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I am having trouble figuring out how to work with xarray DataArrays and DataSets and perform algebra operations; especially when the dimensions have different levels and my cubes have different granularities. I would be very grateful if someone could suggest me some documentation or give me some advice.

In the example below I am trying to compute the contribution of each child (SKU) under a parent (PFS). I found that to get the right values I need to convert the cube slice into a pandas dataframe. Otherwise, Xarray duplicates the dimension I am working with.

import pandas as pd
import numpy as np
import xarray as xr
from itertools import product

# Create hierachies

usage_type_entities = (('Regular',), ('Sample',),
 ('Tender',), ('Clinic Trial',))

usage_type_tree = pd.MultiIndex.from_tuples(
 usage_type_entities, names=('Usage_Type',))

product_tree_hierarchy = (("PF1", "PFS1", "SKU1"),
 ("PF1", "PFS1", "SKU2"),
 ("PF1", "PFS2", "SKU3"),
 ("PF1", "PFS2", "SKU4"),
 ("PF2", "PFS3", "SKU5"))

product_tree_entities = ("PF", "PFS", "SKU")

product_tree = pd.MultiIndex.from_tuples(product_tree_hierarchy,
 names=product_tree_entities)

market_tree_hierarchy = (("Group1", "Region1", "Market1"),
 ("Group1", "Region1", "Market2"),
 ("Group1", "Region2", "Market3"),
 ("Group1", "Region2", "Market4"),
 ("Group2", "Region3", "Market5"))

market_tree_entities = ("Groups", "Regions", "Markets")

market_tree = pd.MultiIndex.from_tuples(market_tree_hierarchy,
 names=market_tree_entities)

time_tree_hierarchy = [(y, y+q) for y, q in product([str(2013+x) for x in range(6)],
 ["Q"+str(int(q)) for q in np.arange(1, 4.1, 1)])][0:22]

time_entities = ("Year", "Quarter")

time_tree = pd.MultiIndex.from_tuples(time_tree_hierarchy, names=time_entities)

# Create X-array Dataset

x1 = np.random.randint(100, size=(len(usage_type_tree), len(
 product_tree), len(market_tree), len(time_tree)))

xda = xr.DataArray(x1, coords=(usage_type_tree, product_tree, market_tree, time_tree),
 dims=("Usage", "Product", "Market", "Time"))

# Operations - I need to convert my slice into a pandas df to get 
the right values. Converting to pandas df works ok. 

market = "Market1"
ut = "Regular"

(xda.sel(Markets=market, Usage_Type=ut)[:, 0].to_pandas() /
 xda.sel(Markets=market, Usage_Type=ut)[:, 0].to_pandas().groupby("PFS").sum(axis=0))

If I don't convert the slice to pandas df and I keep it as a xarray dataset, the dimension gets duplicated. For example, the line below produces a DatArray(Product: 5, Time: 22, PFS: 3), when it should be just (Product: 5, Time: 22)

(xda.sel(Markets=market, Usage_Type=ut)[:, 0] /
 xda.sel(Markets=market, Usage_Type=ut)[:, 0].groupby("PFS").sum(axis=0))