@r-beer I checked back on this and realized I didn't reply to your question: yes re completing #2652, if you're up for giving this a push

@r-beer would be great to finish this off! I think this would be a popular feature. You could take @hrishikeshac 's code (which is close!) and make the final changes.

Would be great to get this in, if anyone wants to have a go. A small, focused, PR would be a good start.

In the meantime you can use one of the solutions above...

@hrishikeshac that looks great! Well done for getting an MVP running.

Do you want to do a PR from this? Should be v close from here.

Others can comment from there. I'd suggest we get something close to this in and iterate from there. How abstract do we want the dimensions to be (i.e. currently we can only pass one dimension in, which is fine, but potentially we could enable multiple).

One nit - no need to use np.sum - that may cause issues with dask arrays - .sum will work fine

Yes for useful, but not sure whether they should be on the same method. They're also fairly easy for a user to construct (call correlation on a .shift copy of the array).

And increments are easy to build on! I'm the worst offender, but don't let completeness get in the way of incremental improvement

(OK, I'll go and finish the fill_value branch...)

I think lagged correlations would be a useful feature.

Hey @hrishikeshac -- any progress on this? Need any help / advice from xarray devs?

And one that handles NaNs:

```python

untested!

def covariance(x, y, dim=None): valid_values = x.notnull() & y.notnull() valid_count = valid_values.sum(dim)

demeaned_x = (x - x.mean(dim)).fillna(0)
demeaned_y = (y - y.mean(dim)).fillna(0)

return xr.dot(demeaned_x, demeaned_y, dims=dim) / valid_count

def correlation(x, y, dim=None): # dim should default to the intersection of x.dims and y.dims return covariance(x, y, dim) / (x.std(dim) * y.std(dim)) ```

For posterity, I made a small adjustment to @shoyer 's draft:

```python

untested!

def covariance(x, y, dim=None): # need to ensure the dim lengths are the same - i.e. no auto-aligning # could use count-1 for sample return xr.dot(x - x.mean(dim), y - y.mean(dim), dims=dim) / x.count(dim)

def correlation(x, y, dim=None): # dim should default to the intersection of x.dims and y.dims return covariance(x, y, dim) / (x.std(dim) * y.std(dim)) ```

Great! Ping me / the issues with any questions at all!

@hrishikeshac if you'd like to contribute, we can help you along - xarray is a v welcoming project!

And from mvstats it looks like you're already up to speed

Let us know

I tend to view the second case as a generalization of the first case. I would also hesitate to implement the n x m array -> m x m correlation matrix version because xarray doesn't handle repeated dimensions well.

I think the basic implementation of this looks quite similar to what I wrote here for calculating the Pearson correlation as a NumPy gufunc: http://xarray.pydata.org/en/stable/dask.html#automatic-parallelization

The main difference is that we might naturally want to support summing over multiple dimensions at once via the dim argument, e.g., something like: ```python

untested!

def covariance(x, y, dim=None): return xarray.dot(x - x.mean(dim), y - y.mean(dim), dim=dim)

def corrrelation(x, y, dim=None): # dim should default to the intersection of x.dims and y.dims return covariance(x, y, dim) / (x.std(dim) * y.std(dim)) ```

If you want to achieve the equivalent of np.corr on an array with dimensions ('n', 'm') with this, you just write something like correlation(x, x.rename({'m': 'm2'}), dim='n').

I'm up for adding .corr to xarray

What do want this to look like? It's a bit different from most xarray functions, which either return the same shape or reduce one dimension. - The basic case here would take a n x m array and return an m x m correlation matrix. We could easily wrap https://docs.scipy.org/doc/numpy/reference/generated/numpy.corrcoef.html - Another case would be take two similarly sized arrays (with the option of broadcasting) and return an array with one dimension reduced. For example 200 x 10 and 200, return a 10 array. - I need to think about how those extrapolate to multiple dimensions

Should I start with the first case and then we can expand as needed?

I'll chime in here to ask a usage question: what is the recommended way to compute correlation maps with xarray? I.e. I have a dataarray of dims (time, lat, lon) and I'd like to correlate every single grid point with a timeseries of dim (time) to get a correlation map of dim (lat, lon). My current strategy is a wonderfully unpythonic double loop over lons and lats, and I wonder if there's better way?

To be clear, I am not say that this does not belong in xarray.

I'm saying that we lack clear general guidelines for how to determine whether a particular function belongs in xarray. The criterion of a "pretty fundamental operation for working with data" is a good starting point. I would add: - used across a wide range of scientific disciplines - clear, unambiguous / uncontroversial definition - numpy implementation already exists

corr meets all of these criteria. Many others (e.g. interpolation, convolution, curve fitting) do as well. Expanding xarray beyond the numpy ufuncs opens the door to supporting these things. I'm just saying it should be conscious, deliberate decision, given the limits on developer time.

Many of these things will be pretty trivial once .apply() is here. So perhaps it's not a big deal.

That said, correlation coefficients are a pretty fundamental operation for working with data. I could see implementing a basic corr in xarray and referring to a separate signal processing package for more options in the docstring.

I agree this would be very useful. But it is also feature creep. There is an extremely wide range of such functions that could hypothetically be put into the xarray package. (all of scipy.signal for example) At some point the community should decide what is the intended scope of xarray itself vs. packages built on top of xarray.

The first step here is to find a library that implements the desired functionality on pure NumPy arrays, ideally in a vectorized fashion. Then it should be pretty straightforward to wrap in xarray.