dpnp.scipy.sparse.linalg.gmres¶

dpnp.scipy.sparse.linalg.gmres(A, b, x0: dpnp_array | None = None, *, rtol: float = 1e-05, atol: float = 0.0, restart: int | None = None, maxiter: int | None = None, M=None, callback: Callable | None = None, callback_type: str | None = None) → tuple[dpnp_array, int][source]¶

Use Generalized Minimal RESidual iteration to solve Ax = b.

For full documentation refer to scipy.sparse.linalg.gmres.

Parameters:

A{dpnp.ndarray, usm_ndarray, LinearOperator, csr_matrix}: The real or complex operator of the linear system, shape (N, N).
b{dpnp.ndarray, usm_ndarray}: Right-hand side of the linear system, shape (N,) or (N, 1).
x0{None, dpnp.ndarray, usm_ndarray}, optional: Starting guess for the solution. Default: None (zeros).
rtol, atolfloat, optional: Convergence tolerance: ||r|| <= max(atol, rtol*||b||). Defaults: rtol=1e-5, atol=0.0.
restart{None, int}, optional: Number of iterations between restarts. Larger values increase the per-iteration cost but may aid convergence. Default: 20.
maxiter{None, int}, optional: Maximum number of iterations. Default: 10 * N.
M{None, dpnp.ndarray, usm_ndarray, LinearOperator}, optional: Preconditioner approximating the inverse of A. Default: None.
callback{None, callable}, optional: Called on every restart as callback(arg), where arg is selected by callback_type. Default: None.
callback_type{None, 'x', 'pr_norm'}, optional: 'x' passes the current solution vector; 'pr_norm' passes the relative (preconditioned) residual norm. Default: 'pr_norm' when a callback is supplied.

Returns:

xdpnp.ndarray: The approximate solution (M @ x in the right-preconditioned formulation, matching CuPy's return value).
infoint: 0 if converged; the iteration count if maxiter was reached.