Should LowRankOperator have a rank-truncation method? #2285

The operator is constructed from the left and right VectorArrays L, R and a core NumPy array C. Consider that L, R have themselves been created as concatenations of VectorArrays and C is the block diagonal NumPy array. The result may very well have (numerical) rank-deficiency, even if the originals were fine. This situation could, e.g., happen for a linear combination of two LowRankOperators. In many situations, it would then be desirable to have a more compact representation of the LowRankOperator, that matches the (numerical) rank.

The easiest truncation procedure would

• compute QR decompositions of L and R,
• form the product of their R factors with C,
• decide the rank by a truncated SVD of that product,
• update the Q factors of L and R with the unitary factors from the SVD.

Obviously, a truncation tolerance on the SVD would then be required.