Dear Roger:
Thanks for you two replies. Yes, I understand now the Vocabulary comment
that the domain of 128!:0 and that of %. are the same. I knew that %. (and
APL before it) could perform left-inverses of matrices of full-column rank.
But I think more as a statistician than as a J programmer. According to J
standards, the Vocabulary offers a sufficient explanation.
My interest in the QR decompositon is to code an efficient eigen
decomposition. I have programmed the Jacobi method; but I'd like a faster
and more accurate routine. Are you aware of good J code for the eigen (or
singular value decomposition) problem?
Sincerely,
Leigh
Leigh Joseph Halliwell, FCAS, MAAA
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L. J. Halliwell, LLC
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-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Roger Hui
Sent: Wednesday, March 25, 2009 11:25 AM
To: Programming forum
Subject: Re: [Jprogramming] QR Decomposition
I should have said that matrix inverse accepts most
"tall" matrices and most square matrices, and rejects
"wide" matrices.
The reason is that the argument matrix must be
non-singular, i.e. having linearly independent columns.
A matrix can have at most {:$y independent columns,
so no wide matrix can qualify. "Most" because most tall
and most square matrices are non-singular.
----- Original Message -----
From: Roger Hui <[email protected]>
Date: Tuesday, March 24, 2009 23:04
Subject: Re: [Jprogramming] QR Decomposition
To: Programming forum <[email protected]>
> The documentation does say that the argument y must be
> in the domain of matrix inverse (%.). Matrix inverse
> accepts "tall" matrices and rejects "wide" matrices.
> (And of course accepts most square matrices.)
>
>
>
> ----- Original Message -----
> From: "Leigh J. Halliwell" <[email protected]>
> Date: Monday, March 23, 2009 16:05
> Subject: [Jprogramming] QR Decomposition
> To: 'Programming forum' <[email protected]>
>
> > Dear J Forum:
> >
> > I've been experimenting with 128!:0 (QR matrix decomposition)
> as
> > follows:
> > B =. |: A =. ? 4 7 $10
> > $ each B;A
> > ----T---+
> > |7 4|4 7|
> > L---+----
> > $ each 128!:0 A
> > |length error
> > | $each 128!:0 A
> > $ each 128!:0 B
> > ----T---+
> > |7 4|4 4|
> > L---+----
> >
> > This suggests that the row dimension of the argument must be
> > greater than or
> > equal to the column dimension, and hence that T(Q) mmult Q is
> > the identity
> > matrix (orthogonal/Hermetian). If so, then noting this in
> > the Vocabulary
> > would be helpful.
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