Forcing positive values when solving system of linear equations

For finding the least squared error solution for X for the equation:

Ax = B

I am currently doing:

x = pinv(A) * B

However, in my case, there are negative values for X in the results, which is non desireable.

Is there a way to force X to be all non-negative values when solving the equation Ax = B using preferably SVD?

Answer 1

[John D'Errico]

Sorry. PINV does not allow you to constrain the sign of your estimates.

You can use LSQNONNEG, which does allow you to do that, or you can use a tool like LSQLIN (from the optimization toolbox.)

For eample here, A is a 100x7 matri, with rank 5 by design.

A = randn(100,5)*randn(5,7);
rank(A)

ans = 5

b = randn(100,1);

As you can see, A\b gets upset at you, because A is singular.

A\b

Warning: Rank deficient, rank = 5, tol = 5.624565e-13.

ans = 7×1

-0.2175 0.0546 0 0 0.0494 0.0315 0.1426

However lsqnonneg does not yell at you about a singular matrix A, so you may prefer that. But does it explicitly use the SVD? No. It uses an active set strategy, choosing a subset of the unknowns to be non-negative.

lsqnonneg(A,b)

ans = 7×1

0 0 0.0487 0 0.0086 0.0056 0.0697