# scipy.linalg.qr¶

scipy.linalg.qr(a, overwrite_a=0, 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. (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))

#### Previous topic

scipy.linalg.cho_solve

#### Next topic

scipy.linalg.schur