> NB. Creat a rotation vector from -n/2 ... 0 ... n/2 Try i: -: y
On Tue, Dec 22, 2015 at 7:50 PM, Richard Donovan <rsdono...@hotmail.com> wrote: > Thanks Thomas, works very well! > > > From: tmcguir...@gmail.com > > Date: Tue, 22 Dec 2015 12:14:31 -0500 > > To: programm...@jsoftware.com > > Subject: Re: [Jprogramming] Magic squares > > > > I haven't tried this in a while but here is one method from an APL book > > transcribed into J > > > > NB. Magic Squares the APL/J way > > NB. From APL An Interactive Approach by Gilman and Rose > > NB. > > NB. Problem 19 page 177 > > NB. > > NB. A magic square of order n made up of the integers from > > NB. 1 through n. > > NB. > > NB. In creating squares of odd order you can use a rotation > > NB. vector constructed from n successive integers with 0 in > > NB. the middle then using the vector to control the rotation > > NB. of the rows and columns of a matrix created with > > NB. successive integers (in J i. n n) > > > > NB. rotr - this uses the rotate operator but sets it to rotate > > NB. an individual row. Otherwise it will try to rotate > > NB. the rows in the matrix as a whole interchanging full > > NB. rows rather than shifting the element in a row and > > NB. leaving the rows in place > > rotr =: |."0 1 > > > > NB. rotc - rotate the elements in their respective columns. > > NB. there is no way to tell J to specifically operate on > > NB. the columns individually so you need to use the > > NB. transpose op. (|:) to turn the columns into rows by > > NB. using the &. operator it will transpose, run the rotate > > NB. then transpose back > > rotc =: |."0 1&.|: > > > > > > NB. MS - magic square routine no bounds check just input an > > NB. odd number greater than or equal to 3 > > > > MS =: 3 : 0 > > NB. Create an initial square matrix order n of numbers 1 to n > > z =. 1 + i. y,y > > > > NB. Creat a rotation vector from -n/2 ... 0 ... n/2 > > q =. ( - (<. 0.5 * y))+ i.y > > > > NB. rotate the rows of the matrix my q then rotate the columns > > NB. of the answer by q. You will get a new matrix that is a > > NB. magic square > > z1 =. q rotc q rotr z > > ) > > > > Tom McGuire > > > > On Dec 22, 2015, at 9:44 AM, Richard Donovan <rsdono...@hotmail.com> > wrote: > > > > > Is there a J routine to construct magic squares of side n? > > > > > > Thanks in advance. > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
