library(phyloseq)
library(ggplot2)
library(sbm)
library(biomformat)

# data("enterotype")
# data("mach")
data <- import_biom("data/chaillou/chaillou.biom")
net_table <- otu_table(data)
dim(net_table)

nb_inter <- sum(net_table > 0)
all_possible_inter <- nrow(net_table) * ncol(net_table)
(density <- nb_inter / all_possible_inter)

res <- estimateBipartiteSBM(net_table, dimLabels = c("OTU", "Sample"), model = "poisson")
res_t <- estimateBipartiteSBM(t(net_table), dimLabels = rev(c("OTU", "Sample")))

plot(res, type = "data")

plot(res_t, type = "data")

sdCol <- function(matrix) {
    sapply(seq_len(ncol(matrix)), function(col) sd(matrix[, col]))
}

t_net_table <- t(net_table)
std_otu <- sdCol(t_net_table)
mean_otu <- rowMeans(net_table)

stats_df <- data.frame(otu = rownames(net_table), mean = mean_otu, std = std_otu, var = std_otu^2)

ggplot(stats_df, aes(x = mean, y = var)) +
    geom_line() +
    geom_point() +
    geom_abline(slope = 1, color = "red") +
    scale_y_log10() +
    scale_x_log10() +
    ggtitle("OTU for log(mean) = log(var)")

ggplot(stats_df, aes(x = mean, y = var / mean)) +
    geom_line() +
    geom_point() +
    geom_hline(yintercept = 1, color = "red") +
    ggtitle("OTU for f(mean) = var/mean = 1")

ggplot(stats_df, aes(x = 1 / mean, y = var / mean^2)) +
    geom_line() +
    geom_point() +
    geom_abline(slope = 1, color = "red") +
    scale_y_log10() +
    scale_x_log10() +
    ggtitle("OTU for log(1/mean) = log(var/mean^2)")