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. 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. 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. Eig (MATLAB Functions) MATLAB Function Reference ? In the paper, they say that phi diagonalizes A=FISH_sp and B=FISH_xc but I can't reproduce it. Which don't give same values for a given column of FISH_sp and FISH_xc) How could I fix this wrong result (I am talking about the ratios : FISH_sp*phi./phi % Check eigen values : OK, columns of eigenvalues D2 found ! % Check eigen values : OK, columns of eigenvalues D1 found ! So, I don't find that matrix of eigenvectors Phi diagonalizes A and B since the eigenvalues expected are not columns of identical values.īy the way, I find the eigenvalues D1 and D2 coming from : = eig(FISH_sp) % Check if phi diagolize FISH_sp : NOT OK, not identical eigenvalues % Check eigen values : OK, columns of eigenvalues found ! % DEBUG : check identity matrix => OK, Identity matrix found ! % V2 corresponds to eigen vectors of FISH_xc Indeed, by doing : % Marginalizing over uncommon parameters between the two matrices I have wrong results if I want to say that phi diagonalizes both A=FISH_sp and B=FISH_xc matrices. From a numerical point of view, why don't I get the same results between the method in 1) and the method in 3) ? I mean about the Phi eigen vectors matrix and the Lambda diagonal matrix.Maybe, we could arrange this relation such that : A*Phi'=Phi'*Lambda_A' Indeed, what I have done up to now is to to find a parallel relation between A*Phi and B*Phi, linked by Lambda diagonal matrix.
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