API design for pointwise indexing

[jhamman]

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There have been a number of threads discussing possible improvements/extensions to xray indexing. The current indexing behavior for isel is orthogonal indexing - in other words, each coordinate is treated independently (see #214 and #411 for more discussion).

So the question: what is the best way to incorporate diagonal or pointwise indexing in xray? I see two main goals / applications:

1. support simple form of numpy style integer array indexing
2. support pointwise array indexing along coordinates via computation of nearest-neighbor indexes - I think this can also be thought of as a form of resampling.

Input from @WeatherGod, @wholmgren, and @shoyer would be great.

[shoyer]

So, the good news is that once we figure out the API for pointwise indexing, I think the nearest-neighbor part could be as simple as supplying method='nearest'.

The challenge is that we want to go from an DataArray that looks like this:

In [4]: arr = xray.DataArray([[1, 2], [3, 4]], dims=['x', 'y'])

In [5]: arr
Out[5]:
<xray.DataArray (x: 2, y: 2)>
array([[1, 2],
       [3, 4]])
Coordinates:
  * x        (x) int64 0 1
  * y        (y) int64 0 1

To one that looks like that:

In [6]: xray.DataArray([1, 4], {'x': ('c', [0, 1]), 'y': ('c', [0, 1])}, dims='c')
Out[6]:
<xray.DataArray (c: 2)>
array([1, 4])
Coordinates:
    y        (c) int64 0 1
    x        (c) int64 0 1
  * c        (c) int64 0 1

Somehow, we need to figure out the name for the new dimension (c in this example).

My thought would be to have methods sel_points and isel_points that work similarly to sel and isel. This is straightforward if you already have xray 1D objects with a labeled dimension: arr.sel_points(x=x, y=y), where x and y are along the c dimension.

If you don't already have 1D xray objects, I suppose we could also allow arr.sel_points(x=('c', [0, 1]), y=('c', [0, 1])) or arr.sel_points('c', x=[0, 1], y=[0, 1]).

[wholmgren]

Seems like if your method is going to be named sel_points then points is a reasonable dimension name. Maybe support a name kwarg?

One thing to keep in mind is that for many of us the "nearest-neighbor" part isn't really method='nearest', but instead more like, method='ingridcell' where the grid cell might be roughly square or might be something pretty different. At least that's how I think of my data. Maybe what I really want is some other kind of more explicit support for gridded data, although my thoughts on this are too half-baked to clearly write down. I thought there was another issue related to this, but I couldn't find it.

[shoyer]

Seems like if your method is going to be named sel_points then points is a reasonable dimension name.

Yes, this is a reasonable choice for the case of 1d indexers.

Maybe support a name kwarg?

This is also a good idea, though I would probably call the parameter dim, not name.

One thing to keep in mind is that for many of us the "nearest-neighbor" part isn't really method='nearest', but instead more like, method='ingridcell' where the grid cell might be roughly square or might be something pretty different.

Indeed. As a start, we should be able to do nearest neighbor lookups with a tolerance soon -- I have a pandas PR that should add some of that basic functionality (https://github.com/pydata/pandas/pull/10411). In the long term, it would be useful to have some sort of representation of grid cells in the index itself, possibly something similar to IntervalIndex (https://github.com/pydata/pandas/pull/8707).

[jhamman]

I like:

DataArray.isel_points(x=[1, 2, 3], y=[0, 1, 2], dim='points')

I also like the nearest-neighbor / resample API of:

DataArray.sel_points(lon=[-123.25, -140.0, 72.5], lat=[45.0, 72.25, 65.75],
                     dim='points', method='nearest')

How do we want to do the nearest-neighbor selection? The simplest case would be to follow the cKDTree example from #214. However, when you're using lat/lon coordinates, it is usually best to map these coordinates from the spherical coordinates to a Cartesian coordinates (see here for a simple example using cKDTree. Is that a road we want to go down here?

Further along that subject, but not directly relate - has anyone used pyresample.

[wholmgren]

Unidata also has a blog post benchmarking cKDTree and other methods and concludes "Your Mileage May Vary". I'd probably just go with a KDTree, but something to aware of.

[rabernat]

There is a great kdtree-based geospatial resampling package you might want to consider building on: https://github.com/pytroll/pyresample It is fast (multithreaded) and has support for different map projections.

[rabernat]

Maybe this is off topic, but are the plans to support more general spatial resampling / regridding? Like if I have two DataArrays a and b with different spatial coords, it would be great to be able to do

c = a.regrid_like(b)

This is a pretty common practice in climate science, since different datasets are provided on different grids with different resolutions.

[shoyer]

I agree that regridding and resample would be very nice, and pyresample looks like a decent option. I have no immediate plans to implement these features but contributions would be very welcome.

For n-dimensional indexing, kdtree seems sensible, especially if we can cache it on the coordinates. We probably want an explicit API for methods that add new coordinates -- something like ds.set_kdtree(['latitude', 'longitude']).

[jhamman]

As a first step, I'll volunteer (unless someone else is more keen on doing this work) to put together a pull request for isel_points.

After that, we'll want to add the sel_points and kdtree API, which will depend on isel_points.

Later on, I'm also interested in regridding and resampling between grids - let's open another issue for that. Maybe we use pyresample for that.

[shoyer]

@jhamman it would be great if you could put together a PR for isel_points. The main complexity is that you'll want to write a version that also works with dask arrays. Let me know if that part is confusing, I can certainly help with that.

As for sel_points, we only need a kdtree if the underlying coordinates are 2D. If latitude and longitude (for example) are 1d, we can just use the existing machinery for remapping label based indexers to integers. This should be pretty straightforward, following the example of isel: https://github.com/xray/xray/blob/v0.5.1/xray/core/dataset.py#L1024 https://github.com/xray/xray/blob/v0.5.1/xray/core/indexing.py#L157

[jhamman]

Good point on the dask array business. From the dask docs:

Dask.array supports most of the NumPy slicing syntax. ... It does not currently support the following:

Slicing one dask.array with another x[x > 0] Slicing with lists in multiple axes x[[1, 2, 3], [3, 2, 1]]

Both of these are straightforward to add though. If you have a use case then raise an issue.

So, from browsing the closed dask issues, it seems like dask has similar support for multi-dimension slicing and indexing as xray. This throws a bit of a wrench in my plan for how I was going to implement isel_points as I had not fully considered the dask array complexities.

I'll have to put a bit more thought into this. Any suggestions on how to index the dask array without looping through individual points would be great.

[shoyer]

Any suggestions on how to index the dask array without looping through individual points would be great.

For now, I actually think selecting individual points and then concatenating the resulting arrays together would be a reasonable start. Yes, it's kind of slow, but once you have a first draft put together that way with the right API we can optimize later.

[jhamman]

Now that the isel_points method is implemented, I think it makes sense to discuss the sel_points method in a bit more detail. The main outstanding question is - do we want to support spherical nearest neighbor mapping. The use case is when you are searching for the nearest neighbor using longitudes and latitudes. This example shows an example of to do this by projecting the coordinates onto a sphere. If we go this route, which is probably the most common use case here, we are committing to the coordinates being latitudes and longitudes. Maybe it is better to use a method='spherical' keyword to fall into this path.

[shoyer]

I would start with the easiest case -- lookups of 1d orthogonal arrays, e.g., grid.sel(latitude=stations.latitude, longitude=stations.longitude, method='nearest'). This would very straightforwardly leverage our current machinery.

For 2D lookups, we need a KDTree. Here are some API ideas, just tossing things around...

>>> ds
<xray.Dataset>
Dimensions:      (x: 4, y: 5)
Coordinates:
    latitude     (x, y) float64 0.49 0.5682 -0.3541 -0.9305 -0.9669 0.01558 ...
    longitude    (x, y) float64 0.3758 1.429 -1.698 -1.344 0.5237 0.6152 ...
  * x            (x) int64 0 1 2 3
  * y            (y) int64 0 1 2 3 4
Data variables:
    temperature  (x, y) float64 0.5735 -0.4871 0.4708 0.4907 -0.3318 0.2883 ...

# perhaps set_ndindex is a better name?
>>> ds = ds.set_kdtree(['latitude', 'longitude'], name='latlon_index', method='spherical')
>>> ds
<xray.Dataset>
Dimensions:      (x: 4, y: 5)
Coordinates:
    latitude     (x, y) float64 0.49 0.5682 -0.3541 -0.9305 -0.9669 0.01558 ...
    longitude    (x, y) float64 0.3758 1.429 -1.698 -1.344 0.5237 0.6152 ...
  * latlon_index (x, y) float64 (0.49, 0.3758) (0.5682, 1.429) ...
  * x            (x) int64 0 1 2 3
  * y            (y) int64 0 1 2 3 4
Data variables:
    temperature  (x, y) float64 0.5735 -0.4871 0.4708 0.4907 -0.3318 0.2883 ...

result = ds.sel_points(latitude=other.latitude, longitude=other.longitude, method='nearest')

[shoyer]

I started playing around with making an array wrapper for KDTree this evening: https://gist.github.com/shoyer/ae30a1200f749c84b4c4

I think it has most of the necessary indexing machinery and you can put it in an xray.Dataset like an array. You could easily imagine hooking in a transform argument to KDTreeIndex to handle projection. But of course it hasn't been hooked up to any API yet.

[jhamman]

Very nice. This is the sort of API I was hoping for. It will be a while before I can come back around on this. In the meantime, if someone else wants to take the sel_points method on, that is fine by me.

[shoyer]

PR #507 implements the my suggested 1d version of sel_points. Maybe we also want reindex_points, i.e., pointwise indexing by label that is gauranteed to succeed even if some labels are missing?

[shoyer]

A few recent developments relevant to this issue:

• #974 discusses how we could add multi-dimensional indexing with broadcasting. This would subsume the need for separate methods like sel_points and allow also handle indexing grids with grids.
• #947 adds first class support for MultiIndex coordinates into xarray. This is good model for how a KDTree could work.

So I'm now thinking an API more like this:

>>> ds = ds.set_kdtree(spatial_index=['latitude', 'longitude'])

>>> ds
<xray.Dataset>
Dimensions:        (x: 4, y: 5)
Coordinates:
  * x              (x) int64 0 1 2 3
  * y              (y) int64 0 1 2 3 4
  * spatial_index  (x, y) KDTree
    - latitude     (x, y) float64 0.49 0.5682 -0.3541 -0.9305 -0.9669 0.01558 ...
    - longitude    (x, y) float64 0.3758 1.429 -1.698 -1.344 0.5237 0.6152 ...
Data variables:
    temperature    (x, y) float64 0.5735 -0.4871 0.4708 0.4907 -0.3318 0.2883 ...

>>> result = ds.sel(latitude=other.latitude, longitude=other.longitude,
...                 method='nearest')

For building a tree with lat/lon remapped to spherical coordinates, we should write a method that converts lat and lon arrays into a tuple of x, y, z arrays (e.g., using apply_ufunc from #964). Then this looks like ds.set_kdtree(spatial_index=latlon_to_xyy(ds.latitude, ds.longitude)). Conceivably, we could add some sugar for this, e.g., ds.geo.set_kdtree(spatial_index=['latitude', 'longitude']).

[burnpanck]

Without following the discussion in detail, what is the status here? In particular, I would like to do pointwise selection on multiple 1D coordinates using multidimensional indexer arrays. I can do this with the current isel_points:

1. construct the multidimensional indexers
2. flatten them
3. create a corresponding MultiIndex
4. apply the flattened indexers using isel_points, and assign the multi-index as the new dimension
5. use unstack on the newly created dimension The first three points can be somewhat simplified by instead putting all of the multidimensional indexer into a Dataset and then stack it to create consistent flat versions and their multi-index.

Given this conceptually easy but somewhat tedious procedure, couldn't that be something that could quite easily be implemented into the current isel_points? Would a PR along that direction have a chance of being accepted?

[shoyer]

@burnpanck I don't think you need to do the flattening/multi-index bit. I believe isel_points/sel_points should just work for you already.

At this point we're really just talking about design refinements (I'll rename the topic).

[burnpanck]

Really? I get a ValueError: Indexers must be 1 dimensional (xarray/core/dataset.py:1031 in isel_points(self, dim, **indexers) when I try. That is xarray 0.8.2, in fact from my fork recently cloned (~2-3 weeks ago), where I changed one or two asarray to asanyarray to work with units. Was there a recent change in this area? EDIT: xarray/core/dataset.py looks very similar also here on master, and there are quite a few lines hinting that really only 1D indexers are supported.

[shoyer]

@burnpanck Nevermind, you are correct! I misread your comment. This cannot be done currently.

You certainly could try to put this into isel_points, and if you can do it in a clean fashion I an open to accepting it, but keep in mind that the method is going to go away when we finally get around to implementing #974. Work on #974 would probably be more productive, ultimately.

[WeatherGod]

So, what has become the consensus for performing regridding/resampling? I see a lot of suggestions, but I have no sense of what is mature enough to use in production-level code. I also haven't seen anything in the documentation about this topic, even if it just refers people to another project.

[jhamman]

@WeatherGod

Short answer. We don't have a tool that is production ready.

Longer answer: xESMF may be the best prospect in the near term. There are two main issues with its current implementation. 1) Lack of out-of-core abilities / integration with dask, and 2) lack of a test suite. Conceptually, it would be great to leverage the low-level remapping tools of ESMPy so I think this is a nice way to move forward as a community but I think everyone agrees it isn't ready for use in any sort of production environment.

This issue introduces the concept of point-wise indexing using nearest neighbor lookups on ND coordinates. @shoyer has an example implementation here but it hasn't moved forward in quite a while.

[WeatherGod]

Yeah, we need to move something forward, because the main benefit of xarray is the ability to manage datasets from multiple sources in a consistent way. And data from different sources will almost always be in different projections.

My current problem that I need to solve right now is that I am ingesting model data that is in a LCC projection and ingesting radar data that is in a simple regular lat/lon grid. Both dataset objects have latitude and longitude coordinate arrays, I just need to get both datasets to have the same lat/lon grid.

I guess I could continue using my old scipy-based solution (using map_coordinates() or RectBivariateSpline), but at the very least, it would make sense to have some documentation demonstrating how one might go about this very common problem, even if it is showing how to use the scipy-based tools with xarrays. If that is of interest, I can see what I can write up after I am done my immediate task.

[shoyer]

Yes, a documentation example would be greatly appreciated. We have been making progress in this direction (especially with the new vectorised indexing support) but it has been slow going to do it right. On Tue, Nov 7, 2017 at 10:29 AM Benjamin Root [email protected] wrote:

Yeah, we need to move something forward, because the main benefit of xarray is the ability to manage datasets from multiple sources in a consistent way. And data from different sources will almost always be in different projections.

My current problem that I need to solve right now is that I am ingesting model data that is in a LCC projection and ingesting radar data that is in a simple regular lat/lon grid. Both dataset objects have latitude and longitude coordinate arrays, I just need to get both datasets to have the same lat/lon grid.

I guess I could continue using my old scipy-based solution (using map_coordinates() or RectBivariateSpline), but at the very least, it would make sense to have some documentation demonstrating how one might go about this very common problem, even if it is showing how to use the scipy-based tools with xarrays. If that is of interest, I can see what I can write up after I am done my immediate task.

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[jhamman]

ping @stefanomattia who seems to be interested in the KDTreeIndex concepts described in this issue.

[rabernat]

Subscribers to this thread will probably be interested in @JiaweiZhuang's recent progress on xESMF. That package is now a viable solution for 2D regridding of xarray datasets. https://github.com/JiaweiZhuang/xESMF

[stefanomattia]

Thanks @jhamman, I'd love to contribute! I'm not that confident in my Python skills, but maybe with a little guidance? Let me know if or how I could help.

[jhamman]

@stefanomattia - I'd be happy to provide guidance and even to contribute to some of the development. Based on your blog post, I think you may be well on your way.