mat: calling qr.Factorize leads to OOM for matrixes with many rows about gonum

[ericwenn]

Minimal reproduction test:

func TestReproduction(t *testing.T) {
	const (
		M = 100_000
		N = 3
	)
	systemMat := mat.NewDense(M, N, make([]float64, M*N))
	measurementsVec := mat.NewVecDense(M, make([]float64, M))

	var results mat.VecDense
	err := results.SolveVec(systemMat, measurementsVec)

	fmt.Println(err)
}

On version 0.14.0 and below this correctly returns error matrix singular or near-singular with condition number +Inf, on version 0.15.0 it crashes due to OOM.

PS I've updated the link in original issue, thanks for pointing that out.

[kortschak]

Can you provide a minimal reproducer for testing and fix the link in the report please?

Note also from the documentation that Q is m×m.

[tvkn]

I believe the issue arises when one tries to solve very large systems.

The issue is introduced by this commit which explicitly computes and stores the Q matrix (instead of just the reflectors tau).

The Q matrix doesn't seem to be explicitly needed in the QR SolveVec, but the new update forces its computation, which in practice can limit the size of the linear systems the function can solve.

[kortschak]

Thanks. Yeah, for situations where the Q is not needed, this is a problem. I think we can get the performance benefit of the single pre-calculation by lazily calculating, but storing the value so the work is only done once. I'll take a look in the weekend.

[ericwenn]

Thanks. Yeah, for situations where the Q is not needed, this is a problem. I think we can get the performance benefit of the single pre-calculation by lazily calculating, but storing the value so the work is only done once. I'll take a look in the weekend.

That would be great, thanks for the quick response!