On Nov 20, 2007 7:30 AM, Viktor Cerovski <[EMAIL PROTECTED]> wrote:
> 2) Gramm-Schmidt orthonormalization:
> (in this example I couldn't find an elegant J code without reduce/fold)
I am going to rephrase your code, since email seems to have mangled it:
mp=: +/ .*
norm=: % %:@mp~
orth=: ] - +/@(mp * [)
GS=: monad :0
v=.,:[EMAIL PROTECTED]
i=.1
while.i<#y do.
v=.v,norm(v orth i{y)
i=.>:i
end.
v
)
You did not specify the domain of any of this, but since GS is usually
for numeric matricies, I believe you use your others with numeric vectors
(and norm is a monad while mp and orth are dyads).
Anyways, here's another approach to GS:
GS1=: [: [EMAIL PROTECTED]/\. [EMAIL PROTECTED]:@]`_1:`]}~
(-: norm"1) GS2 mat=: ?20 20 $ 100
1
This gives you a different result from GS. To get
the result from GS, use GS1&.|. (This issue illustrates
that sets of orthogonal normal vectors spanning a vector
space are not unique.)
Or, using an adverb for this pattern;
foldf=: 2 :'[: [EMAIL PROTECTED]/\. [EMAIL PROTECTED]:@]`_1:`]}~'
GS2=: norm foldf orth
GS1 and GS2 are identical.
--
Raul
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