################################################################################
#
#   Program: Indices.txt
#   Author:  John Fieberg
#
#   Description:    Indices for calculating overlap
#
#
#######################################################################################

#  All of these functions assume that two vectors will be passed (x and y)
#    => x and y represent estimates of the UD at a set of grid points (assumed to be the same 
#       for UD1 and UD2)
#    => dxdy = the area of each grid cell
#    => tol = tolerance level (sets any values of the UD < this level to 0).  This is only
#             needed for those indices that use areas (i.e., HR, PHR, and UDOI).

vi.index<-function(x,y,dxdy){
  z<-sum(pmin(x,y))*dxdy
  z
}

# Note, for HR, dxdy will cancel from numerator and denominator and therefore, we do not need to
#   consider it.  

HR<-function(x,y,dxdy, tol=1*10^(-15)){
  x[x<tol]<-0
  y[y<tol]<-0
  a12<-sum((x>0)*(y>0)>0) # Area of overlap
  a1<-sum((x>0)>0)        # HR area for UD1
  a2<-sum((y>0)>0)        # HR area for UD2
cbind(a12/a1, a12/a2)
}

  
PHR<-function(x,y,dxdy,tol=1*10^(-15)){
  x[x<tol]<-0
  y[y<tol]<-0
  phr12<-sum(y[x>0])*dxdy   # prob. animal 2 is in animal 1's HR
  phr21<-sum(x[y>0])*dxdy   # prob. animal 1 is in animal 2's HR
  cbind(phr12, phr21)
}


BA<-function(x,y,dxdy){
  z<-sum(sqrt(x)*sqrt(y))*dxdy
  z
}


UDOI<-function(x,y,dxdy, tol=1*10^(-15)){
# sum(((x>tol)*(y>tol)>0)*dxdy) = A12
   z<-sum(x*y)*sum(((x>tol)*(y>tol)>0)*dxdy)*dxdy
   z
}
  
 
# Claculate all indices 
allcalc<-function(x,y,dxdy){
  inds<-c(vi.index(x,y,dxdy), HR(x,y,dxdy), PHR(x,y,dxdy), BA(x,y,dxdy), 
         UDOI(x,y,dxdy))
  names(inds)<-c("VI", "HR1,2", "HR2,1", "PHR1,2", "PHR2,1", "BA", "UDOI")
  inds
}