exact align should support a tolerance for agreement in coordinates

[bennyrowland]

What happened:
Using xrft to do 2D Fourier transforms of DataArrays, the coords for transformed axes are modified along with the data. If we do both a forward and inverse transformation, the values are fractionally different to those from the original data, which causes align(join="exact") to fail, and in turn things which depend on this such as where(). This does not seem to happen for a 1D transform, but does for a 2D, for the outer axis. If we use np.allclose() then the coords are shown to be essentially equal to an extremely high tolerance.

What you expected to happen:
align(join="exact") should use np.allclose() or some alternative approach which allows inconsequential differences between coords. This could be supported with a keyword argument to align() with some kind of tolerance to be passed to np.allclose() with a conservative default value to allow xr.where() etc. to succeed without having to call align() manually first.

Minimal Complete Verifiable Example:

import numpy as np
import xarray as xr
import xrft.xrft as xrft

data = np.random.random((150, 150))
coords1 = np.fft.fftshift(np.fft.fftfreq(150, 200/150))
da = xr.DataArray(data, dims=["d1", "d2"], coords={"d1": coords1, "d2": coords1})

fda = xrft.idft(da)
ff_da = xrft.dft(fda)

print(np.allclose(da.d1, ff_da.d1, rtol=1e-14, atol=1e-16))
xr.align(da, ff_da, join='exact')

Anything else we need to know?:
I am happy to work on a PR if the core devs can confirm they would approve the change.

Environment:

Output of xr.show_versions()

INSTALLED VERSIONS

commit: None
python: 3.8.8 (default, Feb 24 2021, 15:54:32) [MSC v.1928 64 bit (AMD64)]
python-bits: 64
OS: Windows
OS-release: 10
machine: AMD64
processor: Intel64 Family 6 Model 142 Stepping 12, GenuineIntel
byteorder: little
LC_ALL: None
LANG: None
LOCALE: English_United Kingdom.1252
libhdf5: 1.10.4
libnetcdf: None

xarray: 0.17.0
pandas: 1.2.3
numpy: 1.19.2
scipy: 1.6.1
netCDF4: None
pydap: None
h5netcdf: None
h5py: 2.10.0
Nio: None
zarr: None
cftime: 1.4.1
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: 1.3.2
dask: 2021.03.0
distributed: 2021.03.0
matplotlib: 3.3.4
cartopy: None
seaborn: None
numbagg: None
pint: None
setuptools: 52.0.0.post20210125
pip: 21.0.1
conda: None
pytest: 6.2.2
IPython: 7.21.0
sphinx: 3.5.2

[keewis]

related to #4489

[bennyrowland]

Indeed, it looks like that will solve my problem when it gets merged. I did a search for existing issues but missed 4489 as a PR. I will close this and keep an eye on 4489 instead. Thanks for bringing it to my attention.