What happened?

In my work, I produced a sequence of covariance matrices for a 2-D quantity. I wanted to extract the diagonal of the covariance matrices, then make that diagonal 2-D so I could plot it.

I could unstack the 2-D dimensions in the sequence of covariance matrices without issue. I figured out how to extract the diagonal of the covariance matrices. Unstacking the diagonal using the same procedure raised a ValueError.

What did you expect to happen?

I expected the sequence of one-dimensional diagonals to unstack into a sequence of two-dimensional fields so I could plot them with pcolormesh.

I can make this happen by unstacking the two dimensions (producing a 5-D DataArray) and extracting the diagonals from that, but I don't see a reason it shouldn't work in the other order.

Minimal Complete Verifiable Example

```Python import numpy as np import xarray

Working:

test = xarray.DataArray( np.eye(12), dims=("dim0", "adj_dim0"), coords={ "dim0_0": (("dim0",), np.repeat(np.arange(3), 4)), "dim0_1": (("dim0",), np.tile(np.arange(4), 3)), }, ) unstacked = test.set_index(dim0=["dim0_0", "dim0_1"]).unstack("dim0") diag_index = xarray.DataArray(np.arange(test.shape[0]), dims=("diag",)) unstacked_diag = ( test.isel(dim0=diag_index, adj_dim0=diag_index) .set_index(diag=["dim0_0", "dim0_1"]) .unstack("diag") )

Not working:

test = xarray.DataArray( dims=("dim1", "dim0", "adj_dim0"), data=np.tile(np.eye(12), (2, 1, 1)), coords={ "dim0": np.arange(12), "dim0_0": (("dim0",), np.repeat(np.arange(3), 4)), "dim0_1": (("dim0",), np.tile(np.arange(4), 3)), "adj_dim0": np.arange(12), "adj_dim0_0": (("adj_dim0",), np.repeat(np.arange(3), 4)), "adj_dim0_1": (("adj_dim0",), np.tile(np.arange(4), 3)), }, ) unstacked = test.set_index( dim0=["dim0_0", "dim0_1"], adj_dim0=["adj_dim0_0", "adj_dim0_1"] ).unstack(["dim0", "adj_dim0"])

diag_index0 = xarray.DataArray(np.arange(unstacked.shape[1]), dims=("diag_0",)) diag_index1 = xarray.DataArray(np.arange(unstacked.shape[2]), dims=("diag_1",)) unstacked_diag = unstacked.isel( dim0_0=diag_index0, dim0_1=diag_index1, adj_dim0_0=diag_index0, adj_dim0_1=diag_index1, )

diag_index = xarray.DataArray(np.arange(test.shape[1]), dims=("diag",)) test.isel(dim0=diag_index, adj_dim0=diag_index).set_index( diag=["dim0_0", "dim0_1"] ).unstack("diag") ```

Relevant log output

Python Traceback (most recent call last): File "./test.py", line 50, in <module> ).unstack("diag") File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/dataarray.py", line 2201, in unstack ds = self._to_temp_dataset().unstack(dim, fill_value, sparse) File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/dataset.py", line 4214, in unstack result = result._unstack_once(dim, fill_value, sparse) File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/dataset.py", line 4070, in _unstack_once variables[name] = var._unstack_once( File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/variable.py", line 1690, in _unstack_once return self._replace(dims=new_dims, data=data) File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/variable.py", line 978, in _replace return type(self)(dims, data, attrs, encoding, fastpath=True) File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/variable.py", line 2668, in __init__ raise ValueError(f"{type(self).__name__} objects must be 1-dimensional") ValueError: IndexVariable objects must be 1-dimensional

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS

commit: None python: 3.10.4 | packaged by conda-forge | (main, Mar 24 2022, 17:39:04) [GCC 10.3.0] python-bits: 64 OS: Linux OS-release: 3.10.0-1160.59.1.el7.x86_64 machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_US.UTF-8 LOCALE: ('en_US', 'UTF-8') libhdf5: 1.12.1 libnetcdf: 4.8.1

xarray: 2022.3.0 pandas: 1.4.2 numpy: 1.22.3 scipy: 1.8.0 netCDF4: 1.5.8 pydap: None h5netcdf: None h5py: None Nio: None zarr: None cftime: 1.6.0 nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: None iris: None bottleneck: None dask: None distributed: None matplotlib: 3.5.1 cartopy: 0.20.2 seaborn: None numbagg: None fsspec: None cupy: None pint: None sparse: None setuptools: 61.3.1 pip: 22.0.4 conda: None pytest: None IPython: None sphinx: None

I prefer having these as coordinates rather than data variables.

This does not cooperate with slicing/pulling out individual variables. grid_mapping should only be associated with variables that have horizontal dimensions or coordinates. bounds should stay associated despite having more dimensions.

I have not implemented similar functionality for the iris conversions.

An alternate approach to dealing with bounds (not used here) is to use a pandas.IntervalIndex http://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.IntervalIndex.html#pandas.IntervalIndex and use where the coordinate is within its cell to determine on which side the intervals are closed (x_dim == x_dim_bnds[:, 0] corresponds to "left", x_dim == x_dim_bnds[:, 1] corresponds to "right", and anything else is "neither"). This would stay through slicing and might already be used for .groupby_bins(), but would not generalize to boundaries of multidimensional coordinates unless someone implements a multidimensional generalization of pd.IntervalIndex

• [ ] Closes #xxxx
• [X] Tests added
• [ ] Fully documented, including whats-new.rst for all changes and api.rst for new API

The documentation seems to imply that passing _FillValue=False in the encoding works to set no fill value for any value. These changes to netCDF4_.py and h5netcdf_.py seem to allow this for variables that are vlen strings (dtype str rather than "S1"): I have used the code-path in netCDF4_.py in real code and know that it at least allows the save to complete.

Allowing _FillValue=False makes it easier to explicitly exclude _FillValue from being written for coordinate variables, which some CF-compliance checkers complain about.

• [ ] Closes #xxxx
• [X] Tests added
• [ ] Fully documented, including whats-new.rst for all changes and api.rst for new API