[Rd] Inaccurate documentation for qr.R and qr.Q (PR#8347)

From: <sims_at_Princeton.EDU>
Date: Wed 23 Nov 2005 - 00:04:05 GMT


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The documentation in QR.Auxiliaries {base} states

|qr.Q| returns part or all of *Q*, the order-nrow(X) orthogonal (unitary) transformation represented by |qr|. If |complete| is |TRUE|, *Q* has |nrow(X)| columns. If |complete| is |FALSE|, *Q* has |ncol(X)| columns. When |Dvec| is specified, each column of *Q* is multiplied by the corresponding value in |Dvec|.
|qr.R| returns *R*, the upper triangular matrix such that |X == Q %*% R|.

This last statement is true if there has been no pivoting, but if the LAPACK=TRUE option is turned on or the x matrix is complex, there is likely to be pivoting, and in that case Q %*% R is X with columns reordered by the pivot. qr.X does return the original x matrix in either case, but a naive user who uses R alone (e.g. thinking that solve(R,crossprod(Q ,y)) will give ols estimates) could be misled.

Example:

> x <- matrix(c(1,2,3,3,6,8),ncol=2)
> qrlin <- qr(x)
> qrla <- qr(x,LAPACK=TRUE)
> qr.Q(qrlin) %*% qr.R(qrlin)

     [,1] [,2]

[1,]    1    3
[2,]    2    6
[3,]    3    8

> qr.Q(qrla) %*% qr.R(qrla)
[,1] [,2] [1,] 3 1

[2,] 6 2
[3,] 8 3
> qr.Q(qrla) %*% qr.R(qrla)[,qrla$pivot]

     [,1] [,2]

[1,]    1    3
[2,]    2    6
[3,]    3    8

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https://stat.ethz.ch/mailman/listinfo/r-devel Received on Wed Nov 23 11:16:45 2005

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