QR decomposition

qr(a)

Compute QR decomposition of a matrix.

Calculate the decomposition A = Q R where Q is unitary/orthogonal and R upper triangular.

Parameters

a : (M, N) array_like

Matrix to be decomposed

Returns

Q : float or complex ndarray

Of shape (M, M), or (M, K) for mode='economic'. Not returned if mode='r'.

R : float or complex ndarray

Of shape (M, N), or (K, N) for mode='economic'. K = min(M, N).

Examples:

a = array([[12, -51,   4],[6, 167, -68],[-4,  24, -41]])
q,r = np.linalg.qr(a)
print q
print r

Result:

>>> run script...
array([[-0.857142857142857, 0.3942857142857143, -0.3314285714285714]
      [-0.42857142857142855, -0.9028571428571428, 0.03428571428571431]
      [0.2857142857142857, -0.17142857142857143, -0.9428571428571428]])
array([[-14.0, -21.000000000000004, 14.0]
      [0.0, -175.0, 69.99999999999999]
      [0.0, 0.0, 35.0]])