Matlab Code for Week 6 - Adam Oberman Math

%% setup for class examples
% first go to the cvx directory and run
cvx_setup

%% tell cvx to be quit
s_quiet = cvx_quiet(true);
s_pause = cvx_pause(false);
cvx_clear; echo on
has_quadprog = 0;

% Input data
m = 16; n = 8;
A = randn(m,n);
b = randn(m,1);
 
% Matlab version
x_ls = A \ b;
 
% cvx version
cvx_begin
    variable x(n);
    minimize( norm(A*x-b) );
cvx_end
echo off
 
plot(1:m, A*x, 1:m, b)
xunc = x;

% Input data
m = 16; n = 8;
%A = randn(m,n);
%b = randn(m,1);
 
% More input data
bnds = randn(n,2);
l = min( bnds, [] ,2 );
u = max( bnds, [], 2 );
 
% cvx version
cvx_begin
    variable x(n);
    minimize( norm(A*x-b) );
    subject to
        x >= l;
        x <= u;
cvx_end
 
echo off
 
figure(2), plot(1:n, x, 1:n, u, 1:n, l)
hold on, plot(1:n, xunc), hold off
figure(4), plot(1:m, A*x-b, 1:m, A*xunc - b); 
norm(A*x-b), 
norm(A*xunc - b),

% Input data
m = 16; n = 8;
A = randn(m,n);
b = randn(m,1);
 
 
% cvx version
cvx_begin
    variable x(n);
    minimize( norm(A*x-b,Inf) );
cvx_end
 
echo off
 
figure(1), plot(A*x-b)
 
%% compare to unconstrained
% cvx version
cvx_begin
    variable xu(n);
    minimize( norm(A*xu-b) );
cvx_end
 
figure(2), plot(1:m,A*x-b, 1:m, A*xu-b)

% cvx version
cvx_begin
    variable x(n);
    minimize( norm(A*x-b,1) );
cvx_end