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: