n = 2;
randn('state',3);
N = 10; M = 6;
Y = [1.5+1*randn(1,M); 2*randn(1,M)];
X = [-1.5+1*randn(1,N); 2*randn(1,N)];
T = [-1 1; 1 1];
Y = T*Y; X = T*X;
fprintf('Finding a separating hyperplane...');
cvx_begin
variables a(n) b(1)
X'*a - b >= 1;
Y'*a - b <= -1;
cvx_end
fprintf(1,'Done! \n');
linewidth = 0.5;
t_min = min([X(1,:),Y(1,:)]);
t_max = max([X(1,:),Y(1,:)]);
t = linspace(t_min-1,t_max+1,100);
p = -a(1)*t/a(2) + b/a(2);
graph = plot(X(1,:),X(2,:), 'o', Y(1,:), Y(2,:), 'o');
set(graph(1),'LineWidth',linewidth);
set(graph(2),'LineWidth',linewidth);
set(graph(2),'MarkerFaceColor',[0 0.5 0]);
hold on;
plot(t,p, '-r');
axis equal
title('Simple classification using an affine function');
Finding a separating hyperplane...
Calling sedumi: 16 variables, 3 equality constraints
For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 3, order n = 17, dim = 17, blocks = 1
nnz(A) = 48 + 0, nnz(ADA) = 9, nnz(L) = 6
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 9.03E+01 0.000
1 : 0.00E+00 3.20E+01 0.000 0.3538 0.9000 0.9000 -2.42 1 1 3.8E+01
2 : 0.00E+00 7.37E+00 0.000 0.2305 0.9000 0.9000 -0.26 1 1 1.4E+01
3 : 0.00E+00 2.38E-01 0.000 0.0323 0.9900 0.9900 0.62 1 1 5.6E-01
4 : 0.00E+00 8.82E-06 0.000 0.0000 1.0000 1.0000 0.99 1 1
iter seconds digits c*x b*y
4 0.0 Inf 0.0000000000e+00 0.0000000000e+00
|Ax-b| = 0.0e+00, [Ay-c]_+ = 0.0E+00, |x|= 0.0e+00, |y|= 5.0e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 3.000E-02 0.000E+00
Max-norms: ||b||=0, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -0
Done!