# Copyright 2022-2023 XProbe Inc.
# derived from copyright 1999-2021 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
from ...core import ENTITY_TYPE
from ..arithmetic import truediv
from .quantile import _quantile_is_valid, _quantile_unchecked
q_error_msg = "Percentiles must be in the range [0, 100]"
[docs]def percentile(
a,
q,
axis=None,
out=None,
overwrite_input=False,
interpolation="linear",
keepdims=False,
):
"""
Compute the q-th percentile of the data along the specified axis.
Returns the q-th percentile(s) of the array elements.
Parameters
----------
a : array_like
Input tensor or object that can be converted to a tensor.
q : array_like of float
Percentile or sequence of percentiles to compute, which must be between
0 and 100 inclusive.
axis : {int, tuple of int, None}, optional
Axis or axes along which the percentiles are computed. The
default is to compute the percentile(s) along a flattened
version of the tensor.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
overwrite_input : bool, optional
Just for compatibility with Numpy, would not take effect.
interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
This optional parameter specifies the interpolation method to
use when the desired percentile lies between two data points
``i < j``:
* '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``.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in
the result as dimensions with size one. With this option, the
result will broadcast correctly against the original array `a`.
Returns
-------
percentile : scalar or ndarray
If `q` is a single percentile and `axis=None`, then the result
is a scalar. If multiple percentiles are given, first axis of
the result corresponds to the percentiles. The other axes are
the axes that remain after the reduction of `a`. If the input
contains integers or floats smaller than ``float64``, the output
data-type is ``float64``. Otherwise, the output data-type is the
same as that of the input. If `out` is specified, that array is
returned instead.
See Also
--------
mean
median : equivalent to ``percentile(..., 50)``
nanpercentile
quantile : equivalent to percentile, except with q in the range [0, 1].
Notes
-----
Given a vector ``V`` of length ``N``, the q-th percentile of
``V`` is the value ``q/100`` of the way from the minimum to the
maximum in a sorted copy of ``V``. The values and distances of
the two nearest neighbors as well as the `interpolation` parameter
will determine the percentile if the normalized ranking does not
match the location of ``q`` exactly. This function is the same as
the median if ``q=50``, the same as the minimum if ``q=0`` and the
same as the maximum if ``q=100``.
Examples
--------
>>> import mars.tensor as mt
>>> a = mt.array([[10, 7, 4], [3, 2, 1]])
>>> a.execute()
array([[10, 7, 4],
[ 3, 2, 1]])
>>> mt.percentile(a, 50).execute()
3.5
>>> mt.percentile(a, 50, axis=0).execute()
array([6.5, 4.5, 2.5])
>>> mt.percentile(a, 50, axis=1).execute()
array([7., 2.])
>>> mt.percentile(a, 50, axis=1, keepdims=True).execute()
array([[7.],
[2.]])
>>> m = mt.percentile(a, 50, axis=0)
>>> out = mt.zeros_like(m)
>>> mt.percentile(a, 50, axis=0, out=out).execute()
array([6.5, 4.5, 2.5])
>>> m.execute()
array([6.5, 4.5, 2.5])
The different types of interpolation can be visualized graphically:
.. plot::
import matplotlib.pyplot as plt
import mars.tensor as mt
import numpy as np
a = mt.arange(4)
p = mt.linspace(0, 100, 6001)
ax = plt.gca()
lines = [
('linear', None),
('higher', '--'),
('lower', '--'),
('nearest', '-.'),
('midpoint', '-.'),
]
for interpolation, style in lines:
ax.plot(
np.asarray(p), np.asarray(mt.percentile(a, p, interpolation=interpolation)),
label=interpolation, linestyle=style)
ax.set(
title='Interpolation methods for list: ' + str(a),
xlabel='Percentile',
ylabel='List item returned',
yticks=np.asarray(a))
ax.legend()
plt.show()
"""
if not isinstance(q, ENTITY_TYPE):
q = np.asanyarray(q)
q = np.true_divide(q, 100)
# do check instantly if q is not a tensor
if not _quantile_is_valid(q):
raise ValueError(q_error_msg)
else:
q = truediv(q, 100)
return _quantile_unchecked(
a,
q,
axis=axis,
out=out,
overwrite_input=overwrite_input,
interpolation=interpolation,
keepdims=keepdims,
q_error_msg=q_error_msg,
)