eigenvector

来源： https://stackoverflow.com/questions/62561548/different-results-in-eigenvector-centrality-numpy

问题 I am trying to compute few (5-500) eigenvectors corresponding to the smallest eigenvalues of large symmetric square sparse-matrices (up to 30000x30000) with less than 0.1% of the values being non-zero. I am currently using scipy.sparse.linalg.eigsh in shift-invert mode (sigma=0.0), which I figured out through various posts on the topic is the prefered solution. However, it takes up to 1h to solve the problem in most cases. On the other hand the function is very fast, if I ask for the largest

问题 I test the theorem that A = Q * Lambda * Q_inverse where Q the Matrix with the Eigenvectors and Lambda the Diagonal matrix having the Eigenvalues in the Diagonal. My code is the following: import numpy as np from numpy import linalg as lg Eigenvalues, Eigenvectors = lg.eigh(np.array([ [1, 3], [2, 5] ])) Lambda = np.diag(Eigenvalues) Eigenvectors @ Lambda @ lg.inv(Eigenvectors) Which returns : array([[ 1., 2.], [ 2., 5.]]) Shouldn't the returned Matrix be the same as the Original one that was

问题 I test the theorem that A = Q * Lambda * Q_inverse where Q the Matrix with the Eigenvectors and Lambda the Diagonal matrix having the Eigenvalues in the Diagonal. My code is the following: import numpy as np from numpy import linalg as lg Eigenvalues, Eigenvectors = lg.eigh(np.array([ [1, 3], [2, 5] ])) Lambda = np.diag(Eigenvalues) Eigenvectors @ Lambda @ lg.inv(Eigenvectors) Which returns : array([[ 1., 2.], [ 2., 5.]]) Shouldn't the returned Matrix be the same as the Original one that was

问题 My problem is this: I'm attempting a spectral decomposition of a random process via a (truncated) Karhunen-Loeve transform, but my covariance matrix is actually a 1-parameter family of matrices, and I need a way to estimate / visualize how my random process depends on this parameter. To do this, I need a way to track the eigenvectors produced by numpy.linalg.eigh(). To give you an idea of my issue, here's a sample toy problem: Suppose I have a set of points {xs}, and a random process R with

问题 In MATLAB I can issue the command: [X,L] = eig(A,'nobalance'); In order to compute the eigenvalues without the balance option. What is the equivalent command in NumPy? When I run the NumPy version of eig, it does not produce the same result as the MATLAB result with nobalance turned on. 回答1: NumPy can't currently do this. As horchler said, there has been an open ticket open for this for a while now. It is, however, possible to do it using external libraries. Here I write up how to do it using

问题 I want to ask some question about eigenvector centrality. I have to compute a eigenvalue using power iteration. This is my code to compute eigenvalue : v=rand(165,1); for k=1:5 w = data_table*v; lamda = norm(w); v = w/lamda; end When I have get a single eigenvalue, I confused to compute eigenvector score using a single eigenvalue that I had get it. for example in my code to compute eigenvalue I get dominant eigenvalue = 78.50. With this eigenvalue score, I want compute eigenvector score.

问题 I am having problems with hd.eigen in Rfast . It gives extremely close results to eigen with most data, but sometimes hd.eign returns an empty $vector , NAs, or other undesirable results. For example: > set.seed(123) > bigm <- matrix(rnorm(2000*2000,mean=0,sd = 3), 2000, 2000) > > e3 = eigen(bigm) > length(e3$values) [1] 2000 > length(e3$vectors) [1] 4000000 > sum(is.na(e3$vectors) == TRUE) [1] 0 > sum(is.na(e3$vectors) == FALSE) [1] 4000000 > > e4 = hd.eigen(bigm, vectors = TRUE) > length(e4

问题 I have seen this question, and it is relevant to my attempt to compute the dominant eigenvector in Python with numPy. I am trying to compute the dominant eigenvector of an n x n matrix without having to get into too much heavy linear algebra. I did cursory research on determinants, eigenvalues, eigenvectors, and characteristic polynomials, but I would prefer to rely on the numPy implementation for finding eigenvalues as I believe it is more efficient than my own would be. The problem I

问题 While using princomp() function in R, the following error is encountered : "covariance matrix is not non-negative definite" . I think, this is due to some values being zero (actually close to zero, but becomes zero during rounding) in the covariance matrix. Is there a work around to proceed with PCA when covariance matrix contains zeros ? [FYI : obtaining the covariance matrix is an intermediate step within the princomp() call. Data file to reproduce this error can be downloaded from here -