Inzynierka/Lib/site-packages/pandas/core/reshape/reshape.py
2023-06-02 12:51:02 +02:00

842 lines
28 KiB
Python

from __future__ import annotations
import itertools
from typing import (
TYPE_CHECKING,
cast,
)
import warnings
import numpy as np
import pandas._libs.reshape as libreshape
from pandas._typing import npt
from pandas.errors import PerformanceWarning
from pandas.util._decorators import cache_readonly
from pandas.util._exceptions import find_stack_level
from pandas.core.dtypes.cast import maybe_promote
from pandas.core.dtypes.common import (
ensure_platform_int,
is_1d_only_ea_dtype,
is_extension_array_dtype,
is_integer,
needs_i8_conversion,
)
from pandas.core.dtypes.dtypes import ExtensionDtype
from pandas.core.dtypes.missing import notna
import pandas.core.algorithms as algos
from pandas.core.arrays.categorical import factorize_from_iterable
from pandas.core.construction import ensure_wrapped_if_datetimelike
from pandas.core.frame import DataFrame
from pandas.core.indexes.api import (
Index,
MultiIndex,
)
from pandas.core.series import Series
from pandas.core.sorting import (
compress_group_index,
decons_obs_group_ids,
get_compressed_ids,
get_group_index,
get_group_index_sorter,
)
if TYPE_CHECKING:
from pandas.core.arrays import ExtensionArray
from pandas.core.indexes.frozen import FrozenList
class _Unstacker:
"""
Helper class to unstack data / pivot with multi-level index
Parameters
----------
index : MultiIndex
level : int or str, default last level
Level to "unstack". Accepts a name for the level.
fill_value : scalar, optional
Default value to fill in missing values if subgroups do not have the
same set of labels. By default, missing values will be replaced with
the default fill value for that data type, NaN for float, NaT for
datetimelike, etc. For integer types, by default data will converted to
float and missing values will be set to NaN.
constructor : object
Pandas ``DataFrame`` or subclass used to create unstacked
response. If None, DataFrame will be used.
Examples
--------
>>> index = pd.MultiIndex.from_tuples([('one', 'a'), ('one', 'b'),
... ('two', 'a'), ('two', 'b')])
>>> s = pd.Series(np.arange(1, 5, dtype=np.int64), index=index)
>>> s
one a 1
b 2
two a 3
b 4
dtype: int64
>>> s.unstack(level=-1)
a b
one 1 2
two 3 4
>>> s.unstack(level=0)
one two
a 1 3
b 2 4
Returns
-------
unstacked : DataFrame
"""
def __init__(self, index: MultiIndex, level=-1, constructor=None) -> None:
if constructor is None:
constructor = DataFrame
self.constructor = constructor
self.index = index.remove_unused_levels()
self.level = self.index._get_level_number(level)
# when index includes `nan`, need to lift levels/strides by 1
self.lift = 1 if -1 in self.index.codes[self.level] else 0
# Note: the "pop" below alters these in-place.
self.new_index_levels = list(self.index.levels)
self.new_index_names = list(self.index.names)
self.removed_name = self.new_index_names.pop(self.level)
self.removed_level = self.new_index_levels.pop(self.level)
self.removed_level_full = index.levels[self.level]
# Bug fix GH 20601
# If the data frame is too big, the number of unique index combination
# will cause int32 overflow on windows environments.
# We want to check and raise an error before this happens
num_rows = np.max([index_level.size for index_level in self.new_index_levels])
num_columns = self.removed_level.size
# GH20601: This forces an overflow if the number of cells is too high.
num_cells = num_rows * num_columns
# GH 26314: Previous ValueError raised was too restrictive for many users.
if num_cells > np.iinfo(np.int32).max:
warnings.warn(
f"The following operation may generate {num_cells} cells "
f"in the resulting pandas object.",
PerformanceWarning,
stacklevel=find_stack_level(),
)
self._make_selectors()
@cache_readonly
def _indexer_and_to_sort(
self,
) -> tuple[
npt.NDArray[np.intp],
list[np.ndarray], # each has _some_ signed integer dtype
]:
v = self.level
codes = list(self.index.codes)
levs = list(self.index.levels)
to_sort = codes[:v] + codes[v + 1 :] + [codes[v]]
sizes = tuple(len(x) for x in levs[:v] + levs[v + 1 :] + [levs[v]])
comp_index, obs_ids = get_compressed_ids(to_sort, sizes)
ngroups = len(obs_ids)
indexer = get_group_index_sorter(comp_index, ngroups)
return indexer, to_sort
@cache_readonly
def sorted_labels(self) -> list[np.ndarray]:
indexer, to_sort = self._indexer_and_to_sort
return [line.take(indexer) for line in to_sort]
def _make_sorted_values(self, values: np.ndarray) -> np.ndarray:
indexer, _ = self._indexer_and_to_sort
sorted_values = algos.take_nd(values, indexer, axis=0)
return sorted_values
def _make_selectors(self):
new_levels = self.new_index_levels
# make the mask
remaining_labels = self.sorted_labels[:-1]
level_sizes = tuple(len(x) for x in new_levels)
comp_index, obs_ids = get_compressed_ids(remaining_labels, level_sizes)
ngroups = len(obs_ids)
comp_index = ensure_platform_int(comp_index)
stride = self.index.levshape[self.level] + self.lift
self.full_shape = ngroups, stride
selector = self.sorted_labels[-1] + stride * comp_index + self.lift
mask = np.zeros(np.prod(self.full_shape), dtype=bool)
mask.put(selector, True)
if mask.sum() < len(self.index):
raise ValueError("Index contains duplicate entries, cannot reshape")
self.group_index = comp_index
self.mask = mask
self.compressor = comp_index.searchsorted(np.arange(ngroups))
@cache_readonly
def mask_all(self) -> bool:
return bool(self.mask.all())
@cache_readonly
def arange_result(self) -> tuple[npt.NDArray[np.intp], npt.NDArray[np.bool_]]:
# We cache this for re-use in ExtensionBlock._unstack
dummy_arr = np.arange(len(self.index), dtype=np.intp)
new_values, mask = self.get_new_values(dummy_arr, fill_value=-1)
return new_values, mask.any(0)
# TODO: in all tests we have mask.any(0).all(); can we rely on that?
def get_result(self, values, value_columns, fill_value) -> DataFrame:
if values.ndim == 1:
values = values[:, np.newaxis]
if value_columns is None and values.shape[1] != 1: # pragma: no cover
raise ValueError("must pass column labels for multi-column data")
values, _ = self.get_new_values(values, fill_value)
columns = self.get_new_columns(value_columns)
index = self.new_index
return self.constructor(
values, index=index, columns=columns, dtype=values.dtype
)
def get_new_values(self, values, fill_value=None):
if values.ndim == 1:
values = values[:, np.newaxis]
sorted_values = self._make_sorted_values(values)
# place the values
length, width = self.full_shape
stride = values.shape[1]
result_width = width * stride
result_shape = (length, result_width)
mask = self.mask
mask_all = self.mask_all
# we can simply reshape if we don't have a mask
if mask_all and len(values):
# TODO: Under what circumstances can we rely on sorted_values
# matching values? When that holds, we can slice instead
# of take (in particular for EAs)
new_values = (
sorted_values.reshape(length, width, stride)
.swapaxes(1, 2)
.reshape(result_shape)
)
new_mask = np.ones(result_shape, dtype=bool)
return new_values, new_mask
dtype = values.dtype
# if our mask is all True, then we can use our existing dtype
if mask_all:
dtype = values.dtype
new_values = np.empty(result_shape, dtype=dtype)
else:
if isinstance(dtype, ExtensionDtype):
# GH#41875
# We are assuming that fill_value can be held by this dtype,
# unlike the non-EA case that promotes.
cls = dtype.construct_array_type()
new_values = cls._empty(result_shape, dtype=dtype)
new_values[:] = fill_value
else:
dtype, fill_value = maybe_promote(dtype, fill_value)
new_values = np.empty(result_shape, dtype=dtype)
new_values.fill(fill_value)
name = dtype.name
new_mask = np.zeros(result_shape, dtype=bool)
# we need to convert to a basic dtype
# and possibly coerce an input to our output dtype
# e.g. ints -> floats
if needs_i8_conversion(values.dtype):
sorted_values = sorted_values.view("i8")
new_values = new_values.view("i8")
else:
sorted_values = sorted_values.astype(name, copy=False)
# fill in our values & mask
libreshape.unstack(
sorted_values,
mask.view("u1"),
stride,
length,
width,
new_values,
new_mask.view("u1"),
)
# reconstruct dtype if needed
if needs_i8_conversion(values.dtype):
# view as datetime64 so we can wrap in DatetimeArray and use
# DTA's view method
new_values = new_values.view("M8[ns]")
new_values = ensure_wrapped_if_datetimelike(new_values)
new_values = new_values.view(values.dtype)
return new_values, new_mask
def get_new_columns(self, value_columns: Index | None):
if value_columns is None:
if self.lift == 0:
return self.removed_level._rename(name=self.removed_name)
lev = self.removed_level.insert(0, item=self.removed_level._na_value)
return lev.rename(self.removed_name)
stride = len(self.removed_level) + self.lift
width = len(value_columns)
propagator = np.repeat(np.arange(width), stride)
new_levels: FrozenList | list[Index]
if isinstance(value_columns, MultiIndex):
# error: Cannot determine type of "__add__" [has-type]
new_levels = value_columns.levels + ( # type: ignore[has-type]
self.removed_level_full,
)
new_names = value_columns.names + (self.removed_name,)
new_codes = [lab.take(propagator) for lab in value_columns.codes]
else:
new_levels = [
value_columns,
self.removed_level_full,
]
new_names = [value_columns.name, self.removed_name]
new_codes = [propagator]
repeater = self._repeater
# The entire level is then just a repetition of the single chunk:
new_codes.append(np.tile(repeater, width))
return MultiIndex(
levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False
)
@cache_readonly
def _repeater(self) -> np.ndarray:
# The two indices differ only if the unstacked level had unused items:
if len(self.removed_level_full) != len(self.removed_level):
# In this case, we remap the new codes to the original level:
repeater = self.removed_level_full.get_indexer(self.removed_level)
if self.lift:
repeater = np.insert(repeater, 0, -1)
else:
# Otherwise, we just use each level item exactly once:
stride = len(self.removed_level) + self.lift
repeater = np.arange(stride) - self.lift
return repeater
@cache_readonly
def new_index(self) -> MultiIndex:
# Does not depend on values or value_columns
result_codes = [lab.take(self.compressor) for lab in self.sorted_labels[:-1]]
# construct the new index
if len(self.new_index_levels) == 1:
level, level_codes = self.new_index_levels[0], result_codes[0]
if (level_codes == -1).any():
level = level.insert(len(level), level._na_value)
return level.take(level_codes).rename(self.new_index_names[0])
return MultiIndex(
levels=self.new_index_levels,
codes=result_codes,
names=self.new_index_names,
verify_integrity=False,
)
def _unstack_multiple(data, clocs, fill_value=None):
if len(clocs) == 0:
return data
# NOTE: This doesn't deal with hierarchical columns yet
index = data.index
# GH 19966 Make sure if MultiIndexed index has tuple name, they will be
# recognised as a whole
if clocs in index.names:
clocs = [clocs]
clocs = [index._get_level_number(i) for i in clocs]
rlocs = [i for i in range(index.nlevels) if i not in clocs]
clevels = [index.levels[i] for i in clocs]
ccodes = [index.codes[i] for i in clocs]
cnames = [index.names[i] for i in clocs]
rlevels = [index.levels[i] for i in rlocs]
rcodes = [index.codes[i] for i in rlocs]
rnames = [index.names[i] for i in rlocs]
shape = tuple(len(x) for x in clevels)
group_index = get_group_index(ccodes, shape, sort=False, xnull=False)
comp_ids, obs_ids = compress_group_index(group_index, sort=False)
recons_codes = decons_obs_group_ids(comp_ids, obs_ids, shape, ccodes, xnull=False)
if not rlocs:
# Everything is in clocs, so the dummy df has a regular index
dummy_index = Index(obs_ids, name="__placeholder__")
else:
dummy_index = MultiIndex(
levels=rlevels + [obs_ids],
codes=rcodes + [comp_ids],
names=rnames + ["__placeholder__"],
verify_integrity=False,
)
if isinstance(data, Series):
dummy = data.copy()
dummy.index = dummy_index
unstacked = dummy.unstack("__placeholder__", fill_value=fill_value)
new_levels = clevels
new_names = cnames
new_codes = recons_codes
else:
if isinstance(data.columns, MultiIndex):
result = data
while clocs:
val = clocs.pop(0)
result = result.unstack(val, fill_value=fill_value)
clocs = [v if v < val else v - 1 for v in clocs]
return result
# GH#42579 deep=False to avoid consolidating
dummy = data.copy(deep=False)
dummy.index = dummy_index
unstacked = dummy.unstack("__placeholder__", fill_value=fill_value)
if isinstance(unstacked, Series):
unstcols = unstacked.index
else:
unstcols = unstacked.columns
assert isinstance(unstcols, MultiIndex) # for mypy
new_levels = [unstcols.levels[0]] + clevels
new_names = [data.columns.name] + cnames
new_codes = [unstcols.codes[0]]
for rec in recons_codes:
new_codes.append(rec.take(unstcols.codes[-1]))
new_columns = MultiIndex(
levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False
)
if isinstance(unstacked, Series):
unstacked.index = new_columns
else:
unstacked.columns = new_columns
return unstacked
def unstack(obj: Series | DataFrame, level, fill_value=None):
if isinstance(level, (tuple, list)):
if len(level) != 1:
# _unstack_multiple only handles MultiIndexes,
# and isn't needed for a single level
return _unstack_multiple(obj, level, fill_value=fill_value)
else:
level = level[0]
if not is_integer(level) and not level == "__placeholder__":
# check if level is valid in case of regular index
obj.index._get_level_number(level)
if isinstance(obj, DataFrame):
if isinstance(obj.index, MultiIndex):
return _unstack_frame(obj, level, fill_value=fill_value)
else:
return obj.T.stack(dropna=False)
elif not isinstance(obj.index, MultiIndex):
# GH 36113
# Give nicer error messages when unstack a Series whose
# Index is not a MultiIndex.
raise ValueError(
f"index must be a MultiIndex to unstack, {type(obj.index)} was passed"
)
else:
if is_1d_only_ea_dtype(obj.dtype):
return _unstack_extension_series(obj, level, fill_value)
unstacker = _Unstacker(
obj.index, level=level, constructor=obj._constructor_expanddim
)
return unstacker.get_result(
obj._values, value_columns=None, fill_value=fill_value
)
def _unstack_frame(obj: DataFrame, level, fill_value=None):
assert isinstance(obj.index, MultiIndex) # checked by caller
unstacker = _Unstacker(obj.index, level=level, constructor=obj._constructor)
if not obj._can_fast_transpose:
mgr = obj._mgr.unstack(unstacker, fill_value=fill_value)
return obj._constructor(mgr)
else:
return unstacker.get_result(
obj._values, value_columns=obj.columns, fill_value=fill_value
)
def _unstack_extension_series(series: Series, level, fill_value) -> DataFrame:
"""
Unstack an ExtensionArray-backed Series.
The ExtensionDtype is preserved.
Parameters
----------
series : Series
A Series with an ExtensionArray for values
level : Any
The level name or number.
fill_value : Any
The user-level (not physical storage) fill value to use for
missing values introduced by the reshape. Passed to
``series.values.take``.
Returns
-------
DataFrame
Each column of the DataFrame will have the same dtype as
the input Series.
"""
# Defer to the logic in ExtensionBlock._unstack
df = series.to_frame()
result = df.unstack(level=level, fill_value=fill_value)
# equiv: result.droplevel(level=0, axis=1)
# but this avoids an extra copy
result.columns = result.columns.droplevel(0)
return result
def stack(frame: DataFrame, level=-1, dropna: bool = True):
"""
Convert DataFrame to Series with multi-level Index. Columns become the
second level of the resulting hierarchical index
Returns
-------
stacked : Series or DataFrame
"""
def factorize(index):
if index.is_unique:
return index, np.arange(len(index))
codes, categories = factorize_from_iterable(index)
return categories, codes
N, K = frame.shape
# Will also convert negative level numbers and check if out of bounds.
level_num = frame.columns._get_level_number(level)
if isinstance(frame.columns, MultiIndex):
return _stack_multi_columns(frame, level_num=level_num, dropna=dropna)
elif isinstance(frame.index, MultiIndex):
new_levels = list(frame.index.levels)
new_codes = [lab.repeat(K) for lab in frame.index.codes]
clev, clab = factorize(frame.columns)
new_levels.append(clev)
new_codes.append(np.tile(clab, N).ravel())
new_names = list(frame.index.names)
new_names.append(frame.columns.name)
new_index = MultiIndex(
levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False
)
else:
levels, (ilab, clab) = zip(*map(factorize, (frame.index, frame.columns)))
codes = ilab.repeat(K), np.tile(clab, N).ravel()
new_index = MultiIndex(
levels=levels,
codes=codes,
names=[frame.index.name, frame.columns.name],
verify_integrity=False,
)
if not frame.empty and frame._is_homogeneous_type:
# For homogeneous EAs, frame._values will coerce to object. So
# we concatenate instead.
dtypes = list(frame.dtypes._values)
dtype = dtypes[0]
if is_extension_array_dtype(dtype):
arr = dtype.construct_array_type()
new_values = arr._concat_same_type(
[col._values for _, col in frame.items()]
)
new_values = _reorder_for_extension_array_stack(new_values, N, K)
else:
# homogeneous, non-EA
new_values = frame._values.ravel()
else:
# non-homogeneous
new_values = frame._values.ravel()
if dropna:
mask = notna(new_values)
new_values = new_values[mask]
new_index = new_index[mask]
return frame._constructor_sliced(new_values, index=new_index)
def stack_multiple(frame, level, dropna: bool = True):
# If all passed levels match up to column names, no
# ambiguity about what to do
if all(lev in frame.columns.names for lev in level):
result = frame
for lev in level:
result = stack(result, lev, dropna=dropna)
# Otherwise, level numbers may change as each successive level is stacked
elif all(isinstance(lev, int) for lev in level):
# As each stack is done, the level numbers decrease, so we need
# to account for that when level is a sequence of ints
result = frame
# _get_level_number() checks level numbers are in range and converts
# negative numbers to positive
level = [frame.columns._get_level_number(lev) for lev in level]
while level:
lev = level.pop(0)
result = stack(result, lev, dropna=dropna)
# Decrement all level numbers greater than current, as these
# have now shifted down by one
level = [v if v <= lev else v - 1 for v in level]
else:
raise ValueError(
"level should contain all level names or all level "
"numbers, not a mixture of the two."
)
return result
def _stack_multi_column_index(columns: MultiIndex) -> MultiIndex:
"""Creates a MultiIndex from the first N-1 levels of this MultiIndex."""
if len(columns.levels) <= 2:
return columns.levels[0]._rename(name=columns.names[0])
levs = [
[lev[c] if c >= 0 else None for c in codes]
for lev, codes in zip(columns.levels[:-1], columns.codes[:-1])
]
# Remove duplicate tuples in the MultiIndex.
tuples = zip(*levs)
unique_tuples = (key for key, _ in itertools.groupby(tuples))
new_levs = zip(*unique_tuples)
# The dtype of each level must be explicitly set to avoid inferring the wrong type.
# See GH-36991.
return MultiIndex.from_arrays(
[
# Not all indices can accept None values.
Index(new_lev, dtype=lev.dtype) if None not in new_lev else new_lev
for new_lev, lev in zip(new_levs, columns.levels)
],
names=columns.names[:-1],
)
def _stack_multi_columns(
frame: DataFrame, level_num: int = -1, dropna: bool = True
) -> DataFrame:
def _convert_level_number(level_num: int, columns: Index):
"""
Logic for converting the level number to something we can safely pass
to swaplevel.
If `level_num` matches a column name return the name from
position `level_num`, otherwise return `level_num`.
"""
if level_num in columns.names:
return columns.names[level_num]
return level_num
this = frame.copy(deep=False)
mi_cols = this.columns # cast(MultiIndex, this.columns)
assert isinstance(mi_cols, MultiIndex) # caller is responsible
# this makes life much simpler
if level_num != mi_cols.nlevels - 1:
# roll levels to put selected level at end
roll_columns = mi_cols
for i in range(level_num, mi_cols.nlevels - 1):
# Need to check if the ints conflict with level names
lev1 = _convert_level_number(i, roll_columns)
lev2 = _convert_level_number(i + 1, roll_columns)
roll_columns = roll_columns.swaplevel(lev1, lev2)
this.columns = mi_cols = roll_columns
if not mi_cols._is_lexsorted():
# Workaround the edge case where 0 is one of the column names,
# which interferes with trying to sort based on the first
# level
level_to_sort = _convert_level_number(0, mi_cols)
this = this.sort_index(level=level_to_sort, axis=1)
mi_cols = this.columns
mi_cols = cast(MultiIndex, mi_cols)
new_columns = _stack_multi_column_index(mi_cols)
# time to ravel the values
new_data = {}
level_vals = mi_cols.levels[-1]
level_codes = sorted(set(mi_cols.codes[-1]))
level_vals_nan = level_vals.insert(len(level_vals), None)
level_vals_used = np.take(level_vals_nan, level_codes)
levsize = len(level_codes)
drop_cols = []
for key in new_columns:
try:
loc = this.columns.get_loc(key)
except KeyError:
drop_cols.append(key)
continue
# can make more efficient?
# we almost always return a slice
# but if unsorted can get a boolean
# indexer
if not isinstance(loc, slice):
slice_len = len(loc)
else:
slice_len = loc.stop - loc.start
if slice_len != levsize:
chunk = this.loc[:, this.columns[loc]]
chunk.columns = level_vals_nan.take(chunk.columns.codes[-1])
value_slice = chunk.reindex(columns=level_vals_used).values
else:
if frame._is_homogeneous_type and is_extension_array_dtype(
frame.dtypes.iloc[0]
):
# TODO(EA2D): won't need special case, can go through .values
# paths below (might change to ._values)
dtype = this[this.columns[loc]].dtypes.iloc[0]
subset = this[this.columns[loc]]
value_slice = dtype.construct_array_type()._concat_same_type(
[x._values for _, x in subset.items()]
)
N, K = subset.shape
idx = np.arange(N * K).reshape(K, N).T.ravel()
value_slice = value_slice.take(idx)
elif frame._is_mixed_type:
value_slice = this[this.columns[loc]].values
else:
value_slice = this.values[:, loc]
if value_slice.ndim > 1:
# i.e. not extension
value_slice = value_slice.ravel()
new_data[key] = value_slice
if len(drop_cols) > 0:
new_columns = new_columns.difference(drop_cols)
N = len(this)
if isinstance(this.index, MultiIndex):
new_levels = list(this.index.levels)
new_names = list(this.index.names)
new_codes = [lab.repeat(levsize) for lab in this.index.codes]
else:
old_codes, old_levels = factorize_from_iterable(this.index)
new_levels = [old_levels]
new_codes = [old_codes.repeat(levsize)]
new_names = [this.index.name] # something better?
new_levels.append(level_vals)
new_codes.append(np.tile(level_codes, N))
new_names.append(frame.columns.names[level_num])
new_index = MultiIndex(
levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False
)
result = frame._constructor(new_data, index=new_index, columns=new_columns)
# more efficient way to go about this? can do the whole masking biz but
# will only save a small amount of time...
if dropna:
result = result.dropna(axis=0, how="all")
return result
def _reorder_for_extension_array_stack(
arr: ExtensionArray, n_rows: int, n_columns: int
) -> ExtensionArray:
"""
Re-orders the values when stacking multiple extension-arrays.
The indirect stacking method used for EAs requires a followup
take to get the order correct.
Parameters
----------
arr : ExtensionArray
n_rows, n_columns : int
The number of rows and columns in the original DataFrame.
Returns
-------
taken : ExtensionArray
The original `arr` with elements re-ordered appropriately
Examples
--------
>>> arr = np.array(['a', 'b', 'c', 'd', 'e', 'f'])
>>> _reorder_for_extension_array_stack(arr, 2, 3)
array(['a', 'c', 'e', 'b', 'd', 'f'], dtype='<U1')
>>> _reorder_for_extension_array_stack(arr, 3, 2)
array(['a', 'd', 'b', 'e', 'c', 'f'], dtype='<U1')
"""
# final take to get the order correct.
# idx is an indexer like
# [c0r0, c1r0, c2r0, ...,
# c0r1, c1r1, c2r1, ...]
idx = np.arange(n_rows * n_columns).reshape(n_columns, n_rows).T.ravel()
return arr.take(idx)