You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: adagrad.m
    path of file: ./repos/TADT/utils/matconvnet/examples/+solver
    
    the code of the file until where you have to start completion: function [w, g_sqr] = adagrad(w, g_sqr, grad, opts, lr)
%ADAGRAD
%   Example AdaGrad solver, for use with CNN_TRAIN and CNN_TRAIN_DAG.
%
%   Set the initial learning rate for AdaGrad in the options for
%   CNN_TRAIN and CNN_TRAIN_DAG. Note that a learning rate that works for
%   SGD may be inappropriate for AdaGrad; the default is 0.001.
%
%   If called without any input argument, returns the default options
%   structure.
%
%   Solver options: (opts.train.solverOpts)
%
%   `epsilon`:: 1e-10
%      Small additive constant to regularize variance estimate.

    
function [w, g_sqr] = adagrad(w, g_sqr, grad, opts, lr)
%ADAGRAD
%   Example AdaGrad solver, for use with CNN_TRAIN and CNN_TRAIN_DAG.
%
%   Set the initial learning rate for AdaGrad in the options for
%   CNN_TRAIN and CNN_TRAIN_DAG. Note that a learning rate that works for
%   SGD may be inappropriate for AdaGrad; the default is 0.001.
%
%   If called without any input argument, returns the default options
%   structure.
%
%   Solver options: (opts.train.solverOpts)
%
%   `epsilon`:: 1e-10
%      Small additive constant to regularize variance estimate.
%
%   `rho`:: 1
%      Moving average window for variance update, between 0 and 1 (larger
%      values result in slower/more stable updating). This is similar to
%      RHO in AdaDelta and RMSProp. Standard AdaGrad is obtained with a RHO
%      value of 1 (use total average instead of a moving average).
%
%   A possibly undesirable effect of standard AdaGrad is that the update
%   will monotonically decrease to 0, until training eventually stops. This
%   is because the AdaGrad update is inversely proportional to the total
%   variance of the gradients seen so far.
%   With RHO smaller than 1, a moving average is used instead. This
%   prevents the final update from monotonically decreasing to 0.

% Copyright (C) 2016 Joao F. Henriques.
% All rights reserved.
%
% This file is part of the VLFeat library and is made available under
% the terms of the BSD license (see the COPYING file).

if nargin == 0 % Return the default solver options
  w = struct('epsilon', 1e-10, 'rho', 1);
  return;
end