gputools (version 1.1)

gpuQr: Estimate the QR decomposition for a matrix

Description

gpuQR estimates the QR decomposition for a matrix using column pivoting and householder matrices. The work is done on a GPU.

Note: a rank-revealing pivoting scheme is employed, potentially resulting in pivot distinctly different from ordinary "qr".

Usage

gpuQr(x, tol = 1e-07)

Arguments

x

a matrix of floating point numbers. This is the matrix that will be decomposed into Q and R factors.

tol

a floating point value. It is used for estimating the rank of matrix x.

Value

an object of class 'qr'. This object has members qr, qraux, pivot, rank. It is meant to be identical to the output of R's base function 'qr'. From the documentation for R's 'qr' function: The attribute qr is a matrix with the same dimension as 'x'. The upper triangle contains the R of the QR decomposition. The lower triangle contains partial information to construct Q. The attribute qraux is a vector of length 'ncol(x)' contains more information to construct Q. The attribute rank is a single integer representing an estimation of the rank of input matrix x based on the results of the QR decomposition. In some cases, this rank can be wildly different from the actual rank of the matrix x and so is only an estimation. The attribute pivot contains the permutation applied to columns of x in the process of calculating the QR decomposition.

References

Bischof, C. B. and Van Loan, C. F. (1987) The WY Representation for Products of Householder Matrices SIAM J Sci. and Stat. Comp, 8, s2--s13.

Bjorck, Ake (1996) Numerical methods for least squares problems. SIAM.

Golub, Gene H. and Van Loan, C. F. (1996) Matrix Computations, Ed. 3, ch. 5.

Examples

# get some random data of any shape at all
x <- matrix(runif(25), 5, 5)
qr <- gpuQr(x)
print(qr)