xarray 等效于 pandas `qcut()` 函数

Question

我想计算Decile Index - 请参阅ex1-Calculate Decile Index (DI) with Python.ipynb。

pandas 实现很简单，但我需要帮助才能使用 groupby_bins() 功能将 bin 标签应用于新的 variable / coordinate。

工作示例（测试数据集）

import pandas as pd
import numpy as np
import xarray as xr

time = pd.date_range('2010-01-01','2011-12-31',freq='M')
lat = np.linspace(-5.175003, -4.7250023, 10)
lon = np.linspace(33.524994, 33.97499, 10)
precip = np.random.normal(0, 1, size=(len(time), len(lat), len(lon)))

ds = xr.Dataset(
    {'precip': (['time', 'lat', 'lon'], precip)},
    coords={
        'lon': lon,
        'lat': lat,
        'time': time,
    }
)

这看起来像：

Out[]:
<xarray.Dataset>
Dimensions:  (lat: 10, lon: 10, time: 24)
Coordinates:
  * lon      (lon) float64 33.52 33.57 33.62 33.67 ... 33.82 33.87 33.92 33.97
  * lat      (lat) float64 -5.175 -5.125 -5.075 -5.025 ... -4.825 -4.775 -4.725
  * time     (time) datetime64[ns] 2010-01-31 2010-02-28 ... 2011-12-31
Data variables:
    precip   (time, lat, lon) float64 0.1638 -1.031 0.2087 ... -0.1147 -0.6863

计算累积频率分布（归一化排名）

# calculate a cumsum over some window size
rolling_window = 3
ds_window = (
    ds.rolling(time=rolling_window, center=True)
    .sum()
    .dropna(dim='time', how='all')
)
# construct a cumulative frequency distribution ranking the precip values
# per month
def rank_norm(ds, dim='time'):
    return (ds.rank(dim=dim) - 1) / (ds.sizes[dim] - 1) * 100

result = ds_window.groupby('time.month').apply(rank_norm, args=('time',))
result = result.rename({variable:'rank_norm'}).drop('month')

Out[]:
<xarray.Dataset>
Dimensions:    (lat: 10, lon: 10, time: 108)
Coordinates:
  * lat        (lat) float64 -5.175 -5.125 -5.075 ... -4.825 -4.775 -4.725
  * lon        (lon) float64 33.52 33.57 33.62 33.67 ... 33.82 33.87 33.92 33.97
  * time       (time) datetime64[ns] 2010-01-31 2010-02-28 ... 2018-12-31
Data variables:
    rank_norm  (time, lat, lon) float64 75.0 75.0 12.5 100.0 ... 87.5 0.0 25.0

熊猫解决方案

我想创建一个变量，它将创建一个新的 variable 或 coordinate 在ds 中，它将具有与bins = [20., 40., 60., 80., np.Inf] 中的箱相对应的整数。

使用 .qcut 功能尝试在 Pandas 中执行此操作相对简单。

test = result.to_dataframe()
bins = pd.qcut(test['rank_norm'], 5, labels=[1, 2, 3, 4, 5])
result = bins.to_xarray().to_dataset().rename({'rank_norm': 'rank_bins'})

Out[]:
<xarray.Dataset>
Dimensions:   (lat: 10, lon: 10, time: 108)
Coordinates:
  * lat       (lat) float64 -5.175 -5.125 -5.075 -5.025 ... -4.825 -4.775 -4.725
  * lon       (lon) float64 33.52 33.57 33.62 33.67 ... 33.82 33.87 33.92 33.97
  * time      (time) datetime64[ns] 2010-01-31 2010-02-28 ... 2018-12-31
Data variables:
    rank_bins  (lat, lon, time) int64 4 4 1 4 3 4 5 1 1 2 ... 2 1 1 4 2 4 3 1 2 2

我的xarray 尝试

# assign bins to variable xarray
bins = [20., 40., 60., 80., np.Inf]
decile_index_gpby = rank_norm.groupby_bins('rank_norm', bins=bins)
out = decile_index_gpby.assign()  # assign_coords()

我得到的错误信息如下：

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-166-8d48b9fc1d56> in <module>
      1 bins = [20., 40., 60., 80., np.Inf]
      2 decile_index_gpby = rank_norm.groupby_bins('rank_norm', bins=bins)
----> 3 out = decile_index_gpby.assign()  # assign_coords()

~/miniconda3/lib/python3.7/site-packages/xarray/core/groupby.py in assign(self, **kwargs)
    772         Dataset.assign
    773         """
--> 774         return self.apply(lambda ds: ds.assign(**kwargs))
    775
    776

~/miniconda3/lib/python3.7/site-packages/xarray/core/groupby.py in apply(self, func, args, **kwargs)
    684         kwargs.pop('shortcut', None)  # ignore shortcut if set (for now)
    685         applied = (func(ds, *args, **kwargs) for ds in self._iter_grouped())
--> 686         return self._combine(applied)
    687
    688     def _combine(self, applied):

~/miniconda3/lib/python3.7/site-packages/xarray/core/groupby.py in _combine(self, applied)
    691         coord, dim, positions = self._infer_concat_args(applied_example)
    692         combined = concat(applied, dim)
--> 693         combined = _maybe_reorder(combined, dim, positions)
    694         if coord is not None:
    695             combined[coord.name] = coord

~/miniconda3/lib/python3.7/site-packages/xarray/core/groupby.py in _maybe_reorder(xarray_obj, dim, positions)
    468
    469 def _maybe_reorder(xarray_obj, dim, positions):
--> 470     order = _inverse_permutation_indices(positions)
    471
    472     if order is None:

~/miniconda3/lib/python3.7/site-packages/xarray/core/groupby.py in _inverse_permutation_indices(positions)
    110         positions = [np.arange(sl.start, sl.stop, sl.step) for sl in positions]
    111
--> 112     indices = nputils.inverse_permutation(np.concatenate(positions))
    113     return indices
    114

~/miniconda3/lib/python3.7/site-packages/xarray/core/nputils.py in inverse_permutation(indices)
     58     # use intp instead of int64 because of windows :(
     59     inverse_permutation = np.empty(len(indices), dtype=np.intp)
---> 60     inverse_permutation[indices] = np.arange(len(indices), dtype=np.intp)
     61     return inverse_permutation
     62

IndexError: index 1304 is out of bounds for axis 0 with size 1000

Answer 1

我不确定pandas.qcut 是否完全符合您的期望；例如在您的示例中查看它返回的垃圾箱：

>>> test = result.to_dataframe()
>>> binned, bins = pd.qcut(test['rank_norm'], 5, labels=[1, 2, 3, 4, 5], retbins=True)

>>> bins
array([  0. ,  12.5,  37.5,  62.5,  87.5, 100. ])

如果我理解正确，您希望根据点所在的 bin 为每个点分配一个整数值。那就是：

• 0.0 <= x < 20.0: 1
• 20.0 <= x < 40.0：2
• 40.0 <= x < 60.0: 3
• 60.0 <= x < 80.0: 4
• 80.0 <= x: 5

对于这项任务，我可能会建议使用通过xarray.apply_ufunc 应用的numpy.digitize：

>>> bins = [0., 20., 40., 60., 80., np.inf]
>>> result = xr.apply_ufunc(np.digitize, result, kwargs={'bins': bins})

Answer 2

看起来如果您使用scalar 来定义您的bins，那么它只会生成 4 个范围。您可以通过查看生成的 GroupBy 对象的length 和groups 的keys 的名称来检查这一点：

mybins = [20., 40., 60., 80., np.inf]

decile_index_gpby = rank_norm.groupby_bins('rank_norm', bins=mybins)

len(decile_index_gpby.groups)
=> 4

decile_index_gpby.groups.keys()
=> [Interval(80.0, inf, closed='right'),
    Interval(20.0, 40.0, closed='right'),
    Interval(60.0, 80.0, closed='right'),
    Interval(40.0, 60.0, closed='right')]

为防止损失 1/5 的值，您必须将 mybins 的定义更改为：

mybins = [np.NINF, 20., 40., 60., np.inf]

这不是你想要的。

所以请改用bins=5：

decile_index_gpby = rank_norm.groupby_bins('rank_norm', bins=5)

len(decile_index_gpby.groups)
=> 5

decile_index_gpby.groups.keys()
=> [Interval(80.0, 100.0, closed='right'),
    Interval(20.0, 40.0, closed='right'),
    Interval(60.0, 80.0, closed='right'),
    Interval(40.0, 60.0, closed='right'),
    Interval(-0.1, 20.0, closed='right')]