Add probabilistic model to shuffled_linklist

[shainova]

prob_model_large_matrix <- function(M, max_attempts=100, verbose=F){
  num_col <- ncol(M)
  num_row <- nrow(M)
  prob_row <- rowSums(M)/num_col # calculate intrarow probabilities 
  prob_column <- colSums(M)/num_row # calculate intracolumn probabilities 
  P <- matrix(0,num_row,num_col) # matrix of probabilities of interactions
  for (i in 1:num_row){
    for(j in 1:num_col){
      # Possible to select one of two null probabilities:
      P[i,j] <- (prob_row[i]+prob_column[j])/2 # Bascompte et al 2003 (commonly used)
      # P[i,j] <- prob_row[i]*prob_column[j] # Configuration model
    }
  }
  
  # Create an empty matrix to fill
  S <- matrix(0,num_row,num_col)
  # Go row by row to ensure each row has at least one value
  for (ridx in 1:num_row){
    col <- sample(1:num_col, 1, prob=prob_column) # Select a column
    S[ridx, col] <- 1
  }
  if(!all(rowSums(S)==1)){print('Something is wrong. All rows should have one edge at this stage.');return(NULL)}
  # Loop through all the columns that have 0 interactions to ensure each column has at least one interaction
  if (any(colSums(S)==0)){
    empty_cols <- which(colSums(S)==0)
    for (cidx in empty_cols){
      row <- sample(1:num_row, 1, prob=prob_row) # Select a row
      S[row, cidx] <- 1
    }
  }
  if(!all(colSums(S)>=0)){print('Something is wrong. All cols should have one or more edge at this stage.');return(NULL)}
  # Now fill in the rest of the interactions by select the rest of the cells at random according to cell probabilities
  cells_to_fill <- sample(which(S==0), size = sum(M)-sum(S), prob = P[which(S==0)], replace = F) # Select a cell to fill by the probability
  S[cells_to_fill] <- 1
  
  if(sum(S)!=sum(M)){print('Something is wrong. Shuffled matrix fill should be the same as the original at this stage.');return(NULL)}
  
  if (verbose){
    print(paste('Created a shuffled matrix with dimensions: ',nrow(S),'x',ncol(S),' and fill of ',sum(S),sep=''))
  }
  return(S)
}