Min-2-norm solution via factorize-and-solve (separating SPQR factorization and solve)

[samiran-kawtikwar]

I'm trying to compute the minimum $\ell_2$-norm solution to an OLS problem min ||Ax - b|| using SuiteSparseQR.

When the system is underdetermined (i.e., fewer rows than columns), the direct solve interface:

cholmod_dense* x_direct = SuiteSparseQR<double>(
    SPQR_ORDERING_DEFAULT,
    SPQR_DEFAULT_TOL,
    A, B, &cc);

does return the minimum 2-norm solution, as expected.

However, I'm looking for a way to reuse the factorization of A across multiple right-hand sides b. So I tried the SuiteSparseQR_factorize + SuiteSparseQR_solve route:

SuiteSparseQR_factorization<double>* QRhandle =
    SuiteSparseQR_factorize<double>(
        SPQR_ORDERING_DEFAULT,
        SPQR_DEFAULT_TOL,
        A, &cc);

cholmod_dense* x_factored =
    SuiteSparseQR_solve<double>(
        SPQR_RETX_EQUALS_B,
        QRhandle,
        B, &cc);

But this does not return the minimum-norm solution—it seems to return a basic solution instead.

I also saw the function SuiteSparseQR_min2norm, but it appears to be a one-shot solve that doesn't let me reuse the factorization when A is fixed.

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❓ My question:

Is there a way to compute the minimum 2-norm solution using SPQR by first factorizing A and then solving multiple times with different b?

See more discussion with a MWE in issue #982