How to tune matrices to specific output?

Hey guys. So I have four matrices that are each 8 by 8: matrix P, matrix Q, matrix R, and matrix G. I have a certain algorithm (I wont go in to too much details about it because its too complicated with multiple files) that depends on those four matrices and uses them to output a single column of values for me. I also have what I call the perfect output, which is what I desire the output single column to look like. Now my question is: How can I use MATLAB to tune those 4 matrices in order for the output column to match the perfect output column?

[Dyuman Joshi]

It is difficult to comment without any specific information.

"I also have what I call the perfect output, which is what I desire the output single column to look like."

What exactly is your "perfect output"? or what are its characteristics?

Maybe try reshape

[Ali Almakhmari]

The perfect output has the exact same format as (single column of values) the estimated output. It just has the desired values of the column output that I would like to estimation to be as close to as possible.

[Torsten]

How can I use MATLAB to tune those 4 matrices in order for the output column to match the perfect output column?

And what are the "free tuning parameters" ? All 4*8*8 matrix entries of the 4 matrices ? Or only some of them and the others are derived from these "free" parameters ?

[Ali Almakhmari]

pretty much all of them yes

[Sam Chak]

Hi @Ali Almakhmari

What is the length of the so-called "Perfect Output" column vector?

numParams = 4*8^2

numParams = 256

If you can mathematically map the 256 free parameters to each element in the Output column vector without any constraint, then solving the problem should be relatively straightforward, isn't it?

[Bruno Luong]

As I said use lsqnonlin

% Initialize P, Q, R, G
x0 = cat(3, P, Q, R, G);
lsqnonlin(@(x) computeOutput(x(:,:,1), x(:,:,2), x(:,:,3), x(:,:,4))-perfectoutput, x0);

function output = computeOutput(P, Q, R, G)
% Out your complicated here.
end

[Ali Almakhmari]

The length of the output is 314.

[Sam Chak]

The code is looking good. 👍

% Initialize P, Q, R, G

P = [0.5 2.5; 3.5 1.5];
Q = P;
R = Q;
G = R;
perfectoutput = [1; 81; 256; 16];

x0 = cat(3, P, Q, R, G);
lsqnonlin(@(x) computeOutput(x(:,:,1), x(:,:,2), x(:,:,3), x(:,:,4)) - perfectoutput, x0)

Warning: Trust-region-reflective algorithm requires at least as many equations as variables; using Levenberg-Marquardt algorithm instead.

Local minimum found.

Optimization completed because the size of the gradient is less than
1e-4 times the value of the function tolerance.

ans = 
ans(:,:,1) =

    1.0000    4.0000
    3.0000    2.0000


ans(:,:,2) =

    1.0000    4.0000
    3.0000    2.0000


ans(:,:,3) =

    1.0000    4.0000
    3.0000    2.0000


ans(:,:,4) =

    1.0000    4.0000
    3.0000    2.0000

function output = computeOutput(P, Q, R, G)
    M      = P.*Q.*R.*G;
    output = [M(1); M(2); M(3); M(4)];
end

Answer 1

[Bruno Luong]

Use lsqnonlin (or such) if you have optimization toolbox.