@jcmgray I had to miss your reply to this issue, I saw it just now. I love your code! I will definitely include xyzpy in my tools from now on ;-).

@shoyer Thanks for your suggestions and linking the other issue. I think this one can also be labelled as the "usage question".

After preparing list similar to [{'x': 0, 'y': 'a'}, {'x': 1, 'y': 'a'}, ...] interaction with cluster is quite efficient. One can easily pass such a thing to async_map of ipyparallel.

Thanks for your suggestion, I need to try few things. I also want to try to extend it to function that computes few different things that could be multi-valued, e.g. ```python def dummy(x, y): ds = xr.Dataset( {'out1': ('n', [1x, 2x, 3*x]), 'out2': ('m', [x, y])}, coords = {'x': x, 'y': y, 'n': range(3), 'm': range(2)} )

return ds

``` and then group together such outputs... Ok, I know. I go from simple problem to much more complicated one, but isn't it the case usually?

For "get done" I had for example the following (similar to what I linked as my initial attempt) ```python coordinates = { 'x': np.linspace(-1, 1), 'y': np.linspace(0, 10), }

constants = { 'a': 1, 'b': 5 }

inps = [{constants, {k: v for k, v in zip(coordinates.keys(), x)}} for x in list(it.product(*coordinates.values()))]

def f(x, y, a, b): """Some dummy function.""" v = a * x2 + b * y2 return xr.DataArray(v, {'x': x, 'y': y, 'a': a, 'b': b})

simulate computation on cluster

values = list(map(lambda s: f(**s), inps))

gather and unstack the inputs

ds = xr.concat(values, dim='new', coords='all') ds = ds.set_index(new=list(set(ds.coords) - set(ds.dims))) ds = ds.unstack('new') ```

It is very close to what you suggest. My main question is if this can be done better. Mainly I am wondering if 1. Is there any built-in iterator over the Cartesian product of coordinates. If no, are there people that also think it would be useful? 2. Gathering together / unstacking of the data. My 3 line combo of concat, set_index and unstack seems to do the trick but it seems a bit like over complication. Ideally I'd expect to have some mechanism that works similar to:

`python inputs = cartesian_product(coordinates) # list similar toinps`` above values = [function(inp) for inp in inputs] # or using ipypparallel map

xarray_data = ... # some empty xarray object for inp, val in zip(inputs, values): xarray_data[inp] = val ```

I asked how to generate product of coordinates from xarray object because I was expecting that I can create xarray_data as an empty object with all coordinates set and then fill it.

Added comment

Having an empty, as filled with nans, object to start with would have this benefit that one could save partial results and have clean information what was already computed.

Let me give a bit of a background what I would like to do:

1. Create an empty Dataset of coordinates I want to explore, i.e. two np.arrays x and y, and two scalars a and b.
2. Generate an list of the Cartesian product of all the coordinates, i.e. [ {'x': -1, 'y': 0, 'a': 1, 'b': 5}, ...] (data format doesn't really matter).
3. For each item of the iterator compute some function: f = f(x, y, a, b). In principle this function can be expensive to compute, therefore I'd compute it for each item of list from 2. separately on the cluster.
4. "merge" it all together into a single xarray object

In principle f should be allowed to return e.g. np.array. An related issue in holoviews and the notebook with my initial attempt. In the linked notebook I managed to achieve the goal however without starting with an xarray object containing coordinates. Also combining the data seems a bit inefficient as it takes more time than generating it for a larger datasets.