| Re: Matrix algebra and index order, A # B vs A ## B [message #79751 is a reply to message #79654] |
Mon, 26 March 2012 06:45  |
Mats Löfdahl
Messages: 263
Registered: January 2012
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Senior Member |
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On Monday, March 26, 2012 3:00:05 PM UTC+2, David Fanning wrote:
> Mats Löfdahl writes:
>
>> IDL has two operators for matrix multiplication, # and ##.
>> The former assumes the matrices involved have colum number as
>> the first index and row number as the second, i.e., A_{rc} =
>> A[c,r] with mathematics on the LHS and IDL on the RHS. The
>> latter operator makes the opposite assumption, A_{rc} = A[r,c].
>>
>> I believe much headache can be avoided if one chooses one
>> notation and sticks with it. If it were only me, I'd choose
>> the A_{rc} = A[r,c] notation. But it isn't only me, because
>> I like to take advantage of IDL routines written by others.
>> So, has there emerged some kind of consensus among influential
>> IDL programmers (those that write publicly available
>> routines that are widely used - thank you BTW!) for
>> which convention to use?
>
> Yes, the consensus that has emerged is that no operation
> is more fraught with ambiguity, anguish, and frustration
> than trying to translate a section of linear algebra code
> from a paper or textbook (say on Principle Components
> Analysis) to IDL than almost anything you can imagine!
> It's like practicing backwards writing in the mirror.
>
> And, of course, while you are doing it you have the
> growing realization that there is no freaking way you
> are EVER going to be able to write the on-line
> documentation to explain this dog's dish of a program
> to anyone else. :-(
>
> The solution, of course, is to stick with the ##
> notation for as long as it makes sense, then throw
> in a couple of # signs whenever needed to make the
> math come out right. :-)
It's that bad? :o)
One thing that had me wondering is the documentation for Craig Markwardt's qrfac routine:
; Given an MxN matrix A (M>N), the procedure QRFAC computes the QR
; decomposition (factorization) of A. This factorization is useful
; in least squares applications solving the equation, A # x = B.
; Together with the procedure QRSOLV, this equation can be solved in
; a least squares sense.
;
; The QR factorization produces two matrices, Q and R, such that
;
; A = Q ## R
;
; where Q is orthogonal such that TRANSPOSE(Q)##Q equals the identity
; matrix, and R is upper triangular.
The ## operator for the matrix-matrix multiplications but # for matrix-vector multiplication! But then I thought this might be IDL 1D arrays being interpreted as row vectors so x # A is actually just another way of writing A ## transpose(x). And the former would be more efficient. Am I on the right track here...?
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