[Rd] (PR#9623) qr.coef: permutes dimnames; inserts NA; promises

[brech at delphioutpost.com]

> From: Prof Brian Ripley <ripley at stats.ox.ac.uk>
> Date: Tue, 1 May 2007 15:01:51 +0100 (BST)
> 
> On Thu, 19 Apr 2007, brech at delphioutpost.com wrote:
> 
> > Full_Name: Christian Brechbuehler
> > Version: 2.4.1 Patched (2007-03-25 r40917)
> > OS: Linux 2.6.15-27-adm64-xeon; Ubuntu 6.06.1 LTS
> > Submission from: (NULL) (24.61.47.236)
> >
> >
> > I believe that R has a bug in that it is not
> > internally consistent, and another separate bug in the documentation.
> 
> I agree with the bug in the dimnames, and and have corrected that in 2.5.0 
> patched.

I see it in svn:

       if(!is.null(nam <- colnames(qr$qr)))
  -       rownames(coef) <- nam
  +        if(k < p) rownames(coef)[qr$pivot] <- nam
  +        else rownames(coef) <- nam
  +

Thank you!


> But I think the rest stems from the following misunderstanding:
> 
> > in math, zero times anything is zero, but in R, NA times
> > anything (even zero) is NA.  This seems somewhat inconvenient.
> 
> That just is not true.

OK, I accept that.

> Stemming from this, what R is reporting is that certain columns are not 
> used in the calculation.

OK, I understand qr.coef indicates with NA that dcrdc2 decided to
exclude the corresponding columns (because of linear dependency).

I still think the documentation is misleading -- trimming to the essence:

> > help(qr):
> >
> >   'solve.qr' is the method for 'solve' for 'qr' objects. 'qr.solve'
> >   solves systems of equations via the QR decomposition: if 'a' is a
> >   QR decomposition it is the same as 'solve.qr', but if 'a' is a
> >   rectangular matrix the QR decomposition is computed first.  Either
> >   will handle over- and under-determined systems, providing a
> >   minimal-length solution or a least-squares fit if appropriate.

(A)
'qr.solve' and 'solve.qr' will NOT handle under-determined systems.
They both perform this check:

    if (a$rank != nc) 
        stop("singular matrix 'a' in solve")

But 'qr.coef', which they call when all is well, does.

(B)
Help promises a minimal-length solution, but QR does not deliver that.

> >     > qr.coef(qr(t(1:2)), 5)
> >
> >     [1]  5 NA

> > 1*5 + 2*0 does equal 5, so this is a solution, but it is
> > NOT minimal-length.  OTOH
> >
> >     > d <- svd(t(1:2));  5 %*% d$u %*% (d$d^-1 * t(d$v))
> >          [,1] [,2]
> >     [1,]    1    2
> >
> > This *is* minimum length, and 1*1 + 2*2 == 5.
> >
> > The documentation should clarify when minimal-length solution is
> > provided.

Maybe the phrase "a minimal-length solution or" should be removed?

/Christian Brechbuehler