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PYTHON CODE

Given a unit lower triangular matrix L and an upper triangular matrix U.

Write the forward and backward elimination solves (Ly = b and U x = y) assuming that L and U are stored in compressed sparse row (CSR) format. Estimate the cost of memory and operations.

Lets say our test matrices are stored in adjacency list (in each row of the file we have three numbers) something like this (it is also .txt file):

row index, column index, and value

23 3 0.000001370542294

4 4 0.107816040610854

7 4 0.022782277293175

11 4 -0.00921782470662

But this file might have 25 or 50 rows.

Factor them into LD^{-1}L^T form, either using some library, or implementing it yourself. Store the resulting unit triangular matrix L in CSR format (do not store the zeros).

The txt file contains only the nonzero entries of the matrix. The data should give s.p.d. matrices.