xarray_curvigrad3D

PlasmaCalcs.tools.xarray_tools.xarray_sci.xarray_curvigrad3D(array, x=None, xyz=('x', 'y', 'z'))

return d(array)/dx, for curvilinear coordinates in 3D,

i.e. where x, y, z might each be up to 3D arrays instead of 1D.

For example, might have x varying across underlying dimensions i, j, k,

while y varies across only i, j and z varies across only j, k.

Or, maybe all three of them vary across i, j, and k.

array: xarray.DataArray or Dataset

array to be differentiated.

Must contain x, y, z coords, each of which can be up to 3D,

and which together share some set of up to 3 underlying dimensions.

x: None, str, or iterable of str.

tells which coord(s) to differentiate with respect to.

str –> result will be d(array)/dx.

None –> equivalent to using x=xyz

iterable of str –> result is a Dataset with data_vars dd{x[0]}, dd{x[1]}, dd{x[2]}.

(e.g., x=(‘x’, ‘y’) –> result has data_vars ‘ddx’ and ‘ddy’.)

If array was already a Dataset, result is a dict with those keys instead.

xyz: iterable of 3 strings, default (‘x’, ‘y’, ‘z’)

tells which 3 coords form a basis for the curvilinear coordinates.

Even if only getting ‘x’ derivative, the result can depend on ‘y’ and ‘z’

due to the Jacobian. Really, it is because, what does “d/dx” really mean?

It means “derivative when moving along x BUT not moving along y and z”.

With that framing, it is clear that d/dx depends, in general, on how

the underlying grid varies with all three variables.