from __future__ import annotations
import warnings
from collections.abc import Iterator
from functools import wraps
from numbers import Number
import numpy as np
from tlz import merge
from dask.array.core import Array
from dask.array.numpy_compat import NUMPY_GE_122
from dask.array.numpy_compat import percentile as np_percentile
from dask.base import tokenize
from dask.highlevelgraph import HighLevelGraph
@wraps(np.percentile)
def _percentile(a, q, method="linear"):
n = len(a)
if not len(a):
return None, n
if isinstance(q, Iterator):
q = list(q)
if a.dtype.name == "category":
result = np_percentile(a.cat.codes, q, method=method)
import pandas as pd
return pd.Categorical.from_codes(result, a.dtype.categories, a.dtype.ordered), n
if type(a.dtype).__name__ == "DatetimeTZDtype":
import pandas as pd
if isinstance(a, (pd.Series, pd.Index)):
a = a.values
if np.issubdtype(a.dtype, np.datetime64):
values = a
if type(a).__name__ in ("Series", "Index"):
from dask.dataframe._compat import PANDAS_GE_200
if PANDAS_GE_200:
a2 = values.astype("i8")
else:
a2 = values.view("i8")
else:
a2 = values.view("i8")
result = np_percentile(a2, q, method=method).astype(values.dtype)
if q[0] == 0:
# https://github.com/dask/dask/issues/6864
result[0] = min(result[0], values.min())
return result, n
if not np.issubdtype(a.dtype, np.number):
method = "nearest"
return np_percentile(a, q, method=method), n
def _tdigest_chunk(a):
from crick import TDigest
t = TDigest()
t.update(a)
return t
def _percentiles_from_tdigest(qs, digests):
from crick import TDigest
t = TDigest()
t.merge(*digests)
return np.array(t.quantile(qs / 100.0))
[docs]def percentile(a, q, method="linear", internal_method="default", **kwargs):
"""Approximate percentile of 1-D array
Parameters
----------
a : Array
q : array_like of float
Percentile or sequence of percentiles to compute, which must be between
0 and 100 inclusive.
method : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}, optional
The interpolation method to use when the desired percentile lies
between two data points ``i < j``. Only valid for ``internal_method='dask'``.
- 'linear': ``i + (j - i) * fraction``, where ``fraction``
is the fractional part of the index surrounded by ``i``
and ``j``.
- 'lower': ``i``.
- 'higher': ``j``.
- 'nearest': ``i`` or ``j``, whichever is nearest.
- 'midpoint': ``(i + j) / 2``.
.. versionchanged:: 2022.1.0
This argument was previously called "interpolation"
internal_method : {'default', 'dask', 'tdigest'}, optional
What internal method to use. By default will use dask's internal custom
algorithm (``'dask'``). If set to ``'tdigest'`` will use tdigest for
floats and ints and fallback to the ``'dask'`` otherwise.
.. versionchanged:: 2022.1.0
This argument was previously called “method”.
interpolation : str, optional
Deprecated name for the method keyword argument.
.. deprecated:: 2022.1.0
See Also
--------
numpy.percentile : Numpy's equivalent Percentile function
"""
from dask.array.dispatch import percentile_lookup as _percentile
from dask.array.utils import array_safe, meta_from_array
allowed_internal_methods = ["default", "dask", "tdigest"]
if method in allowed_internal_methods:
warnings.warn(
"In Dask 2022.1.0, the `method=` argument was renamed to `internal_method=`",
FutureWarning,
)
internal_method = method
if "interpolation" in kwargs:
if NUMPY_GE_122:
warnings.warn(
"In Dask 2022.1.0, the `interpolation=` argument to percentile was renamed to "
"`method= ` ",
FutureWarning,
)
method = kwargs.pop("interpolation")
if kwargs:
raise TypeError(
f"percentile() got an unexpected keyword argument {kwargs.keys()}"
)
if not a.ndim == 1:
raise NotImplementedError("Percentiles only implemented for 1-d arrays")
if isinstance(q, Number):
q = [q]
q = array_safe(q, like=meta_from_array(a))
token = tokenize(a, q, method)
dtype = a.dtype
if np.issubdtype(dtype, np.integer):
dtype = (array_safe([], dtype=dtype, like=meta_from_array(a)) / 0.5).dtype
meta = meta_from_array(a, dtype=dtype)
if internal_method not in allowed_internal_methods:
raise ValueError(
f"`internal_method=` must be one of {allowed_internal_methods}"
)
# Allow using t-digest if method is allowed and dtype is of floating or integer type
if (
internal_method == "tdigest"
and method == "linear"
and (np.issubdtype(dtype, np.floating) or np.issubdtype(dtype, np.integer))
):
from dask.utils import import_required
import_required(
"crick", "crick is a required dependency for using the t-digest method."
)
name = "percentile_tdigest_chunk-" + token
dsk = {
(name, i): (_tdigest_chunk, key) for i, key in enumerate(a.__dask_keys__())
}
name2 = "percentile_tdigest-" + token
dsk2 = {(name2, 0): (_percentiles_from_tdigest, q, sorted(dsk))}
# Otherwise use the custom percentile algorithm
else:
# Add 0 and 100 during calculation for more robust behavior (hopefully)
calc_q = np.pad(q, 1, mode="constant")
calc_q[-1] = 100
name = "percentile_chunk-" + token
dsk = {
(name, i): (_percentile, key, calc_q, method)
for i, key in enumerate(a.__dask_keys__())
}
name2 = "percentile-" + token
dsk2 = {
(name2, 0): (
merge_percentiles,
q,
[calc_q] * len(a.chunks[0]),
sorted(dsk),
method,
)
}
dsk = merge(dsk, dsk2)
graph = HighLevelGraph.from_collections(name2, dsk, dependencies=[a])
return Array(graph, name2, chunks=((len(q),),), meta=meta)
def merge_percentiles(finalq, qs, vals, method="lower", Ns=None, raise_on_nan=True):
"""Combine several percentile calculations of different data.
Parameters
----------
finalq : numpy.array
Percentiles to compute (must use same scale as ``qs``).
qs : sequence of :class:`numpy.array`s
Percentiles calculated on different sets of data.
vals : sequence of :class:`numpy.array`s
Resulting values associated with percentiles ``qs``.
Ns : sequence of integers
The number of data elements associated with each data set.
method : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
Specify the interpolation method to use to calculate final
percentiles. For more information, see :func:`numpy.percentile`.
Examples
--------
>>> finalq = [10, 20, 30, 40, 50, 60, 70, 80]
>>> qs = [[20, 40, 60, 80], [20, 40, 60, 80]]
>>> vals = [np.array([1, 2, 3, 4]), np.array([10, 11, 12, 13])]
>>> Ns = [100, 100] # Both original arrays had 100 elements
>>> merge_percentiles(finalq, qs, vals, Ns=Ns)
array([ 1, 2, 3, 4, 10, 11, 12, 13])
"""
from dask.array.utils import array_safe
if isinstance(finalq, Iterator):
finalq = list(finalq)
finalq = array_safe(finalq, like=finalq)
qs = list(map(list, qs))
vals = list(vals)
if Ns is None:
vals, Ns = zip(*vals)
Ns = list(Ns)
L = list(zip(*[(q, val, N) for q, val, N in zip(qs, vals, Ns) if N]))
if not L:
if raise_on_nan:
raise ValueError("No non-trivial arrays found")
return np.full(len(qs[0]) - 2, np.nan)
qs, vals, Ns = L
# TODO: Perform this check above in percentile once dtype checking is easy
# Here we silently change meaning
if vals[0].dtype.name == "category":
result = merge_percentiles(
finalq, qs, [v.codes for v in vals], method, Ns, raise_on_nan
)
import pandas as pd
return pd.Categorical.from_codes(result, vals[0].categories, vals[0].ordered)
if not np.issubdtype(vals[0].dtype, np.number):
method = "nearest"
if len(vals) != len(qs) or len(Ns) != len(qs):
raise ValueError("qs, vals, and Ns parameters must be the same length")
# transform qs and Ns into number of observations between percentiles
counts = []
for q, N in zip(qs, Ns):
count = np.empty_like(finalq, shape=len(q))
count[1:] = np.diff(array_safe(q, like=q[0]))
count[0] = q[0]
count *= N
counts.append(count)
# Sort by calculated percentile values, then number of observations.
combined_vals = np.concatenate(vals)
combined_counts = array_safe(np.concatenate(counts), like=combined_vals)
sort_order = np.argsort(combined_vals)
combined_vals = np.take(combined_vals, sort_order)
combined_counts = np.take(combined_counts, sort_order)
# percentile-like, but scaled by total number of observations
combined_q = np.cumsum(combined_counts)
# rescale finalq percentiles to match combined_q
finalq = array_safe(finalq, like=combined_vals)
desired_q = finalq * sum(Ns)
# the behavior of different interpolation methods should be
# investigated further.
if method == "linear":
rv = np.interp(desired_q, combined_q, combined_vals)
else:
left = np.searchsorted(combined_q, desired_q, side="left")
right = np.searchsorted(combined_q, desired_q, side="right") - 1
np.minimum(left, len(combined_vals) - 1, left) # don't exceed max index
lower = np.minimum(left, right)
upper = np.maximum(left, right)
if method == "lower":
rv = combined_vals[lower]
elif method == "higher":
rv = combined_vals[upper]
elif method == "midpoint":
rv = 0.5 * (combined_vals[lower] + combined_vals[upper])
elif method == "nearest":
lower_residual = np.abs(combined_q[lower] - desired_q)
upper_residual = np.abs(combined_q[upper] - desired_q)
mask = lower_residual > upper_residual
index = lower # alias; we no longer need lower
index[mask] = upper[mask]
rv = combined_vals[index]
else:
raise ValueError(
"interpolation method can only be 'linear', 'lower', "
"'higher', 'midpoint', or 'nearest'"
)
return rv