# Copyright 2018 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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import autograd.numpy as np
from pennylane.utils import _flatten, unflatten

learning rate in each dimension.

Adagrad adjusts the learning rate for each parameter :math:x_i
in :math:x based on past gradients. We therefore have to consider
each parameter update individually,

.. math::
x^{(t+1)}_i = x^{(t)}_i - \eta_i^{(t+1)} \partial_{w_i} f(x^{(t)}),

where the gradient is replaced by a (scalar) partial derivative.

The learning rate in step :math:t is given by

.. math::
\eta_i^{(t+1)} = \frac{ \eta_{\mathrm{init}} }{ \sqrt{a_i^{(t+1)} + \epsilon } },
~~~ a_i^{(t+1)} = \sum_{k=1}^t (\partial_{x_i} f(x^{(k)}))^2.

The offset :math:\epsilon avoids division by zero.

:math:\eta is the step size, a user defined parameter.

Args:
stepsize (float): the user-defined hyperparameter :math:\eta
eps (float): offset :math:\epsilon added for numerical stability
"""
def __init__(self, stepsize=0.01, eps=1e-8):
super().__init__(stepsize)
self.eps = eps
self.accumulation = None

r"""Update the variables x to take a single optimization step. Flattens and unflattens
the inputs to maintain nested iterables as the parameters of the optimization.

Args:
grad (array): The gradient of the objective
function at point :math:x^{(t)}: :math:\nabla f(x^{(t)})
x (array): the current value of the variables :math:x^{(t)}

Returns:
array: the new values :math:x^{(t+1)}
"""

x_flat = _flatten(x)

if self.accumulation is None:
self.accumulation = [g*g for g in grad_flat]
else:
self.accumulation = [a + g*g for a, g in zip(self.accumulation, grad_flat)]

x_new_flat = [e - (self._stepsize / np.sqrt(a + self.eps)) * g for a, g, e in zip(self.accumulation, grad_flat, x_flat)]

return unflatten(x_new_flat, x)

[docs]    def reset(self):
"""Reset optimizer by erasing memory of past steps."""
self.accumulation = None