28 48 22 %. m 0.909091 2.18182 2.9697 Istvan
2011/3/23 Ben Gorte - LR <[email protected]> > For further appreciation of the inverse of a function ^:_1 I was > looking at the dot product > > dp =: +/ . * > > With a 3x3 matrix > > ]m =: ?3 3$10 > 9 5 3 > 9 6 9 > 0 6 3 > > and a vector 1 2 3 it gives: > > m dp 1 2 3 > 28 48 21 > > Here comes the inverse: > > m dp^:_1 (28 48 21) > 1 2 3 > > Wow! But it even produces least squares solutions: > > m dp^:_1 (28 48 22) > 0.909091 2.18182 2.9697 > > Amazing :-) > > Ben > > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Linda Alvord > Sent: dinsdag 22 maart 2011 2:24 > To: 'Programming forum' > Subject: Re: [Jprogramming] Adding up digits in a long number > > > n =. <.@o. 10^50x > n > 314159265358979323846264338327950288419716939937510 > > 10#.^:_1 n > 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 > 4 1 > 9 7 1 6 9 3 9 9 3 7 5 1 0 > > 10#.10#.^:_1 n > 314159265358979323846264338327950288419716939937510 > > This is such a clear example of the power of an inverse of a function > ^:_1 > it is a shame not to stop a while and appreciate it. > > > a=:2%:3 > a > 1.73205 > > 2%:^:_1 a > 3 > 2%:2%:^:_1 a > 1.73205 > > > Linda > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
