dpnp.linalg.qr

dpnp.linalg.qr(a, mode='reduced')[source]

Compute the qr factorization of a matrix.

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

For full documentation refer to numpy.linalg.qr.

Parameters:

  • a ({dpnp.ndarray, usm_ndarray}) -- The input array with the dimensionality of at least 2.

  • mode ({"reduced", "complete", "r", "raw"}, optional) --

    If K = min(M, N), then

    • "reduced" : returns Q, R with dimensions (…, M, K), (…, K, N)

    • "complete" : returns Q, R with dimensions (…, M, M), (…, M, N)

    • "r" : returns R only with dimensions (…, K, N)

    • "raw" : returns h, tau with dimensions (…, N, M), (…, K,)

    Default: "reduced".

Returns:

  • When mode is "reduced" or "complete", the result will be a namedtuple with

  • the attributes Q and R.

  • Q (dpnp.ndarray) -- A matrix with orthonormal columns. When mode = "complete" the result is an orthogonal/unitary matrix depending on whether or not a is real/complex. The determinant may be either +/- 1 in that case. In case the number of dimensions in the input array is greater than 2 then a stack of the matrices with above properties is returned.

  • R (dpnp.ndarray) -- The upper-triangular matrix or a stack of upper-triangular matrices if the number of dimensions in the input array is greater than 2.

  • (h, tau) (tuple of dpnp.ndarray) -- The h array contains the Householder reflectors that generate Q along with R. The tau array contains scaling factors for the reflectors.

Examples

>>> import dpnp as np
>>> a = np.random.randn(9, 6)
>>> Q, R = np.linalg.qr(a)
>>> np.allclose(a, np.dot(Q, R))  # a does equal QR
array([ True])
>>> R2 = np.linalg.qr(a, mode='r')
>>> np.allclose(R, R2)  # mode='r' returns the same R as mode='full'
array([ True])
>>> a = np.random.normal(size=(3, 2, 2)) # Stack of 2 x 2 matrices as input
>>> Q, R = np.linalg.qr(a)
>>> Q.shape
(3, 2, 2)
>>> R.shape
(3, 2, 2)
>>> np.allclose(a, np.matmul(Q, R))
array([ True])