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. Relative separation of the desired eigenvalues from the rest Randomly distributed around the origin vectors work well if no better eigifp is a MATLAB program for computing a few algebraically smallest or largest eigenvalues and their corresponding eigenvectors of the generalized eigenvalue prob-lem Ax Bx (1) where A and B are large (and typically sparse) symmetric matrices and B is positive denite. Quality of the initial approximations X to the seeking eigenvectors. The convergence speed depends basically on three factors: It you call LOBPCG with k=1Īnd n=10, it works though n is small. It is not that n should be large for the LOBPCG to work, but rather the ![]() Now I tried to convert the same for a ellipsoid. 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. achisquarevalsqrt (largesteigenval) bchisquarevalsqrt (smallesteigenval) Therefore I could extract the needed parameters to plot the ellipse. 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 Thanks in advance for your helpful comments. 'sa' means Smallest Algebraic lambda2 D (2, 2) getting the second smallest eigenvalue. Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG). 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). 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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