higher accuracy in diagonialzation
Dear all, I am now diagonalizing a 200-by-200 symmetric matrix. But the two methods, scipy.linalg.eigh and numpy.linalg.eigh give significantly different result. The results from two methods are different within 10^-4 order. One of them is inaccurate or both two of them are inaccurate within that range. Which one is more accurate? or Are there any ways to control the accuracy for diagonalization? If you have some idea please let me know. Sunghwan Choi Ph. D. candidator Department of Chemistry KAIST (South Korea)
On 2014-10-27 10:37:58, Sunghwan Choi <sunghwanchoi91@gmail.com> wrote:
I am now diagonalizing a 200-by-200 symmetric matrix. But the two methods, scipy.linalg.eigh and numpy.linalg.eigh give significantly different result. The results from two methods are different within 10^-4 order. One of them is inaccurate or both two of them are inaccurate within that range. Which one is more accurate? or Are there any ways to control the accuracy for diagonalization? If you have some idea please let me know.
My first (naive) attempt would be to set up a matrix, M, in sympy and then use M.diagonalize() to find the symbolic expression of the solution. You can then do the same numerically to see which method yields a result closest to the desired answer. Stéfan
On 27 October 2014 09:37, Sunghwan Choi <sunghwanchoi91@gmail.com> wrote:
One of them is inaccurate or both two of them are inaccurate within that range. Which one is more accurate?
You can check it yourself using the eigenvectors. The cosine distance between v and M.dot(v) will give you the error in the eigenvectors, and the difference between ||lambda*v|| and ||M.dot(v)|| the error in the eigenvalue. I would also check the condition numbers, maybe your matrix is just not well conditioned. You would have to look at preconditioners. /David.
participants (3)
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Daπid -
Stefan van der Walt -
Sunghwan Choi