Robert O'Boyle wrote:

> It could be that the Rarg matrix in the second situation is close to
> singular and that both languages are giving non-sensical results but I am
> not sure. Could anyone explain the difference between what %. And Domino
> are
> doing?

I think they are doing the same thing and that the matrix is bad.

In J, x %. y minimizes the norm of x - y mp x %. y.  If we do the
calculation for both results (note: data will wrap):

Rarg=:11 3 $ 0.273501 33.6993  _15.6811 0.505944 50.5733  _10.6639
0.700719 52.4143  _6.45982 0.796474 47.0372    _4.393 0.861592 39.7353 
_2.98746 0.905876 32.2908  _2.03162 0.935991 25.5423  _1.38161  0.95647
19.8067 _0.939561 0.970398 15.1266 _0.638949 0.979869 11.4137 _0.434517 
0.98631 8.52817 _0.295493

Larg2=:0.0387946 0.0263726 0.0159726 0.0108677 0.00739584 0.00503257
0.00340808 0.00233151 0.00157923 0.00107516 0.000729004

div2=:_0.000007023400888 2.333431673e_7 _0.002473197439

mp=:+/ .*

x=:Larg2
y=:Rarg

d=:x-y mp x %.y
d2=:x-y mp div2

   +/ d*+d
3.33231e_10
   +/ d2*+d2
5.26306e_10

Both of these are effectively zero when doing matrix calculations of this
size.

Best wishes,

John Randall


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