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- the problem of eigenvalues&eigenvectors of sparse matrix.

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han_N_

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02-09-2015
06:36 PM

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Alexander_K_Intel2

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02-09-2015
06:59 PM

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Hi,

You can use Extended EigenSolver functionality. Just make any estimation on eigenvalues (for example norm of matrix) and set small interval near its boundaries to EE functionality with any estimation on number of eigenvalues. If your estimation of number eigenvalues less than real number functionality return correspondent error, if bigger - functionality provide correct answer.

Thanks,

Alex

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Alexander_K_Intel2

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02-09-2015
06:59 PM

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Hi,

You can use Extended EigenSolver functionality. Just make any estimation on eigenvalues (for example norm of matrix) and set small interval near its boundaries to EE functionality with any estimation on number of eigenvalues. If your estimation of number eigenvalues less than real number functionality return correspondent error, if bigger - functionality provide correct answer.

Thanks,

Alex

han_N_

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02-09-2015
07:13 PM

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Alexander Kalinkin (Intel) wrote:

Hi,

You can use Extended EigenSolver functionality. Just make any estimation on eigenvalues (for example norm of matrix) and set small interval near its boundaries to EE functionality with any estimation on number of eigenvalues. If your estimation of number eigenvalues less than real number functionality return correspondent error, if bigger - functionality provide correct answer.

Thanks,

Alex

It means that I should try some [min max] interval set until it meet the number of j I want?

Alexander_K_Intel2

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02-09-2015
07:26 PM

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Just to verify - you need to find smallest eigenvalue or j-th eigenvalue?

han_N_

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02-09-2015
07:33 PM

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Alexander Kalinkin (Intel) wrote:

Just to verify - you need to find smallest eigenvalue or j-th eigenvalue?

Hi

I need to find from smallest to the j-th smallest eigenvalues and the eigenvectors associated with the the eigenvalues (smallest Top J)

Thanks

Alexander_K_Intel2

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02-09-2015
07:43 PM

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In such case make sense to achieve this interval using inertia functionality from PARDISO. So you have initial searching interval (a, b), set c = (a+b)/2 and set matrix B = A-cE. After call PARDISO reordering and factorization phase and get number of negative pivot. If this number less than j than number of eigenvalue in interval (a,c) less than j and you need to increase c and decrease otherwise. After you got new c and new matrix B and repeat pardiso call...

Thanks,

Alex

han_N_

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02-09-2015
07:53 PM

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Alexander Kalinkin (Intel) wrote:

In such case make sense to achieve this interval using inertia functionality from PARDISO. So you have initial searching interval (a, b), set c = (a+b)/2 and set matrix B = A-cE. After call PARDISO reordering and factorization phase and get number of negative pivot. If this number less than j than number of eigenvalue in interval (a,c) less than j and you need to increase c and decrease otherwise. After you got new c and new matrix B and repeat pardiso call...

Thanks,

Alex

Oh I got it, it seems like a good way to approach the j-th value and get the interval.

Thanks again

Alexander_K_Intel2

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02-09-2015
08:00 PM

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han_N_

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02-09-2015
09:16 PM

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Alexander Kalinkin (Intel) wrote:

- I wanna use spectral clustertng algorithm to divide a graph into some clusters, the algorithm need to get some eigenvalues and eigenvectors in order to dimensionality reduciton.
- Can MKL just calculate the eigenvalues from sparse matrix? That would be easier to locate the interval.

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