code: def _bicgstab_solve(
      A, b, x0=None, *, maxiter, tol=1e-5, atol=0.0, M=_identity
  ):
      # tolerance handling uses the "non-legacy" behavior of scipy.sparse.linalg.bicgstab
      bs = _vdot_real_tree(b, b)
      atol2 = jnp.maximum(jnp.square(tol) * bs, jnp.square(atol))
  
      # https://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method#Preconditioned_BiCGSTAB
  
      def cond_fun(value):
          x, r, *_, k = value
          rs = _vdot_real_tree(r, r)
          # the last condition checks breakdown
          return (rs > atol2) & (k < maxiter) & (k >= 0)
  
      def body_fun(value):
          x, r, rhat, alpha, omega, rho, p, q, k = value
          rho_ = _vdot_tree(rhat, r)
          beta = rho_ / rho * alpha / omega
          p_ = _add(r, _mul(beta, _sub(p, _mul(omega, q))))
          phat = M(p_)
          q_ = A(phat)
          alpha_ = rho_ / _vdot_tree(rhat, q_)
          s = _sub(r, _mul(alpha_, q_))
          exit_early = _vdot_real_tree(s, s) < atol2
          shat = M(s)
          t = A(shat)
          omega_ = _vdot_tree(t, s) / _vdot_tree(t, t)  # make cases?
          x_ = tree_map(
              partial(jnp.where, exit_early),
              _add(x, _mul(alpha_, phat)),
              _add(x, _add(_mul(alpha_, phat), _mul(omega_, shat))),
          )
          r_ = tree_map(
              partial(jnp.where, exit_early),
              s,
              _sub(s, _mul(omega_, t)),
          )
          k_ = jnp.where((omega_ == 0) | (alpha_ == 0), -11, k + 1)
          k_ = jnp.where((rho_ == 0), -10, k_)
          return x_, r_, rhat, alpha_, omega_, rho_, p_, q_, k_
  
      r0 = _sub(b, A(x0))
      rho0 = alpha0 = omega0 = lax_internal._convert_element_type(
          1, *dtypes._lattice_result_type(*tree_leaves(b))
      )
      initial_value = (x0, r0, r0, alpha0, omega0, rho0, r0, r0, 0)
  
      x_final, *_ = lax.while_loop(cond_fun, body_fun, initial_value)
  
      return x_final
  
imports: from functools import partial
  import operator
  import numpy
  import jax
  import jax.numpy
  from jax import device_put
  from jax import lax
  from jax import scipy
  from jax.tree_util import tree_leaves, tree_map, tree_structure, tree_reduce, Partial
  from jax._src import dtypes
  from jax._src.lax import lax
  from jax._src.util import safe_map
label_desc: Use image node_id 10 for calling a global function with example usage: _bicgstab_solve(A, b, x0) and returns: x_final, unknown, x_,  r_,  rhat,  alpha_,  omega_,  rho_,  p_,  q_,  k_