maxframe.tensor.linalg.lu#

maxframe.tensor.linalg.lu(a)[source]#

LU decomposition

The decomposition is::: A = P L U

where P is a permutation matrix, L lower triangular with unit diagonal elements, and U upper triangular.

Parameters:

a ((M, N) array_like) – Array to decompose

Returns:

p ((M, M) ndarray) – Permutation matrix
l ((M, K) ndarray) – Lower triangular or trapezoidal matrix with unit diagonal. K = min(M, N)
u ((K, N) ndarray) – Upper triangular or trapezoidal matrix

Examples

>>> import maxframe.tensor as mt

>>> A = mt.array([[1,2],[2,3]])
>>> A.execute()
array([[ 1,  2],
       [ 2,  3]])
>>> P, L, U = mt.linalg.lu(A)
>>> P.execute()
array([[ 0,  1],
       [ 1,  0]])
>>> L.execute()
array([[ 1,  0],
       [ 0.5,  1]])
>>> U.execute()
array([[ 2,  3],
       [ 0,  0.5]])
>>> mt.dot(P.dot(L), U).execute() # verify that PL * U = A
array([[ 1,  2],
       [ 2,  3]])