Uses the simple linear quotient technique as follows:
$$lq_i = \frac{X_i^r / X^r}{X_i^n / X^n}$$
where \(X^n\) is the total production, \(X^r\) is the total production for region r, \(X^r_i\) is the production for region r sector i, and \(X^n_i\) is the total production for the ith sector.
Then lq is converted such that if \(lq_i > 1\), then \(lq_i = 1\). Then lq is converted into a diagonal matrix of values less than or equal to 1, which gives us our final results
$$\hat{A} = A lq$$