As = {}; bs = {}; cs = {};
As{1} = [ 0.1355 0.1148; 0.1148 0.4398];
As{2} = [ 0.6064 -0.1022; -0.1022 0.7344];
As{3} = [ 0.7127 -0.0559; -0.0559 0.9253];
As{4} = [ 0.2706 -0.1379; -0.1379 0.2515];
As{5} = [ 0.4008 -0.1112; -0.1112 0.2107];
bs{1} = [ -0.2042 0.0264]';
bs{2} = [ 0.8259 -2.1188]';
bs{3} = [ -0.0256 1.0591]';
bs{4} = [ 0.1827 -0.3844]';
bs{5} = [ 0.3823 -0.8253]';
cs{1} = 0.2351;
cs{2} = 5.8250;
cs{3} = 0.9968;
cs{4} = -0.2981;
cs{5} = 2.6735;
n = 2;
m = size(bs,2);
cvx_begin sdp
variable Asqr(n,n) symmetric
variable btilde(n)
variable t(m)
maximize( det_rootn( Asqr ) )
subject to
t >= 0;
for i = 1:m
[ -(Asqr - t(i)*As{i}), -(btilde - t(i)*bs{i}), zeros(n,n);
-(btilde - t(i)*bs{i})', -(- 1 - t(i)*cs{i}), -btilde';
zeros(n,n), -btilde, Asqr] >= 0;
end
cvx_end
A = sqrtm(Asqr);
b = A\btilde;
noangles = 200;
angles = linspace( 0, 2 * pi, noangles );
clf
for i=1:m
Ai = sqrtm(As{i}); bi = Ai\bs{i};
alpha = bs{i}'*inv(As{i})*bs{i} - cs{i};
ellipse = Ai \ [ sqrt(alpha)*cos(angles)-bi(1) ; sqrt(alpha)*sin(angles)-bi(2) ];
plot( ellipse(1,:), ellipse(2,:), 'b-' );
hold on
end
ellipse = A \ [ cos(angles) - b(1) ; sin(angles) - b(2) ];
plot( ellipse(1,:), ellipse(2,:), 'r--' );
axis square
axis off
hold off
Calling sedumi: 94 variables, 15 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 = 15, order n = 38, dim = 152, blocks = 8
nnz(A) = 98 + 0, nnz(ADA) = 119, nnz(L) = 67
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 6.88E+00 0.000
1 : 2.21E-01 1.98E+00 0.000 0.2884 0.9000 0.9000 1.26 1 1 5.3E+00
2 : 2.53E-01 6.02E-01 0.000 0.3035 0.9000 0.9000 1.69 1 1 1.4E+00
3 : 1.05E-01 1.53E-01 0.000 0.2534 0.9000 0.9000 1.81 1 1 3.7E-01
4 : 7.56E-02 1.52E-02 0.000 0.0993 0.9900 0.9900 1.34 1 1 5.2E-02
5 : 7.86E-02 3.47E-03 0.000 0.2290 0.9000 0.9000 0.90 1 1 1.3E-02
6 : 7.87E-02 1.80E-04 0.000 0.0518 0.9900 0.9900 0.99 1 1 7.1E-04
7 : 7.87E-02 6.81E-06 0.000 0.0379 0.9901 0.9900 1.00 1 1 2.7E-05
8 : 7.87E-02 1.10E-06 0.000 0.1608 0.9030 0.9000 1.00 1 1 4.3E-06
9 : 7.87E-02 6.40E-08 0.340 0.0584 0.9901 0.9900 1.00 1 1 2.6E-07
10 : 7.87E-02 1.71E-08 0.000 0.2674 0.9010 0.9000 1.00 1 2 7.0E-08
11 : 7.87E-02 6.21E-10 0.271 0.0362 0.9903 0.9900 1.00 1 2 2.1E-09
iter seconds digits c*x b*y
11 0.1 8.5 7.8681465732e-02 7.8681465493e-02
|Ax-b| = 1.0e-09, [Ay-c]_+ = 2.6E-10, |x|= 2.4e+00, |y|= 2.6e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 1.100E-01 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 10265.2.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.0786815