cupyx.scipy.sparse.linalg.gmres#

cupyx.scipy.sparse.linalg.gmres(A, b, x0=None, *, rtol=1e-05, atol=0.0, restart=None, maxiter=None, M=None, callback=None, callback_type=None)[source]#

Uses Generalized Minimal RESidual iteration to solve Ax = b.

Parameters:

A (ndarray, spmatrix or LinearOperator) – The real or complex matrix of the linear system with shape (n, n). A must be cupy.ndarray, cupyx.scipy.sparse.spmatrix or cupyx.scipy.sparse.linalg.LinearOperator.
b (cupy.ndarray) – Right hand side of the linear system with shape (n,) or (n, 1).
x0 (cupy.ndarray) – Starting guess for the solution.
rtol (float) – Tolerance for convergence.
atol (float) – Tolerance for convergence.
restart (int) – Number of iterations between restarts. Larger values increase iteration cost, but may be necessary for convergence.
maxiter (int) – Maximum number of iterations.
M (ndarray, spmatrix or LinearOperator) – Preconditioner for A. The preconditioner should approximate the inverse of A. M must be cupy.ndarray, cupyx.scipy.sparse.spmatrix or cupyx.scipy.sparse.linalg.LinearOperator.
callback (function) – User-specified function to call on every restart. It is called as callback(arg), where arg is selected by callback_type.
callback_type (str) – ‘x’ or ‘pr_norm’. If ‘x’, the current solution vector is used as an argument of callback function. if ‘pr_norm’, relative (preconditioned) residual norm is used as an argument.

Returns:

It returns x (cupy.ndarray) and info (int) where x is the converged solution and info provides convergence information.

Return type:

tuple

Reference:: M. Wang, H. Klie, M. Parashar and H. Sudan, “Solving Sparse Linear Systems on NVIDIA Tesla GPUs”, ICCS 2009 (2009).