Niclas
53 lines
1.9 KiB
R
53 lines
1.9 KiB
R
create_matrix_Q <- function(
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qgraphon,
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a,
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K,
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Fv,
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matrix_X = NULL,
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scaled = FALSE
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) {
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## 1.1 Check inputs ==========================================================
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if (!is.numeric(a) || !is.vector(a)) stop("'a' must be a numeric vector")
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if (!is.numeric(K) || length(K) != 1 || K <= 0) stop("'K' must be a positive integer")
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if (!is.function(Fv)) stop("'F_v' must be a function")
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if (!is.matrix(matrix_X)) stop("matrix_X must be a matrix")
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if (!is.logical(scaled)) stop("`scaled` must be a logical!")
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if (ncol(matrix_X) != length(a)) {
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stop("Number of columns of `matrix_X` (", ncol(matrix_X), ") must equal length(a) (", length(a), ")")
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}
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## 1.3 Compute the graphon quantiles =========================================
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k <- seq(0, K) / K
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n <- nrow(matrix_X)
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# here there is an automatic switch included, if fX is not null and we have a
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# scalar case, then qpgrahon automatically switches to the analytical
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# expression. The intended use is for small values of n
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graphon_quantiles <- qgraphon(k)
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## 1.4 Build the matrix Q ====================================================
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inner_products = as.vector(matrix_X %*% a)
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# outer(y, x, "-") gives a matrix with entry (j,i) = y[j] - x[i]
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# then we apply the CDF `F_v` to the whole matrix at once.
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# finally we take the difference of successive rows (j) to obtain the
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# increments required by equation (3.1).
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cdf_mat <- Fv(outer(graphon_quantiles, inner_products, "-")) # (K +1) x n matrix
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Q <- diff(cdf_mat, lag=1) # operates along rows
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if (scaled) { Q <- 1 / sqrt(n) * Q }
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Q
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}
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source(here::here("R", "distributionfunctions.R"))
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n <- 100
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K <- 3
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a <- c(2.0, -0.5)
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X <- matrix(rnorm(2 * n), nrow = n, ncol = 2)
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Fv <- function(x) {dnorm(x, mean=0, sd=1)}
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qgraphon <- make_distribution_func(a=a, Fv=Fv, X_matrix=X)
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Q <- create_matrix_Q(qgraphon, a, K, Fv, X)
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Q
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