code: def adagrad(step_size, momentum=0.9):
      """Construct optimizer triple for Adagrad.
  
      Adaptive Subgradient Methods for Online Learning and Stochastic Optimization:
      http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf
  
      Args:
        step_size: positive scalar, or a callable representing a step size schedule
          that maps the iteration index to a positive scalar.
        momentum: optional, a positive scalar value for momentum
  
      Returns:
        An (init_fun, update_fun, get_params) triple.
      """
      step_size = make_schedule(step_size)
  
      def init(x0):
          g_sq = jnp.zeros_like(x0)
          m = jnp.zeros_like(x0)
          return x0, g_sq, m
  
      def update(i, g, state):
          x, g_sq, m = state
          g_sq += jnp.square(g)
          g_sq_inv_sqrt = jnp.where(g_sq > 0, 1.0 / jnp.sqrt(g_sq), 0.0)
          m = (1.0 - momentum) * (g * g_sq_inv_sqrt) + momentum * m
          x = x - step_size(i) * m
          return x, g_sq, m
  
      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 5 for calling a global function with example usage: adagrad(step_size, momentum) and returns: init,  update,  get_params, x0,  g_sq,  m, x,  g_sq,  m, x