SUBROUTINE weightfromdata(m,x,maxiter,weight)
    implicit none
    
    integer :: m,maxiter
    real*8 :: x(m),weight
    real*8 :: thr,mu,sigma,Xvec,normconstants,fx,z,bfx,wlo
    real*8 :: pi,phix(m),dnorm0,shi,slo,temp(m),beta(m),initialwlo,tmpweight,temp_deltaweight(100),wmid,smid,whi,conTol,wtol,stol
    integer :: ii,tnum,i
    
    pi = 3.1415926
    thr = sqrt(2.0*log(real(m)))
    mu = 0
    sigma = 1
    Xvec = abs((thr-mu)**2)
    normconstants = 1.0/(sqrt(2.0*pi)*sigma)
    fx = normconstants*exp(-Xvec/(2.0*sigma))
    z = (thr-mu)/sigma
    bfx = 1.0/2.0*erfc(-z/sqrt(2.0))
    
    wlo = 1 + (bfx - thr*fx - 1.0/2)/(sqrt(pi/2.0)*fx*thr**2)
    if(isnan(wlo)) wlo = 1
    wlo = 1.0/wlo
    
    phix = abs((x-mu)**2)
    phix = normconstants*exp(-phix/(2.0*sigma))
    dnorm0 = 0.398942280401433
    
    do i=1,m
        if(abs(phix(i) - dnorm0)>5.55111512312578e-14) then
            beta(i) = (dnorm0/phix(i)-1.0)/x(i)**2-1.0
        else
            beta(i) = -0.5
        end if
    end do
    
    shi = sum(beta/(1.0 + beta))
    if(shi>=0) then
        weight = 1
        goto 10
    end if
    
    temp = wlo*beta
    slo = sum(beta/(1.0+temp))
    if(slo<=0) then
        tmpweight = wlo
        initialwlo = wlo
    end if
    
    conTol = 1.0e30
    wtol = 2.22044604925031e-14
    stol = 1e-7
    ii = 1
    
    temp_deltaweight = 0
    temp_deltaweight(1) = 1.0-wlo
    tnum = 1
    
    whi = 1
    do while(conTol>wtol)
        wmid = sqrt(whi*wlo)
        smid = sum(beta/(1.0+wmid*beta))
        
        if(abs(smid)<stol) then
            tmpweight = wmid
            weight = tmpweight
            goto 10
        end if
        
        if(smid>0) wlo = wmid
        if(smid<0) whi = wmid
        
        tnum = tnum+1
        temp_deltaweight(tnum) = whi-wlo
    
        conTol = abs(temp_deltaweight(ii+1) - temp_deltaweight(ii))
        ii = ii+1
        if(ii>maxiter) exit
    end do
    
    tmpweight = sqrt(wlo*whi)
    if(slo <= 0) tmpweight = initialwlo
    weight = tmpweight
    
10  end subroutine