burn::tensor::linalg

Function lu_decomposition

pub fn lu_decomposition<B>(
    tensor: Tensor<B, 2>,
) -> (Tensor<B, 2>, Tensor<B, 1, Int>)
where
    B: Backend,
Expand description

Performs PLU decomposition of a square matrix.

The function decomposes a given square matrix A into three matrices: a permutation vector p, a lower triangular matrix L, and an upper triangular matrix U, such that PA = LU. The permutation vector p represents the row swaps made during the decomposition process. The lower triangular matrix L has ones on its diagonal and contains the multipliers used during the elimination process below the diagonal. The upper triangular matrix U contains the resulting upper triangular form of the matrix after the elimination process.

§Arguments

  • tensor - A square matrix to decompose, represented as a 2D tensor.

§Returns

A tuple containing:

  • A 2D tensor representing the combined L and U matrices.
  • A 1D tensor representing the permutation vector p.

§Panics and numerical issues

  • The function will panic if the input matrix is singular or near-singular.
  • The function will panic if the input matrix is not square.

§Performance note (synchronization / device transfers)

This function may involve multiple synchronizations and device transfers, especially when determining pivot elements and performing row swaps. This can impact performance,