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gen.gaussian <- function() {
    sign <- sample(c(-1, 1), 1)
    alpha <- runif(1, 0, 1)
    beta <- runif(1, 0, 3)
    return(list(fun = function(x) {sign * alpha * exp(- beta * x^2)}, 
    sign = sign, alpha = alpha, beta = beta, type = "gaussian"))
}

gen.sine <- function() {
    alpha <- runif(1, 0, 1)
    beta <- runif(1, 0, 3)
    return(list(fun = function(x) {beta * sin(2 * pi * alpha * x)}, 
    alpha = alpha, beta = beta, type = "sine"))
}

gen.cos <- function() {
    alpha <- runif(1, 0, 1)
    beta <- runif(1, 0, 3)
    return(list(fun = function(x) {beta * cos(2 * pi * alpha * x)}, 
    alpha = alpha, beta = beta, type = "cosine"))
}

gen.logis <- function() {
    alpha <- runif(1, 0, 1)
    beta <- runif(1, 0, 3)
    return(list(fun = function(x) {beta/(1 + exp(-alpha * x))}, 
    alpha = alpha, beta = beta, type = "logistic"))
}

function.list <- list(gen.gaussian, gen.sine, gen.cos, gen.logis)

gen.mixing.matrix <- function(d, seed = 7) {
    set.seed(seed)
    foos.idx <- sample(1:length(function.list), d^2, T)

    return(function(x) {
        m <- matrix(0, nrow = d, ncol = d)
        cnt <- 1
        for (i in 1:d) {
            for (j in 1:d) {
                set.seed(seed)
                foo <- function.list[[foos.idx[cnt]]]()
                m[i, j] <- foo$fun(x)
                cnt <- cnt + 1
            }
        }
        m
    })
}