dpnp.scipy.sparse.linalg.minres¶

dpnp.scipy.sparse.linalg.minres(A, b, x0: dpnp_array | None = None, *, rtol: float = 1e-05, shift: float = 0.0, maxiter: int | None = None, M=None, callback: Callable | None = None, show: bool = False, check: bool = False) → tuple[dpnp_array, int][source]¶

Use MINimum RESidual iteration to solve Ax = b.

Solves the symmetric (possibly indefinite) system Ax = b or, if shift is nonzero, (A - shift*I)x = b. All computation stays on the SYCL device; only scalar recurrence coefficients and norms are transferred to the host for branching.

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

Parameters:

A{dpnp.ndarray, usm_ndarray, LinearOperator, csr_matrix}: The real symmetric or complex Hermitian operator, shape (N, N).
b{dpnp.ndarray, usm_ndarray}: Right-hand side, shape (N,) or (N, 1).
x0{None, dpnp.ndarray, usm_ndarray}, optional: Starting guess for the solution. Default: None (zeros).
shiftfloat, optional: If nonzero, solve (A - shift*I)x = b. Default: 0.0.
rtolfloat, optional: Relative convergence tolerance. Default: 1e-5.
maxiter{None, int}, optional: Maximum number of iterations. Default: 5 * N.
M{None, dpnp.ndarray, usm_ndarray, LinearOperator}, optional: Preconditioner approximating the inverse of A. Default: None.
callback{None, callable}, optional: Called as callback(xk) after each iteration. Default: None.
showbool, optional: If True, print a convergence summary each iteration. Default: False.
checkbool, optional: If True, verify that A and M are symmetric before iterating (costs extra matvecs). Default: False.

Returns:

xdpnp.ndarray: The converged (or best) solution.
infoint: 0 if converged, maxiter if the iteration limit was reached.