# 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/numerics.py
# def abs_sq(x: chex.Array) -> chex.Array:
# def safe_norm(x: chex.Array,
#               min_norm: chex.Numeric,
#               ord: Optional[Union[int, float, str]] = None,  # pylint: disable=redefined-builtin
#               axis: Union[None, Tuple[int, ...], int] = None,
#               keepdims: bool = False) -> chex.Array:
# def safe_root_mean_squares(x: chex.Array, min_rms: chex.Numeric) -> chex.Array:
# def safe_int32_increment(count: chex.Numeric) -> chex.Numeric:
# 
# Path: optax/_src/utils.py
# def tile_second_to_last_dim(a):
# def canonicalize_dtype(dtype):
# def cast_tree(tree, dtype):
# def set_diags(a, new_diags):
# def multi_normal(loc, log_scale):
#   def __init__(self, loc, log_scale):
#   def sample(self, shape, seed):
#   def log_prob(self, x):
#   def log_scale(self):
#   def params(self):
# def _scale_gradient(inputs: chex.Array, scale: float)  -> chex.ArrayTree:
# def _scale_gradient_fwd(inputs, scale):
# def _scale_gradient_bwd(scale, g):
# def scale_gradient(inputs: chex.ArrayTree, scale: float) -> chex.ArrayTree:
# class MultiNormalDiagFromLogScale():


import dataclasses
import chex
import jax
import jax.numpy as jnp
import numpy as np
from typing import NamedTuple, Optional, Tuple, Callable
from optax._src import base
from optax._src import numerics
from optax._src import utils
      raise ValueError(base.NO_PARAMS_MSG)

    def _update(grad, v_row, v_col, v, param, step):
      shape = param.shape
      decay_rate_t = decay_rate_fn(step - step_offset, decay_rate)

      # Scaled by factorized second moment statistics.
      new_v_row = jnp.zeros((1,))
      new_v_col = jnp.zeros((1,))
      new_v = jnp.zeros((1,))

      factored_dims = _factored_dims(shape, factored, min_dim_size_to_factor)
      if factored_dims is not None:
        d1, d0 = factored_dims
        grad_sqr = numerics.abs_sq(grad) + epsilon
        new_v_row = (
            decay_rate_t * v_row +
            (1. - decay_rate_t) * jnp.mean(grad_sqr, axis=d0))
        new_v_col = (
            decay_rate_t * v_col +
            (1. - decay_rate_t) * jnp.mean(grad_sqr, axis=d1))
        reduced_d1 = d1-1 if d1 > d0 else d1
        row_col_mean = jnp.mean(new_v_row, axis=reduced_d1, keepdims=True)
        row_factor = (new_v_row / row_col_mean) ** -0.5
        col_factor = (new_v_col) ** -0.5
        update = (
            grad *
            jnp.expand_dims(row_factor, axis=d0) *
            jnp.expand_dims(col_factor, axis=d1))
      else:

# 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/numerics.py
# def abs_sq(x: chex.Array) -> chex.Array:
# def safe_norm(x: chex.Array,
#               min_norm: chex.Numeric,
#               ord: Optional[Union[int, float, str]] = None,  # pylint: disable=redefined-builtin
#               axis: Union[None, Tuple[int, ...], int] = None,
#               keepdims: bool = False) -> chex.Array:
# def safe_root_mean_squares(x: chex.Array, min_rms: chex.Numeric) -> chex.Array:
# def safe_int32_increment(count: chex.Numeric) -> chex.Numeric:
# 
# Path: optax/_src/utils.py
# def tile_second_to_last_dim(a):
# def canonicalize_dtype(dtype):
# def cast_tree(tree, dtype):
# def set_diags(a, new_diags):
# def multi_normal(loc, log_scale):
#   def __init__(self, loc, log_scale):
#   def sample(self, shape, seed):
#   def log_prob(self, x):
#   def log_scale(self):
#   def params(self):
# def _scale_gradient(inputs: chex.Array, scale: float)  -> chex.ArrayTree:
# def _scale_gradient_fwd(inputs, scale):
# def _scale_gradient_bwd(scale, g):
# def scale_gradient(inputs: chex.ArrayTree, scale: float) -> chex.ArrayTree:
# class MultiNormalDiagFromLogScale():


# Path: optax/_src/factorized.py
import dataclasses
import chex
import jax
import jax.numpy as jnp
import numpy as np
from typing import NamedTuple, Optional, Tuple, Callable
from optax._src import base
from optax._src import numerics
from optax._src import utils

      raise ValueError(base.NO_PARAMS_MSG)

    def _update(grad, v_row, v_col, v, param, step):
      shape = param.shape
      decay_rate_t = decay_rate_fn(step - step_offset, decay_rate)

      # Scaled by factorized second moment statistics.
      new_v_row = jnp.zeros((1,))
      new_v_col = jnp.zeros((1,))
      new_v = jnp.zeros((1,))

      factored_dims = _factored_dims(shape, factored, min_dim_size_to_factor)
      if factored_dims is not None:
        d1, d0 = factored_dims
        grad_sqr = numerics.abs_sq(grad) + epsilon
        new_v_row = (
            decay_rate_t * v_row +
            (1. - decay_rate_t) * jnp.mean(grad_sqr, axis=d0))
        new_v_col = (
            decay_rate_t * v_col +
            (1. - decay_rate_t) * jnp.mean(grad_sqr, axis=d1))
        reduced_d1 = d1-1 if d1 > d0 else d1
        row_col_mean = jnp.mean(new_v_row, axis=reduced_d1, keepdims=True)
        row_factor = (new_v_row / row_col_mean) ** -0.5
        col_factor = (new_v_col) ** -0.5
        update = (
            grad *
            jnp.expand_dims(row_factor, axis=d0) *
            jnp.expand_dims(col_factor, axis=d1))
      else:

        grad_sqr = numerics.abs_sq(grad) + epsilon