Better error message for when Hilbert space is smaller than requested eigenvalues

[hankarls]

When using eigs_lanczos, if I request more eigenvalues than the Hilbert space allows, the error is a bit difficult to understand. The current error message is "ERROR: LoadError: Mat::submat(): indices out of bounds or incorrectly used", when preferably it should tell that the requested number of eigenvalues is too large, or perhaps even better, default neigvals to the largest value allowed. A minimal example follows below:

  using XDiag

  let

     L=10    # systemsize
     N = 0   # number of particles

     block = Electron(L, N ÷ 2, N ÷ 2)
     ops = OpSum()

     # Hubbard model as example
     for i in 1:L-1
         ops += "t" * Op("Hop",[i,i+1])
     end

     ops += "U" * Op("HubbardU")

     ops["t"] = -1.0
     ops["U"] = -6.0

     res = eigs_lanczos(ops,block,neigvals=2)    # ask for two converged eigenvalues

  end

[awietek]

This issue should be addressed now with commit 48fab79 in the C++ version. Now, if the number of requested eigenvalues is larger then the block dimension, then neigvals is reset to the block dimension. Let me know if this works now.

[physicsmonk]

I encountered the same error for the eigs_lanczos function (version 0.4.1) but for my case neigvals is way smaller than the dimension of the Hilbert space. When neigvals=1 it works but neigvals=2 will throw "libc++abi: terminating due to uncaught exception of type std::out_of_range: Mat::submat(): indices out of bounds or incorrectly used".

[awietek]

Dear @physicsmonk

thank you for reporting this issue. Could you provide me with a minimal example to reproduce the error, such that I can fix this more quickly?

Best,
Alex

[physicsmonk]

I found where this error comes. In function eigs_lanczos when you do

eigenvectors.matrixC(false) += kron(v, revecs.submat(iter - 1, 0, iter - 1, neigvals - 1));

it could cause out-of-bounds because the number of columns of revecs could be smaller than neigvals. This is because of the deflation of the Lanczos iteration, namely, the iteration could be stopped way before the neigvalsth step so that the Krylov space is way smaller than neigvals.

I don't know much about the deflation process, but I searched on the internet and it seems that the Lanczos iteration should be continued after the deflation. Can you elaborate on this?

Also it seems function eigs_lanczos does not do re-orthogonalization after each Lanczos iteration. I don't know but I am wondering if this is a common practice in many-body computations?