qmr(A, b, x0=None, tol=1e-05, maxiter=None, M1=None, M2=None, callback=None, atol=None)
Starting guess for the solution.
Tolerances for convergence, norm(residual) <= max(tol*norm(b), atol)
. The default for atol
is 'legacy'
, which emulates a different legacy behavior.
The default value for :None:None:`atol` will be changed in a future release. For future compatibility, specify :None:None:`atol` explicitly.
Maximum number of iterations. Iteration will stop after maxiter steps even if the specified tolerance has not been achieved.
Left preconditioner for A.
Right preconditioner for A. Used together with the left preconditioner M1. The matrix M1@A@M2 should have better conditioned than A alone.
User-supplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector.
The real-valued N-by-N matrix of the linear system. Alternatively, A
can be a linear operator which can produce Ax
and A^T x
using, e.g., scipy.sparse.linalg.LinearOperator
.
Right hand side of the linear system. Has shape (N,) or (N,1).
Use Quasi-Minimal Residual iteration to solve Ax = b
.
>>> from scipy.sparse import csc_matrix
... from scipy.sparse.linalg import qmr
... A = csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
... b = np.array([2, 4, -1], dtype=float)
... x, exitCode = qmr(A, b)
... print(exitCode) # 0 indicates successful convergence 0
>>> np.allclose(A.dot(x), b) TrueSee :
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