Normalization of Parsed Cartesian Coordinates

[philipc2]

Closes #872

Overview

• Adds a helper uxarray.grid.validation._check_normalization() to check if the Cartesian coordinates stored under a Grid are normalized.
• Adds Grid.normalize_cartesian_coordinates() to normalize coordinates if they were initially stored as non-normalized.

Expected Usage

import uxarray as ux

grid_path = "/path/to/grid.nc"
data_path = "/path/to/data.nc"

uxds = ux.open_dataset(grid_path, data_path)

# normalize coordinates
uxds.uxgrid.normalize_cartesian_coordinates()

[philipc2]

@hongyuchen1030

Do you recall which MPAS dataset had the non-normalized Cartesian coordinates? The two we have in testing both are already normalized.

EDIT: Might have checked something wrong, looking into it now

[hongyuchen1030]

@hongyuchen1030

We should expect the coordinates to be in the [-1, 1] range as well correct?

Yes, correct.

And unfortunately, I don't remember which dataset I ran into, but I will like you know once I saw it.

[github-actions]

ASV Benchmarking

Benchmark Comparison Results

Benchmarks that have improved:

Change	Before [92f38db]	After [2b92c7b]	Ratio	Benchmark (Parameter)
	failed	659±7μs	n/a	mpas_ocean.CheckNorm.time_check_norm('120km')
	failed	430±7μs	n/a	mpas_ocean.CheckNorm.time_check_norm('480km')
-	408M	354M	0.87	mpas_ocean.Integrate.peakmem_integrate('480km')

Benchmarks that have stayed the same:

Change	Before [92f38db]	After [2b92c7b]	Ratio	Benchmark (Parameter)
	failed	failed	n/a	face_bounds.Bounds.time_bounds
	383M	383M	1.00	face_bounds.FaceBounds.peakmem_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/mpas/QU/oQU480.231010.nc'))
	385M	384M	1.00	face_bounds.FaceBounds.peakmem_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/scrip/outCSne8/outCSne8.nc'))
	384M	387M	1.01	face_bounds.FaceBounds.peakmem_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/ugrid/geoflow-small/grid.nc'))
	382M	385M	1.01	face_bounds.FaceBounds.peakmem_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/ugrid/quad-hexagon/grid.nc'))
	1.57±0.01s	1.57±0.01s	1.00	face_bounds.FaceBounds.time_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/mpas/QU/oQU480.231010.nc'))
	226±3ms	222±2ms	0.98	face_bounds.FaceBounds.time_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/scrip/outCSne8/outCSne8.nc'))
	2.02±0.01s	2.02±0.01s	1.00	face_bounds.FaceBounds.time_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/ugrid/geoflow-small/grid.nc'))
	7.65±0.1ms	7.74±0.2ms	1.01	face_bounds.FaceBounds.time_face_bounds(PosixPath('/home/runner/work/uxarray/uxarray/test/meshfiles/ugrid/quad-hexagon/grid.nc'))
	1.77±0.01s	1.76±0.02s	0.99	import.Imports.timeraw_import_uxarray
	652±5ms	642±6ms	0.99	mpas_ocean.ConnectivityConstruction.time_face_face_connectivity('120km')
	42.0±0.7ms	41.1±0.7ms	0.98	mpas_ocean.ConnectivityConstruction.time_face_face_connectivity('480km')
	493±4μs	506±10μs	1.03	mpas_ocean.ConnectivityConstruction.time_n_nodes_per_face('480km')
	1.33±0.01μs	1.31±0.01μs	0.99	mpas_ocean.ConstructTreeStructures.time_ball_tree('120km')
	304±2ns	313±0.9ns	1.03	mpas_ocean.ConstructTreeStructures.time_ball_tree('480km')
	867±6ns	860±5ns	0.99	mpas_ocean.ConstructTreeStructures.time_kd_tree('120km')
	291±5ns	300±4ns	1.03	mpas_ocean.ConstructTreeStructures.time_kd_tree('480km')
	399M	399M	1.00	mpas_ocean.GeoDataFrame.peakmem_to_geodataframe('120km', False)
	389M	389M	1.00	mpas_ocean.GeoDataFrame.peakmem_to_geodataframe('120km', True)
	362M	362M	1.00	mpas_ocean.GeoDataFrame.peakmem_to_geodataframe('480km', False)
	361M	361M	1.00	mpas_ocean.GeoDataFrame.peakmem_to_geodataframe('480km', True)
	1.04±0.01s	1.05±0.01s	1.01	mpas_ocean.GeoDataFrame.time_to_geodataframe('120km', False)
	57.7±0.4ms	58.3±0.5ms	1.01	mpas_ocean.GeoDataFrame.time_to_geodataframe('120km', True)
	78.3±0.3ms	80.1±0.6ms	1.02	mpas_ocean.GeoDataFrame.time_to_geodataframe('480km', False)
	5.57±0.2ms	5.88±0.2ms	1.06	mpas_ocean.GeoDataFrame.time_to_geodataframe('480km', True)
	264M	263M	1.00	mpas_ocean.Gradient.peakmem_gradient('120km')
	241M	241M	1.00	mpas_ocean.Gradient.peakmem_gradient('480km')
	2.69±0.01ms	2.70±0.02ms	1.00	mpas_ocean.Gradient.time_gradient('120km')
	289±4μs	290±1μs	1.01	mpas_ocean.Gradient.time_gradient('480km')
	243±2μs	237±3μs	0.98	mpas_ocean.HoleEdgeIndices.time_construct_hole_edge_indices('120km')
	122±0.7μs	121±0.8μs	0.99	mpas_ocean.HoleEdgeIndices.time_construct_hole_edge_indices('480km')
	370M	371M	1.00	mpas_ocean.Integrate.peakmem_integrate('120km')
	177±1ms	173±0.7ms	0.98	mpas_ocean.Integrate.time_integrate('120km')
	12.0±0.08ms	11.9±0.05ms	0.99	mpas_ocean.Integrate.time_integrate('480km')
	349±3ms	350±3ms	1.00	mpas_ocean.MatplotlibConversion.time_dataarray_to_polycollection('120km', 'exclude')
	347±4ms	348±2ms	1.00	mpas_ocean.MatplotlibConversion.time_dataarray_to_polycollection('120km', 'include')
	349±4ms	350±0.5ms	1.00	mpas_ocean.MatplotlibConversion.time_dataarray_to_polycollection('120km', 'split')
	22.9±0.4ms	22.3±0.2ms	0.97	mpas_ocean.MatplotlibConversion.time_dataarray_to_polycollection('480km', 'exclude')
	22.8±0.7ms	22.6±0.5ms	0.99	mpas_ocean.MatplotlibConversion.time_dataarray_to_polycollection('480km', 'include')
	22.7±0.4ms	22.6±0.1ms	1.00	mpas_ocean.MatplotlibConversion.time_dataarray_to_polycollection('480km', 'split')
	54.9±0.2ms	53.7±0.3ms	0.98	mpas_ocean.RemapDownsample.time_inverse_distance_weighted_remapping
	44.4±0.2ms	43.5±0.05ms	0.98	mpas_ocean.RemapDownsample.time_nearest_neighbor_remapping
	361±1ms	356±1ms	0.99	mpas_ocean.RemapUpsample.time_inverse_distance_weighted_remapping
	263±0.3ms	260±0.5ms	0.99	mpas_ocean.RemapUpsample.time_nearest_neighbor_remapping
	237M	237M	1.00	quad_hexagon.QuadHexagon.peakmem_open_dataset
	236M	236M	1.00	quad_hexagon.QuadHexagon.peakmem_open_grid
	6.66±0.05ms	6.49±0.07ms	0.97	quad_hexagon.QuadHexagon.time_open_dataset
	5.78±0.07ms	5.63±0.04ms	0.97	quad_hexagon.QuadHexagon.time_open_grid

Benchmarks that have got worse:

Change	Before [92f38db]	After [2b92c7b]	Ratio	Benchmark (Parameter)
+	1.86±0.2ms	2.17±0.03ms	1.17	mpas_ocean.ConnectivityConstruction.time_n_nodes_per_face('120km')

[philipc2]

@hongyuchen1030 @amberchen122

This should be ready for review.

[erogluorhan]

This looks good to me with the application of global error tolerance to isclose checks.