code: def test_custom_linear_solve_batching_with_aux(self):
      def solve(mv, b):
          aux = (np.array(1.0), True, 0)
          return mv(b), aux
  
      def solve_aux(x):
          matvec = lambda y: tree_util.tree_map(partial(jnp.dot, A), y)
          return lax.custom_linear_solve(
              matvec, (x, x), solve, solve, symmetric=True, has_aux=True
          )
  
      rng = self.rng()
      A = rng.randn(3, 3)
      A = A + A.T
      b = rng.randn(3, 3)
  
      # doesn't crash
      jax.vmap(solve_aux)(b)
  
imports: from functools import partial
  import re
  import unittest
  from absl.testing import absltest
  from absl.testing import parameterized
  import numpy
  import jax
  from jax import lax
  from jax.ad_checkpoint import checkpoint
  from jax._src import test_util
  from jax import tree_util
  import jax.numpy
  import jax.scipy
  from jax import config
label_desc: Use image node_id 13 for calling the CustomLinearSolveTest obj's underlying member method code with example usage: obj.test_custom_linear_solve_batching_with_aux() and returns: mv,  aux, lax