Repository: fatiando/harmonica (python)

Issue:
Coordinates decimal issue in filters
**Description of the problem:**
<!--
Please be as detailed as you can when describing an issue. The more information
we have, the easier it will be for us to track this down.
-->

When using the new grid transformations, I noticed that several (at least `derivative_upward` and `gaussian_lowpass`) functions are slightly changing the easting coordinates of the dataarrays. I was attempting to add the resulting grids as a new dataset variable with:
```python
magnetic_grid_padded['deriv_upward'] = hm.derivative_upward(magnetic_grid_padded)
```
Plotting the new grid shows:
![image](https://user-images.githubusercontent.com/81199856/225128479-bdca1ee7-5873-4d27-89d5-dd97f0726a7f.png)

Compared to the normal method of creating a new array shows an issue with the high and low easting values.
```python
deriv_upward = hm.derivative_upward(magnetic_grid_padded)
```
![image](https://user-images.githubusercontent.com/81199856/225128711-fc0a8e08-b976-4d45-af7e-89f90b86c4a4.png)

Numpy testing confirms that the easting values of the produced grid don't match the original past the 10th decimal place.

```python
np.testing.assert_almost_equal(
    deriv_upward.easting.values, 
    magnetic_grid_padded.easting.values, 
    decimal=11,
)
```
```
AssertionError: 
Arrays are not almost equal to 11 decimals

Mismatched elements: 391 / 576 (67.9%)
Max absolute difference: 1.16415322e-10
Max relative difference: 2.53196054e-16
 x: array([459783.31767976726, 459833.31767976726, 459883.31767976726,
       459933.31767976726, 459983.31767976726, 460033.31767976726,
       460083.31767976726, 460133.31767976726, 460183.31767976726,...
 y: array([459783.31767976715, 459833.31767976715, 459883.31767976715,
       459933.31767976715, 459983.31767976715, 460033.31767976715,
       460083.31767976715, 460133.31767976715, 460183.31767976715,...
```
The northing coordinates are exactly equal for this dataset, but northing and easting both fail the test on a dataset of min. 

I have a workaround, which is to round the coordinate values to the same number of decimal places before merging, which gives the desired results.

```python
magnetic_grid_padded = magnetic_grid_padded.assign_coords(
    {
        "easting":np.round(magnetic_grid_padded.easting.values),
        "northing":np.round(magnetic_grid_padded.northing.values)
    })

deriv_upward = hm.derivative_upward(magnetic_grid_padded)
deriv_upward = deriv_upward.assign_coords(
    {
        "easting":np.round(deriv_upward.easting.values),
        "northing":np.round(deriv_upward.northing.values)
    })

magnetic_grid_padded['deriv_upward'] = deriv_upward
```

I need to add the resulting data back to the original dataset since my grid has NaN's, which I've filled with -999 and need to mask the results with the original data extent. 

Any ideas what's causing this issue?

Otherwise, these new functions are great!

**System information**

* Operating system: Linux
* Python installation (Anaconda, system, ETS):  mambaforge
* Version of Python: 3.10.9
* Version of this package: 0.6.0.post1+g627fbfa.d20230310 
* If using conda, paste the output of `conda list` below:

<details>
<summary>Output of conda list</summary>
<pre>

# Name                    Version                   Build  Channel
_libgcc_mutex             0.1                 conda_forge    conda-forge
_openmp_mutex             4.5                       2_gnu    conda-forge
aiofiles                  22.1.0             pyhd8ed1ab_0    conda-forge
aiosqlite                 0.18.0             pyhd8ed1ab_0    conda-forge
anyio                     3.6.2              pyhd8ed1ab_0    conda-forge
argon2-cffi               21.3.0             pyhd8ed1ab_0    conda-forge
argon2-cffi-bindings      21.2.0          py310h5764c6d_3    conda-forge
asttokens                 2.2.1              pyhd8ed1ab_0    conda-forge
attrs                     22.2.0             pyh71513ae_0    conda-forge
babel                     2.12.1             pyhd8ed1ab_1    conda-forge
backcall                  0.2.0              pyh9f0ad1d_0    conda-forge
backports                 1.0                pyhd8ed1ab_3    conda-forge
backports.functools_lru_cache 1.6.4              pyhd8ed1ab_0    conda-forge
beautifulsoup4            4.11.2             pyha770c72_0    conda-forge
bleach                    6.0.0              pyhd8ed1ab_0    conda-forge
bokeh                     2.4.3              pyhd8ed1ab_3    conda-forge
boule                     0.4.1              pyhd8ed1ab_0    conda-forge
brotli                    1.0.9                h166bdaf_8    conda-forge
brotli-bin                1.0.9                h166bdaf_8    conda-forge
brotlipy                  0.7.0           py310h5764c6d_1005    conda-forge
bzip2                     1.0.8                h7f98852_4    conda-forge
c-ares                    1.18.1               h7f98852_0    conda-forge
ca-certificates           2022.12.7            ha878542_0    conda-forge
cached-property           1.5.2                hd8ed1ab_1    conda-forge
cached_property           1.5.2              pyha770c72_1    conda-forge
cartopy                   0.21.1          py310hcb7e713_0    conda-forge
certifi                   2022.12.7          pyhd8ed1ab_0    conda-forge
cffi                      1.15.1          py310h255011f_3    conda-forge
cftime                    1.6.2           py310hde88566_1    conda-forge
charset-normalizer        2.1.1              pyhd8ed1ab_0    conda-forge
click                     8.1.3           unix_pyhd8ed1ab_2    conda-forge
cloudpickle               2.2.1              pyhd8ed1ab_0    conda-forge
comm                      0.1.2              pyhd8ed1ab_0    conda-forge
contourpy                 1.0.7           py310hdf3cbec_0    conda-forge
cryptography              39.0.2          py310h34c0648_0    conda-forge
curl                      7.88.1               hdc1c0ab_0    conda-forge
cycler                    0.11.0             pyhd8ed1ab_0    conda-forge
cytoolz                   0.12.0          py310h5764c6d_1    conda-forge
dask                      2023.3.0           pyhd8ed1ab_0    conda-forge
dask-core                 2023.3.0           pyhd8ed1ab_0    conda-forge
debugpy                   1.6.6           py310heca2aa9_0    conda-forge
decorator                 5.1.1              pyhd8ed1ab_0    conda-forge
defusedxml                0.7.1              pyhd8ed1ab_0    conda-forge
distributed               2023.3.0           pyhd8ed1ab_0    conda-forge
docrep                    0.3.2              pyh44b312d_0    conda-forge
ensaio                    0.5.0              pyhd8ed1ab_0    conda-forge
entrypoints               0.4                pyhd8ed1ab_0    conda-forge
executing                 1.2.0              pyhd8ed1ab_0    conda-forge
flit-core                 3.8.0              pyhd8ed1ab_0    conda-forge
fonttools                 4.39.0          py310h1fa729e_0    conda-forge
freetype                  2.12.1               hca18f0e_1    conda-forge
fsspec                    2023.3.0           pyhd8ed1ab_1    conda-forge
future                    0.18.3             pyhd8ed1ab_0    conda-forge
geos                      3.11.1               h27087fc_0    conda-forge
h5netcdf                  1.1.0              pyhd8ed1ab_1    conda-forge
h5py                      3.8.0           nompi_py310h0311031_100    conda-forge
harmonica                 0.6.0.post1+g627fbfa.d20230310          pypi_0    pypi
hdf4                      4.2.15               h501b40f_6    conda-forge
hdf5                      1.12.2          nompi_h4df4325_101    conda-forge
heapdict                  1.0.1                      py_0    conda-forge
icu                       70.1                 h27087fc_0    conda-forge
idna                      3.4                pyhd8ed1ab_0    conda-forge
importlib-metadata        6.0.0              pyha770c72_0    conda-forge
importlib_metadata        6.0.0                hd8ed1ab_0    conda-forge
importlib_resources       5.12.0             pyhd8ed1ab_0    conda-forge
ipykernel                 6.21.3             pyh210e3f2_0    conda-forge
ipython                   8.11.0             pyh41d4057_0    conda-forge
ipython_genutils          0.2.0                      py_1    conda-forge
jedi                      0.18.2             pyhd8ed1ab_0    conda-forge
jinja2                    3.1.2              pyhd8ed1ab_1    conda-forge
joblib                    1.2.0              pyhd8ed1ab_0    conda-forge
json5                     0.9.5              pyh9f0ad1d_0    conda-forge
jsonschema                4.17.3             pyhd8ed1ab_0    conda-forge
jupyter_client            8.0.3              pyhd8ed1ab_0    conda-forge
jupyter_core              5.2.0           py310hff52083_0    conda-forge
jupyter_events            0.6.3              pyhd8ed1ab_0    conda-forge
jupyter_server            2.4.0              pyhd8ed1ab_0    conda-forge
jupyter_server_fileid     0.8.0              pyhd8ed1ab_0    conda-forge
jupyter_server_terminals  0.4.4              pyhd8ed1ab_1    conda-forge
jupyter_server_ydoc       0.6.1              pyhd8ed1ab_0    conda-forge
jupyter_ydoc              0.2.2              pyhd8ed1ab_0    conda-forge
jupyterlab                3.6.1              pyhd8ed1ab_0    conda-forge
jupyterlab_pygments       0.2.2              pyhd8ed1ab_0    conda-forge
jupyterlab_server         2.20.0             pyhd8ed1ab_0    conda-forge
keyutils                  1.6.1                h166bdaf_0    conda-forge
kiwisolver                1.4.4           py310hbf28c38_1    conda-forge
krb5                      1.20.1               h81ceb04_0    conda-forge
lcms2                     2.15                 haa2dc70_1    conda-forge
ld_impl_linux-64          2.40                 h41732ed_0    conda-forge
lerc                      4.0.0                h27087fc_0    conda-forge
libaec                    1.0.6                hcb278e6_1    conda-forge
libblas                   3.9.0           16_linux64_openblas    conda-forge
libbrotlicommon           1.0.9                h166bdaf_8    conda-forge
libbrotlidec              1.0.9                h166bdaf_8    conda-forge
libbrotlienc              1.0.9                h166bdaf_8    conda-forge
libcblas                  3.9.0           16_linux64_openblas    conda-forge
libcurl                   7.88.1               hdc1c0ab_0    conda-forge
libdeflate                1.17                 h0b41bf4_0    conda-forge
libedit                   3.1.20191231         he28a2e2_2    conda-forge
libev                     4.33                 h516909a_1    conda-forge
libffi                    3.4.2                h7f98852_5    conda-forge
libgcc-ng                 12.2.0              h65d4601_19    conda-forge
libgfortran-ng            12.2.0              h69a702a_19    conda-forge
libgfortran5              12.2.0              h337968e_19    conda-forge
libgomp                   12.2.0              h65d4601_19    conda-forge
libiconv                  1.17                 h166bdaf_0    conda-forge
libjpeg-turbo             2.1.5.1              h0b41bf4_0    conda-forge
liblapack                 3.9.0           16_linux64_openblas    conda-forge
libllvm11                 11.1.0               he0ac6c6_5    conda-forge
libnetcdf                 4.9.1           nompi_hd2e9713_102    conda-forge
libnghttp2                1.52.0               h61bc06f_0    conda-forge
libnsl                    2.0.0                h7f98852_0    conda-forge
libopenblas               0.3.21          pthreads_h78a6416_3    conda-forge
libpng                    1.6.39               h753d276_0    conda-forge
libsodium                 1.0.18               h36c2ea0_1    conda-forge
libsqlite                 3.40.0               h753d276_0    conda-forge
libssh2                   1.10.0               hf14f497_3    conda-forge
libstdcxx-ng              12.2.0              h46fd767_19    conda-forge
libtiff                   4.5.0                hddfeb54_5    conda-forge
libuuid                   2.32.1            h7f98852_1000    conda-forge
libwebp-base              1.2.4                h166bdaf_0    conda-forge
libxcb                    1.13              h7f98852_1004    conda-forge
libxml2                   2.10.3               h7463322_0    conda-forge
libzip                    1.9.2                hc929e4a_1    conda-forge
libzlib                   1.2.13               h166bdaf_4    conda-forge
llvmlite                  0.39.1          py310h58363a5_1    conda-forge
locket                    1.0.0              pyhd8ed1ab_0    conda-forge
lz4                       4.3.2           py310h0cfdcf0_0    conda-forge
lz4-c                     1.9.4                hcb278e6_0    conda-forge
markupsafe                2.1.2           py310h1fa729e_0    conda-forge
matplotlib-base           3.7.1           py310he60537e_0    conda-forge
matplotlib-inline         0.1.6              pyhd8ed1ab_0    conda-forge
mistune                   2.0.5              pyhd8ed1ab_0    conda-forge
msgpack-python            1.0.5           py310hdf3cbec_0    conda-forge
munkres                   1.1.4              pyh9f0ad1d_0    conda-forge
nbclassic                 0.5.3              pyhb4ecaf3_3    conda-forge
nbclient                  0.7.2              pyhd8ed1ab_0    conda-forge
nbconvert                 7.2.9              pyhd8ed1ab_0    conda-forge
nbconvert-core            7.2.9              pyhd8ed1ab_0    conda-forge
nbconvert-pandoc          7.2.9              pyhd8ed1ab_0    conda-forge
nbformat                  5.7.3              pyhd8ed1ab_0    conda-forge
ncurses                   6.3                  h27087fc_1    conda-forge
nest-asyncio              1.5.6              pyhd8ed1ab_0    conda-forge
netcdf4                   1.6.3           nompi_py310h0feb132_100    conda-forge
notebook                  6.5.3              pyha770c72_0    conda-forge
notebook-shim             0.2.2              pyhd8ed1ab_0    conda-forge
numba                     0.56.4          py310ha5257ce_0    conda-forge
numpy                     1.23.5          py310h53a5b5f_0    conda-forge
openjpeg                  2.5.0                hfec8fc6_2    conda-forge
openssl                   3.0.8                h0b41bf4_0    conda-forge
packaging                 23.0               pyhd8ed1ab_0    conda-forge
pandas                    1.5.3           py310h9b08913_0    conda-forge
pandoc                    2.19.2               h32600fe_2    conda-forge
pandocfilters             1.5.0              pyhd8ed1ab_0    conda-forge
parso                     0.8.3              pyhd8ed1ab_0    conda-forge
partd                     1.3.0              pyhd8ed1ab_0    conda-forge
pexpect                   4.8.0              pyh1a96a4e_2    conda-forge
pickleshare               0.7.5                   py_1003    conda-forge
pillow                    9.4.0           py310h065c6d2_2    conda-forge
pip                       23.0.1             pyhd8ed1ab_0    conda-forge
pkgutil-resolve-name      1.3.10             pyhd8ed1ab_0    conda-forge
platformdirs              3.1.0              pyhd8ed1ab_0    conda-forge
pooch                     1.7.0              pyhd8ed1ab_0    conda-forge
proj                      9.1.1                h8ffa02c_2    conda-forge
prometheus_client         0.16.0             pyhd8ed1ab_0    conda-forge
prompt-toolkit            3.0.38             pyha770c72_0    conda-forge
prompt_toolkit            3.0.38               hd8ed1ab_0    conda-forge
psutil                    5.9.4           py310h5764c6d_0    conda-forge
pthread-stubs             0.4               h36c2ea0_1001    conda-forge
ptyprocess                0.7.0              pyhd3deb0d_0    conda-forge
pure_eval                 0.2.2              pyhd8ed1ab_0    conda-forge
pycparser                 2.21               pyhd8ed1ab_0    conda-forge
pygments                  2.14.0             pyhd8ed1ab_0    conda-forge
pyopenssl                 23.0.0             pyhd8ed1ab_0    conda-forge
pyparsing                 3.0.9              pyhd8ed1ab_0    conda-forge
pyproj                    3.4.1           py310h15e2413_1    conda-forge
pyrsistent                0.19.3          py310h1fa729e_0    conda-forge
pyshp                     2.3.1              pyhd8ed1ab_0    conda-forge
pysocks                   1.7.1              pyha2e5f31_6    conda-forge
python                    3.10.9          he550d4f_0_cpython    conda-forge
python-dateutil           2.8.2              pyhd8ed1ab_0    conda-forge
python-fastjsonschema     2.16.3             pyhd8ed1ab_0    conda-forge
python-json-logger        2.0.7              pyhd8ed1ab_0    conda-forge
python_abi                3.10                    3_cp310    conda-forge
pytz                      2022.7.1           pyhd8ed1ab_0    conda-forge
pyyaml                    6.0             py310h5764c6d_5    conda-forge
pyzmq                     25.0.0          py310h059b190_0    conda-forge
readline                  8.1.2                h0f457ee_0    conda-forge
requests                  2.28.2             pyhd8ed1ab_0    conda-forge
rfc3339-validator         0.1.4              pyhd8ed1ab_0    conda-forge
rfc3986-validator         0.1.1              pyh9f0ad1d_0    conda-forge
scikit-learn              1.2.2           py310h209a8ca_0    conda-forge
scipy                     1.10.1          py310h8deb116_0    conda-forge
send2trash                1.8.0              pyhd8ed1ab_0    conda-forge
setuptools                67.6.0             pyhd8ed1ab_0    conda-forge
shapely                   2.0.1           py310h8b84c32_0    conda-forge
six                       1.16.0             pyh6c4a22f_0    conda-forge
sniffio                   1.3.0              pyhd8ed1ab_0    conda-forge
sortedcontainers          2.4.0              pyhd8ed1ab_0    conda-forge
soupsieve                 2.3.2.post1        pyhd8ed1ab_0    conda-forge
sqlite                    3.40.0               h4ff8645_0    conda-forge
stack_data                0.6.2              pyhd8ed1ab_0    conda-forge
tblib                     1.7.0              pyhd8ed1ab_0    conda-forge
terminado                 0.17.1             pyh41d4057_0    conda-forge
threadpoolctl             3.1.0              pyh8a188c0_0    conda-forge
tinycss2                  1.2.1              pyhd8ed1ab_0    conda-forge
tk                        8.6.12               h27826a3_0    conda-forge
tomli                     2.0.1              pyhd8ed1ab_0    conda-forge
toolz                     0.12.0             pyhd8ed1ab_0    conda-forge
tornado                   6.2             py310h5764c6d_1    conda-forge
traitlets                 5.9.0              pyhd8ed1ab_0    conda-forge
typing-extensions         4.4.0                hd8ed1ab_0    conda-forge
typing_extensions         4.4.0              pyha770c72_0    conda-forge
tzdata                    2022g                h191b570_0    conda-forge
unicodedata2              15.0.0          py310h5764c6d_0    conda-forge
urllib3                   1.26.14            pyhd8ed1ab_0    conda-forge
verde                     1.7.0              pyhd8ed1ab_0    conda-forge
wcwidth                   0.2.6              pyhd8ed1ab_0    conda-forge
webencodings              0.5.1                      py_1    conda-forge
websocket-client          1.5.1              pyhd8ed1ab_0    conda-forge
wheel                     0.38.4             pyhd8ed1ab_0    conda-forge
xarray                    2023.2.0           pyhd8ed1ab_0    conda-forge
xorg-libxau               1.0.9                h7f98852_0    conda-forge
xorg-libxdmcp             1.1.3                h7f98852_0    conda-forge
xrft                      1.0.1                    pypi_0    pypi
xz                        5.2.6                h166bdaf_0    conda-forge
y-py                      0.5.9           py310h4426083_0    conda-forge
yaml                      0.2.5                h7f98852_2    conda-forge
ypy-websocket             0.8.2              pyhd8ed1ab_0    conda-forge
zeromq                    4.3.4                h9c3ff4c_1    conda-forge
zict                      2.2.0              pyhd8ed1ab_0    conda-forge
zipp                      3.15.0             pyhd8ed1ab_0    conda-forge
zstd                      1.5.2                h3eb15da_6    conda-forge

</pre>
</details>


Pull request:
Fix coordinate rounding errors in FFT
Here is a quick fix for the rounding error of the coordinate values during the FFTs. I've simply copied the original grid coordinates back to the grid after filtering.

This now allows users to add the filtered results as a new variable to the dataset/dataarray:
```python
magnetic_grid_padded["upward_continued"] = hm.upward_continuation(magnetic_grid_padded, height_displacement=500)
```
<!--
Thank you for contributing a pull request to Fatiando! 💖

👆🏽 ABOVE: Describe the changes proposed and WHY you made them.

👇🏽 BELOW: Link to any relevant issue or pull request.

Please ensure you have taken a look at the CONTRIBUTING.md file 
in this repository (if available) and the general guidelines at 
https://github.com/fatiando/community/blob/main/CONTRIBUTING.md
-->

**Relevant issues/PRs:**
<!--
Example: "Fixes #1234" / "See also #345" / "Relevant to #111"
Use keywords (e.g., Fixes, Closes) to create the links and automatically
close issues when this PR is merged. 
See https://github.com/blog/1506-closing-issues-via-pull-requests
-->
Fixes #395 

Patch:
diff --git a/harmonica/filters/_utils.py b/harmonica/filters/_utils.py
index bd2b7c4..0325386 100644
--- a/harmonica/filters/_utils.py
+++ b/harmonica/filters/_utils.py
@@ -61,4 +61,10 @@ def apply_filter(grid, fft_filter, **kwargs):
     filtered_fft_grid = fft_grid * da_filter
     # Compute inverse FFT
     filtered_grid = ifft(filtered_fft_grid).real
+
+    # use original coordinates on the filtered grid
+    filtered_grid = filtered_grid.assign_coords(
+        {dims[1]: grid[dims[1]].values, dims[0]: grid[dims[0]].values}
+    )
+
     return filtered_grid


Test patch:
diff --git a/harmonica/tests/test_filters.py b/harmonica/tests/test_filters.py
index 42fe0e7..035af9d 100644
--- a/harmonica/tests/test_filters.py
+++ b/harmonica/tests/test_filters.py
@@ -220,6 +220,18 @@ def test_apply_filter_grid_with_nans(invalid_grid_with_nans):
         apply_filter(invalid_grid_with_nans, dummy_filter)
 
 
+def test_coordinate_rounding_fix(sample_grid):
+    """
+    Check that the transformed grid has the same coordinates as the input grid.
+    """
+    # Apply the dummy filter
+    filtered_grid = apply_filter(sample_grid, dummy_filter)
+
+    # Compare coordinates of original grid with coordinates of filtered grid
+    npt.assert_array_equal(filtered_grid.easting.values, sample_grid.easting.values)
+    npt.assert_array_equal(filtered_grid.northing.values, sample_grid.northing.values)
+
+
 # -----------------------------
 # Test upward derivative filter
 # -----------------------------