Problem, a good simple preconditioner function would be a linear solveįor A, which is easy to code since A is tridiagonal. Slow, unless efficient preconditioning is used. Proper preconditioning to shrink the spectral spread.įor example, a rod vibration test problem (under testsĭirectory) is ill-conditioned for large n, so convergence will be One can vary k to improve the separation. Thanks in advance for your helpful comments. 'sa' means Smallest Algebraic lambda2 D (2, 2) getting the second smallest eigenvalue. Relative separation of the desired eigenvalues from the rest In Matlab, for example, the line that I use to code is:, D eigs (lap, 2, 'sa') getting the first two eigenvalues of laplacian (lap). Randomly distributed around the origin vectors work well if no better ![]() Quality of the initial approximations X to the seeking eigenvectors. The convergence speed depends basically on three factors: Manotosh Mandal Matlab codes for Power Method to find dominant eigenvalue and the corresponding eigenvector. For diagonal matrix D as the sum of the weights, adjacency matrix A with weighted degrees, and Laplacian matrix L (which is a positive semidefinite matrix), the normalized Laplacian is: D (1/2)L (D1/2) Therefore I compute the following: Theme. It you call LOBPCG with k=1Īnd n=10, it works though n is small. Power Method to find dominant eigenvalue Version 1.0.02 (1.32 KB) by Dr. It is not that n should be large for the LOBPCG to work, but rather the Y ndarray, float32 or float64, default: NoneĪn n-by-sizeY ndarray of constraints with sizeY n, it would likelyīreak internally, so the code calls the standard function eigh instead. Preconditioner aiming to accelerate convergence. By default M = None, which is equivalent to identity. Hermitian definite generalized eigenproblems. ![]() ![]() LOBPCG is a preconditioned eigensolver for large real symmetric and complex Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG). lobpcg ( A, X, B = None, M = None, Y = None, tol = None, maxiter = None, largest = True, verbosityLevel = 0, retLambdaHistory = False, retResidualNormsHistory = False, restartControl = 20 ) #
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