SUBROUTINE postmedcauchy(m,x,weight,maxiter,muhat)
    implicit none
    
    integer :: m,maxiter
    real*8 :: x(m),weight,muhat(m)
    
    real*8 :: magdata(m),magdatatmp(m),weight2(m),hi(m),Tol,conTol,lo(m),midpoint(m),y(m),pi,Xvec(m),normconstants,fx(m),delta(maxiter)
    real*8 :: z(m),y2(m),y3(m),fx2(m),fmidpoint(m),zeromd(m),mu,sigma,yr(m),FUNC_sign
    integer :: i,idx(m),numiter
    
    muhat = 0
    magdata = abs(x)
    magdatatmp = magdata
    idx = 1
    delta = 0
    
    do i=1,m
        if(magdata(i)>=20) then
            idx(i)=0
            magdata(i) = sqrt(-1.0)
        end if
    end do
    
    weight2 = weight
    lo = 0
    hi = maxval(magdata)
    Tol = 1e-9
    numiter = 0
    conTol = 1e30
    mu = 0
    sigma = 1
    pi = 3.1415926
    zeromd = 0
    
    do while(conTol>Tol)
        numiter = numiter +1
        midpoint = (lo+hi)/2.0
        
        y = magdata-midpoint
        Xvec = abs((y-mu)**2)
        normconstants = 1.0/(sqrt(2.0*pi)*sigma)
        fx = normconstants*exp(-Xvec/(2.0*sigma))
        
        z = (y-mu)/sigma
        y2 = 1.0/2.0*erfc(-z/sqrt(2.0))
        
        z = (-midpoint-mu)/sigma
        y3 = 1.0/2.0*erfc(-z/sqrt(2.0))
        
        Xvec = abs((midpoint-mu)**2)
        fx2 = normconstants*exp(-Xvec/(2.0*sigma))
        
        yr = y2 - magdata*fx + ((magdata*midpoint-1)*fx*y3/fx2)
        
        y3 = magdata**2.0*(1.0/weight2-1.0)-1.0
        
        y2 = 1+exp(-magdata**2/2.0)*y3
        
        fmidpoint = y2/2.0-yr
        
        do i=1,m
            if(fmidpoint(i) <= zeromd(i)) then
                lo(i) = midpoint(i)
            else
                hi(i) = midpoint(i)
            end if
        end do
        delta(numiter) = maxval(abs(hi-lo))
        conTol = delta(numiter)
        if(numiter > maxiter) exit
    end do
    
    muhat = (lo+hi)/2.0
    
    do i=1,m
        if(idx(i)==0) then
            muhat(i) = magdatatmp(i)-2.0/magdatatmp(i)
        end if
        if(muhat(i)<1e-7) muhat(i)=0
        muhat(i) = FUNC_sign(x(i))*muhat(i)
        if(abs(muhat(i)) > abs(x(i))) muhat(i) = x(i)
    end do
    
    end subroutine