topic Quote:Alexander Kalinkin in Intel® oneAPI Math Kernel Library

the problem of eigenvalues&eigenvectors of sparse matrix.

han_N_ — Tue, 10 Feb 2015 02:36:08 GMT

If I just want to get smallest eigenvalues and its' eigenvectorsj(0<=j<=n) from a sparse matrix(n*n),'cause the dimension of matrix is too large to calculate all the eigenvalues&eigenvectors at the same time(memory limited) and the smallest j is meet the need, Which funciton should I use?(Matrix store as CSC or CSR format)

Hi,

Alexander_K_Intel2 — Tue, 10 Feb 2015 02:59:12 GMT

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

Quote:Alexander Kalinkin

han_N_ — Tue, 10 Feb 2015 03:13:24 GMT

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?

Just to verify - you need to

Alexander_K_Intel2 — Tue, 10 Feb 2015 03:26:59 GMT

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

Quote:Alexander Kalinkin

han_N_ — Tue, 10 Feb 2015 03:33:00 GMT

Alexander Kalinkin (Intel) wrote:

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

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

Thanks

In such case make sense to

Alexander_K_Intel2 — Tue, 10 Feb 2015 03:43:40 GMT

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

Quote:Alexander Kalinkin

han_N_ — Tue, 10 Feb 2015 03:53:03 GMT

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

No problem, you are welcome.

Alexander_K_Intel2 — Tue, 10 Feb 2015 04:00:19 GMT

No problem, you are welcome. If it is not a secret, could you explain your application? What is it name or goal?

Quote:Alexander Kalinkin

han_N_ — Tue, 10 Feb 2015 05:16:35 GMT

Alexander Kalinkin (Intel) wrote:

No problem, you are welcome. If it is not a secret, could you explain your application? What is it name or goal?

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.