
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}}
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NODE_CLASSES = {}
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{{for dtype, dtype_title, closed, closed_title, cmp_left, cmp_right,
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cmp_left_converse, cmp_right_converse, fused_prefix in nodes}}
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@cython.internal
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cdef class {{dtype_title}}Closed{{closed_title}}IntervalNode(IntervalNode):
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"""Non-terminal node for an IntervalTree
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Categorizes intervals by those that fall to the left, those that fall to
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the right, and those that overlap with the pivot.
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"""
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cdef readonly:
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{{dtype_title}}Closed{{closed_title}}IntervalNode left_node, right_node
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{{dtype}}_t[:] center_left_values, center_right_values, left, right
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int64_t[:] center_left_indices, center_right_indices, indices
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{{dtype}}_t min_left, max_right
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{{dtype}}_t pivot
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def __init__(self,
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ndarray[{{dtype}}_t, ndim=1] left,
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ndarray[{{dtype}}_t, ndim=1] right,
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ndarray[int64_t, ndim=1] indices,
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int64_t leaf_size):
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self.n_elements = len(left)
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self.leaf_size = leaf_size
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# min_left and min_right are used to speed-up query by skipping
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# query on sub-nodes. If this node has size 0, query is cheap,
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# so these values don't matter.
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if left.size > 0:
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self.min_left = left.min()
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self.max_right = right.max()
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else:
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self.min_left = 0
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self.max_right = 0
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if self.n_elements <= leaf_size:
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# make this a terminal (leaf) node
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self.is_leaf_node = True
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self.left = left
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self.right = right
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self.indices = indices
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self.n_center = 0
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else:
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# calculate a pivot so we can create child nodes
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self.is_leaf_node = False
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self.pivot = np.median(left / 2 + right / 2)
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if np.isinf(self.pivot):
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self.pivot = cython.cast({{dtype}}_t, 0)
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if self.pivot > np.max(right):
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self.pivot = np.max(left)
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if self.pivot < np.min(left):
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self.pivot = np.min(right)
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left_set, right_set, center_set = self.classify_intervals(
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left, right)
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self.left_node = self.new_child_node(left, right,
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indices, left_set)
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self.right_node = self.new_child_node(left, right,
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indices, right_set)
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self.center_left_values, self.center_left_indices = \
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sort_values_and_indices(left, indices, center_set)
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self.center_right_values, self.center_right_indices = \
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sort_values_and_indices(right, indices, center_set)
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self.n_center = len(self.center_left_indices)
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@cython.wraparound(False)
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@cython.boundscheck(False)
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cdef classify_intervals(self, {{dtype}}_t[:] left, {{dtype}}_t[:] right):
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"""Classify the given intervals based upon whether they fall to the
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left, right, or overlap with this node's pivot.
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"""
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cdef:
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Int64Vector left_ind, right_ind, overlapping_ind
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Py_ssize_t i
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left_ind = Int64Vector()
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right_ind = Int64Vector()
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overlapping_ind = Int64Vector()
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for i in range(self.n_elements):
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if right[i] {{cmp_right_converse}} self.pivot:
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left_ind.append(i)
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elif self.pivot {{cmp_left_converse}} left[i]:
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right_ind.append(i)
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else:
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overlapping_ind.append(i)
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return (left_ind.to_array(),
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right_ind.to_array(),
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overlapping_ind.to_array())
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cdef new_child_node(self,
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ndarray[{{dtype}}_t, ndim=1] left,
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ndarray[{{dtype}}_t, ndim=1] right,
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ndarray[int64_t, ndim=1] indices,
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ndarray[int64_t, ndim=1] subset):
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"""Create a new child node.
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"""
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left = take(left, subset)
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right = take(right, subset)
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indices = take(indices, subset)
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return {{dtype_title}}Closed{{closed_title}}IntervalNode(
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left, right, indices, self.leaf_size)
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@cython.wraparound(False)
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@cython.boundscheck(False)
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@cython.initializedcheck(False)
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cpdef query(self, Int64Vector result, {{fused_prefix}}scalar_t point):
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"""Recursively query this node and its sub-nodes for intervals that
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overlap with the query point.
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"""
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cdef:
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int64_t[:] indices
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{{dtype}}_t[:] values
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Py_ssize_t i
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if self.is_leaf_node:
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# Once we get down to a certain size, it doesn't make sense to
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# continue the binary tree structure. Instead, we use linear
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# search.
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for i in range(self.n_elements):
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if self.left[i] {{cmp_left}} point {{cmp_right}} self.right[i]:
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result.append(self.indices[i])
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else:
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# There are child nodes. Based on comparing our query to the pivot,
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# look at the center values, then go to the relevant child.
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if point < self.pivot:
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values = self.center_left_values
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indices = self.center_left_indices
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for i in range(self.n_center):
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if not values[i] {{cmp_left}} point:
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break
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result.append(indices[i])
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if point {{cmp_right}} self.left_node.max_right:
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self.left_node.query(result, point)
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elif point > self.pivot:
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values = self.center_right_values
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indices = self.center_right_indices
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for i in range(self.n_center - 1, -1, -1):
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if not point {{cmp_right}} values[i]:
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break
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result.append(indices[i])
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if self.right_node.min_left {{cmp_left}} point:
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self.right_node.query(result, point)
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else:
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result.extend(self.center_left_indices)
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NODE_CLASSES['{{dtype}}',
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'{{closed}}'] = {{dtype_title}}Closed{{closed_title}}IntervalNode
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{{endfor}}
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