![]() ![]() ![]() How can I build these common eigenvectors and finding also the eigenvalues associated? I am a little lost between all the potential methods that exist to carry it out. In a first time, I prefer to conclude in Matlab as if it was a prototype, and after if it works, look for doing this synthesis with MKL or with Python functions. So surely, I must have done an error in my code snippet above. % Compute the final endomorphism : F = P D P^-1įISH_final = V*eye(7).*eigen_final*inv(V)īut the matrix FISH_final don't give good results since I can do other computations from this matrix FISH_final (this is actually a Fisher matrix) and the results of these computations are not valid. % Diagonalize the matrix (A B^-1) to compute Lambda since we have AX=Lambda B X I tried to use it like this : % Search for common build eigen vectors between FISH_sp and FISH_xc Particularly, I am interested by the eig(A,B) Matlab function. I have also read the wikipedia topic and this interesting paper but couldn't have to extract methods pretty easy to implement. I took a look in a similar post but had not managed to conclude, i.e having valid results when I build the final wanted endomorphism F defined by : F = P D P^-1 Where A and B are square and diagonalizable matrices. I am looking for finding or rather building common eigenvectors matrix X between 2 matrices A and B such as : AX=aX with "a" the diagonal matrix corresponding to the eigenvaluesīX=bX with "b" the diagonal matrix corresponding to the eigenvalues ? 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. Now, I would like to do the link between this generalized problem and the eventual common eigenvectors between A and B matrices (respectively Fish_sp and Fish_xc).So at the end, I find phi eigenvectors matrix (phi) and lambda diagonal matrix (D1). ![]() % Applying each step of algorithm 1 on page 7 Here my little Matlab script for this method : % Diagonalize A = FISH_sp and B = Fish_xc Here the interested part (sorry, I think Latex is not available on stakoverflow) : I have followed all the steps of this algorithm and it seems to give better results when I make the Fisher synthesis. To summarize, the algorithm used is described on page 7. the second method comes from the following paper.I don't know why I don't get the same results than the second ones below. So, from a theorical point of view, it is the simple and classical eigen values problem.įinally, in Matlab, I simply did, with A=FISH_sp and B=FISH_xc : = eig(inv(FISH_xc)*FISH_sp) īut results are not correct when I make after a simple Fisher synthesis (constraints are too bad and also making appear nan values. Then, we could multiply by B^(-1) on each side, such as : if Generalized problem is formulated as :.I am looking for solving a generalized eigenvectors and eigen value problem in Matlab. ![]()
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