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I have a feeling this should be very simple, but I somehow got stuck thinking about it.

I have $\it X$, which is a 15 x 18 matrix containing non-negative real values. I smoothed this matrix using a moving window smoother, which resulted in a matrix $\it Y$ of the same dimensions, but unfortunately the total sum for this new matrix changed.

My question is, how do I create a 15 x 18 matrix $\it W$ containing adjustment weights, such that the marginals sums of $\mathit{Y \cdot W}$ after smoothing agree with the corresponding row and column sums of $\it X$ prior to smoothing?

Thanks very much for your help!

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Could it be quadratic programming problem of sort?

min z(t)Iz

subject to

Ay*=c

where y* is adjusted vector, c is an vector for marginal values and z = y - y*, meaning discrepancy vector. A would be restriction matrix with 1, 0 and 1/n elements depending on your problem.

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  • $\begingroup$ Thank you for your reply! Yes, it certainly looks like an optimization problem. I am, however, still unsure how to implement it. What is it exactly that I am minimizing here? I need the row and column marginal sums in my smoothed matrix to be the same as in the original matrix, while the values in each cell can differ. I think this is what you meant by z = y - y*, if I consider one vector (row or column from my matrix) at a time. So, is it possible to optimize cell values in rows while keeping in the respective column sums in check? $\endgroup$
    – Denys D.
    Jun 15, 2018 at 23:49

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