scipy.linalg.qr

scipy.linalg.qr(a, overwrite_a=False, lwork=None, econ=None, mode='qr')

Compute QR decomposition of a matrix.

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

Parameters :

a : array, shape (M, N)

Matrix to be decomposed

overwrite_a : boolean

Whether data in a is overwritten (may improve performance)

lwork : integer

Work array size, lwork >= a.shape[1]. If None or -1, an optimal size is computed.

econ : boolean

Whether to compute the economy-size QR decomposition, making shapes of Q and R (M, K) and (K, N) instead of (M,M) and (M,N). K=min(M,N). Default is False.

mode : {‘qr’, ‘r’}

Determines what information is to be returned: either both Q and R or only R.

Returns :

(if mode == ‘qr’) :

Q : double or complex array, shape (M, M) or (M, K) for econ==True

(for any mode) :

R : double or complex array, shape (M, N) or (K, N) for econ==True

Size K = min(M, N)

Raises LinAlgError if decomposition fails :

Notes

This is an interface to the LAPACK routines dgeqrf, zgeqrf, dorgqr, and zungqr.

Examples

>>> from scipy import random, linalg, dot
>>> a = random.randn(9, 6)
>>> q, r = linalg.qr(a)
>>> allclose(a, dot(q, r))
True
>>> q.shape, r.shape
((9, 9), (9, 6))

>>> r2 = linalg.qr(a, mode='r')
>>> allclose(r, r2)

>>> q3, r3 = linalg.qr(a, econ=True)
>>> q3.shape, r3.shape
((9, 6), (6, 6))