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
