Error raised when array has additional 2D coordinates

In Harmonica we usually produce 2D grids out of scattered data whose dimensions are northing and easting. In addition, we often have an extra coordinate: the upward, which is the vertical coordinate of each point of the grid. The upward coordinate is included into the list of coordinates inside the array, but as a 2D array with the same dimensions as the grid itself.

When trying to compute the fft over this kind of arrays, xrft is raising and error because it recognizes the upward as a bad coordinate. I leave a minimal working example to reproduce the error:

import numpy as np
import xarray as xr
import xrft

# Build a sample array
# --------------------
# Generate easting and northing
easting = np.linspace(-5e3, 3e3, 91)
northing = np.linspace(4e3, 10e3, 61)

# Generate sample data and the upward coordinate
ee, nn = np.meshgrid(easting, northing)
upward = np.ones_like(ee)
data = ee ** 2 + nn ** 2

# Build the array
dims = ("northing", "easting")
da = xr.DataArray(
    data,
    coords={"easting": easting, "northing": northing, "upward": (dims, upward)},
    dims=dims,
)
print(da)

# Compute FFT
# -----------
xrft.fft(da, true_phase=True, true_amplitude=True)

<xarray.DataArray (northing: 61, easting: 91)>
array([[4.10000000e+07, 4.01190123e+07, 3.92538272e+07, ...,
        2.39649383e+07, 2.44745679e+07, 2.50000000e+07],
       [4.18100000e+07, 4.09290123e+07, 4.00638272e+07, ...,
        2.47749383e+07, 2.52845679e+07, 2.58100000e+07],
       [4.26400000e+07, 4.17590123e+07, 4.08938272e+07, ...,
        2.56049383e+07, 2.61145679e+07, 2.66400000e+07],
       ...,
       [1.21040000e+08, 1.20159012e+08, 1.19293827e+08, ...,
        1.04004938e+08, 1.04514568e+08, 1.05040000e+08],
       [1.23010000e+08, 1.22129012e+08, 1.21263827e+08, ...,
        1.05974938e+08, 1.06484568e+08, 1.07010000e+08],
       [1.25000000e+08, 1.24119012e+08, 1.23253827e+08, ...,
        1.07964938e+08, 1.08474568e+08, 1.09000000e+08]])
Coordinates:
  * easting   (easting) float64 -5e+03 -4.911e+03 -4.822e+03 ... 2.911e+03 3e+03
  * northing  (northing) float64 4e+03 4.1e+03 4.2e+03 ... 9.8e+03 9.9e+03 1e+04
    upward    (northing, easting) float64 1.0 1.0 1.0 1.0 ... 1.0 1.0 1.0 1.0
Traceback (most recent call last):
  File "/home/santi/tmp/test.py", line 27, in <module>
    xrft.fft(da, true_phase=True, true_amplitude=True)
  File "/home/santi/.miniforge3/envs/default/lib/python3.9/site-packages/xrft/xrft.py", line 392, in fft
    raise ValueError(
ValueError: The input array contains coordinate variable(s) (['upward']) whose dims include the transform dimension(s) `northing`. Please drop these coordinates (`.drop(['upward']`) before invoking xrft.

Version of xrft: v0.4.0

---

I think we could improve the detection of the bad coordinates in a way that it doesn’t include any n-dimensional coordinate (where n > 1) so we don’t need to drop them before passing them to fft.

What do you think?

[santisoler]

I’ve just noticed that pad has a similar problem: it raises a cryptic xarray error when trying to pad a grid with the extra upward coordinate. So probably a single private function should take care of the task of ignoring additional coordinates for both cases, and only a simple call to it inside fft and pad should do the trick.

[roxyboy]

PR #163 was where we implemented the error detection as an easy fix to issue #162 .