Re: [Rd] transpose of complex matrices in R
Robin Hankin wrote:
Hello everybody
When one is working with complex matrices, transpose very nearly
always means
*Hermitian* transpose, that is, A[i,j] - Conj(A[j,i]).
One often writes A^* for the Hermitian transpose.
I have only once seen a real-life case
where transposition does not occur simultaneously with complex conjugation.
And I'm not 100% sure that that wasn't a mistake.
Matlab and Octave sort of recognize this, as A' means the Hermitian
transpose of A.
In R, this issue makes t(), crossprod(), and tcrossprod() pretty much
useless to me.
OK, so what to do? I have several options:
1. define functions myt(), and mycrossprod() to get round the problem:
myt - function(x){t(Conj(x))}
2. Try to redefine t.default():
t.default - function(x){if(is.complex(x)){return(base::t(Conj(x)))}
else {return(base::t(x))}}
(This fails because of infinite recursion, but I don't quite understand
why).
You should call base::t.default, not base::t. Then this will work. The
same solution fixes the one below, though you won't even need the base::
prefix on t.default.
Duncan Murdoch
3. Try to define a t.complex() function:
t.complex - function(x){t(Conj(x))}
(also fails because of recursion)
4. Try a kludgy workaround:
t.complex - function(x){t(Re(x)) - 1i*t(Im(x))}
Solution 1 is not good because it's easy to forget to use myt() rather
than t()
and it does not seem to be good OO practice.
As Martin Maechler points out, solution 2 (even if it worked as desired)
would break the code of everyone who writes a myt() function.
Solution 3 fails and solution 4 is kludgy and inefficient.
Does anyone have any better ideas?
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Re: [Rd] transpose of complex matrices in R
Hello Peter thanks for this. On 07/30/2010 11:01 AM, peter dalgaard wrote: What's wrong with t.complex- function(x) t.default(Conj(x)) M- matrix(rnorm(4)+1i*rnorm(4),2) M It's not going to help with the cross products though. As a general matter, in my book, transpose is transpose and the other thing is called adjoint. So another option is to use adj(A) for what you call myt(A), and then just remember to transcribe A^* to adj(A). That's a good way to think about it. Perhaps this is one case where thinking too literally in terms of OO-style programming [ie wanting to overload t()] is harmful. I didn't realize until an email just now that octave has a transpose() function which does *not* take the complex conjugate. You live and learn! I forget whether the cross products A^*A and AA^* have any special names in abstract linear algebra/functional analysis. Well they sort of do. I'd call A^* %*% A an inner product, or possibly an Hermitian inner product. Would it hurt to redefine crossprod(A,B) to mean t(Conj(A)) %*% B and tcrossprod(A,B) to A %*% t(Conj(B))? (we could include an optional 'Hermitian' argument to crossprod() in the complex case, defaulting to TRUE?) rksh -- Robin K. S. Hankin Uncertainty Analyst University of Cambridge 19 Silver Street Cambridge CB3 9EP 01223-764877 __ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
[Rd] transpose of complex matrices in R
When one is working with complex matrices, transpose very nearly always means *Hermitian* transpose, that is, A[i,j] - Conj(A[j,i]). One often writes A^* for the Hermitian transpose. I believe that I have actually (many years ago) used a true complex transpose, but I agree that one more often needs the conjugate transpose. I would not be in favour of changing t() because I feel transpose means transpose -- certainly where there are non-square matrices. But I'd be in favour of adding a conjt() (or some similar function) that does the conjugate transpose efficiently. JN __ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
Re: [Rd] transpose of complex matrices in R
Hi,
On 30.07.2010, at 11:35, Robin Hankin wrote:
3. Try to define a t.complex() function:
t.complex - function(x){t(Conj(x))}
(also fails because of recursion)
Try this version:
t.complex - function(x) {
xx - Conj(x)
.Internal(t.default(xx))
}
You get infinite recursion in your example because you keep dispatching on the
(complex) result of Conj(x) in t(Conj(x)). I'm not sure if the use of .Internal
in user code is sanctioned but it does work for me.
Cheers,
Olaf
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Re: [Rd] transpose of complex matrices in R
-Original Message-
From: r-devel-boun...@r-project.org
[mailto:r-devel-boun...@r-project.org] On Behalf Of Olaf Mersmann
Sent: Friday, July 30, 2010 3:01 AM
To: Robin Hankin
Cc: R-devel@r-project.org; Martin Maechler
Subject: Re: [Rd] transpose of complex matrices in R
Hi,
On 30.07.2010, at 11:35, Robin Hankin wrote:
3. Try to define a t.complex() function:
t.complex - function(x){t(Conj(x))}
(also fails because of recursion)
The NextMethod() function exists to avoid
this sort of infinite recursion in S3 methods.
E.g.,
t.complex - function(x)NextMethod(Conj(x))
or
t.complex-function(x)Conj(NextMethod(x))
would do what you wanted.
Using NextMethod means you cannot call this as
t.complex(nonComplexMatrix)
but I think that is generally a good thing.
Bill Dunlap
Spotfire, TIBCO Software
wdunlap tibco.com
Try this version:
t.complex - function(x) {
xx - Conj(x)
.Internal(t.default(xx))
}
You get infinite recursion in your example because you keep
dispatching on the (complex) result of Conj(x) in t(Conj(x)).
I'm not sure if the use of .Internal in user code is
sanctioned but it does work for me.
Cheers,
Olaf
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