This submission was written by request - as a tool to handle linear least squares problems, subject to linear equality constraints that may potentially be rank deficient. (It handles problems with full rank constraints of course too.) In the event of a rank deficient constraint system, it tests for consistency of the constraints.
I added a few other features to LSE:
- It allows multiple right hand sides to the least squares problem, fully vectorized of course.
- Weights may be supplied.
- You are offered a choice of least squares solvers, either backslash or pinv.
LSE solves the problem (for an unknown vector x)
argmin norm(A*x - b)
subject to the constraints
C*x = d
As an example, consider the random system
A = rand(10,3);
b = rand(10,1);
With a rank deficient constraint set
C = [1 1 1;1 1 1];
d = [1;1];
X = lse(A,b,C,d)
Verify that the constraints are satisfied
Column pivoting is used to eliminate variables from the constraint system when \ is specified, and when pinv is specified, an svd is used for the final solution.
John D'Errico (2023). LSE (https://www.mathworks.com/matlabcentral/fileexchange/13835-lse), MATLAB Central File Exchange. Retrieved .
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Bug fix - Single constraint problems on R2009 releases failed due to a qr issue - this fix repairs that bug.