Python - Multiply sparse matrix row with non-sparse vector by index

2
votes

My current software project involves implementing a numeric method for solving linear systems with python (the so called SOR-Method). It basically works like this:

Given a linear system:

ax1 + bx2 + cx3 = b1
dx1 + ex2 + fx3 = b2
gx1 + hx2 + ix3 = b3

Re-arrange the equations to:

x1_new = (b1 - (bx2 + cx3)) / a
x2_new = (b2 - (dx1_new + fx3)) / e
x3_new = (b3 - (gx1_new + hx2_new)) / i

As you can see, the x*_new values are updating with each line - that's the unfortunate reason why I can't use simple vector-vector prodcuts (I also have to divide by the diagonal element - not multiply it). I have to go element by element.

I would like to work with sparse-Matrices. But I didn't find a way yet how to index a sparse matrix and how to perform the operation described above? Like, the only thing I found (regarding this https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html) is to use A[i].data which returns the non-zero elements of the row i. But there can be a lot of zeros in a row. And also working with a lot of if/else to get the element at the index is not very efficient with a 100.000 x 100.000 matrix.

Any ideas?

pythonnumpymatrixscipynumerical-methods
A[i] is a new sparse matrix (not a view). A[i].A is a dense version of that matrix, with all the zeros restored. (lil format does have a version of sparse row views). Working with elements, rows or columns of sparse matrices is not efficient unless you are willing to get your hands dirty and play with the data, indices, indptr attributes directly. – hpaulj
@hpaulj Do you have any idea, what A[i, j] does? Because somehow that is exactly doing what I need. – binaryBigInt