Eigenvalues experiment

; Aims to emonstrate the eigenvectors of a 2x2 matrix

; Created by Francisco Restivo, frestivo@gmail.com

globals [tr det delta EV1 EV2 alpha x0 y0 x1 y1]

to go
 clear-all
 crt 128 ; 128 turtles, for 128 unit vectors
 set tr A11 + A22
 set det A11 * A22 - A12 * A21
 set delta tr * tr - 4 * det
 set EV1 0
 set EV2 0
 if delta >= 0 [
   set delta sqrt (delta)
   set EV1 (tr + delta) / 2
   set EV2 (tr - delta) / 2 ]
 ask turtles [
   pd
   set shape "circle"
   set size 0
   set color green + who / 28
   set alpha 360 * who / 128
   set x0 Scale * cos alpha
   set y0 Scale * sin alpha
   setxy x0 y0
   setxy 0 0
   set x1 A11 * x0 + A12 * y0
   set y1 A21 * x0 + A22 * y0
   setxy x1 y1 ]
end