Solve a system of linear equations

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Chubashini
Chubashini el 28 de Feb. de 2024
Editada: John D'Errico el 28 de Feb. de 2024
Hello,
I would like to solve a system of linear equations for the unknowns xj using a least-squared approximation procedure with a non-negative constraint (using the lsqnonneg function in MATLAB). The linear equation system is represented as S=YA, where S is a 30-element vector containing all the si values, Y is a 30×n matrix containing all the yj,i values, and A is an n-element vector containing the unknowns xj. While I can solve each equation for individual sample using the lsnonneg function in MATLAB, I am seeking guidance on how to solve the equations for many samples simultaneously..
Thanks,

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John D'Errico
John D'Errico el 28 de Feb. de 2024
Editada: John D'Errico el 28 de Feb. de 2024
I am confused. You say that you know how to solve the problem using lsqnonneg. So just use it!
n = 30;
Y = rand(30,n);
S = rand(30,1);
See, that if I just use backslash here, it will produce a result that is not bounded to be nonnegative.
xslash = Y\S
xslash = 30×1
0.3452 -0.8259 -2.7427 -0.2307 -2.4206 -0.3200 -1.8315 -1.9436 -1.1118 4.4774
As such, you use lsqnonneg. And you do not use lsqnonneg one equation at a time. It applies to the entire system.
x = lsqnonneg(Y,S)
x = 30×1
0.0204 0.0166 0.4094 0 0 0 0 0.1144 0 0

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