Product-manifold-definition function

Product manifold definition

Define a product manifold composed of simpler manifolds

get.product.defn(...)

Arguments

• ...: One or more simpler Manifold definitions

Returns

List containing manifold definitions for the product manifold

Examples

mani.defn1 <- get.product.defn(get.sphere.defn(n=5), get.spd.defn(n=5))
mani.defn2 <- get.product.defn(
    get.stiefel.defn(n=10, p=5),
    get.stiefel.defn(n=7, p=3),
    get.grassmann.defn(n=10, p=5)
)

## Not run:

# --- Estimate jointly: Sigma in SPD manifold and mu in sphere manifold ---
library(mvtnorm)
n <- 400
p <- 3
mu.true <- rep(1/sqrt(p), p)
Sigma.true <- diag(2,p) + 0.1
y <- rmvnorm(n, mean = mu.true, sigma = Sigma.true)

tx <- function(x) {
    idx.mu <- 1:p
    idx.S <- 1:p^2 + p
    mu <- x[idx.mu]
    S <- matrix(x[idx.S], p, p)
    list(mu = mu, Sigma = S)
}
f <- function(x) {
    par <- tx(x)
    -sum(dmvnorm(y, mean = par$mu, sigma = par$Sigma, log = TRUE))
}

mod <- Module("ManifoldOptim_module", PACKAGE = "ManifoldOptim")
prob <- new(mod$RProblem, f)

mu0 <- diag(1, p)[,1]
Sigma0 <- diag(1, p)
x0 <- c(mu0, as.numeric(Sigma0))

mani.defn <- get.product.defn(get.sphere.defn(p), get.spd.defn(p))
mani.params <- get.manifold.params()
solver.params <- get.solver.params(isconvex = TRUE)

res <- manifold.optim(prob, mani.defn, method = "LRBFGS", 
    mani.params = mani.params, solver.params = solver.params, x0 = x0)
## End(Not run)