LU decomposition with partial pivoting.
Computes the matrix decomposition:\[P.A = L.U\]
where \(P\) is a permutation of the rows of \(A\), \(L\) is a lower-triangular matrix with unit-diagonal elements, and \(U\) is an upper-triangular matrix.
- Return type:
(lu, pivots, permutation).
luis a batch of matrices with the same shape and dtype as
xcontaining the \(L\) matrix in its lower triangle and the \(U\) matrix in its upper triangle. The (unit) diagonal elements of \(L\) are not represented explicitly.
pivotsis an int32 array with shape
[..., min(m, n)]representing a sequence of row swaps that should be performed on \(A\).
permutationis an alternative representation of the sequence of row swaps as a permutation, represented as an int32 array with shape