# mxnet.np.linalg.qr¶

qr(a, mode='reduced')

Compute the qr factorization of a matrix a. Factor the matrix a as qr, where q is orthonormal and r is upper-triangular.

Parameters
• a ((.., M, N) ndarray) – Matrix or stack of matrices to be qr factored.

• mode ({‘reduced’, ‘complete’, ‘r’, ‘raw’, ‘full’, ‘economic’}, optional) – Only default mode, ‘reduced’, is implemented. If K = min(M, N), then * ‘reduced’ : returns q, r with dimensions (M, K), (K, N) (default)

Returns

• q ((…, M, K) ndarray) – A matrix or stack of matrices with K orthonormal columns, with K = min(M, N).

• r ((…, K, N) ndarray) – A matrix or stack of upper triangular matrices.

Raises

MXNetError – If factoring fails.

Notes

Currently, the gradient for the QR factorization is well-defined only when the first K columns of the input matrix are linearly independent.

Examples

>>> from mxnet import np
>>> a = np.random.uniform(-10, 10, (2, 2))
>>> q, r = np.linalg.qr(a)
>>> q
array([[-0.22121978, -0.97522414],
[-0.97522414,  0.22121954]])
>>> r
array([[-4.4131265 , -7.1255064 ],
[ 0.        , -0.28771925]])
>>> a = np.random.uniform(-10, 10, (2, 3))
>>> q, r = np.linalg.qr(a)
>>> q
array([[-0.28376842, -0.9588929 ],
[-0.9588929 ,  0.28376836]])
>>> r
array([[-7.242763  , -0.5673361 , -2.624416  ],
[ 0.        , -7.297918  , -0.15949416]])
>>> a = np.random.uniform(-10, 10, (3, 2))
>>> q, r = np.linalg.qr(a)
>>> q
array([[-0.34515655,  0.10919492],
[ 0.14765628, -0.97452265],
[-0.92685735, -0.19591334]])
>>> r
array([[-8.453794,  8.4175  ],
[ 0.      ,  5.430561]])