我们从Python开源项目中，提取了以下5个代码示例，用于说明如何使用scipy.sparse.linalg.gmres()。
def krylovMethod(self,tol=1e-8): """ We obtain ``pi`` by using the :func:``gmres`` solver for the system of linear equations. It searches in Krylov subspace for a vector with minimal residual. The result is stored in the class attribute ``pi``. Example ------- >>> P = np.array([[0.5,0.5],[0.6,0.4]]) >>> mc = markovChain(P) >>> mc.krylovMethod() >>> print(mc.pi) [ 0.54545455 0.45454545] Parameters ---------- tol : float, optional(default=1e-8) Tolerance level for the precision of the end result. A lower tolerance leads to more accurate estimate of ``pi``. Remarks ------- For large state spaces, this method may not always give a solution. Code due to http://stackoverflow.com/questions/21308848/ """ P = self.getIrreducibleTransitionMatrix() #if P consists of one element, then set self.pi = 1.0 if P.shape == (1, 1): self.pi = np.array([1.0]) return size = P.shape[0] dP = P - eye(size) #Replace the first equation by the normalizing condition. A = vstack([np.ones(size), dP.T[1:,:]]).tocsr() rhs = np.zeros((size,)) rhs[0] = 1 pi, info = gmres(A, rhs, tol=tol) if info != 0: raise RuntimeError("gmres did not converge") self.pi = pi
def _declare_options(self): """ Declare options before kwargs are processed in the init method. """ self.options.declare('solver', default='gmres', values=tuple(_SOLVER_TYPES.keys()), desc='function handle for actual solver') self.options.declare('restart', default=20, types=int, desc='Number of iterations between restarts. Larger values increase ' 'iteration cost, but may be necessary for convergence. This ' 'option applies only to gmres.') # changing the default maxiter from the base class self.options['maxiter'] = 1000 self.options['atol'] = 1.0e-12
def __init__(self, M, ifunc=gmres, tol=0): if tol <= 0: # when tol=0, ARPACK uses machine tolerance as calculated # by LAPACK's _LAMCH function. We should match this tol = 2 * np.finfo(M.dtype).eps self.M = M self.ifunc = ifunc self.tol = tol if hasattr(M, 'dtype'): self.dtype = M.dtype else: x = np.zeros(M.shape[1]) self.dtype = (M * x).dtype self.shape = M.shape
def __init__(self, A, M, sigma, ifunc=gmres, tol=0): if tol <= 0: # when tol=0, ARPACK uses machine tolerance as calculated # by LAPACK's _LAMCH function. We should match this tol = 2 * np.finfo(A.dtype).eps self.A = A self.M = M self.sigma = sigma self.ifunc = ifunc self.tol = tol def mult_func(x): return A.matvec(x) - sigma * M.matvec(x) def mult_func_M_None(x): return A.matvec(x) - sigma * x x = np.zeros(A.shape[1]) if M is None: dtype = mult_func_M_None(x).dtype self.OP = LinearOperator(self.A.shape, mult_func_M_None, dtype=dtype) else: dtype = mult_func(x).dtype self.OP = LinearOperator(self.A.shape, mult_func, dtype=dtype) self.shape = A.shape
def solve(A, b, method, tol=1e-3): """ General sparse solver interface. method can be one of - spsolve_umfpack_mmd_ata - spsolve_umfpack_colamd - spsolve_superlu_mmd_ata - spsolve_superlu_colamd - bicg - bicgstab - cg - cgs - gmres - lgmres - minres - qmr - lsqr - lsmr """ if method == 'spsolve_umfpack_mmd_ata': return spla.spsolve(A,b,use_umfpack=True, permc_spec='MMD_ATA') elif method == 'spsolve_umfpack_colamd': return spla.spsolve(A,b,use_umfpack=True, permc_spec='COLAMD') elif method == 'spsolve_superlu_mmd_ata': return spla.spsolve(A,b,use_umfpack=False, permc_spec='MMD_ATA') elif method == 'spsolve_superlu_colamd': return spla.spsolve(A,b,use_umfpack=False, permc_spec='COLAMD') elif method == 'bicg': res = spla.bicg(A,b,tol=tol) return res[0] elif method == 'bicgstab': res = spla.bicgstab(A,b,tol=tol) return res[0] elif method == 'cg': res = spla.cg(A,b,tol=tol) return res[0] elif method == 'cgs': res = spla.cgs(A,b,tol=tol) return res[0] elif method == 'gmres': res = spla.gmres(A,b,tol=tol) return res[0] elif method == 'lgmres': res = spla.lgmres(A,b,tol=tol) return res[0] elif method == 'minres': res = spla.minres(A,b,tol=tol) return res[0] elif method == 'qmr': res = spla.qmr(A,b,tol=tol) return res[0] elif method == 'lsqr': res = spla.lsqr(A,b,atol=tol,btol=tol) return res[0] elif method == 'lsmr': res = spla.lsmr(A,b,atol=tol,btol=tol) return res[0] else: raise Exception('UnknownSolverType')
