Feature Request: Conversion Utilities for Complex Data – Dtype & Dimension Transformations

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Description:
I’d like to propose adding utility functions to xarray to convert complex-valued DataArrays into a real-valued form with a separate dimension for real and imaginary parts, and back. Since netCDF doesn't support complex numbers yet, this would offer a practical workaround for saving, plotting, and processing complex data using existing xarray tools.

Proposed Approaches:

1. Using “to_”/“from_” Naming:

   • to_complex_dim: Converts a complex dtype DataArray to a new DataArray with an extra dimension (e.g., "complex") that holds the real and imaginary components. Something in the style of:

     def to_complex_dim(da: xr.DataArray, dim: str = "complex", labels: list = ["Real", "Imag"]) -> xr.DataArray:
         if not np.iscomplexobj(da.data):
             raise ValueError("DataArray must be complex-valued.")
         return xr.DataArray(
             np.stack([da.real, da.imag], axis=-1),
             dims=da.dims + (dim,),
             coords={**da.coords, dim: labels},
             attrs=da.attrs,
         )
     

   • to_complex_dtype: Reconstructs a complex dtype DataArray from a DataArray that contains real and imaginary parts along a dedicated dimension.

     def to_complex_dtype(da: xr.DataArray, dim: str = "complex", labels: list = ["Real", "Imag"]) -> xr.DataArray:
         return da.sel({dim: labels[0]}) + 1j * da.sel({dim: labels[1]})
     

2. Using “pack”/“unpack” Naming:

   • pack_complex: “Packs” a real/imaginary DataArray (with an extra dimension) back into a complex dtype DataArray.
   • unpack_complex: “Unpacks” the real and imaginary parts from a complex dtype DataArray into separate values along a new dimension.

3. Accessor-Based Integration:
   Alternatively, these functions could be incorporated as a DataArray accessor (?)

Would love to hear your thoughts on this.

Describe the solution you'd like

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Describe alternatives you've considered

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Additional context

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Start with issue #10213 and compare the proposed to_complex_dim/to_complex_dtype and pack_complex/unpack_complex APIs, including the possible DataArray accessor. Before implementation, clarify naming, dimension labels, validation, metadata, and the expected complex round trip; done should be a decided API with agreed behavior and tests.