Spectrahedral Shadow
In CORA, spectrahedral shadows are instantiated by
% SpS = spectraShadow(A,c,G);
where A is the horizontal concatenation of the coefficient matrices, c is the center vector, and G is the generator matrix.
Alternatively, a spectrahedral shadow can be instantiated as
% SpS = spectraShadow(E);
where E is a 1x2 cell array, where the first element is a matrix A that is the concatenation of the coefficient matrices, and the second element is a matrix B that is the concatenation of the additional coefficient matrices.
Example:
% create two simple spectrahedral shadows
% an ellipsoid, using the first type of instantiation
A1 = [0 1 0; 1 0 0; 0 0 0];
A2 = [0 0 1; 0 0 0; 1 0 0];
SpS_ellipsoid = spectraShadow(A,c,G);
% a small zonotope, using the second type of instantiation
A0 = diag([-19 1 11 21 1 -9]);
A1 = diag([10 10 0 -10 -10 0]);
A2 = (10/3)*diag([1 -1 2 -1 1 -2]);
B = 0.5774*diag([-1 1 1 1 -1 -1]);
SpS_zonotope = spectraShadow(ESumRep);
% we can construct more complicated sets
% based on the two above, such as the
% convex hull of the two previous spectrahedral shadows
SpS = convHull(SpS_ellipsoid, SpS_zonotope);
For more information, type
help spectraShadow
spectraShadow - object constructor for spectraShadow objects
Description:
This class represents spectrahedral shadow objects defined as
SpS = {Gx+c|A0 + x1*A1 + ... + xm*Am >= 0}
(projection representation)
or, equivalently,
SpS = {y|