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title: 'Xarray Indexes: Exciting new ways to slice and dice your data!' | ||||||
date: '2025-08-11' | ||||||
authors: | ||||||
- name: Benoît Bovy | ||||||
github: benbovy | ||||||
- name: Scott Henderson | ||||||
github: scottyhq | ||||||
- name: Deepak Cherian | ||||||
github: dcherian | ||||||
- name: Justus Magin | ||||||
github: keewis | ||||||
summary: 'An introduction to customizable coordinate-based data selection and alignment for more efficient handling of both traditional and more exotic data structures' | ||||||
--- | ||||||
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\_TLDR: Xarray>2025.6 has been through a major refactoring of its internals that makes coordinate-based data selection and alignment customizable, enabling more efficient handling of both traditional and more exotic data structures. In this post we highlight a few examples that take advantage of this new superpower! | ||||||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. The TLDR looks a bit weird with the leading underscore after rendering, and I'd probably write the version comparison as There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more.
While some pieces of this have been around longer, I know there have been a lot of incremental improvements, so I thought I'd play it safe and go very recent. @benbovy do you have a preference? There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. the version itself is fine (but I didn't check for anything specific that we'd need), I just found the |
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<figure> | ||||||
<img src='/posts/flexible-indexing/summary-slide.png' /> | ||||||
<figcaption> | ||||||
*Summary schematic from Deepak Cherian's [2025 SciPy | ||||||
Presentation](https://www.youtube.com/watch?v=I-NHCuLhRjY) highlighting new | ||||||
custom Indexes and usecases. [Link to full slide | ||||||
deck](https://docs.google.com/presentation/d/1sQU2N0-ThNZM8TUhsZy-kT0bZnu0H5X0FRJz2eKwEpA/edit?slide=id.g37373ba88e6_0_214#slide=id.g37373ba88e6_0_214)* | ||||||
</figcaption> | ||||||
</figure> | ||||||
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{/* This is a comment that won't be rendered! */} | ||||||
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Suggested change
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Yeah, I'll add a small section to the readme on authoring tips. I was commenting some things out while testing the build locally and had to search around to figure out this syntax! Eventually it would be nice for a more streamlined blogging interface, just using mystmd or jupyterbook, I'll open an issue with a couple ideas. |
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## Indexing basics | ||||||
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First thing's first, _what is an `index` and why is it helpful?_ | ||||||
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> In brief, an _index_ makes repeated selection of data more efficient. Xarray Indexes connect coordinate labels to associated data values and encode important contextual information about the coordinate space. | ||||||
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Examples of indexes are all around you and are a fundamental way to organize and simplify access to information. | ||||||
If you want a book about Natural Sciences, you can go to your local library branch and head straight to section `500`, or if you're in the mood for a good novel go to section `800`. Connecting thematic labels with numbers is a classic indexing system that's been around for hundreds of years [(Dewey Decimal System, 1876)](https://en.wikipedia.org/wiki/Dewey_Decimal_Classification). | ||||||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. this might be a US thing, I've never seen this kind of numbering scheme (although admittedly I've not been to a lot of libraries with science sections). Still, the example is interesting and I would keep it, I'd just qualify it with something like "In the US ..." (or whatever fits) There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Good call, definitely Dewey Decimal is a US thing, and there are plenty of alternatives :) |
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The need for an index becomes critical as the size of data grows - just imagine the time it would take to find a specific novel amongst a million uncategorized books! | ||||||
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The same efficiencies arise in computing. Consider a simple 1D dataset consisting of measurements `Y=[10,20,30,40,50,60]` at six coordinate positions `X=[1, 2, 4, 8, 16, 32]`. _What was our measurement at `X=8`?_ | ||||||
To answer this in code, we have need an index that is simply a key:value mapping between the coordinate values and integer positions `i=[0,1,2,3,4,5]` in the coordinates array. | ||||||
With only 6 coordinates, we easily see `X[3]=8` so our measurement of interest is `Y[3]=40`. | ||||||
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> 💡 **Note:** for large datasets we should loop over _all_ the coordinates to ensure there are no repeated values! This initial pass over all the coordinates to build an _index_ may take significant time and may not always be desirable. | ||||||
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## Pandas.Index | ||||||
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Xarray's [label-based selection](https://docs.xarray.dev/en/latest/user-guide/indexing.html#indexing-with-dimension-names) allows a more expressive and simple syntax in which you don't have to think about the index (`da.sel(x=8) = 40`). Up until now, Xarray has relied exclusively on [Pandas.Index](https://pandas.pydata.org/docs/user_guide/indexing.html), which is still used by default: | ||||||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. to be closer to the import
Suggested change
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. also, should this mention databases and hash-tables? It doesn't have to, just a thought. There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more.
I'm actually not sure what you mean here? I thought pandas.Index is a hash-table? But my understanding of this space is admittedly not that great 😅 . If you have a sentence or two please suggest! There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. that's correct. I think I remember hearing that hash tables were created for databases, so that's why I mentioned both (but either way, I don't think it's necessary to follow this, and I don't have any specific sentences in mind). |
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```python | ||||||
x = np.array([1, 2, 4, 8, 16, 32]) | ||||||
y = np.array([10, 20, 30, 40, 50, 60]) | ||||||
da = xr.DataArray(y, coords={'x': x}) | ||||||
da | ||||||
``` | ||||||
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<RawHTML filePath='/posts/flexible-indexing/da-pandas-repr.html' /> | ||||||
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```python | ||||||
da.sel(x=8) | ||||||
# 40 | ||||||
``` | ||||||
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## Alternatives to Pandas.Index | ||||||
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Importantly, a loop over all the coordinate values is not the only way to create an index. | ||||||
You might recognize that our coordinates about can in fact be represented by a function `X(i)=2**i` where `i` is the integer position! Given that function we can quickly get measurement values at any position: `Y(X=4)` = `Y[sqrt(4)]` = `Y[2]=30`. Xarray now has a [CoordinateTransformIndex](https://xarray-indexes.readthedocs.io/blocks/transform.html) to handle this type of on-demand lookup of coordinate positions. | ||||||
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### Xarray RangeIndex | ||||||
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A simple special case of `CoordinateTransformIndex` is a `RangeIndex` where coordinates can be defined by a start, stop, and uniform step size. `Pandas.RangeIndex` only supports _integers_, whereas Xarray handles floating-point values. Coordinate look-up is performed on-the-fly rather than loading all values into memory up-front when creating a Dataset, which is critical for the example below that has a coordinate array of 7TB! | ||||||
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```python | ||||||
from xarray.indexes import RangeIndex | ||||||
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index = RangeIndex.arange(0.0, 1000.0, 1e-9, dim='x') # 7TB coordinate array! | ||||||
ds = xr.Dataset(coords=xr.Coordinates.from_xindex(index)) | ||||||
ds | ||||||
``` | ||||||
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<RawHTML filePath='/posts/flexible-indexing/ds-range-repr.html' /> | ||||||
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Selection preserves the RangeIndex and does not require loading all the coordinates into memory. | ||||||
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``` | ||||||
sliced = ds.isel(x=slice(1_000, 50_000, 100)) | ||||||
sliced.x | ||||||
``` | ||||||
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<RawHTML filePath='/posts/flexible-indexing/ds-range-slice-repr.html' /> | ||||||
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## Third-party custom Indexes | ||||||
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In addition to a few new built-in indexes, Xarray can be extended by third party indexes defined outside of the core codebase. This capability is very important to support a multitude of domain-specific data structures. | ||||||
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### Rasterix RasterIndex | ||||||
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Earlier we mentioned that coordinates often have a _functional representation_. | ||||||
For 2D raster images, this function often takes the form of an [Affine Transform](https://en.wikipedia.org/wiki/Affine_transformation). | ||||||
The [rasterix](https://github.com/xarray-contrib/rasterix) library extends Xarray with a `RasterIndex` which computes coordinates for geospatial images such as GeoTiffs via Affine Transform. | ||||||
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Below is a simple example of slicing a large mosaic of GeoTiffs without ever loading the coordinates into memory, note that a new Affine is defined after the slicing operation: | ||||||
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```python | ||||||
# 811816322401 values! | ||||||
import rasterix | ||||||
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#26475 GeoTiffs represented by a GDAL VRT | ||||||
da = xr.open_dataarray('https://opentopography.s3.sdsc.edu/raster/COP30/COP30_hh.vrt', | ||||||
engine='rasterio', | ||||||
parse_coordinates=False).squeeze().pipe( | ||||||
rasterix.assign_index | ||||||
) | ||||||
da | ||||||
``` | ||||||
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<RawHTML filePath='/posts/flexible-indexing/da-rasterix-repr.html' /> | ||||||
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```python | ||||||
print('Original geotransform:\n', da.xindexes['x'].transform()) | ||||||
da_sliced = da.sel(x=slice(-122.4, -120.0), y=slice(-47.1,-49.0)) | ||||||
print('Sliced geotransform:\n', da_sliced.xindexes['x'].transform()) | ||||||
``` | ||||||
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``` | ||||||
Original geotransform: | ||||||
| 0.00, 0.00,-180.00| | ||||||
| 0.00,-0.00, 84.00| | ||||||
| 0.00, 0.00, 1.00| | ||||||
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Sliced geotransform: | ||||||
| 0.00, 0.00,-122.40| | ||||||
| 0.00,-0.00,-47.10| | ||||||
| 0.00, 0.00, 1.00| | ||||||
``` | ||||||
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### XProj CRSIndex | ||||||
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> real-world datasets are usually more than just raw numbers; they have labels which encode information about how the array values map to locations in space, time, etc. [Xarray Docs](https://docs.xarray.dev/en/stable/getting-started-guide/why-xarray.html#what-labels-enable) | ||||||
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We often think about metadata providing context for _measurement values_ but metadata is also critical for coordinates! | ||||||
In particular, to align two different datasets we must ask if the coordinates are in the same coordinate system. | ||||||
In other words, do they share the same origin and scale? | ||||||
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There are currently over 7000 commonly used [Coordinate Reference Systems (CRS)](https://spatialreference.org/ref/epsg/) for geospatial data in the authoritative EPSG database! | ||||||
And of course an infinite number of custom-defined CRSs. | ||||||
[xproj.CRSIndex](https://xproj.readthedocs.io/en/latest/) gives Xarray objects an automatic awareness of the coordinate reference system operations like `xr.align()`, which can raise an an informative error when there is a CRS mismatch: | ||||||
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Suggested change
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```python | ||||||
from xproj import CRSIndex | ||||||
lons1 = np.arange(-125, -120, 1) | ||||||
lons2 = np.arange(-122, -118, 1) | ||||||
ds1 = xr.Dataset(coords={'longitude': lons1}).proj.assign_crs(crs=4267) | ||||||
ds2 = xr.Dataset(coords={'longitude': lons2}).proj.assign_crs(crs=4326) | ||||||
ds1 + ds2 | ||||||
``` | ||||||
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```pytb | ||||||
MergeError: conflicting values/indexes on objects to be combined for coordinate 'crs' | ||||||
``` | ||||||
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### XVec GeometryIndex | ||||||
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A "vector data cube" is an n-D array that has at least one dimension indexed by a 2-D array of vector geometries. | ||||||
Large vector cubes can take advantage of an [R-tree spatial index](https://en.wikipedia.org/wiki/R-tree) for efficiently selecting vector geometries within a given bounding box. | ||||||
The `XVec.GeometryIndex` provides this functionality, below is a short code snippet but please refer to the [documentation for more](https://xvec.readthedocs.io/en/stable/indexing.html)! | ||||||
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```python | ||||||
import xvec | ||||||
import geopandas as gpd | ||||||
from geodatasets import get_path | ||||||
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# Dataset that contains demographic data indexed by U.S. counties | ||||||
counties = gpd.read_file(get_path("geoda.natregimes")) | ||||||
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cube = xr.Dataset( | ||||||
data_vars=dict( | ||||||
population=(["county", "year"], counties[["PO60", "PO70", "PO80", "PO90"]]), | ||||||
unemployment=(["county", "year"], counties[["UE60", "UE70", "UE80", "UE90"]]), | ||||||
), | ||||||
coords=dict(county=counties.geometry, year=[1960, 1970, 1980, 1990]), | ||||||
).xvec.set_geom_indexes("county", crs=counties.crs) | ||||||
cube | ||||||
``` | ||||||
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<RawHTML filePath='/posts/flexible-indexing/xvec-repr.html' /> | ||||||
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```python | ||||||
# Efficient selection using shapely.STRtree | ||||||
from shapely.geometry import box | ||||||
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subset = cube.xvec.query( | ||||||
"county", | ||||||
box(-125.4, 40, -120.0, 50), | ||||||
predicate="intersects", | ||||||
) | ||||||
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subset['population'].xvec.plot(col='year'); | ||||||
``` | ||||||
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<p align='center'> | ||||||
<img src='/posts/flexible-indexing/xvecfig.png' /> | ||||||
</p> | ||||||
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### Even more examples! | ||||||
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Be sure to check out the [Gallery of Custom Index Examples](https://xarray-indexes.readthedocs.io) for more detailed examples of all the indexes mentioned in this post and more! | ||||||
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## What's next? | ||||||
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While we're extremely excited about what can _already_ be accomplished with the new indexing capabilities, there are plenty of exciting ideas for future work. | ||||||
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Have an idea for your own custom index? Check out [this section of the Xarray documentation](https://docs.xarray.dev/en/stable/internals/how-to-create-custom-index.html). | ||||||
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## Acknowledgments | ||||||
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This work would not have been possible without technical input from the Xarray core team and community! | ||||||
Several developers received essential funding from a [CZI Essential Open Source Software for Science (EOSS) grant](https://xarray.dev/blog/czi-eoss-grant-conclusion) as well as NASA's Open Source Tools, Frameworks, and Libraries (OSTFL) grant 80NSSC22K0345. |
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remove? Or did you want to leave that as an example?
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I could go either way, I commented instead of deleting to more easily go back to the existing multi-line banner