# mars.tensor.linalg.qr#

mars.tensor.linalg.qr(a, method='tsqr')[source]#

Compute the qr factorization of a matrix.

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

Parameters
• a (array_like, shape (M, N)) – Matrix to be factored.

• method ({'tsqr', 'sfqr'}, optional) –

method to calculate qr factorization, tsqr as default

TSQR is presented in:

A. Benson, D. Gleich, and J. Demmel. Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures. IEEE International Conference on Big Data, 2013. http://arxiv.org/abs/1301.1071

FSQR is a QR decomposition for fat and short matrix:

A = [A1, A2, A3, …], A1 may be decomposed as A1 = Q1 * R1, for A = Q * R, Q = Q1, R = [R1, R2, R3, …] where A2 = Q1 * R2, A3 = Q1 * R3, …

Returns

• q (Tensor of float or complex, optional) – 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.

• r (Tensor of float or complex, optional) – The upper-triangular matrix.

Raises

LinAlgError – If factoring fails.

Notes

For more information on the qr factorization, see for example: http://en.wikipedia.org/wiki/QR_factorization

Examples

```>>> import mars.tensor as mt
```
```>>> a = mt.random.randn(9, 6)
>>> q, r = mt.linalg.qr(a)
>>> mt.allclose(a, mt.dot(q, r)).execute()  # a does equal qr
True
```