Finding largest eigenvalue in sparse matrix - python

I'm using numpy and scipy. I have a large sparse matrix and I want to find the largest eigenvalue of the sparse matrix. How can I do that?


I use scipy.sparse.linalg.eigsh for symmetric sparse matrices passing which="LM":
eigvals, eigvecs = eigsh(A, k=10, which='LM', sigma=1.)
but you should definitely read the documentation.

Related

How do I do this calculation most efficiently with scipy sparse matrices?

Suppose I have the following:
A complex-valued sparse matrix Q (and its conjugate transpose is Q^H)
A complex-valued diagonal matrix D
A real-valued sparse vector v
and I wish to compute as efficiently as possible, using scipy sparse matrices, the product
Q # (D # (Q^H # v)),
where the #s are matrix-vector multiplication and the bracketed order is chosen to avoid matrix-matrix multiplication. I am new to use of sparse matrices, and the available types confuse me. How would I best compute this in scipy? In particular, I'm wondering:
Is it inefficient to mix matrix types? (e.g. would it be inefficient if Q were a CSC matrix and v were a CSR matrix - is there any general requirement for them all to be the same?)
For each of Q, D, and v, which scipy sparse representation would be best to do efficient matrix-vector multiplication?
If I were to port the code to run on my GPU using cupy, are there any additional factors I'd need to consider for efficiency?

Eigenvalues and Eigenvectors of large sparse matrix in Python Scipy

My Python code generates upper triangle of a matrix in coordinate (COO) format (row,col,mat_element) and stores non-zero elements only to decrease memory usage. However, it is sparse symmetric matrix and I wish to obtain it's eigenvalues and eigenvectors using 'eigsh' from 'scipy.sparse.linalg'. How can I do this?
I would prefer to convert COO to CSR matrix directly and give it as an input for 'eigsh'. But if that is not possible I would like to make the matrix symmetric first and then convert it to CSR format.
COO and CSR matrix wiki:
https://en.wikipedia.org/wiki/Sparse_matrix

Finding out eigen values and vectors of huge sparse matrices in python is horribly slower than Matlab

I am trying to find 100 eigen values and vectors of a huge sparse matrix of size 409600x409600. I am using scipy.sparse.linalg.eigs for this and it's taking ages to find the result whereas eigs on matlab solves it within 10 mins.Any suggestions on how to speed it up?
Python:
eigenvectors, eigenvalues = scipy.sparse.linalg.eigs(Laplacian, k=100, which='SM')
Matlab:
eigCnt = 100;
[eigenvectors, eigenvalues] = eigs(Laplacian, eigCnt, 'SM');
where Laplacian is a sparse matrix of size 409600x409600 with 10418204 non zero entries
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How to obtain correct L and U matrices from LU decomposition of a sparse matrix A, without using scipy.sparse.linalg.splu()?

I have noticed that scipy.sparse.linalg.splu() does not allow me to decompose a sparse matrix A into the correct L and U matrix that I can call separately. The command ''merely'' allows me to decompose the matrix and reconstruct it later on using the permutation matrix. However, for my code I need to decompose a sparse matrix A into a sparse matrix L and U and then be able to call the L and U matrices separately (without permutation matrices etc.). This does not work when using the scipy.sparse.linalg.splu() command. I could use scipy.linalg.lu() but I cannot apply this to a matrix A in sparse format. Are there any other methods out there for obtaining the correct L and U decomposition matrices from a sparse matrix A? Thanks in advance.

Determine sparsity of sparse matrix ( Lil matrix )

I have a large sparse matrix, implemented as a lil sparse matrix from sci-py. I just want a statistic for how sparse the matrix is once populated. Is there a method to find out this?

m.nnz is the number of nonzero elements in the matrix m, you can use m.size to get the total number of elements.

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