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from itertools import zip_longest
from numbers import Integral
import numba
import numpy as np
from .._slicing import normalize_index
from .._utils import _zero_of_dtype, equivalent
def getitem(x, index):
"""
This function implements the indexing functionality for COO.
The overall algorithm has three steps:
1. Normalize the index to canonical form. Function: normalize_index
2. Get the mask, which is a list of integers corresponding to
the indices in coords/data for the output data. Function: _mask
3. Transform the coordinates to what they will be in the output.
Parameters
----------
x : COO
The array to apply the indexing operation on.
index : {tuple, str}
The index into the array.
"""
from .core import COO
# If string, this is an index into an np.void
# Custom dtype.
if isinstance(index, str):
data = x.data[index]
idx = np.where(data)
data = data[idx].flatten()
coords = list(x.coords[:, idx[0]])
coords.extend(idx[1:])
fill_value_idx = np.asarray(x.fill_value[index]).flatten()
fill_value = fill_value_idx[0] if fill_value_idx.size else _zero_of_dtype(data.dtype)[()]
if not equivalent(fill_value, fill_value_idx).all():
raise ValueError("Fill-values in the array are inconsistent.")
return COO(
coords,
data,
shape=x.shape + x.data.dtype[index].shape,
has_duplicates=False,
sorted=True,
fill_value=fill_value,
)
# Otherwise, convert into a tuple.
if not isinstance(index, tuple):
index = (index,)
# Check if the last index is an ellipsis.
last_ellipsis = len(index) > 0 and index[-1] is Ellipsis
# Normalize the index into canonical form.
index = normalize_index(index, x.shape)
# zip_longest so things like x[..., None] are picked up.
if len(index) != 0 and all(
isinstance(ind, slice) and ind == slice(0, dim, 1) for ind, dim in zip_longest(index, x.shape)
):
return x
# Get the mask
mask, adv_idx = _mask(x.coords, index, x.shape)
# Get the length of the mask
n = len(range(mask.start, mask.stop, mask.step)) if isinstance(mask, slice) else len(mask)
coords = []
shape = []
i = 0
sorted = adv_idx is None or adv_idx.pos == 0
adv_idx_added = False
for ind in index:
# Nothing is added to shape or coords if the index is an integer.
if isinstance(ind, Integral):
i += 1
continue
# Add to the shape and transform the coords in the case of a slice.
if isinstance(ind, slice):
shape.append(len(range(ind.start, ind.stop, ind.step)))
coords.append((x.coords[i, mask] - ind.start) // ind.step)
i += 1
if ind.step < 0:
sorted = False
# Add the index and shape for the advanced index.
if isinstance(ind, np.ndarray):
if not adv_idx_added:
shape.append(adv_idx.length)
coords.append(adv_idx.idx)
adv_idx_added = True
i += 1
# Add a dimension for None.
if ind is None:
coords.append(np.zeros(n, dtype=np.intp))
shape.append(1)
# Join all the transformed coords.
if coords:
coords = np.stack(coords, axis=0)
else:
# If index result is a scalar, return a 0-d COO or
# a scalar depending on whether the last index is an ellipsis.
if last_ellipsis:
coords = np.empty((0, n), dtype=np.uint8)
else:
if n != 0:
return x.data[mask][0]
return x.fill_value
shape = tuple(shape)
data = x.data[mask]
return COO(
coords,
data,
shape=shape,
has_duplicates=False,
sorted=sorted,
fill_value=x.fill_value,
)
def _mask(coords, indices, shape):
indices = _prune_indices(indices, shape)
indices, adv_idx, adv_idx_pos = _separate_adv_indices(indices)
if len(adv_idx) != 0:
if len(adv_idx) != 1:
# Ensure if multiple advanced indices are passed, all are of the same length
# Also check each advanced index to ensure each is only a one-dimensional iterable
adv_ix_len = len(adv_idx[0])
for ai in adv_idx:
if len(ai) != adv_ix_len:
raise IndexError(
"shape mismatch: indexing arrays could not be broadcast together. Ensure all indexing arrays "
"are of the same length."
)
if ai.ndim != 1:
raise IndexError("Only one-dimensional iterable indices supported.")
mask, aidxs = _compute_multi_axis_multi_mask(
coords,
_ind_ar_from_indices(indices),
np.array(adv_idx, dtype=np.intp),
np.array(adv_idx_pos, dtype=np.intp),
)
return mask, _AdvIdxInfo(aidxs, adv_idx_pos, adv_ix_len)
adv_idx = adv_idx[0]
adv_idx_pos = adv_idx_pos[0]
if adv_idx.ndim != 1:
raise IndexError("Only one-dimensional iterable indices supported.")
mask, aidxs = _compute_multi_mask(coords, _ind_ar_from_indices(indices), adv_idx, adv_idx_pos)
return mask, _AdvIdxInfo(aidxs, adv_idx_pos, len(adv_idx))
mask, is_slice = _compute_mask(coords, _ind_ar_from_indices(indices))
if is_slice:
return slice(mask[0], mask[1], 1), None
return mask, None
def _ind_ar_from_indices(indices):
"""
Computes an index "array" from indices, such that ``indices[i]`` is
transformed to ``ind_ar[i]`` and ``ind_ar[i].shape == (3,)``. It has the
format ``[start, stop, step]``. Integers are converted into steps as well.
Parameters
----------
indices : Iterable
Input indices (slices and integers)
Returns
-------
ind_ar : np.ndarray
The output array.
Examples
--------
>>> _ind_ar_from_indices([1])
array([[1, 2, 1]])
>>> _ind_ar_from_indices([slice(5, 7, 2)])
array([[5, 7, 2]])
"""
ind_ar = np.empty((len(indices), 3), dtype=np.intp)
for i, idx in enumerate(indices):
if isinstance(idx, slice):
ind_ar[i] = [idx.start, idx.stop, idx.step]
elif isinstance(idx, Integral):
ind_ar[i] = [idx, idx + 1, 1]
return ind_ar
def _prune_indices(indices, shape, prune_none=True):
"""
Gets rid of the indices that do not contribute to the
overall mask, e.g. None and full slices.
Parameters
----------
indices : tuple
The indices to the array.
shape : tuple[int]
The shape of the array.
Returns
-------
indices : tuple
The filtered indices.
Examples
--------
>>> _prune_indices((None, 5), (10,)) # None won't affect the mask
[5]
>>> _prune_indices((slice(0, 10, 1),), (10,)) # Full slices don't affect the mask
[]
"""
if prune_none:
indices = [idx for idx in indices if idx is not None]
i = 0
for idx, sh in zip(indices[::-1], shape[::-1], strict=True):
if not isinstance(idx, slice):
break
if idx.start == 0 and idx.stop == sh and idx.step == 1:
i += 1
continue
if idx.start == sh - 1 and idx.stop == -1 and idx.step == -1:
i += 1
continue
break
if i != 0:
indices = indices[:-i]
return indices
def _separate_adv_indices(indices):
"""
Separates advanced from normal indices.
Parameters
----------
indices : list
The input indices
Returns
-------
new_idx : list
The normal indices.
adv_idx : list
The advanced indices.
adv_idx_pos : list
The positions of the advanced indices.
"""
adv_idx_pos = []
new_idx = []
adv_idx = []
for i, idx in enumerate(indices):
if isinstance(idx, np.ndarray):
adv_idx.append(idx)
adv_idx_pos.append(i)
else:
new_idx.append(idx)
return new_idx, adv_idx, adv_idx_pos
@numba.jit(nopython=True, nogil=True)
def _compute_multi_axis_multi_mask(coords, indices, adv_idx, adv_idx_pos): # pragma: no cover
"""
Computes a mask with the advanced index, and also returns the advanced index
dimension.
Parameters
----------
coords : np.ndarray
Coordinates of the input array.
indices : np.ndarray
The indices in slice format.
adv_idx : np.ndarray
List of advanced indices.
adv_idx_pos : np.ndarray
The position of the advanced indices.
Returns
-------
mask : np.ndarray
The mask.
aidxs : np.ndarray
The advanced array index.
"""
n_adv_idx = len(adv_idx_pos)
mask = numba.typed.List.empty_list(numba.types.intp)
a_indices = numba.typed.List.empty_list(numba.types.intp)
full_idx = np.empty((len(indices) + len(adv_idx_pos), 3), dtype=np.intp)
# Get location of non-advanced indices
if len(indices) != 0:
ixx = 0
for ix in range(coords.shape[0]):
isin = False
for ax in adv_idx_pos:
if ix == ax:
isin = True
break
if not isin:
full_idx[ix] = indices[ixx]
ixx += 1
for i in range(len(adv_idx[0])):
for ii in range(n_adv_idx):
full_idx[adv_idx_pos[ii]] = [adv_idx[ii][i], adv_idx[ii][i] + 1, 1]
partial_mask, is_slice = _compute_mask(coords, full_idx)
if is_slice:
slice_mask = numba.typed.List.empty_list(numba.types.intp)
for j in range(partial_mask[0], partial_mask[1]):
slice_mask.append(j)
partial_mask = array_from_list_intp(slice_mask)
for j in range(len(partial_mask)):
mask.append(partial_mask[j])
a_indices.append(i)
return array_from_list_intp(mask), array_from_list_intp(a_indices)
@numba.jit(nopython=True, nogil=True)
def _compute_multi_mask(coords, indices, adv_idx, adv_idx_pos): # pragma: no cover
"""
Computes a mask with the advanced index, and also returns the advanced index
dimension.
Parameters
----------
coords : np.ndarray
Coordinates of the input array.
indices : np.ndarray
The indices in slice format.
adv_idx : list(int)
The advanced index.
adv_idx_pos : list(int)
The position of the advanced index.
Returns
-------
mask : np.ndarray
The mask.
aidxs : np.ndarray
The advanced array index.
"""
mask = numba.typed.List.empty_list(numba.types.intp)
a_indices = numba.typed.List.empty_list(numba.types.intp)
full_idx = np.empty((len(indices) + 1, 3), dtype=np.intp)
full_idx[:adv_idx_pos] = indices[:adv_idx_pos]
full_idx[adv_idx_pos + 1 :] = indices[adv_idx_pos:]
for i, aidx in enumerate(adv_idx):
full_idx[adv_idx_pos] = [aidx, aidx + 1, 1]
partial_mask, is_slice = _compute_mask(coords, full_idx)
if is_slice:
slice_mask = numba.typed.List.empty_list(numba.types.intp)
for j in range(partial_mask[0], partial_mask[1]):
slice_mask.append(j)
partial_mask = array_from_list_intp(slice_mask)
for j in range(len(partial_mask)):
mask.append(partial_mask[j])
a_indices.append(i)
return array_from_list_intp(mask), array_from_list_intp(a_indices)
@numba.jit(nopython=True, nogil=True)
def _compute_mask(coords, indices): # pragma: no cover
"""
Gets the mask for the coords given the indices in slice format.
Works with either start-stop ranges of matching indices into coords
called "pairs" (start-stop pairs) or filters the mask directly, based
on which is faster.
Exploits the structure in sorted coords, which is that for a constant
value of coords[i - 1], coords[i - 2] and so on, coords[i] is sorted.
Concretely, ``coords[i, coords[i - 1] == v1 & coords[i - 2] = v2, ...]``
is always sorted. It uses this sortedness to find sub-pairs for each
dimension given the previous, and so on. This is efficient for small
slices or ints, but not for large ones.
After it detects that working with pairs is rather inefficient (or after
going through each possible index), it constructs a filtered mask from the
start-stop pairs.
Parameters
----------
coords : np.ndarray
The coordinates of the array.
indices : np.ndarray
The indices in the form of slices such that indices[:, 0] are starts,
indices[:, 1] are stops and indices[:, 2] are steps.
Returns
-------
mask : np.ndarray
The starts and stops in the mask.
is_slice : bool
Whether or not the array represents a continuous slice.
Examples
--------
Let's create some mock coords and indices
>>> import numpy as np
>>> coords = np.array([[0, 0, 1, 1, 2, 2]])
>>> indices = np.array([[0, 3, 2]]) # Equivalent to slice(0, 3, 2)
Now let's get the mask. Notice that the indices of ``0`` and ``2`` are matched.
>>> _compute_mask(coords, indices)
(array([0, 1, 4, 5]), False)
Now, let's try with a more "continuous" slice. Matches ``0`` and ``1``.
>>> indices = np.array([[0, 2, 1]])
>>> _compute_mask(coords, indices)
(array([0, 4]), True)
This is equivalent to mask being ``slice(0, 4, 1)``.
"""
# Set the initial mask to be the entire range of coordinates.
starts = numba.typed.List.empty_list(numba.types.intp)
starts.append(0)
stops = numba.typed.List.empty_list(numba.types.intp)
stops.append(coords.shape[1])
n_matches = np.intp(coords.shape[1])
i = 0
while i < len(indices):
# Guesstimate whether working with pairs is more efficient or
# working with the mask directly.
# One side is the estimate of time taken for binary searches
# (n_searches * log(avg_length))
# The other is an estimated time of a linear filter for the mask.
n_pairs = len(starts)
n_current_slices = len(range(indices[i, 0], indices[i, 1], indices[i, 2])) * n_pairs + 2
if n_current_slices * np.log(n_current_slices / max(n_pairs, 1)) > n_matches + n_pairs:
break
# For each of the pairs, search inside the coordinates for other
# matching sub-pairs.
# This gets the start-end coordinates in coords for each 'sub-array'
# Which would come out of indexing a single integer.
starts, stops, n_matches = _get_mask_pairs(starts, stops, coords[i], indices[i])
i += 1
# Combine adjacent pairs
starts, stops = _join_adjacent_pairs(starts, stops)
# If just one pair is left over, treat it as a slice.
if i == len(indices) and len(starts) == 1:
return np.array([starts[0], stops[0]]), True
# Convert start-stop pairs into mask, filtering by remaining
# coordinates.
mask = _filter_pairs(starts, stops, coords[i:], indices[i:])
return array_from_list_intp(mask), False
@numba.jit(nopython=True, nogil=True)
def _get_mask_pairs(starts_old, stops_old, c, idx): # pragma: no cover
"""
Gets the pairs for a following dimension given the pairs for
a dimension.
For each pair, it searches in the following dimension for
matching coords and returns those.
The total combined length of all pairs is returned to
help with the performance guesstimate.
Parameters
----------
starts_old, stops_old : list[int]
The starts and stops from the previous index.
c : np.ndarray
The coords for this index's dimension.
idx : np.ndarray
The index in the form of a slice.
idx[0], idx[1], idx[2] = start, stop, step
Returns
-------
starts, stops: list
The starts and stops after applying the current index.
n_matches : int
The sum of elements in all ranges.
Examples
--------
>>> c = np.array([1, 2, 1, 2, 1, 1, 2, 2])
>>> starts_old = numba.typed.List()
>>> starts_old.append(4)
>>> stops_old = numba.typed.List()
>>> stops_old.append(8)
>>> idx = np.array([1, 2, 1])
>>> _get_mask_pairs(starts_old, stops_old, c, idx)
(ListType[int64]([4]), ListType[int64]([6]), 2)
"""
starts = numba.typed.List.empty_list(numba.types.intp)
stops = numba.typed.List.empty_list(numba.types.intp)
n_matches = np.intp(0)
for j in range(len(starts_old)):
# For each matching "integer" in the slice, search within the "sub-coords"
# Using binary search.
for p_match in range(idx[0], idx[1], idx[2]):
start = np.searchsorted(c[starts_old[j] : stops_old[j]], p_match, side="left") + starts_old[j]
stop = np.searchsorted(c[starts_old[j] : stops_old[j]], p_match, side="right") + starts_old[j]
if start != stop:
starts.append(start)
stops.append(stop)
n_matches += stop - start
return starts, stops, n_matches
@numba.jit(nopython=True, nogil=True)
def _filter_pairs(starts, stops, coords, indices): # pragma: no cover
"""
Converts all the pairs into a single integer mask, additionally filtering
by the indices.
Parameters
----------
starts, stops : list[int]
The starts and stops to convert into an array.
coords : np.ndarray
The coordinates to filter by.
indices : np.ndarray
The indices in the form of slices such that indices[:, 0] are starts,
indices[:, 1] are stops and indices[:, 2] are steps.
Returns
-------
mask : list
The output integer mask.
Examples
--------
>>> import numpy as np
>>> starts = numba.typed.List()
>>> starts.append(2)
>>> stops = numba.typed.List()
>>> stops.append(7)
>>> coords = np.array([[0, 1, 2, 3, 4, 5, 6, 7]])
>>> indices = np.array([[2, 8, 2]]) # Start, stop, step pairs
>>> _filter_pairs(starts, stops, coords, indices)
ListType[int64]([2, 4, 6])
"""
mask = numba.typed.List.empty_list(numba.types.intp)
# For each pair,
for i in range(len(starts)):
# For each element match within the pair range
for j in range(starts[i], stops[i]):
match = True
# Check if it matches all indices
for k in range(len(indices)):
idx = indices[k]
elem = coords[k, j]
match &= (elem - idx[0]) % idx[2] == 0 and (
(idx[2] > 0 and idx[0] <= elem < idx[1]) or (idx[2] < 0 and idx[0] >= elem > idx[1])
)
# and append to the mask if so.
if match:
mask.append(j)
return mask
@numba.jit(nopython=True, nogil=True)
def _join_adjacent_pairs(starts_old, stops_old): # pragma: no cover
"""
Joins adjacent pairs into one. For example, 2-5 and 5-7
will reduce to 2-7 (a single pair). This may help in
returning a slice in the end which could be faster.
Parameters
----------
starts_old, stops_old : list[int]
The input starts and stops
Returns
-------
starts, stops : list[int]
The reduced starts and stops.
Examples
--------
>>> starts = numba.typed.List()
>>> starts.append(2)
>>> starts.append(5)
>>> stops = numba.typed.List()
>>> stops.append(5)
>>> stops.append(7)
>>> _join_adjacent_pairs(starts, stops)
(ListType[int64]([2]), ListType[int64]([7]))
"""
if len(starts_old) <= 1:
return starts_old, stops_old
starts = numba.typed.List.empty_list(numba.types.intp)
starts.append(starts_old[0])
stops = numba.typed.List.empty_list(numba.types.intp)
for i in range(1, len(starts_old)):
if starts_old[i] != stops_old[i - 1]:
starts.append(starts_old[i])
stops.append(stops_old[i - 1])
stops.append(stops_old[-1])
return starts, stops
@numba.jit(nopython=True, nogil=True)
def array_from_list_intp(x): # pragma: no cover
n = len(x)
a = np.empty(n, dtype=np.intp)
for i in range(n):
a[i] = x[i]
return a
class _AdvIdxInfo:
def __init__(self, idx, pos, length):
self.idx = idx
self.pos = pos
self.length = length
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