######   WEIGHTED MEDIANS  ######

###   CONSTRUCTING THE "BIVARIATE SORTING" FUNCTION
###   This function sorts "y" keeping the pairs (x_i,y_i) together

my.sort = function(x,y)
{
mm = sort(y,index.return =  T)$ix
x = x[mm]
y = y[mm]
cbind(x,y)
}

##########################################################################
##########################################################################


###  FUNCTION TO FORM A DISTRIBUTION FUNCTION
###  GIVEN A SET OF WEIGHTS 

F = function(y,x=rep(1,length(y)))
{
##  y: vector of dim "n". It can have repeated values.
##  x: vector of dim "n". The weight of y[i] is  proportional to abs(x_i)
  
	w = abs(x)/sum(abs(x))
	re = my.sort(w,y)
	y = re[,2]
	w = re[,1] 
	l_y = length(y)
	yy = unique(y)
	l_yy = length(yy); 
	ww = rep(0,l_yy)
	i = 1
	for(j in 1:l_yy)
	{
		while(y[i]==yy[j] & i <= l_y)
		{
			ww[j] = ww[j]+w[i]
			i = i+1 
		}
	}
ww = cumsum(ww)
re = cbind(yy,ww)
re
}

#########################################################################
#########################################################################

###  FUNCTION TO COMPUTE  THE "WEIGHTED MEDIAN"
my.median = function(y,x=rep(1,length(y)),full = FALSE)
{
re = F(y,x)

## COMPUTING THE "LOWER" AND "UPPER" MEDIANS, AND THE MEDIAN

test = which(re[,2]==1/2)

if(length(test)==1) {
med_low = re[test,1];
med_up = re[test+1,1]
med = (med_low +med_up)/2
if(full == TRUE){
                res = list("med_low" = med_low,"med_up"=med_up,"med"=med)
               } else
               {
                res = med               
               }
			}

if(length(test)<1)
{
i = 1
while( re[i,2] < 1/2)
	{
	  ss = re[i,2]
	  i = i+1 
	}
med_low = med_up = med =  re[i,1]
if(full == TRUE){
                res = list("med_low" = med_low,"med_up"=med_up,"med"=med)
               } else
               {
                res = med               
               }
			}
res
res
}

my.median(y)

my.median(y,x)


#########################################################################
#############################  TESTING THE FUNCTIONS ####################
#########################################################################

### "BIVARIATE SORTING" FUNCTION

set.seed(123)
y = sample(1:10,replace = T)   
x = 1:length(y)
cbind(x,y)
my.sort(x,y)

###  "CUMMULATIVE DISTRIBUTION" FUNCTION 

set.seed(123)
y = sample(1:10,replace=T)
x = rep(1,length(y))
cbind(x,y) # To see the data
F(y,x)  # To see the cummulative distribution



set.seed(124)
y = sample(1:10,replace=T)
x = rep(1,length(y))
cbind(x,y)
F(y,x)  # To see the cummulative distribution


###  "WEIGHTED MEDIAN"  FUNCTION 
re = my.median(y,x,full = T)
re
median(y)


set.seed(123)
y = sample(1:15,replace=T)
x = rep(1,length(y))
cbind(x,y) # To see the data
F(y,x)  # To see the cummulative distribution
re = my.median(y,x)
re
median(y)


set.seed(123)
x = round(rnorm(length(y)),2)
cbind(x,y)
F(y,x)  # To see the cummulative distribution
re = my.median(y,x)
re

set.seed(123)
y = sample(1:15,replace=T)
x = rep(1,length(y))
cbind(x,y) # To see the data
F(y,x)  # To see the cummulative distribution
re = my.median(y,x)
re
median(y)


set.seed(123)
y = sample(1:100,replace = T)   
x = 1:length(y)
cbind(x,y)
my.median(y,x)