# Path: optax/_src/base.py
# NO_PARAMS_MSG = (
#     'You are using a transformation that requires the current value of '
#     'parameters, but you are not passing `params` when calling `update`.')
# class TransformInitFn(typing_extensions.Protocol):
# class TransformUpdateFn(typing_extensions.Protocol):
# class GradientTransformation(NamedTuple):
# class EmptyState(NamedTuple):
#   def __call__(self, params: Params) -> OptState:
#   def __call__(
#       self,
#       updates: Updates,
#       state: OptState,
#       params: Optional[Params] = None
#     ) -> Tuple[Updates, OptState]:
# def identity() -> GradientTransformation:
#   def init_fn(_):
#   def update_fn(updates, state, params=None):
# def set_to_zero() -> GradientTransformation:
#   def init_fn(params):
#   def update_fn(updates, state, params=None):
# def stateless(
#     f: Callable[[Updates, Optional[Params]], Updates],
# ) -> GradientTransformation:
#   def init_fn(_):
#   def update_fn(updates, state, params=None):
# def stateless_with_tree_map(
#     f: Callable[[chex.Array, Optional[chex.Array]], chex.Array],
# ) -> GradientTransformation:
#   def init_fn(_):
#   def update_fn(updates, state, params=None):
# 
# Path: optax/_src/linear_algebra.py
# def global_norm(updates: base.Updates) -> base.Updates:
# def power_iteration(
#     matrix,
#     num_iters=100,
#     error_tolerance=1e-6,
#     precision=lax.Precision.HIGHEST):
#   def _iter_condition(state):
#   def _iter_body(state):
# def matrix_inverse_pth_root(
#     matrix,
#     p,
#     num_iters=100,
#     ridge_epsilon=1e-6,
#     error_tolerance=1e-6,
#     precision=lax.Precision.HIGHEST):
#   def _unrolled_mat_pow_1(mat_m):
#   def _unrolled_mat_pow_2(mat_m):
#   def _unrolled_mat_pow_4(mat_m):
#   def _unrolled_mat_pow_8(mat_m):
#   def mat_power(mat_m, p):
#   def _iter_condition(state):
#   def _iter_body(state):


from typing import NamedTuple
from optax._src import base
from optax._src import linear_algebra
import jax
import jax.numpy as jnp

  Returns:
    A `GradientTransformation`.
  """
  noise_std = l2_norm_clip * noise_multiplier

  def init_fn(params):
    del params
    return DifferentiallyPrivateAggregateState(rng_key=jax.random.PRNGKey(seed))

  def update_fn(updates, state, params=None):
    del params
    grads_flat, grads_treedef = jax.tree_flatten(updates)
    bsize = grads_flat[0].shape[0]

    if any(g.ndim == 0 or bsize != g.shape[0] for g in grads_flat):
      raise ValueError(
          'Unlike other transforms, `differentially_private_aggregate` expects'
          ' `updates` to have a batch dimension in the 0th axis. That is, this'
          ' function expects per-example gradients as input.')

    new_key, *rngs = jax.random.split(state.rng_key, len(grads_flat)+1)
    global_grad_norms = jax.vmap(linear_algebra.global_norm)(grads_flat)
    divisors = jnp.maximum(global_grad_norms / l2_norm_clip, 1.0)
    clipped = [(jnp.moveaxis(g, 0, -1) / divisors).sum(-1) for g in grads_flat]
    noised = [(g + noise_std * jax.random.normal(r, g.shape, g.dtype)) / bsize
              for g, r in zip(clipped, rngs)]
    return (jax.tree_unflatten(grads_treedef, noised),
            DifferentiallyPrivateAggregateState(rng_key=new_key))


# Path: optax/_src/base.py
# NO_PARAMS_MSG = (
#     'You are using a transformation that requires the current value of '
#     'parameters, but you are not passing `params` when calling `update`.')
# class TransformInitFn(typing_extensions.Protocol):
# class TransformUpdateFn(typing_extensions.Protocol):
# class GradientTransformation(NamedTuple):
# class EmptyState(NamedTuple):
#   def __call__(self, params: Params) -> OptState:
#   def __call__(
#       self,
#       updates: Updates,
#       state: OptState,
#       params: Optional[Params] = None
#     ) -> Tuple[Updates, OptState]:
# def identity() -> GradientTransformation:
#   def init_fn(_):
#   def update_fn(updates, state, params=None):
# def set_to_zero() -> GradientTransformation:
#   def init_fn(params):
#   def update_fn(updates, state, params=None):
# def stateless(
#     f: Callable[[Updates, Optional[Params]], Updates],
# ) -> GradientTransformation:
#   def init_fn(_):
#   def update_fn(updates, state, params=None):
# def stateless_with_tree_map(
#     f: Callable[[chex.Array, Optional[chex.Array]], chex.Array],
# ) -> GradientTransformation:
#   def init_fn(_):
#   def update_fn(updates, state, params=None):
# 
# Path: optax/_src/linear_algebra.py
# def global_norm(updates: base.Updates) -> base.Updates:
# def power_iteration(
#     matrix,
#     num_iters=100,
#     error_tolerance=1e-6,
#     precision=lax.Precision.HIGHEST):
#   def _iter_condition(state):
#   def _iter_body(state):
# def matrix_inverse_pth_root(
#     matrix,
#     p,
#     num_iters=100,
#     ridge_epsilon=1e-6,
#     error_tolerance=1e-6,
#     precision=lax.Precision.HIGHEST):
#   def _unrolled_mat_pow_1(mat_m):
#   def _unrolled_mat_pow_2(mat_m):
#   def _unrolled_mat_pow_4(mat_m):
#   def _unrolled_mat_pow_8(mat_m):
#   def mat_power(mat_m, p):
#   def _iter_condition(state):
#   def _iter_body(state):


# Path: optax/_src/privacy.py
from typing import NamedTuple
from optax._src import base
from optax._src import linear_algebra
import jax
import jax.numpy as jnp


  Returns:
    A `GradientTransformation`.
  """
  noise_std = l2_norm_clip * noise_multiplier

  def init_fn(params):
    del params
    return DifferentiallyPrivateAggregateState(rng_key=jax.random.PRNGKey(seed))

  def update_fn(updates, state, params=None):
    del params
    grads_flat, grads_treedef = jax.tree_flatten(updates)
    bsize = grads_flat[0].shape[0]

    if any(g.ndim == 0 or bsize != g.shape[0] for g in grads_flat):
      raise ValueError(
          'Unlike other transforms, `differentially_private_aggregate` expects'
          ' `updates` to have a batch dimension in the 0th axis. That is, this'
          ' function expects per-example gradients as input.')

    new_key, *rngs = jax.random.split(state.rng_key, len(grads_flat)+1)
    global_grad_norms = jax.vmap(linear_algebra.global_norm)(grads_flat)
    divisors = jnp.maximum(global_grad_norms / l2_norm_clip, 1.0)
    clipped = [(jnp.moveaxis(g, 0, -1) / divisors).sum(-1) for g in grads_flat]
    noised = [(g + noise_std * jax.random.normal(r, g.shape, g.dtype)) / bsize
              for g, r in zip(clipped, rngs)]
    return (jax.tree_unflatten(grads_treedef, noised),
            DifferentiallyPrivateAggregateState(rng_key=new_key))


  return base.GradientTransformation(init_fn, update_fn)