I am porting an application to eigen that requires solving Ax=b where A is numerically singular, i.e. it has vanishing singular values less than a specified threshold. I was able to get the application to work with eigen by making a few small modifications to the solve functions in the ColPivHouseholderQR, JacobiSVD and FullPivLU classes. These amount to replacing the nonzero_pivots or nonzeroSingVals variable by the numerical rank, e.g. ColPivHouseholderQR.h line 462, JacobiSVD.h line 841 and FullPivLU.h line 676. I wonder if this should be the default behaviour, or at least a supported option.
It would also be nice if the JacobiSVD class had functions to set the threshold and return the rank and kernel.