tol parameter wrong for isolve routines (Trac #939) #1466
Description
Original ticket http://projects.scipy.org/scipy/ticket/939 on 2009-05-03 by @pv, assigned to @wnbell.
The tol parameter in the scipy.sparse.linalg.isolve.* routines is documented wrong. The documentation says:
tol : float
Relative tolerance to achieve before terminating.
However, the algorithms terminate as if tol was absolute tolerance (in addition to being relative tolerance; STOPTEST2 anyway treats tol as relative tolerance only):
>>> import scipy.sparse.linalg as la
>>> import numpy as np
>>> A = np.array([[1,0],[0,-1]])
>>> A = np.array([[1,0],[0,-1.]])
>>> b = np.array([1,-1]) * 1e-9
>>> la.gmres(A, b, tol=1e-8)
(array([ 0., 0.]), 0)
>>> la.gmres(A, b, tol=1e-12)
(array([ 1.00000000e-09, 1.00000000e-09]), 0)
>>> la.bicgstab(A, b, tol=1e-8)
(array([ 0., 0.]), 0)
>>> la.bicgstab(A, b, tol=1e-12)
(array([ NaN, NaN]), 1)
Is this the intended behaviour? Should the documentation or the code be fixed?
Some changes to behavior were apparently made in 9a40153, possibly erroneously.