The on_axis_* statistics copy the whole state to the host on device builds #359

What is missing

The on_axis_* statistics (SEP 19) read one row of the field at the axis. On a device build the native backend copies the whole state to the host and scans the row there, once per saved plane that asks for them. SEP 19 left the device form out on purpose, as "needed only to avoid the state copy on a GPU", and deferred it to GPU qualification.

Why it matters

Possibly not much. On a large Cartesian run the copy is the whole state at each such plane. Its cost has not been measured on a GPU, so that is the first step. Read, not run.

To do

• Time a saved plane with and without on_axis_* on a data-centre GPU, on a Cartesian run of at least 384 x 384.
• If the copy matters, add a one-row device scan through the existing plasma scan, keeping tests/backends/test_on_axis_statistics.py's parity against numpy_ref. If not, close this with the number.

Done when

The cost is recorded with device, grid and date, and either the statistics no longer copy the state on a device, with parity holding on a CUDA and a HIP build, or the issue closes because the copy is under 1 % of the run's time at one plane per 100 steps.

Checked against commit 8a9f764. Takes over the roadmap's entry "The on-axis statistics on device builds".