import scipy.sparse.linalg as la import scipy.io as io import numpy as np import sys #problem = "SPARSKIT/drivcav/e05r0100" problem = "SPARSKIT/drivcav/e05r0200" #problem = "Harwell-Boeing/sherman/sherman1" #problem = "misc/hamm/add32" mm = np.lib._datasource.Repository('https://math.nist.gov/pub/MatrixMarket2/') f = mm.open(f'{problem}.mtx.gz') Am = io.mmread(f).tocsr() f.close() f = mm.open(f'{problem}_rhs1.mtx.gz') b = np.array(io.mmread(f)).ravel() f.close() bnorm = np.linalg.norm(b) count = [0] def matvec(v): count[0] += 1 sys.stderr.write(f"{count[0]}\r") return Am@v A = la.LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype) M = 100 print("MatrixMarket problem %s" % problem) print(f"Invert {Am.shape[0]} x {Am.shape[1]} matrix; nnz = {Am.nnz}") count[0] = 0 x0, info = la.gmres(A, b, restrt=M, tol=1e-14) count_0 = count[0] err0 = np.linalg.norm(Am@x0 - b) / bnorm print(f"GMRES({M}): {count_0} matvecs, relative residual: {err0}") if info != 0: print("Didn't converge") count[0] = 0 x1, info = la.lgmres(A, b, inner_m=M-6*2, outer_k=6, tol=1e-14) count_1 = count[0] err1 = np.linalg.norm(Am@x1 - b) / bnorm print(f"LGMRES({M - 2*6}, 6) [same memory req.]: {count_1} " f"matvecs, relative residual: {err1}") if info != 0: print("Didn't converge") count[0] = 0 x2, info = la.lgmres(A, b, inner_m=M-6, outer_k=6, tol=1e-14) count_2 = count[0] err2 = np.linalg.norm(Am@x2 - b) / bnorm print(f"LGMRES({M - 6}, 6) [same subspace size]: {count_2} " f"matvecs, relative residual: {err2}") if info != 0: print("Didn't converge")