Hfunctions <- function(times1,d1,R1,n,times2,d2,R2,m,points,eta=1,lam){
#### This function computes the check-functions for 2 samples EL
#### under several equality constraints. 
#### times12, d12, R12 --- the 2 sample observations, required inputs.
#### The times12 should be ordered. d/R must be < 1, if the last value 
#### of (d/R) is 1, then delete it!!!
#### points, --- a set of given t's used to get constraints. The
#### constraints are: 1-F(t's) = [1-G(t's)]^eta .
#### We assume  min(times12) < points < max(times12).Last changed 6/25/2001
    d12 <- c(d1, d2)
    R12 <- c(R1, R2)
    w012 <- d12/R12       # the Nelson-Aalen, unconstrained max location
    u012 <- log(1-w012)

    N<-n+m

    A21 <- outer(times1, points, FUN="<=")
    A22 <- outer(times2, points, FUN="<=")
    A2 <- rbind(A21, - eta*A22)  # the constrain matrix

 if(length(lam)!=length(points)) stop("the length of lam not compatible")

    v <- d1/(R1+N*crossprod(lam, t(A21)) ) 

    u <- d2/(R2-eta*N*crossprod(lam, t(A22)) ) 

    u12 <- c(log(1-v), log(1-u))
    return(u12 %*% A2)
}