> In the Dictionary, I think there's no pointer to a definition of > the general case.
Not so. The general case is described twice in http://www.jsoftware.com/help/dictionary/d300.htm More generally, the phrase u . v is defined in terms of a recursive expansion by minors along the first column, as discussed below. and DET=: 2 : 'v/@,`({."1 u . v $:@minors)@.(0<{:@$) @ ,. "2' minors=: }."1 @ (1&([\.)) ----- Original Message ----- From: John Wilson <[email protected]> Date: Monday, May 25, 2009 15:03 Subject: Re: [Jprogramming] determinant of 16x15 matrix seems to hang J To: Programming forum <[email protected]> > It was inadvertent. > > In the Dictionary, I think there's no pointer to a definition of > the general > case. > /J > > ----- Original Message ----- > From: "Roger Hui" <[email protected]> > To: "Programming forum" <[email protected]> > Sent: Monday, May 25, 2009 1:53 PM > Subject: Re: [Jprogramming] determinant of 16x15 matrix seems to > hang J > > > > It just takes a long time. > > > > Do you really mean to compute the determinant > > of a non-square matrix? For a square matrix > > the interpreter uses fast (n^3) special code; > > for a non-square matrix, it uses the general !n code. > > e.g. > > > > 6!:2 '-/ .* m' [ m=: 8 8 ?...@$ 10 > > 9.24699e_5 > > 6!:2 '-/ .* m' [ m=: 8 7 ?...@$ 10 > > 0.0602373 > > > > 6!:2 '-/ .* m' [ m=: 9 9 ?...@$ 10 > > 5.81079e_5 > > 6!:2 '-/ .* m' [ m=: 9 8 ?...@$ 10 > > 0.602606 > > > > 6!:2 '-/ .* m' [ m=: 10 10 ?...@$ 10 > > 0.000100013 > > 6!:2 '-/ .* m' [ m=: 10 9 ?...@$ 10 > > 5.56612 > > > > 6!:2 '-/ .* m' [ m=: 11 11 ?...@$ 10 > > 6.70476e_5 > > 6!:2 '-/ .* m' [ m=: 11 10 ?...@$ 10 > > 61.0679 > > > > > > > > ----- Original Message ----- > > From: John Wilson <[email protected]> > > Date: Monday, May 25, 2009 10:33 > > Subject: [Jprogramming] determinant of 16x15 matrix seems to > hang J > > To: Programming forum <[email protected]> > > > >> This appears to hang J. > >> > >> M =: ? 16 15$10 > >> det =: -/ . * > >> N =: det M ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
