I reduced the problem to a difference of results with eigsh when
working in shift-invert mode and when not. Notice that the following
works with sigma=None but not with sigma=0. , thus seems to me that we
should fall back to non invert-mode for singular matrices (see
asociated pull request).
```
In [8]: M = sparse.csr_matrix([[1, 1, 1], [1, 1, 1], [1, 1, 1.]])
In [9]: linalg.eigsh(M, 1)
Out[9]:
(array([ 3.]),
array([[-0.57735027],
[-0.57735027],
[-0.57735027]]))
In [10]: linalg.eigsh(M, 1, sigma=0.)
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call last)
/home/fabian/dev/sandbox/<ipython-input-10-f646f5be93ec> in <module>()
----> 1 linalg.eigsh(M, 1, sigma=0.)
/home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
in eigsh(A, k, M, sigma, which, v0, ncv, maxiter, tol,
return_eigenvectors, Minv, OPinv, mode)
1484 if OPinv is None:
1485 Minv_matvec = get_OPinv_matvec(A, M, sigma,
-> 1486 symmetric=True, tol=tol)
1487 else:
1488 OPinv = _aslinearoperator_with_dtype(OPinv)
/home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
in get_OPinv_matvec(A, M, sigma, symmetric, tol)
1004 def get_OPinv_matvec(A, M, sigma, symmetric=False, tol=0):
1005 if sigma == 0:
-> 1006 return get_inv_matvec(A, symmetric=symmetric, tol=tol)
1007
1008 if M is None:
/home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
in get_inv_matvec(M, symmetric, tol)
997 if isspmatrix_csr(M) and symmetric:
998 M = M.T
--> 999 return SpLuInv(M).matvec
1000 else:
1001 return IterInv(M, tol=tol).matvec
/home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
in __init__(self, M)
890 """
891 def __init__(self, M):
--> 892 self.M_lu = splu(M)
893 LinearOperator.__init__(self, M.shape, self._matvec,
dtype=M.dtype)
894 self.isreal = not np.issubdtype(self.dtype, np.complexfloating)
/home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/dsolve/linsolve.pyc
in splu(A, permc_spec, diag_pivot_thresh, drop_tol, relax, panel_size,
options)
171 _options.update(options)
172 return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
--> 173 ilu=False, options=_options)
174
175 def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None,
permc_spec=None,
RuntimeError: Factor is exactly singular
In [11]:
```
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