问题

I want to calculate the Decile Index - see the ex1-Calculate Decile Index (DI) with Python.ipynb.

The pandas implementation is simple enough but I need help with applying the bin labels to a new variable / coordinate using the groupby_bins() functionality.

working example (test dataset)

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,
    }
)

This looks like:

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

Calculating the cumulative frequency distribution (normalised rank)

# 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

Pandas Solution

I want to create a variable which will create a new variable or coordinate in ds that will have the the integers corresponding to the bins from the bins = [20., 40., 60., 80., np.Inf].

Trying to do it in Pandas is relatively simple with the .qcut functionality.

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

My `xarray` attempt

# 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()

The error message I get is as follows:

---------------------------------------------------------------------------
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

回答1:

I'm not sure pandas.qcut is giving you exactly what you expect; e.g. see the bins it returns in your example:

>>> 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. ])

If I understand correctly, you are looking to assign an integer value at each point based on the bin the point falls into. That is:

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

For this task I would probably recommend using numpy.digitize applied via xarray.apply_ufunc:

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

回答2:

It looks like if you use a scalar to define your bins then it will only generate 4 ranges. You can check this by looking at the length and the name of the keys of the groups of the resulting GroupBy object:

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')]

To prevent the loss of 1/5th of the values, you would have to change your definition of mybins to something like:

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

which is not what you want.

So use bins=5 instead:

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')]

来源：https://stackoverflow.com/questions/56485160/xarray-equivalent-of-pandas-qcut-function

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