jacprojs.m

sba, a C/C++ package for generic sparse bundle adjustment is almost invariably used as the last step

function jst=jacprojS(rt, xyz, a)
% symbolic projection function Jacobian
  a1=a(1); a2=a(2); a4=a(4); %a3=a(3); a5=a(5);
  qr2=rt(1); qr3=rt(2); qr4=rt(3);
  t1=rt(4); t2=rt(5); t3=rt(6);
  X=xyz(1); Y=xyz(2); Z=xyz(3);

  qr1=sqrt(1-(qr2^2+qr3^2+qr4^2));
  
  jst=[-(((-2*qr1*Z-2*qr1*t3)*qr4+(-2*qr1*Y-2*t2*qr1)*qr3+((2*t2-2*Y)*qr4+(2*Z-2*t3)*qr3)*qr2)*a2+(-Z-t3+(2*t3+2*Z)*qr4^2+(2*qr4*Y-2*t1*qr1+2*qr3*t3)*qr3+(2*t1*qr4-2*qr1*Y+2*qr2*Z)*qr2)*a1)/(-Z-t3+(2*qr1*X-2*qr4*Y+2*qr3*Z)*qr3+(-2*qr4*X-2*qr1*Y+2*qr2*Z)*qr2)^2,...
  ((Z+t3+(-2*t3-2*Z)*qr4^2+(-2*qr1*X-2*t2*qr4-2*qr3*Z)*qr3+(-2*qr4*X-2*t2*qr1-2*t3*qr2)*qr2)*a2+((-2*qr1*Z-2*qr1*t3)*qr4+(-2*t1+2*X)*qr4*qr3+(-2*t1*qr1-2*qr1*X+(2*t3-2*Z)*qr3)*qr2)*a1)/(-Z-t3+(2*qr1*X-2*qr4*Y+2*qr3*Z)*qr3+(-2*qr4*X-2*qr1*Y+2*qr2*Z)*qr2)^2,...
  ((-t2-Y+(-2*qr1*X+2*qr4*Y)*qr4+(2*qr4*t3+(2*t2+2*Y)*qr3)*qr3+(-2*qr1*t3+2*qr3*X+2*t2*qr2)*qr2)*a2+(-X-t1+(2*qr1*Y+2*qr4*X)*qr4+(2*qr1*t3+2*t1*qr3)*qr3+(2*qr3*Y+2*qr4*t3+(2*t1+2*X)*qr2)*qr2)*a1)/(-Z-t3+(2*qr1*X-2*qr4*Y+2*qr3*Z)*qr3+(-2*qr4*X-2*qr1*Y+2*qr2*Z)*qr2)^2,...
  2*a4*((qr1*Z+qr1*t3)*qr4+(qr1*Y+t2*qr1)*qr3+((Y-t2)*qr4+(t3-Z)*qr3)*qr2)/(-Z-t3+(2*qr1*X-2*qr4*Y+2*qr3*Z)*qr3+(-2*qr4*X-2*qr1*Y+2*qr2*Z)*qr2)^2,...
  -a4*(-Z-t3+(2*Z+2*t3)*qr4^2+(2*qr1*X+2*t2*qr4+2*qr3*Z)*qr3+(2*qr4*X+2*t2*qr1+2*t3*qr2)*qr2)/(-Z-t3+(2*qr1*X-2*qr4*Y+2*qr3*Z)*qr3+(-2*qr4*X-2*qr1*Y+2*qr2*Z)*qr2)^2,...
  a4*(-t2-Y+(-2*qr1*X+2*qr4*Y)*qr4+(2*qr4*t3+(2*t2+2*Y)*qr3)*qr3+(-2*qr1*t3+2*qr3*X+2*t2*qr2)*qr2)/(-Z-t3+(2*qr1*X-2*qr4*Y+2*qr3*Z)*qr3+(-2*qr4*X-2*qr1*Y+2*qr2*Z)*qr2)^2];