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Implements scipy.stats.rankdata (#3218)
* Implement rankdata * linting * Linting * adding copyright header * Increasing coverage * increasing coverage * linting * Sorting imports alphabetically
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# 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, | ||
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
# See the License for the specific language governing permissions and | ||
# limitations under the License. | ||
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from ... import tensor as mt | ||
import numpy as np | ||
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def rankdata(a, method="average", *, axis=None): | ||
"""Assign ranks to data, dealing with ties appropriately. | ||
By default (``axis=None``), the data array is first flattened, and a flat | ||
array of ranks is returned. Separately reshape the rank array to the | ||
shape of the data array if desired (see Examples). | ||
Ranks begin at 1. The `method` argument controls how ranks are assigned | ||
to equal values. See [1]_ for further discussion of ranking methods. | ||
Parameters | ||
---------- | ||
a : array_like | ||
The array of values to be ranked. | ||
method : {'average', 'min', 'max', 'dense', 'ordinal'}, optional | ||
The method used to assign ranks to tied elements. | ||
The following methods are available (default is 'average'): | ||
* 'average': The average of the ranks that would have been assigned to | ||
all the tied values is assigned to each value. | ||
* 'min': The minimum of the ranks that would have been assigned to all | ||
the tied values is assigned to each value. (This is also | ||
referred to as "competition" ranking.) | ||
* 'max': The maximum of the ranks that would have been assigned to all | ||
the tied values is assigned to each value. | ||
* 'dense': Like 'min', but the rank of the next highest element is | ||
assigned the rank immediately after those assigned to the tied | ||
elements. | ||
* 'ordinal': All values are given a distinct rank, corresponding to | ||
the order that the values occur in `a`. | ||
axis : {None, int}, optional | ||
Axis along which to perform the ranking. If ``None``, the data array | ||
is first flattened. | ||
Returns | ||
------- | ||
ranks : ndarray | ||
An array of size equal to the size of `a`, containing rank | ||
scores. | ||
References | ||
---------- | ||
.. [1] "Ranking", https://en.wikipedia.org/wiki/Ranking | ||
Examples | ||
-------- | ||
>>> from mars.tensor.stats import rankdata | ||
>>> rankdata([0, 2, 3, 2]).execute() | ||
array([ 1. , 2.5, 4. , 2.5]) | ||
>>> rankdata([0, 2, 3, 2], method='min').execute() | ||
array([ 1, 2, 4, 2]) | ||
>>> rankdata([0, 2, 3, 2], method='max').execute() | ||
array([ 1, 3, 4, 3]) | ||
>>> rankdata([0, 2, 3, 2], method='dense').execute() | ||
array([ 1, 2, 3, 2]) | ||
>>> rankdata([0, 2, 3, 2], method='ordinal').execute() | ||
array([ 1, 2, 4, 3]) | ||
>>> rankdata([[0, 2], [3, 2]]).reshape(2,2).execute() | ||
array([[1. , 2.5], | ||
[4. , 2.5]]) | ||
>>> rankdata([[0, 2, 2], [3, 2, 5]], axis=1).execute() | ||
array([[1. , 2.5, 2.5], | ||
[2. , 1. , 3. ]]) | ||
""" | ||
if method not in ("average", "min", "max", "dense", "ordinal"): | ||
raise ValueError('unknown method "{0}"'.format(method)) | ||
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if axis is not None: | ||
a = np.asarray(a) | ||
if a.size == 0: | ||
np.core.multiarray.normalize_axis_index(axis, a.ndim) | ||
dt = np.float64 if method == "average" else np.int_ | ||
return mt.empty(a.shape, dtype=dt) | ||
return mt.tensor(np.apply_along_axis(rankdata, axis, a, method)) | ||
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arr = mt.ravel(mt.asarray(a)) | ||
algo = "mergesort" if method == "ordinal" else "quicksort" | ||
sorter = mt.argsort(arr, kind=algo) | ||
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inv = mt.empty(sorter.size, dtype=np.intp) | ||
inv[sorter] = mt.arange(sorter.size, dtype=np.intp) | ||
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if method == "ordinal": | ||
return inv + 1 | ||
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arr = arr[sorter] | ||
obs = mt.r_[True, arr[1:] != arr[:-1]] | ||
dense = obs.cumsum()[inv] | ||
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if method == "dense": | ||
return dense | ||
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count = mt.r_[mt.nonzero(obs)[0], len(obs)] | ||
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if method == "max": | ||
return count[dense] | ||
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if method == "min": | ||
return count[dense - 1] + 1 | ||
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return 0.5 * (count[dense] + count[dense - 1] + 1) |
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