html_url,issue_url,id,node_id,user,created_at,updated_at,author_association,body,reactions,performed_via_github_app,issue
https://github.com/pydata/xarray/pull/5390#issuecomment-850843957,https://api.github.com/repos/pydata/xarray/issues/5390,850843957,MDEyOklzc3VlQ29tbWVudDg1MDg0Mzk1Nw==,56925856,2021-05-29T14:37:48Z,2021-05-31T10:27:06Z,CONTRIBUTOR,"@willirath this is cool, but I think it doesn't explain why the tests fail. Currently `da_a.mean()` and the `da_b.mean()` calls *do* know about each other's missing data! That's what we're doing in [these lines](https://github.com/pydata/xarray/blob/master/xarray/core/computation.py#L1370_L1371).
@dcherian, I think I've got it to work, but you need to account for the length(s) of the dimension you're calculating the correlation over. (i.e. `(da-da.mean('time')).sum('time')` is not the same as `da.sum('time') - da.mean('time')` because you should _actually_ do `da.sum('time') - da.mean('time')*length_of_time_dim`)
This latest commit does this, but I'm not sure whether the added complication is worth it yet? Thoughts welcome.
```python3
def _mean(da):
return (da.sum(dim=dim, skipna=True, min_count=1) / (valid_count))
dim_length = da_a.notnull().sum(dim=dim, skipna=True)
def _mean_detrended_term(da):
return (dim_length * da / (valid_count))
cov = _mean(da_a * da_b) - _mean_detrended_term(da_a.mean(dim=dim) * da_b.mean(dim=dim))
```","{""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,904153867
https://github.com/pydata/xarray/pull/5390#issuecomment-850690985,https://api.github.com/repos/pydata/xarray/issues/5390,850690985,MDEyOklzc3VlQ29tbWVudDg1MDY5MDk4NQ==,56925856,2021-05-28T21:43:52Z,2021-05-28T21:44:12Z,CONTRIBUTOR,"> is it just
>
> ```
> cov = _mean(da_a * da_b) - da_a.mean(dim=dim) * da_b.mean(dim=dim)
> ```
I think you'd still have to normalize the second term by `1 / (valid_count)`. However, I just tried both of these approaches and neither pass the test suite, so we may need to do more thinking... ","{""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,904153867
https://github.com/pydata/xarray/pull/5390#issuecomment-850556738,https://api.github.com/repos/pydata/xarray/issues/5390,850556738,MDEyOklzc3VlQ29tbWVudDg1MDU1NjczOA==,56925856,2021-05-28T17:12:52Z,2021-05-28T17:14:08Z,CONTRIBUTOR,"@willirath this is great stuff, thanks again! So generally it looks like the graph is more efficient when doing operations of the form:
```python3
(X * Y).mean('time') - (X.mean('time') * Y.mean('time'))
```
than doing
```python3
((X - X.mean('time')) * (Y-Y.mean('time'))).mean('time')
```
or like what I've implemented (see screenshot)?
```python3
intermediate = (X * Y) - (X.mean('time') * Y.mean('time'))
intermediate.mean('time')
```
If so, it seems like the most efficient(?) way to do the computation in [_cov_corr()](https://github.com/pydata/xarray/blob/master/xarray/core/computation.py#L1373_L1383) is to combine it all into one line? I can't think of how to do this though...
","{""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,904153867
https://github.com/pydata/xarray/pull/5390#issuecomment-850276619,https://api.github.com/repos/pydata/xarray/issues/5390,850276619,MDEyOklzc3VlQ29tbWVudDg1MDI3NjYxOQ==,56925856,2021-05-28T09:15:30Z,2021-05-28T09:17:48Z,CONTRIBUTOR,"@willirath , thanks for your example notebook! I'm still trying to get my head around this a bit though.
Say you have `da_a` and `da_b` defined as:
```python3
da_a = xr.DataArray(
np.array([[1, 2, 3, 4], [1, 0.1, 0.2, 0.3], [2, 3.2, 0.6, 1.8]]),
dims=(""space"", ""time""),
coords=[
(""space"", [""IA"", ""IL"", ""IN""]),
(""time"", pd.date_range(""2000-01-01"", freq=""1D"", periods=4)),
],
).chunk()
da_b = xr.DataArray(
np.array([[0.2, 0.4, 0.6, 2], [15, 10, 5, 1], [1, 3.2, np.nan, 1.8]]),
dims=(""space"", ""time""),
coords=[
(""space"", [""IA"", ""IL"", ""IN""]),
(""time"", pd.date_range(""2000-01-01"", freq=""1D"", periods=4)),
],
).chunk()
```
The [original computation](https://github.com/pydata/xarray/blob/master/xarray/core/computation.py#L1373_L1375) in `_cov_corr` has a graph something like:
Whereas my alteration now has a graph more like this:
Am I correct in thinking that this is a 'better' computational graph? Because the original chunks are not passed onto later points in the computation? ","{""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,904153867