Implementation of LU Decomposition

[rabbull]

This PR implements LU decomposition by enhancing gaussian_elimination to support step-by-step recording of row operations. These recorded steps can then be replayed on an identity matrix to construct the L matrix.

Four new methods are introduced:

• gaussian_elimination_ex: An extended version of Gaussian elimination that includes an option to record the steps performed during row operations. The existing gaussian_elimination method now serves as a wrapper for this function.
• lu_decomposition: Computes the LU decomposition of a matrix. This method returns the lower triangular matrix L, the upper triangular matrix U, and a permutation vector pv (if row permutations occur during Gaussian elimination).
• lu_decomposition_in_place: A more memory-efficient variant of lu_decomposition. Instead of returning U, it modifies the original matrix (self) in place to represent U.
• permute_rows: A utility function that applies a permutation vector pv to a matrix, enabling consistent handling of row permutations.

EDIT: APIs are updated, and explained in a seperate comment.

[CLAassistant]

All committers have signed the CLA.

[rabbull]

APIs are updated after rework, the new interfaces provided are:

• permute_rows: A utility function that applies a permutation vector pv to a matrix, enabling consistent handling of row permutations.
• partial_row_reduce_impl: An extended version of row reduce that includes an option to record the steps performed during row operations. The existing partial_row_reduce method now serves as a wrapper for this function.
• lu_decompose: Computes the LU decomposition of a matrix. This method returns a permutation vector pv, the lower triangular matrix L, and the upper triangular matrix U.

Example usage can be refered to the tests added.