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flag can be:Ĭomputes the generalized eigenvalues of A and B using the Cholesky factorization of B. Specifies the algorithm used to compute eigenvalues and eigenvectors.
#EIG MATLAB FULL#
Produces a diagonal matrix D of generalized eigenvalues and a full matrix V whose columns are the corresponding eigenvectors so that A*V = B*V*D. See the balance function for more details. However, if a matrix contains small elements that are really due to roundoff error, balancing may scale them up to make them as significant as the other elements of the original matrix, leading to incorrect eigenvectors. Ordinarily, balancing improves the conditioning of the input matrix, enabling more accurate computation of the eigenvectors and eigenvalues.
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Use = eig(A.') W = conj(W) to compute the left eigenvectors.įinds eigenvalues and eigenvectors without a preliminary balancing step. If W is a matrix such that W'*A = D*W', the columns of W are the left eigenvectors of A. Matrix V is the modal matrix-its columns are the eigenvectors of A. Matrix D is the canonical form of A-a diagonal matrix with A's eigenvalues on the main diagonal. Produces matrices of eigenvalues ( D) and eigenvectors ( V) of matrix A, so that A*V = V*D. To request eigenvectors, and in all other cases, use eigs to find the eigenvalues or eigenvectors of sparse matrices. If S is sparse and symmetric, you can use d = eig(S) to returns the eigenvalues of S. Returns a vector containing the generalized eigenvalues, if A and B are square matrices. Returns a vector of the eigenvalues of matrix A. The only case in which the scaling has to be defined exactly, is when you are going to give a graphic representation of the eigenvalues.Eig (MATLAB Functions) MATLAB Function Reference
#EIG MATLAB HOW TO#
In this case I'm not able to give you advice on how to exactly replicate matlab: knowledge of the internal working of matlab is required.Īs a general remark, in linear algebra usually one does not care too much about eigenvector scaling, since this is usually completely irrelevant for the problem solved, when the eigenvectors are just used as intermediate results. This unfortunately means that the scaling is not unique, and probably depends on intermediate results of the generalised eigenvector algorithm used. all(imag(V(end,:))=0) (the last component of each eigenvector is real)īut not imposing other constraints.By quickly inspecting your example, I would say that in this case matlab is enforcing following condition:
#EIG MATLAB DRIVER#
The main problem with exactly replicating the scaling chosen by matlab is that eig(A,B) is a driver routine, which depending from the different properties of A and B may call different libraries/routines, and apply extra steps like balancing the matrices and so on.
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It is quite common that different linear algebra libraries compute different eigenvectors, but this does not mean that one of the two codes is wrong: it simply means that they choose a different scaling of the eigenvectors. if v is an eigenvector the same holds for alpha*v, where alpha is a non zero complex scalar.) Please remember from basic linear algebra that eigenvector are determined up to an arbitrary scaling factor. In fact for the second example run, Matlab and Eigen produced the very same result. I've rewritten matrices manually to C++ and performed eig(A,B) again with matrices meeting requirements: Matrix4cd x Ġ.0208 - 0.0218i 0.2425 + 0.0753i -0.1242 + 0.3753i eigenvalues() for the same matrices are not the same at all: eigenvalues() doesn't return complex values where Matlab does. My implementation looks like this: std::pair eig(const Matrix4cd& A, const Matrix4cd& B)Įigen::GeneralizedSelfAdjointEigenSolver solver(A, B) īut first thing that comes to my mind is, that I can't use Vector4cd as. Matlab definition of eig function I need: = eig(A,B) produces a diagonal matrix D of generalizedĮigenvalues and a full matrix V whose columns are the corresponding Do anyone have any idea how can I rewrite eig(A,B) from Matlab used to calculate generalized eigenvector/eigenvalues? I've been struggling with this problem lately.