[Code scan] Make mhcustom honor burn-in state and nsamples

[njzjz]

This issue comes from a Codex global repository scan.

Problem

The vendored MCMC custom sampler computes a post-burn-in state, then discards it and collects the wrong number of samples:

dftio/dftio/dep/_xitorch/_impls/integrate/mcsamples/mcmc.py

Lines 76 to 77 in c9d128f

	x, dtype, device = _mhcustom_sample(logpfcn, x0, pparams, nburnout, custom_step, False)
	xsamples = _mhcustom_sample(logpfcn, x0, pparams, nburnout, custom_step, True)

It calls _mhcustom_sample(..., x0, ..., nburnout, ..., True) instead of starting from x and collecting nsamples. Whenever nsamples != nburnout, the returned chain has the wrong length and starts from the unburned initial state.

Reproduction

Use custom_step=lambda x: x + 1, x0=0, nsamples=3, and nburnout=2; the current output has length 2 and starts at [0, 1].

Suggested fix

Collect from the burned-in state and use nsamples:

xsamples = _mhcustom_sample(logpfcn, x, pparams, nsamples, custom_step, True)