Weighted Average and its Uncertainty

// after e.g. J.R. Taylor 1997, Introduction to error analysis, 2nd Ed., University Science Books, p175
// input waves MUST NOT contain NaNs or INFs
function/WAVE WeightedAvg(data, error)
    wave data, error    
    
    // define weight
    MatrixOP/O/FREE w = rec(magSqr(error))
    
    // weighted average
    MatrixOP/O/FREE avg = sum(w * data) * rec(sum(w))
    
    // uncertainty
    MatrixOP/O/FREE sigma = rec(sqrt(sum(w)))
    
    // Combine results into 2D wave, 1st col = wAvg, 2nd col = error
    Concatenate/O {avg,sigma}, W_wAvg
    
    return W_wAvg
end