#' @export
ising_m2 <- function(
    params, use_MC = NULL, nr_samples = 10000L,
    warmup = 15L, nr_threads = 1L
) {
    if (missing(use_MC)) {
        use_MC <- if (is.matrix(params)) 19 < nrow(params) else 190 < length(params)
    }

    m2 <- .Call("C_ising_m2", params, use_MC, nr_samples, warmup, nr_threads,
            PACKAGE = "tensorPredictors"
    )

    M2 <- vech.pinv(m2)
    attr(M2, "prob_0") <- attr(m2, "prob_0")

    M2
}


# library(tensorPredictors)

# dimX <- c(3, 4)
# dimF <- rep(1L, length(dimX))

# betas <- Map(diag, 1, dimX, dimF)
# Omegas <- list(
#     1 - diag(dimX[1]),
#     toeplitz(rev(seq(0, len = dimX[2])) / dimX[2])
# )
# Omega <- Reduce(kronecker, rev(Omegas))

# y <- array(1, dimF)
# params <- diag(as.vector(mlm(y, betas))) + Omega

# # params <- array(0, dim(Omega))

# (prob_0 <- attr(ising_m2(params), "prob_0"))
# (probs <- replicate(20, attr(ising_m2(params, use_MC = TRUE, nr_threads = 8), "prob_0")))[1]
# m <- mean(probs)
# s <- sd(probs)

# (prob_a <- (function(p, M2) {
#     (1 + p * (p + 1) / 2 + 2 * sum(M2) - 2 * (p + 1) * sum(diag(M2))) / 2^p
# })(prod(dimX), ising_m2(params, use_MC = FALSE)))

# par(mar = c(1, 2, 1, 2) + 0.1)
# plot(probs, ylim = pmax(0, range(probs, prob_0, prob_a)), pch = 16, cex = 1,
#     xaxt = "n", xlab = "", col = "gray", log = "y", bty = "n")
# lines(cumsum(probs) / seq_along(probs), lty = 2, lwd = 2)
# abline(h = c(m - s, m, m + s), lty = c(3, 2, 3), col = "red", lwd = 2)
# abline(h = c(prob_0, prob_a), lwd = 2)
# axis(4, at = prob_0, labels = sprintf("%.1e", prob_0))
# axis(4, at = prob_a, labels = sprintf("%.1e", prob_a))