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. Find the largest element in the magnitude of matrix Y and assign it to K. 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 How can I modify the power method so that it computes the smallest eigenvalue my power method algorithm : 1. By taking advantage of this feature, as well as the power method, we are able to obtain the smallest eigenvalue of A this will be basis of the inverse power method. One can vary k to improve the separation. The eigenvalues of the inverse matrix A 1 are the reciprocals of the eigenvalues of A.
Relative separation of the desired eigenvalues from the rest 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: 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 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. Now I tried to convert the same for a ellipsoid. LOBPCG is a preconditioned eigensolver for large real symmetric and complex achisquarevalsqrt (largesteigenval) bchisquarevalsqrt (smallesteigenval) Therefore I could extract the needed parameters to plot the ellipse. 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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