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:

• Batch and Online Processing
• Distributed Processing

Examples

C++ (CPU)Python*

Batch Processing:

• qr_dense_batch.cpp

Online Processing:

• qr_dense_online.cpp

Distributed Processing:

• qr_dense_distr.cpp