# jax.scipy.linalg.qr¶

`jax.scipy.linalg.``qr`(a, overwrite_a=False, lwork=None, mode='full', pivoting=False, check_finite=True)[source]

Compute QR decomposition of a matrix.

LAX-backend implementation of `qr()`.

Original docstring below.

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

• overwrite_a (bool, optional) – Whether data in a is overwritten (may improve performance if overwrite_a is set to True by reusing the existing input data structure rather than creating a new one.)

• lwork (int, optional) – Work array size, lwork >= a.shape. If None or -1, an optimal size is computed.

• mode ({'full', 'r', 'economic', 'raw'}, optional) – Determines what information is to be returned: either both Q and R (‘full’, default), only R (‘r’) or both Q and R but computed in economy-size (‘economic’, see Notes). The final option ‘raw’ (added in SciPy 0.11) makes the function return two matrices (Q, TAU) in the internal format used by LAPACK.

• pivoting (bool, optional) – Whether or not factorization should include pivoting for rank-revealing qr decomposition. If pivoting, compute the decomposition `A P = Q R` as above, but where P is chosen such that the diagonal of R is non-increasing.

• 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

• 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)`.

• P (int ndarray) – Of shape (N,) for `pivoting=True`. Not returned if `pivoting=False`.