code: def _expand(x, shape):
      prepend_dim = len(shape) - np.ndim(x)
      assert prepend_dim >= 0
      shape = shape[:prepend_dim] + tuple(
          dx if size == -1 else size
          for dx, size in zip(np.shape(x), shape[prepend_dim:])
      )
      return np.broadcast_to(x, shape)
  
imports: import numbers
  import typing
  import jax.numpy
  import jax.random
  import numpy
  from jax import lax
  from jax.core import Tracer
  from jax.scipy.linalg import cho_solve, solve_triangular
  from jax.scipy.special import expit, gammaln, logsumexp
  from ..None import ops
label_desc: Use image node_id 20 for calling a global function with example usage: _expand(x, shape) and returns: np