Least squares on a sparse matrix - excluding terms from RSS?

[Kadence]

Is is possible in LAPACK to perform least squares on a sparse matrix - a matrix with missing elements? In other words, if in AX=B, a certain B.ij=0, then the residual given by row A.i times column X.j is not counted in the residual sum of squares.

[Kadence]

I'm looking into that, thanks.

Does anyone know of an open-source least squares solver (usuable in C++) where one can directly modify the residual sum of squares? For instance to ignore certain elements, or for regularization purposes. Preferably one that's really really fast :)