Code Sample

I am having some troubles understanding apply_ufunc broadcasting rules. As I had some trouble understanding the docs, I am not 100% sure it is a bug, but I am quite sure. I will try to explain why with the following really simple example.

```python import xarray as xr import numpy as np

a = xr.DataArray(data=np.random.normal(size=(7, 3)), dims=["dim1", "dim2"]) c = xr.DataArray(data=np.random.normal(size=(5, 6)), dims=["dim3", "dim4"])

def func(x,y): print(x.shape) print(y.shape) return ```

The function defined always raises an error when trying to call apply_ufunc, but this is intended, as the shapes have already been printed by then, and this keeps the example as simple as possible.

Problem description

```python xr.apply_ufunc(func, a, c)

Out

(7, 3, 1, 1)

(5, 6)

```

Here, a has been kind of broadcasted, but I would expect the shapes of a and c to be the same as when calling xr.broadcast, as there are no input core dims, so all dimensions are broadcasted. However:

```python print([ary.shape for ary in xr.broadcast(a,c)])

[(7, 3, 5, 6), (7, 3, 5, 6)]

```

Using different input core dims does not get rid of the problem, instead I believe it shows some more issues:

```python xr.apply_ufunc(func, a, c, input_core_dims=[["dim1"],[]])

(3, 1, 1, 7), expected (3, 5, 6, 7)

(5, 6), expected (3, 5, 6)

xr.apply_ufunc(func, a, c, input_core_dims=[[],["dim3"]])

(7, 3, 1), expected (7, 3, 6)

(6, 5), expected (7, 3, 6, 5)

xr.apply_ufunc(func, a, c, input_core_dims=[["dim1"],["dim3"]])

(3, 1, 7), expected (3, 6, 7)

(6, 5), expected (3, 6, 5)

```

Is this current behaviour what should be expected?

Output of xr.show_versions()

INSTALLED VERSIONS ------------------ commit: None python: 3.6.8 (default, Jan 14 2019, 11:02:34) [GCC 8.0.1 20180414 (experimental) [trunk revision 259383]] python-bits: 64 OS: Linux OS-release: 4.15.0-52-generic machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_US.UTF-8 LOCALE: en_US.UTF-8 libhdf5: 1.10.2 libnetcdf: 4.6.3 xarray: 0.12.1 pandas: 0.24.2 numpy: 1.16.4 scipy: 1.3.0 netCDF4: 1.5.1.2 pydap: None h5netcdf: None h5py: 2.9.0 Nio: None zarr: None cftime: 1.0.3.4 nc_time_axis: None PseudonetCDF: None rasterio: None cfgrib: None iris: None bottleneck: None dask: None distributed: None matplotlib: 3.1.0 cartopy: None seaborn: None setuptools: 41.0.0 pip: 19.1.1 conda: None pytest: 4.5.0 IPython: 7.5.0 sphinx: 2.0.1