function check_grad_example_vector(feature_dim, sample_size)
% an example of check_grad on the Lasso 
%          min_{x} || A * x - y ||_F^2
%
% by Jiayu Zhou. Dec 2, 2015.

if nargin < 1, feature_dim = 500; end
if nargin < 3, sample_size = 30; end

A  = randn(sample_size, feature_dim);
y  = randn(sample_size, 1);
x0 = rand(feature_dim, 1);

% closure on the constant variables.
test_func = @(x) dic_obj(x, A, y);

% perform testing.
check_grad(test_func, x0)


function [f, g] = dic_obj(x, A, y)
% The function value and gradient of the following objective
%     min_{x} || A * x - y ||_F^2
% where
% INPUT
%   [X(:); alpha]
% OUTPUT
% given the search point, variable_vect
%   f - function value
%   g - the vectorized gradient

Axy = (A * x - y);
g = A' * Axy;
f = 0.5 * sum(Axy.^2);