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If you wish to verify this experimentally, I guess you'll have a hard time getting an exact zero out of Matlab, since this sum converges quite slowly to its asymptotical value usually. If another eigenvector were to be nonnegative, then the scalar product with the dominant eigenvector $u^^n (\phi_t-\mu) (\phi'_t-\mu)'^T=0$, where $\mu$ and $\mu'$ are the means of the two time series. There are some classes of matrices (such as Z-matrices or nonnegative matrices) for which it is known that the largest or smallest eigenvector is nonnegative.
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No, the eigenvalues could come in any order there is no guarantee that they are ordered. I suppose your matrix is symmetric, since you say that the eigenvectors are orthogonal and try to order the eigenvalues. LOTS of questions, I know, but I would REALLY appreciate if you could help me answer some of them!
Matlab 2012 left eigenvectors how to#
Out of curiosity, but what does it mean "the two times-series Fi and Fi' are uncorrelated in the sense that their empirical correlation vanishes for i != i' ? How to check that in MATLAB?.
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The generalized eigenvalue problem is to determine the solution to the equation Av Bv, where A and B are n-by-n matrices, v is a column vector of length n, and is a scalar.
Matlab 2012 left eigenvectors full#
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For systems with large numbers of degrees of freedom, however, the function mphinputmatrix fails due to limitations of the Java Heap Memory ( OutOfMemoryError: Java heap space) in Matlab, although the Java heap space was already increased to a maximum value of 8GB.Īs the manipulation of the load vector is more convenient to do in Matlab, the reduced order model simulations are preferred to also being performed in Matlab.The following MATLAB function produces the Eigenvalues and Eigenvectors of matrix X. So far, transposing the system matrices in Matlab and returning them to COMSOL via mphinputmatrix did the trick to get the left eigenvector. However, for the model order reduction the right AND left eigenvectors are required but only the right eigenvector can be extracted in a straightforward manner. The model order reduction is then performed in a second step in Matlab. Therefore, in a first step I execute an eigenvalue study and extract the system matrices, the eigenvalues and the (right) eigenvectors via the COMSOL LiveLink for Matlab using the functions mphmatrix and mphgetu. The governing equations are implemented using the Weak Form PDE Physics in COMSOL 4.4 (newer releases are available but rarely used). After quite some research, I still haven't found a way to calculate and export the left eigenvector to Matlab when performing an eigenvalue study in COMSOL.Ĭurrently I am trying to perform reduced order model simulations in time domain for acoustic wave propagation.