library(sbm)
library(ggplot2)
library(readr)

source("load-full.R")

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

net_table <- otu_table(cpd_phyloseq)
rm(cpd_phyloseq)
write.csv(net_table, "data/otu_matrix.csv")
zip("data/otu_matrix.csv.zip", "data/otu_matrix.csv")
unlink("data/otu_matrix.csv")
# Ne tourne pas, probablement gros calculs matriciel
# res <- estimateBipartiteSBM(netMat = net_table, dimLabels = c("OTU", "Sample"), model = "poisson")

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

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(y = otu, x = mean)) +
    geom_point() +
    geom_errorbarh(aes(xmin = mean - std, xmax = mean + std), orientation = "y") +
    theme(
        axis.title.y = element_blank(),
        axis.text.y = element_blank(),
        axis.ticks.y = element_blank()
    )

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)")

lambdas <- seq(1, 100)
realization_pois <- sapply(lambdas, rpois, n = 1000)
r_pois_df <- data.frame(mean = colMeans(realization_pois), var = sdCol(realization_pois)^2)

ggplot(r_pois_df, aes(x = mean, y = var)) +
    geom_line() +
    geom_point() +
    geom_abline(slope = 1, color = "red") +
    ggtitle("Poisson for mean = var")

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


ggplot(r_pois_df, aes(x = 1 / mean, y = var / mean^2)) +
    geom_line() +
    geom_point() +
    geom_abline(slope = 1, color = "red") +
    ggtitle("Poisson for 1/lambda = var/mean^2")