issues: 844827026

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id node_id number title user state locked assignee milestone comments created_at updated_at closed_at author_association active_lock_reason draft pull_request body reactions performed_via_github_app state_reason repo type
844827026 MDU6SXNzdWU4NDQ4MjcwMjY= 5094 exact align should support a tolerance for agreement in coordinates 5189118 closed 0     2 2021-03-30T16:21:59Z 2021-03-31T20:00:40Z 2021-03-31T20:00:40Z NONE      

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:

```python 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 <tt>xr.show_versions()</tt> 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 
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