Intel® oneAPI Math Kernel Library
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## the problem of eigenvalues&eigenvectors of sparse matrix. Beginner
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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)

1 Solution Employee
189 Views

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

8 Replies Employee
190 Views

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 Beginner
189 Views

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? Employee
189 Views

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

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 Employee
189 Views

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 Beginner
189 Views

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 Employee
189 Views

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