User ManualSEE WHAT THE WEB GUI LOOKS LIKEWHAT I NEED TO KNOW ABOUT EDIDREMOTE CONTROL HEX CODESQ: I see the the HDMI extenders come with 2-remote IR cables, will the remote IR work with this matrix? A: The IR repeater works well with 26 KHz single band remotes but may not work with multi-band remotes used on a few satellite boxes. Stack Overflow is a community of 4.7 million programmers, just like you, helping each other.

For a given integer n I will seek to reduce the size of the matrix by kicking people out, such that I am left with a n-by-n correlation matrix that minimises the total sum of the elements. As a starting point I take A = tril(A), which will remove redundant off-diagonal elements from the correlation matrix. So, if n = 4 and we have the hypothetical 5-by-5 matrix above, it's very clear that person 5 should be kicked out of the matrix, since that person is contributing a lot of very high correlations. It's also clear that person 1 should not be kicked out, since that person contributes a lot of negative correlations, and thus brings down the sum of the matrix elements. I noticed a similar question Finding sub-matrix with minimum elementwise sum, which has a brute force solution as the accepted answer.

EDIT: I had thought of iterating, but I don't think that truly minimizes the sum of elements in the reduced matrix.

I vaguely recalled that sometimes these n choose k problems can be resolved with dynamic programming approaches that avoid recomputing things, but I can't work out how to solve this, and nor did googling enlighten me. I'm willing to sacrifice precision for speed if there's no other option, or the best program will take more than a week to generate a precise solution.

If it's not possible for a program to optimise the matrix within an reasonable timeframe, then I would accept an answer that explains why n choose k tasks of this particular sort can't be resolved within reasonable timeframes. Are you able to expand on how that code can help find the n-by-n abbreviated version of the matrix that minimises the sum of the matrix elements? The gatool enables you to change hundreds of parameters, so you can trade speed for precision in the selected output. If I have understood you problem statement, you have a N x N matrix M (which happens to be a correlation matrix), and you wish to find for integer n where 2 <= n < N, a n x n matrix m which minimises the sum over all elements of m which I denote f(m)?

In Matlab it is fairly easy and fast to obtain a sub-matrix of a matrix (see for example Removing rows and columns from matrix in Matlab), and the function f is relatively inexpensive to evaluate for n = 151. Appreciate your comment by the complexity you see comes from your chosen approach to the solution by seeing it as a combinatorial problem.

Disclaimer: I'm not an expert on binary quadratic programming, and you may want to consult the academic literature for more sophisticated algorithms. This is a quadratic programming problem where the vector x is restricted to taking only binary values.

If you don't need a precise solution, something to play around with might be a relaxed version of the problem: drop the binary constraint.

Note also that the relaxed problem gives you a lower bound on the optimal value of the original problem. You should check out this link and go down to the section on Mixed Integer Quadratic Programming (MIQP). It's true that the problem is equivalent to what you just stated, aside from one thing.

Working on a suggestion from Matthew Gunn and also some advice at the Gurobi forums, I came up with the following function.

I will award it the answer, but if someone can come up with code that works better I'll remove the tick from this answer and place it on their answer instead.

Not the answer you're looking for?Browse other questions tagged matlab optimization quadratic-programming or ask your own question. Is it possible to have a research career while checking the proof of every theorem that you cite? Each source can be routed to any display using the front-panel push buttons, IR remote control, web GUI interface and RS-232 interface.

You may be tired of losing your television signal and thus losing a certain amount of sound quality once that signal returns.

They can't be used with this matrix and need to be set aside and not used.Q: Will the Remote IR work with all remote controls? It's a correlation matrix, so there are 1s on the main diagonal and repeated values above and below the main diagonal. In addition to obtaining the abbreviated matrix, I also need to know the row number of the people who should be booted out of the original matrix (or their column number - they'll be the same number). Below I have a 4-by-4 correlation matrix in bold, with sums of rows and columns on the edges.

However, I'm happy to let a program run for up to a week if it will generate a precise solution.

The problem is to choose a vector x to minimize x'*S*x where S is a given symmetric, positive definite matrix and x is subject to the constraints that the entries of x are either 1 or 0 and the elements of x sum to n.

Your understanding of the question is correct, except that S is a correlation matrix, and thus is necessarily positive semidefinite and not necessarily positive definite. Given a matrix of size M, we can easily find the solution to the problem if we simply wish to reduce the dimension by 1, i.e.

Quadratic programming where the domain is restricted to a set of discrete values is called mixed integer quadratic programming (MIQP).

If you drop the constraint that x(i) is either 1 or 0 for all i, then the problem becomes a trivial convex optimization problem and can be solved nearly instantaneously (eg.

If your discretized version of the solution to the relaxed problem leads to a value for the objective function close to the lower bound, there may be a sense in which this ad-hoc solution can't be that far off from the true solution. You can get a zero eigenvalue (hence semi-definite rather than definite) if some linear combination of random variables is perfectly correlated with another. It's the elements in S that have to be between 0 and 1, whereas the elements in x have to be either 0 or 1. I just put it in there so I could CLEANLY argue the latter problem is simply a less constrained version of the former.

If you are pre-wiring make sure to run a 3rd cat5 cable so you can add an IR system that can handle multi-band remotes.

It's apparent that with n = 2 the optimal matrix is the 2-by-2 identity matrix involving Persons 1 and 4, but according to the iterative scheme I would have kicked out Person 1 in the first phase of iteration, and so the algorithm makes a solution that is not optimal. You want to make sure that you have the technology that amplifies the sound from a show in a correct fashion.

If you have multi-band remotes you might want to upgrade your remotes to UHF, which goes through walls. I wrote a program that always generated optimal solutions, and it works well when n or k are small, but when trying to make an optimal 75-by-75 matrix from a 151-by-151 matrix I realised my program would take billions of years to terminate.

The last restriction, that x is binary, makes the problem substantially more difficult; it destroys the problem's convexity! You could try removing entries that, on the relaxed problem, quadprog assigns the lowest values in the x vector, but this does not truly solve the original problem! People are worried about sound and visual quality when it comes to OTT content and making sure that content streams correctly. It allows any source (Blue-Ray player, HD DVD player, satellite receiver, game system, etc.) to be shown on the any of the displays simultaneously, no matter the source is HDCP or not.

The information is stored in the display and is used to communicate with the system through a Display Data Channel (DDC ), which sites between the monitor and the source device.

The system uses this information for configuration purposes, so the HDTV and system can work together.

For a given integer n I will seek to reduce the size of the matrix by kicking people out, such that I am left with a n-by-n correlation matrix that minimises the total sum of the elements. As a starting point I take A = tril(A), which will remove redundant off-diagonal elements from the correlation matrix. So, if n = 4 and we have the hypothetical 5-by-5 matrix above, it's very clear that person 5 should be kicked out of the matrix, since that person is contributing a lot of very high correlations. It's also clear that person 1 should not be kicked out, since that person contributes a lot of negative correlations, and thus brings down the sum of the matrix elements. I noticed a similar question Finding sub-matrix with minimum elementwise sum, which has a brute force solution as the accepted answer.

EDIT: I had thought of iterating, but I don't think that truly minimizes the sum of elements in the reduced matrix.

I vaguely recalled that sometimes these n choose k problems can be resolved with dynamic programming approaches that avoid recomputing things, but I can't work out how to solve this, and nor did googling enlighten me. I'm willing to sacrifice precision for speed if there's no other option, or the best program will take more than a week to generate a precise solution.

If it's not possible for a program to optimise the matrix within an reasonable timeframe, then I would accept an answer that explains why n choose k tasks of this particular sort can't be resolved within reasonable timeframes. Are you able to expand on how that code can help find the n-by-n abbreviated version of the matrix that minimises the sum of the matrix elements? The gatool enables you to change hundreds of parameters, so you can trade speed for precision in the selected output. If I have understood you problem statement, you have a N x N matrix M (which happens to be a correlation matrix), and you wish to find for integer n where 2 <= n < N, a n x n matrix m which minimises the sum over all elements of m which I denote f(m)?

In Matlab it is fairly easy and fast to obtain a sub-matrix of a matrix (see for example Removing rows and columns from matrix in Matlab), and the function f is relatively inexpensive to evaluate for n = 151. Appreciate your comment by the complexity you see comes from your chosen approach to the solution by seeing it as a combinatorial problem.

Disclaimer: I'm not an expert on binary quadratic programming, and you may want to consult the academic literature for more sophisticated algorithms. This is a quadratic programming problem where the vector x is restricted to taking only binary values.

If you don't need a precise solution, something to play around with might be a relaxed version of the problem: drop the binary constraint.

Note also that the relaxed problem gives you a lower bound on the optimal value of the original problem. You should check out this link and go down to the section on Mixed Integer Quadratic Programming (MIQP). It's true that the problem is equivalent to what you just stated, aside from one thing.

Working on a suggestion from Matthew Gunn and also some advice at the Gurobi forums, I came up with the following function.

I will award it the answer, but if someone can come up with code that works better I'll remove the tick from this answer and place it on their answer instead.

Not the answer you're looking for?Browse other questions tagged matlab optimization quadratic-programming or ask your own question. Is it possible to have a research career while checking the proof of every theorem that you cite? Each source can be routed to any display using the front-panel push buttons, IR remote control, web GUI interface and RS-232 interface.

You may be tired of losing your television signal and thus losing a certain amount of sound quality once that signal returns.

They can't be used with this matrix and need to be set aside and not used.Q: Will the Remote IR work with all remote controls? It's a correlation matrix, so there are 1s on the main diagonal and repeated values above and below the main diagonal. In addition to obtaining the abbreviated matrix, I also need to know the row number of the people who should be booted out of the original matrix (or their column number - they'll be the same number). Below I have a 4-by-4 correlation matrix in bold, with sums of rows and columns on the edges.

However, I'm happy to let a program run for up to a week if it will generate a precise solution.

The problem is to choose a vector x to minimize x'*S*x where S is a given symmetric, positive definite matrix and x is subject to the constraints that the entries of x are either 1 or 0 and the elements of x sum to n.

Your understanding of the question is correct, except that S is a correlation matrix, and thus is necessarily positive semidefinite and not necessarily positive definite. Given a matrix of size M, we can easily find the solution to the problem if we simply wish to reduce the dimension by 1, i.e.

Quadratic programming where the domain is restricted to a set of discrete values is called mixed integer quadratic programming (MIQP).

If you drop the constraint that x(i) is either 1 or 0 for all i, then the problem becomes a trivial convex optimization problem and can be solved nearly instantaneously (eg.

If your discretized version of the solution to the relaxed problem leads to a value for the objective function close to the lower bound, there may be a sense in which this ad-hoc solution can't be that far off from the true solution. You can get a zero eigenvalue (hence semi-definite rather than definite) if some linear combination of random variables is perfectly correlated with another. It's the elements in S that have to be between 0 and 1, whereas the elements in x have to be either 0 or 1. I just put it in there so I could CLEANLY argue the latter problem is simply a less constrained version of the former.

If you are pre-wiring make sure to run a 3rd cat5 cable so you can add an IR system that can handle multi-band remotes.

It's apparent that with n = 2 the optimal matrix is the 2-by-2 identity matrix involving Persons 1 and 4, but according to the iterative scheme I would have kicked out Person 1 in the first phase of iteration, and so the algorithm makes a solution that is not optimal. You want to make sure that you have the technology that amplifies the sound from a show in a correct fashion.

If you have multi-band remotes you might want to upgrade your remotes to UHF, which goes through walls. I wrote a program that always generated optimal solutions, and it works well when n or k are small, but when trying to make an optimal 75-by-75 matrix from a 151-by-151 matrix I realised my program would take billions of years to terminate.

The last restriction, that x is binary, makes the problem substantially more difficult; it destroys the problem's convexity! You could try removing entries that, on the relaxed problem, quadprog assigns the lowest values in the x vector, but this does not truly solve the original problem! People are worried about sound and visual quality when it comes to OTT content and making sure that content streams correctly. It allows any source (Blue-Ray player, HD DVD player, satellite receiver, game system, etc.) to be shown on the any of the displays simultaneously, no matter the source is HDCP or not.

The information is stored in the display and is used to communicate with the system through a Display Data Channel (DDC ), which sites between the monitor and the source device.

The system uses this information for configuration purposes, so the HDTV and system can work together.

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