`scipy.sparse.linalg._isolve._gcrotmk:_fgmres`

source: /scipy/sparse/linalg/_isolve/_gcrotmk.py :14

Signature

   def     _fgmres (    matvec    ,    v0    ,    m    ,    atol    ,    lpsolve    =  None   ,    rpsolve    =  None   ,    cs    =  ()   ,    outer_v    =  ()   ,    prepend_outer_v    =  False     )

Summary

FGMRES Arnoldi process, with optional projection or augmentation

Parameters

matvec : callable: Operation A*x
v0 : ndarray: Initial vector, normalized to nrm2(v0) == 1
m : int: Number of GMRES rounds
atol : float: Absolute tolerance for early exit
lpsolve : callable: Left preconditioner L
rpsolve : callable: Right preconditioner R
cs : list of (ndarray, ndarray): Columns of matrices C and U in GCROT
outer_v : list of ndarrays: Augmentation vectors in LGMRES
prepend_outer_v : bool, optional: Whether augmentation vectors come before or after Krylov iterates

Returns

Q, R : ndarray: QR decomposition of the upper Hessenberg H=QR
B : ndarray: Projections corresponding to matrix C
vs : list of ndarray: Columns of matrix V
zs : list of ndarray: Columns of matrix Z
y : ndarray: Solution to ||H y - e_1||_2 = min!
res : float: The final (preconditioned) residual norm

Raises

: LinAlgError: If nans encountered

Aliases

scipy.sparse.linalg._isolve._gcrotmk._fgmres