library(igraph)


NC <- function(x) {
    N <- vcount(x)
    log(sum(exp(eigen(get.adjacency(x))$values)) / N) / (N-log(N))
}

# ig -> igraph object
robustnessNC <- function(ig, nrand=0) {

## Order by betweenness
btw <- centralization.betweenness(ig, directed=FALSE)$res
btw <- order(btw, decreasing=TRUE)
nv <- vcount(ig)

btw_ncvec <- vector('numeric', nv-1)
#tmpgr <- ig
for (i in 1:(nv-1)) {
#    tmpgr <- delete_vertices(ig, which(btw > i))
    tmpgr <- delete_edges(ig, E(ig)[from(V(ig)[which(btw > i)])])
    btw_ncvec[i] <- NC(tmpgr)
}

## Order by degree
deg <- degree(ig)
deg <- order(deg, decreasing=TRUE)

#tmpgr <- ig
deg_ncvec <- vector('numeric', nv-1)
for (i in 1:(nv-1)) {
#    tmpgr <- delete_vertices(ig, which(deg > i))
    tmpgr <- delete_edges(ig, E(ig)[from(V(ig)[which(deg > i)])])
    deg_ncvec[i] <- NC(tmpgr)
}

if (nrand > 0) {
  randmat <- replicate(nrand, {
    rand_ncvec <- vector('numeric', nv-1)
    rand <- sample(1:(nv-1))
    for (i in 1:(nv-1)) {
        tmpgr <- delete_edges(ig, E(ig)[from(V(ig)[which(rand > i)])])
        rand_ncvec[i] <- NC(tmpgr)
    }
     return(rand_ncvec)
  }, simplify='matrix')
} else randmat <- NULL

list(vert=(nv-1):1, btw=btw_ncvec, deg=deg_ncvec, rand=randmat)
}


number_to_sign <- function(number,signal=c("-",".","+")){
  number[number<0] = "-"
  number[number==0] = "."
  number[number>0] = "+"
  return(number)
}
get_Oxf_interaction <- function(biom_to_use,minimum_prevalence,lambda,type="signal"){
  # type can be mean, summary, sign
  biom_to_use <- prune_taxa(rowSums(biom_to_use@otu_table@.Data)!=0, biom_to_use)
  tax_table(biom_to_use) <- t(sapply(taxa_names(biom_to_use), parse_taxonomy_qiime))
  biom_to_use.filt <-  prune_taxa(rowSums(sign(biom_to_use@otu_table@.Data)) > nsamples(biom_to_use)*minimum_prevalence, biom_to_use)
  if(length(grep("formigenes",taxa_names(biom_to_use.filt)))==0){
    print("O. formigenes is not present in 20% of the samples" )
  }
  else{
    temp = spiec.easi(biom_to_use.filt, method='mb', sel.criterion='bstars', lambda.min.ratio=lambda,
                      nlambda=100, pulsar.params=list(rep.num=20, ncores=2))
    Of_index = grep("formigenes",taxa_names(biom_to_use.filt))
    taxa_itrt = taxa_names(biom_to_use.filt)[as(temp$refit,"matrix")[Of_index,]==1]
    #return(taxa_itrt)
    taxa_itrt_index = which(taxa_names(biom_to_use.filt)%in%taxa_itrt)
    taxa_itrt_beta = as.data.frame(lapply(temp$est$beta,function(x) as(x,"matrix")[Of_index,taxa_itrt_index]))
    rownames(taxa_itrt_beta) = taxa_itrt
    if(type=="signal"){return(number_to_sign(apply(taxa_itrt_beta,1,mean)))}
    else if(type=="mean"){return(apply(taxa_itrt_beta,1,mean))}
    else if(type=="summary"){return(apply(taxa_itrt_beta,1,summary))}
  }
}