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#' Sample a random edgelist from a random dot product graph
#'
#' There are two steps to using the `fastRG` package. First,
#' you must parameterize a random dot product graph by
#' sampling the latent factors. Use functions such as
#' [dcsbm()], [sbm()], etc, to perform this specification.
#' Then, use `sample_*()` functions to generate a random graph
#' in your preferred format.
#'
#' @param factor_model A [directed_factor_model()] or
#' [undirected_factor_model()].
#'
#' @param ... Ignored. Do not use.
#'
#' @return A single realization of a random Poisson (or Bernoulli)
#' Dot Product Graph, represented as a [tibble::tibble()] with two
#' integer columns, `from` and `to`.
#'
#' **NOTE**: Indices for isolated nodes will not appear in the edgelist!
#' This can lead to issues if you construct network objects from the
#' edgelist directly.
#'
#' In the undirected case, `from` and `to` do not encode
#' information about edge direction, but we will always have
#' `from <= to` for convenience of edge identification.
#'
#' To avoid handling such considerations yourself, we recommend using
#' [sample_sparse()], [sample_igraph()], and [sample_tidygraph()]
#' over [sample_edgelist()].
#'
#' @export
#' @family samplers
#'
#' @details This function implements the `fastRG` algorithm as
#' described in Rohe et al (2017). Please see the paper
#' (which is short and open access!!) for details.
#'
#' @references Rohe, Karl, Jun Tao, Xintian Han, and Norbert Binkiewicz. 2017.
#' "A Note on Quickly Sampling a Sparse Matrix with Low Rank Expectation."
#' Journal of Machine Learning Research; 19(77):1-13, 2018.
#' <https://www.jmlr.org/papers/v19/17-128.html>
#'
#' @examples
#'
#' library(igraph)
#' library(tidygraph)
#'
#' set.seed(27)
#'
#' ##### undirected examples ----------------------------
#'
#' n <- 100
#' k <- 5
#'
#' X <- matrix(rpois(n = n * k, 1), nrow = n)
#' S <- matrix(runif(n = k * k, 0, .1), nrow = k)
#'
#' # S will be symmetrized internal here, or left unchanged if
#' # it is already symmetric
#'
#' ufm <- undirected_factor_model(
#' X, S,
#' expected_density = 0.1
#' )
#'
#' ufm
#'
#' ### sampling graphs as edgelists ----------------------
#'
#' edgelist <- sample_edgelist(ufm)
#' edgelist
#'
#' ### sampling graphs as sparse matrices ----------------
#'
#' A <- sample_sparse(ufm)
#'
#' inherits(A, "dsCMatrix")
#' isSymmetric(A)
#' dim(A)
#'
#' B <- sample_sparse(ufm)
#'
#' inherits(B, "dsCMatrix")
#' isSymmetric(B)
#' dim(B)
#'
#' ### sampling graphs as igraph graphs ------------------
#'
#' sample_igraph(ufm)
#'
#' ### sampling graphs as tidygraph graphs ---------------
#'
#' sample_tidygraph(ufm)
#'
#' ##### directed examples ----------------------------
#'
#' n2 <- 100
#'
#' k1 <- 5
#' k2 <- 3
#'
#' d <- 50
#'
#' X <- matrix(rpois(n = n2 * k1, 1), nrow = n2)
#' S <- matrix(runif(n = k1 * k2, 0, .1), nrow = k1, ncol = k2)
#' Y <- matrix(rexp(n = k2 * d, 1), nrow = d)
#'
#' fm <- directed_factor_model(X, S, Y, expected_in_degree = 2)
#' fm
#'
#' ### sampling graphs as edgelists ----------------------
#'
#' edgelist2 <- sample_edgelist(fm)
#' edgelist2
#'
#' ### sampling graphs as sparse matrices ----------------
#'
#' A2 <- sample_sparse(fm)
#'
#' inherits(A2, "dgCMatrix")
#' isSymmetric(A2)
#' dim(A2)
#'
#' B2 <- sample_sparse(fm)
#'
#' inherits(B2, "dgCMatrix")
#' isSymmetric(B2)
#' dim(B2)
#'
#' ### sampling graphs as igraph graphs ------------------
#'
#' # since the number of rows and the number of columns
#' # in `fm` differ, we will get a bipartite igraph here
#'
#' # creating the bipartite igraph is slow relative to other
#' # sampling -- if this is a blocker for
#' # you please open an issue and we can investigate speedups
#'
#' dig <- sample_igraph(fm)
#' is_bipartite(dig)
#'
#' ### sampling graphs as tidygraph graphs ---------------
#'
#' sample_tidygraph(fm)
#'
sample_edgelist <- function(
factor_model,
...) {
ellipsis::check_dots_unnamed()
UseMethod("sample_edgelist")
}
#' @rdname sample_edgelist
#' @export
sample_edgelist.undirected_factor_model <- function(
factor_model,
...) {
X <- factor_model$X
S <- factor_model$S
sample_edgelist(
X, S, X,
FALSE,
factor_model$poisson_edges,
factor_model$allow_self_loops
)
}
#' @rdname sample_edgelist
#' @export
sample_edgelist.directed_factor_model <- function(
factor_model,
...) {
X <- factor_model$X
S <- factor_model$S
Y <- factor_model$Y
sample_edgelist(
X, S, Y,
TRUE,
factor_model$poisson_edges,
factor_model$allow_self_loops
)
}
#' Low level interface to sample RPDG edgelists
#'
#' **This is a breaks-off, no safety checks interface.**
#' We strongly recommend that you do not call
#' `sample_edgelist.matrix()` unless you know what you are doing,
#' and even then, we still do not recommend it, as you will
#' bypass all typical input validation.
#' ***extremely loud coughing*** All those who bypass input
#' validation suffer foolishly at their own hand.
#' ***extremely loud coughing***
#'
#' @param factor_model An `n` by `k1` [matrix()] or [Matrix::Matrix()]
#' of latent node positions encoding incoming edge community membership.
#' The `X` matrix in Rohe et al (2017). Naming differs only for
#' consistency with the S3 generic.
#'
#' @param S A `k1` by `k2` mixing [matrix()] or [Matrix::Matrix()]. In
#' the undirect case this is assumed to be symmetric but **we do not
#' check that this is the case**.
#'
#' @param Y A `d` by `k2` [matrix()] or [Matrix::Matrix()] of latent
#' node positions encoding outgoing edge community membership.
#'
#' @param directed Logical indicating whether or not the graph should be
#' directed. When `directed = FALSE`, symmetrizes `S` internally.
#' `Y = X` together with a symmetric `S` implies a symmetric
#' expectation (although not necessarily an undirected graph).
#' When `directed = FALSE`, samples a directed graph with
#' symmetric expectation, and then adds edges until symmetry
#' is achieved.
#'
#' @param poisson_edges Whether or not to remove duplicate edges
#' after sampling. See Section 2.3 of Rohe et al. (2017)
#' for some additional details. Defaults to `TRUE`.
#'
#' @param allow_self_loops Logical indicating whether or not
#' nodes should be allowed to form edges with themselves.
#' Defaults to `TRUE`. When `FALSE`, sampling proceeds allowing
#' self-loops, and these are then removed after the fact.
#'
#' @param ... Ignored, for generic consistency only.
#'
#' @inherit sample_edgelist return details references
#'
#' @export
#' @importFrom stats rpois rmultinom
#' @family samplers
#'
#' @examples
#'
#' set.seed(46)
#'
#' n <- 10000
#' d <- 1000
#'
#' k1 <- 5
#' k2 <- 3
#'
#' X <- matrix(rpois(n = n * k1, 1), nrow = n)
#' S <- matrix(runif(n = k1 * k2, 0, .1), nrow = k1)
#' Y <- matrix(rpois(n = d * k2, 1), nrow = d)
#'
#' sample_edgelist(X, S, Y, TRUE, TRUE, TRUE)
#'
sample_edgelist.matrix <- function(
factor_model, S, Y,
directed,
poisson_edges,
allow_self_loops,
...) {
X <- factor_model
stopifnot(is.logical(directed))
stopifnot(is.logical(poisson_edges))
stopifnot(is.logical(allow_self_loops))
n <- nrow(X)
d <- nrow(Y)
k1 <- ncol(X)
k2 <- ncol(Y)
Cx <- Diagonal(n = k1, x = colSums(X))
Cy <- Diagonal(n = k2, x = colSums(Y))
# passed to rmultinom, so Matrix objects will break things
S_tilde <- as.matrix(Cx %*% S %*% Cy)
expected_edges <- sum(S_tilde)
m <- rpois(n = 1, lambda = expected_edges)
if (m == 0) {
edge_list <- matrix(0, nrow = 0, ncol = 2)
colnames(edge_list) <- c("from", "to")
return(edge_list)
}
# varpi in section 2.4 of Rohe et al (2017), the number of
# edges between all pairs of blocks
block_sizes <- matrix(
rmultinom(n = 1, size = m, prob = S_tilde),
nrow = k1,
ncol = k2
)
# allocate space for the edgelist
from <- integer(m)
to_tmp <- integer(m)
to <- integer(m)
# intuition: each column works just like a block in a stochastic
# block model. sample one column of X (variously denoted by U in
# the paper) at a time
u_block_start <- 1
u_block_sizes <- rowSums(block_sizes)
for (u in 1:k1) {
if (u_block_sizes[u] > 0) {
indices <- u_block_start:(u_block_start + u_block_sizes[u] - 1)
# the prob argument should be \tilde X from the paper, but \tilde X
# is just the l1 normalized version of X[, u], and sample()
# will automatically normalize for us
from[indices] <- sample(
n,
size = u_block_sizes[u],
replace = TRUE,
prob = X[, u]
)
u_block_start <- u_block_start + u_block_sizes[u]
}
}
v_block_start <- 1
v_block_sizes <- colSums(block_sizes)
for (v in 1:k2) {
if (v_block_sizes[v] > 0) {
indices <- v_block_start:(v_block_start + v_block_sizes[v] - 1)
# note same lack of \tilde Y as in the X/U case
to_tmp[indices] <- sample(
d,
size = v_block_sizes[v],
replace = TRUE,
prob = Y[, v]
)
v_block_start <- v_block_start + v_block_sizes[v]
}
}
# if the model is undirected, i think to and to_tmp are sufficient since
# the U and V blocks should line up since block memberships match?
# put to_tmp in the correct order, to match up with from
u_block_start <- 1
# i believe the move from the commented out line of code to the new
# version should fix #13, but if something goes horribly wrong, revert this,
# it's fine if #13 remains buggy
# v_block_start <- c(1, cumsum(v_block_sizes))
v_block_start <- cumsum(c(1, v_block_sizes))
for (u in 1:k1) {
for (v in 1:k2) {
if (block_sizes[u, v] > 0) {
to_index <- u_block_start:(u_block_start + block_sizes[u, v] - 1)
tmp_index <- v_block_start[v]:(v_block_start[v] + block_sizes[u, v] - 1)
to[to_index] <- to_tmp[tmp_index]
v_block_start[v] <- v_block_start[v] + block_sizes[u, v]
u_block_start <- u_block_start + block_sizes[u, v]
}
}
}
if (directed) {
edgelist <- tibble(from = from, to = to)
} else {
# in the undirected case, sort the indices so that the *directed*
# representations lives all in the same triangle (upper or lower i
# didn't work it out)
# *do not* move these into the tibble call otherwise you'll run
# into a nasty NSE scoping issue is that is super hard to detect
tibble_from <- pmin(from, to)
tibble_to <- pmax(from, to)
edgelist <- tibble(
from = tibble_from,
to = tibble_to
)
}
if (!poisson_edges) {
# need to deduplicate edgelist. the number of times a given
# (to, from) pair appears in the edgelist is the weight of
# that edge (i.e. we're really working with a multigraph)
edgelist <- dplyr::distinct(edgelist)
}
if (!allow_self_loops) {
edgelist <- dplyr::filter(edgelist, to != from)
}
edgelist
}
#' @rdname sample_edgelist.matrix
#' @export
sample_edgelist.Matrix <- sample_edgelist.matrix
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