LU decomposition

lu(a)

Compute pivoted LU decomposition of a matrix.

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, M) array_like

Array to decompose

permute_l : bool, optional

Perform the multiplication P*L (Default: do not permute)

overwrite_a : bool, optional

Whether to overwrite data in a (may improve performance)

check_finite : bool, optional

Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns

p : (M, M) ndarray

Permutation matrix

l : (M, M) ndarray

Lower triangular or trapezoidal matrix with unit diagonal.

u : (M, M) ndarray

Upper triangular or trapezoidal matrix

Examples:

a = array([[1,3,5],[2,4,7],[1,1,0]])
p,l,u = np.linalg.lu(a)
print p
print l
print u

Result:

>>> run script...
array([[0.0, 1.0, 0.0]
      [1.0, 0.0, 0.0]
      [0.0, 0.0, 1.0]])
array([[1.0, 0.0, 0.0]
      [0.5, 1.0, 0.0]
      [0.5, -1.0, 1.0]])
array([[2.0, 4.0, 7.0]
      [0.0, 1.0, 1.5]
      [0.0, 0.0, -2.0]])