Solve a system of linear equations

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=Y⋅A, 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,

Answer 1

[John D'Errico]

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