code: def adam(step_size, b1=0.9, b2=0.999, eps=1e-8):
      """Construct optimizer triple for Adam.
  
      Args:
        step_size: positive scalar, or a callable representing a step size schedule
          that maps the iteration index to a positive scalar.
        b1: optional, a positive scalar value for beta_1, the exponential decay rate
          for the first moment estimates (default 0.9).
        b2: optional, a positive scalar value for beta_2, the exponential decay rate
          for the second moment estimates (default 0.999).
        eps: optional, a positive scalar value for epsilon, a small constant for
          numerical stability (default 1e-8).
  
      Returns:
        An (init_fun, update_fun, get_params) triple.
      """
      step_size = make_schedule(step_size)
  
      def init(x0):
          m0 = jnp.zeros_like(x0)
          v0 = jnp.zeros_like(x0)
          return x0, m0, v0
  
      def update(i, g, state):
          x, m, v = state
          m = (1 - b1) * g + b1 * m  # First  moment estimate.
          v = (1 - b2) * jnp.square(
              g
          ) + b2 * v  # Second moment estimate.
          mhat = m / (
              1 - jnp.asarray(b1, m.dtype) ** (i + 1)
          )  # Bias correction.
          vhat = v / (1 - jnp.asarray(b2, m.dtype) ** (i + 1))
          x = x - step_size(i) * mhat / (jnp.sqrt(vhat) + eps)
          return x, m, v
  
      def get_params(state):
          x, _, _ = state
          return x
  
      return init, update, get_params
  
imports: from __future__ import annotations
  from typing import Any, Callable, NamedTuple
  from collections import namedtuple
  import functools
  from functools import partial
  import jax.numpy
  from jax._src.util import safe_zip, safe_map, unzip2
  from jax import tree_util
  from jax.tree_util import tree_map, tree_flatten, tree_unflatten, register_pytree_node
label_desc: Use image node_id 8 for calling a global function with example usage: adam(step_size, b1, b2, eps) and returns: init,  update,  get_params, x0,  m0,  v0, x,  m,  v, x