Spectrahedron-class {volesti}

An R class to represent a Spectrahedron

Description

A spectrahedron is a convex body defined by a linear matrix inequality of the form A_0 + x_1 A_1 + ... + x_n A_n \preceq 0. The matrices A_i are symmetric m \times m real matrices and \preceq 0 denoted negative semidefiniteness.

Details

matrices

A List that contains the matrices A_0, A_1, ..., A_n.

Examples

A0 = matrix(c(-1,0,0,0,-2,1,0,1,-2), nrow=3, ncol=3, byrow = TRUE)
A1 = matrix(c(-1,0,0,0,0,1,0,1,0), nrow=3, ncol=3, byrow = TRUE)
A2 = matrix(c(0,0,-1,0,0,0,-1,0,0), nrow=3, ncol=3, byrow = TRUE)
lmi = list(A0, A1, A2)
S = Spectrahedron(matrices = lmi);