mapZX | R Documentation |
Map from zonotope Z to the convex projection of A Y (E)
mapZX(z, A, eps = 1e-06, Amat = NULL, Aind = NULL)
z |
matrix of low-dimensional coordinates in the zonotope, one point per row |
A |
random embedding matrix, such that |
eps |
to avoid some numerical issues with quadratic programming |
Aind, Amat |
optional matrices to be passed to |
Numerical problems may occur, then the equality constraints are slightly relaxed.
Mickael Binois
M. Binois, D. Ginsbourger, O. Roustant (2018), On the choice of the low-dimensional domain for global optimization via random embeddings, arXiv:1704.05318
## Example of forward - backward mapping
d <- 5; D <- 26
A <- selectA(d, D, type = 'Gaussian')
n <- 10000
size <- 10
Y <- size * (2 * matrix(runif(n * d), n) - 1)
X <- randEmb(Y, A)
Z <- ortProj(X, t(A))
# Errors are catched and the problem slightly relaxed
Xback <- mapZX(Z, A)
print(max(abs(Xback - X)))
print(mean(Xback - X))
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