code: def test_walkers_dependent_subtle():
      nwalkers, ndim = 30, 10
      w = np.random.randn(nwalkers, ndim)
      assert walkers_independent(w)
      # random unit vector
      p = np.random.randn(ndim)
      p /= np.sqrt(np.dot(p, p))
      # project away the direction of p
      w -= np.sum(p[None, :] * w, axis=1)[:, None] * p[None, :]
      assert not walkers_independent(w)
      # shift away from the origin
      w += p[None, :]
      assert not walkers_independent(w)
  
imports: import pickle
  from itertools import islice, product
  import numpy
  import pytest
  from emcee import EnsembleSampler, backends, moves, walkers_independent
label_desc: Use image node_id 15 for calling a global function with example usage: test_walkers_dependent_subtle() without return types