Overview - 2023.2 English

Vitis Libraries

Release Date
2023-12-20
Version
2023.2 English

QR decomposition, is a decomposition of a matrix \(A\) into a product of an orthogonal matrix \(Q\) and an upper triangular matrix \(R\).

This API shown a very high performance design of QRD in Versal device. For complex float 1024*256 matrix, this design could achieve 790+ GFLOPS on VCK190.

For DSP performance, near 100% sustained to peak performance is achieved.

This design structure is highly scalable. In the smaller dimension of 256*64, resources and performance are linearly related to the case of 1024*256.

QRD is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm.

\[A = Q R\]

There are several methods for actually computing the QR decomposition, such as by means of the Gram-Schmidt process, Householder transformations, or Givens rotations. Each has a number of advantages and disadvantages. For more details, please refer: QR_decomposition.

In our design, Gram-Schmidt is used.