% l1qc_example.m
%
% Test out l1qc code (l1 minimization with quadratic constraint).
%
% Written by: Justin Romberg, Caltech
% Email: jrom@acm.caltech.edu
% Created: October 2005
%

% put optimization code in path if not already there
path(path, './Optimization');

% signal length
N = 512;

% number of spikes to put down
T = 20;

% number of observations to make
K = 120;

% random +/- 1 signal
x = zeros(N,1);
q = randperm(N);
x(q(1:T)) = sign(randn(T,1));

% measurement matrix
disp('Creating measurment matrix...');
A = randn(K,N);
A = orth(A')';
disp('Done.');
	
% noisy observations
sigma = 0.005;
e = sigma*randn(K,1);
y = A*x + e;

% initial guess = min energy
x0 = A'*y;

% take epsilon a little bigger than sigma*sqrt(K)
epsilon =  sigma*sqrt(K)*sqrt(1 + 2*sqrt(2)/sqrt(K));
                                                                                                                           
tic
xp = l1qc_logbarrier(x0, A, [], y, epsilon, 1e-3);
toc

% large scale
% Afun = @(z) A*z;
% Atfun = @(z) A'*z;
% tic
% xp = l1qc_logbarrier(x0, Afun, Atfun, y, epsilon, 1e-3, 50, 1e-8, 500);
% toc