# QR Decomposition without Pivoting¶

Given the matrix $$X$$ of size $$n \times p$$, the problem is to compute the QR decomposition $$X = QR$$, where

• $$Q$$ is an orthogonal matrix of size $$n \times n$$

• $$R$$ is a rectangular upper triangular matrix of size $$n \times p$$

The library requires $$n > p$$. In this case:

$\begin{split}X = QR = [Q_1, Q_2] \cdot \begin{bmatrix} R_1 \\ 0 \end{bmatrix} = Q_1 R_1\end{split}$

where the matrix $$Q_1$$ has the size $$n \times p$$ and $$R_1$$ has the size $$p \times p$$.

## Computation¶

The following computation modes are available:

## Examples¶

Batch Processing:

Online Processing:

Distributed Processing:

Note

There is no support for Java on GPU.

Batch Processing:

Online Processing:

Distributed Processing:

Batch Processing:

Online Processing:

Distributed Processing: