rand('state',0);
N = 100;
M = 120;
X = 2 * rand(2,N) - 1;
X = X * diag(0.9*rand(1,N)./sqrt(sum(X.^2)));
Y = 2 * rand(2,M) - 1;
Y = Y * diag((1.1+rand(1,M))./sqrt(sum(Y.^2)));
d = sqrt(sum((X-[1.1;0]*ones(1,N)).^2));
Y = [ Y, X(:,d<0.9) ];
X = X(:,d>1);
N = size(X,2);
M = size(Y,2);
p1 = [0,0,1,0,1,2,0,1,2,3,0,1,2,3,4]';
p2 = [0,1,1,2,2,2,3,3,3,3,4,4,4,4,4]'-p1;
np = length(p1);
op = ones(np,1);
monX = X(op,:) .^ p1(:,ones(1,N)) .* X(2*op,:) .^ p2(:,ones(1,N));
monY = Y(op,:) .^ p1(:,ones(1,M)) .* Y(2*op,:) .^ p2(:,ones(1,M));
fprintf(1,'Finding the optimal polynomial of order 4 that separates the 2 classes...');
cvx_begin
variables a(np) t(1)
minimize ( t )
a'*monX <= t;
a'*monY >= -t;
norm(a) <= 1;
cvx_end
fprintf(1,'Done! \n');
nopts = 2000;
angles = linspace(0,2*pi,nopts);
cont = zeros(2,nopts);
for i=1:nopts
v = [cos(angles(i)); sin(angles(i))];
l = 0; u = 1;
while ( u - l > 1e-3 )
s = (u+l)/2;
x = s * v;
if a' * ( x(op,:) .^ p1 .* x(2*op) .^ p2 ) > 0,
u = s;
else
l = s;
end
end;
s = (u+l)/2;
cont(:,i) = s*v;
end;
graph = plot(X(1,:),X(2,:),'o', Y(1,:), Y(2,:),'o', cont(1,:), cont(2,:), '-');
set(graph(2),'MarkerFaceColor',[0 0.5 0]);
title('Optimal order-4 polynomial that separates the 2 classes')
Finding the optimal polynomial of order 4 that separates the 2 classes...
Calling sedumi: 228 variables, 17 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 = 17, order n = 215, dim = 229, blocks = 2
nnz(A) = 3393 + 0, nnz(ADA) = 287, nnz(L) = 152
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 5.60E+02 0.000
1 : -4.97E-01 2.36E+02 0.000 0.4220 0.9000 0.9000 2.73 1 1 1.3E+02
2 : -1.84E-01 1.51E+02 0.000 0.6389 0.9000 0.9000 5.08 1 1 2.9E+01
3 : -2.46E-02 7.59E+01 0.000 0.5024 0.9000 0.9000 4.64 1 1 5.1E+00
4 : -1.13E-02 3.19E+01 0.000 0.4205 0.9000 0.9000 1.51 1 1 1.9E+00
5 : -6.08E-03 1.48E+01 0.000 0.4643 0.9000 0.9000 0.80 1 1 1.1E+00
6 : -8.09E-04 4.48E+00 0.000 0.3024 0.9000 0.9000 0.10 1 1 9.3E-01
7 : 7.49E-03 2.84E+00 0.000 0.6334 0.9000 0.9000 -0.40 1 1 7.1E-01
8 : 2.80E-02 1.50E+00 0.000 0.5302 0.9000 0.9000 0.36 1 1 3.8E-01
9 : 3.40E-02 5.24E-01 0.000 0.3483 0.9000 0.9000 0.52 1 1 1.5E-01
10 : 3.73E-02 2.14E-01 0.000 0.4080 0.9000 0.9000 0.67 1 1 7.4E-02
11 : 3.89E-02 1.01E-01 0.000 0.4702 0.9000 0.9000 0.68 1 1 3.9E-02
12 : 3.98E-02 5.69E-02 0.000 0.5662 0.9000 0.9000 0.60 1 1 2.6E-02
13 : 4.03E-02 3.12E-02 0.000 0.5481 0.9000 0.9000 0.67 1 1 1.5E-02
14 : 4.07E-02 1.69E-02 0.000 0.5430 0.9000 0.9000 0.65 1 1 9.2E-03
15 : 4.09E-02 4.50E-03 0.000 0.2655 0.9000 0.9000 0.86 1 1 2.5E-03
16 : 4.10E-02 1.14E-03 0.000 0.2530 0.9000 0.9000 0.88 1 1 6.7E-04
17 : 4.10E-02 2.30E-05 0.000 0.0202 0.9900 0.9900 0.99 1 1 1.4E-05
18 : 4.10E-02 6.03E-06 0.000 0.2622 0.9000 0.8743 1.00 1 1 3.3E-06
19 : 4.10E-02 1.39E-06 0.000 0.2306 0.9003 0.9000 1.00 1 1 7.6E-07
20 : 4.10E-02 1.93E-07 0.000 0.1390 0.9107 0.9000 1.00 1 1 1.3E-07
21 : 4.10E-02 3.64E-08 0.000 0.1883 0.9106 0.9000 1.00 1 1 3.1E-08
22 : 4.10E-02 9.83E-09 0.046 0.2700 0.9169 0.9000 1.00 2 2 1.0E-08
iter seconds digits c*x b*y
22 0.1 7.9 4.0993225478e-02 4.0993225002e-02
|Ax-b| = 9.0e-09, [Ay-c]_+ = 0.0E+00, |x|= 5.6e-01, |y|= 1.0e+00
Detailed timing (sec)
Pre IPM Post
2.000E-02 1.300E-01 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 26.9346.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -0.0409932
Done!