hifir4py.ksp.pipit_hifir

pipit_hifir(A, b: numpy.ndarray, n_null: int, M=None, **kw) → Tuple[numpy.ndarray, Dict[str, numpy.ndarray], int, dict]

PIPIT solver for solving the pseudoinverse solution

PIPIT implements a pseudoinverse solution solver with small dimension of nullspace. The system can be potentially inconsistent in that the RHS vector may not fully in the range of A.

Parameters:

• A (csr_matrix) – User input matrix
• b (ndarray) – User input RHS
• n_null (int) – Nullspace dimension (>0)
• M (HIF, optional) – HIF preconditioner
• x0 (ndarray, optional) – Initial guess, default is zeros; if passed in, this will be overwritten by the solution.
• verbose ({0,1,2}, optional) – Verbose level, 0 disables the verbose printing, while 1 enables HIF verbose logging; default is 1.
• restart (int, optional) – Restart dimension, default is 30
• rtols (list, optional) – Legnth-two list storing the relative tolerance thresholds, default is [1e-6, 1e-12], where the former is for solving least-squares solution using HIF-GMRES, and the latter is for solving nullspaces.
• work (FGMRES_WorkSpace, optional) – Workspace buffer, by default, the solver creates all buffer space.
• vs (ndarray, optional) – User-provided right nullspace; if not given, then vs will be computed on-the-fly.

Returns:

• x (ndarray) – The computed pseudoinverse solution, which overwrites x0 if provided
• ns (dict) – A dictionary of {"us": lns, "vs": rns} where lns and rns are left and right null-space components, respectively.
• flag (int) – Termination flag for LS solver.
• info (dict) – Statistics for LS solver plus runtimes for factorization, left nullspace computation, LS computation, and right nullspace computation stages, i.e., info["times"]=[t_fac,t_lns,t_ls,t_rns].

See also

gmres_hif