code: def _gmres_solve(
      A, b, x0, atol, ptol, restart, maxiter, M, gmres_func
  ):
      """
      The main function call wrapped by custom_linear_solve. Repeatedly calls GMRES
      to find the projected solution within the order-``restart``
      Krylov space K(A, x0, restart), using the result of the previous projection
      in place of x0 each time. Parameters are the same as in ``gmres`` except:
  
      atol: Tolerance for norm(A(x) - b), used between restarts.
      ptol: Tolerance for norm(M(A(x) - b)), used within a restart.
      gmres_func: A function performing a single GMRES restart.
  
      Returns: The solution.
      """
      residual = M(_sub(b, A(x0)))
      unit_residual, residual_norm = _safe_normalize(residual)
  
      def cond_fun(value):
          _, k, _, residual_norm = value
          return jnp.logical_and(k < maxiter, residual_norm > atol)
  
      def body_fun(value):
          x, k, unit_residual, residual_norm = value
          x, unit_residual, residual_norm = gmres_func(
              A, b, x, unit_residual, residual_norm, ptol, restart, M
          )
          return x, k + 1, unit_residual, residual_norm
  
      initialization = (x0, 0, unit_residual, residual_norm)
      x_final, k, _, err = lax.while_loop(
          cond_fun, body_fun, initialization
      )
      _ = k  # Until we can pass this out
      _ = err
      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 24 for calling a global function with example usage: _gmres_solve(A, b, x0, atol, ptol, restart, maxiter, M, gmres_func) and returns: x_final, jnp, x,  unknown,  unit_residual,  residual_norm