... !define derivatives of b_{k+1,1},b_{k+1,2},b_{k+1,3},c_{k+1} wrt th(k) for k=0,...,n-1 do k=0,n-1 dbdth(k+1,k,1) = dsin(psi(k))*dcos(th(k))*dcos(th(k+1))+dsin(th(k))*dsin(psi(k+1))*dsin(th(k+1)) dbdth(k+1,k,2) = dcos(psi(k))*dcos(th(k))*dcos(th(k+1))+dsin(th(k))*dcos(psi(k+1))*dsin(th(k+1)) dbdth(k+1,k,3) = dcos(psi(k))*dcos(th(k))*dsin(psi(k+1))*dsin(th(k+1)) & -dsin(psi(k))*dcos(th(k))*dcos(psi(k+1))*dsin(th(k+1)) dcdth(k+1,k) = dcos(psi(k))*dcos(th(k))*dcos(psi(k+1))*dsin(th(k+1)) & +dsin(psi(k))*dcos(th(k))*dsin(psi(k+1))*dsin(th(k+1)) & -dsin(th(k))*dcos(th(k+1)) enddo !define the derivative of R_{k} wrt psi(k) for k=1,...,n do k=1,n dRdpsi(k,k,1,1) = (1d0-h(k)*h(k)*b(k,1)*b(k,1))*dcdpsi(k,k)+2d0*h(k)*b(k,1)*dbdpsi(k,k,1)dRdpsi(k,k,1,2) = h(k)*b(k,1)*dbdpsi(k,k,2)+h(k)*b(k,2)*dbdpsi(k,k,1)-h(k)*h(k)*b(k,1)*b(k,2)*dcdpsi(k,k)-dbdpsi(k,k,3) dRdpsi(k,k,1,3) = h(k)*b(k,1)*dbdpsi(k,k,3)+h(k)*b(k,3)*dbdpsi(k,k,1)-h(k)*h(k)*b(k,1)*b(k,3)*dcdpsi(k,k)+dbdpsi(k,k,2) dRdpsi(k,k,2,1) = h(k)*b(k,1)*dbdpsi(k,k,2)+h(k)*b(k,2)*dbdpsi(k,k,1)-h(k)*h(k)*b(k,1)*b(k,2)*dcdpsi(k,k)+dbdpsi(k,k,3) dRdpsi(k,k,2,2) = (1d0-h(k)*h(k)*b(k,2)*b(k,2))*dcdpsi(k,k)+2d0*h(k)*b(k,2)*dbdpsi(k,k,2) dRdpsi(k,k,2,3) = h(k)*b(k,2)*dbdpsi(k,k,3)+h(k)*b(k,3)*dbdpsi(k,k,2)-h(k)*h(k)*b(k,2)*b(k,3)*dcdth(k,k)-dbdpsi(k,k,1) dRdpsi(k,k,3,1) = h(k)*b(k,1)*dbdpsi(k,k,3)+h(k)*b(k,3)*dbdpsi(k,k,1)-h(k)*h(k)*b(k,1)*b(k,3)*dcdth(k,k)-dbdpsi(k,k,2) dRdpsi(k,k,3,2) = h(k)*b(k,2)*dbdpsi(k,k,3)+h(k)*b(k,3)*dbdpsi(k,k,2)-h(k)*h(k)*b(k,2)*b(k,3)*dcdth(k,k)+dbdpsi(k,k,1)dRdpsi(k,k,3,3) = (1d0-h(k)*h(k)*b(k,3)*b(k,3))*dcdpsi(k,k)+2d0*h(k)*b(k,3)*dbdpsi(k,k,3) enddo !define the derivative of R_{k+1} wrt psi(k) for k=0,...,n-1 do k=0,n-1 dRdpsi(k+1,k,1,1) = (1d0-h(k+1)*h(k+1)*b(k+1,1)*b(k+1,1))*dcdpsi(k+1,k)+2d0*h(k+1)*b(k+1,1)*dbdpsi(k+1,k,1) dRdpsi(k+1,k,1,2) = h(k+1)*b(k+1,1)*dbdpsi(k+1,k,2)+h(k+1)*b(k+1,2)*dbdpsi(k+1,k,1) & -h(k+1)*h(k+1)*b(k+1,1)*b(k+1,2)*dcdpsi(k+1,k)-dbdpsi(k+1,k,3) dRdpsi(k+1,k,1,3) = h(k+1)*b(k+1,1)*dbdpsi(k+1,k,3)+h(k+1)*b(k+1,3)*dbdpsi(k+1,k,1) &-h(k+1)*h(k+1)*b(k+1,1)*b(k+1,3)*dcdpsi(k+1,k)+dbdpsi(k+1,k,2) dRdpsi(k+1,k,2,1) = h(k+1)*b(k+1,1)*dbdpsi(k+1,k,2)+h(k+1)*b(k+1,2)*dbdpsi(k+1,k,1) & -h(k+1)*h(k+1)*b(k+1,1)*b(k+1,2)*dcdpsi(k+1,k)+dbdpsi(k+1,k,3) dRdpsi(k+1,k,2,2) = (1d0-h(k+1)*h(k+1)*b(k+1,2)*b(k+1,2))*dcdpsi(k+1,k)+2d0*h(k+1)*b(k+1,2)*dbdpsi(k+1,k,2) dRdpsi(k+1,k,2,3) = h(k+1)*b(k+1,2)*dbdpsi(k+1,k,3)+h(k+1)*b(k+1,3)*dbdpsi(k+1,k,2) & -h(k+1)*h(k+1)*b(k+1,2)*b(k+1,3)*dcdpsi(k+1,k)-dbdpsi(k+1,k,1) dRdpsi(k+1,k,3,1) = h(k+1)*b(k+1,1)*dbdpsi(k+1,k,3)+h(k+1)*b(k+1,3)*dbdpsi(k+1,k,1) & -h(k+1)*h(k+1)*b(k+1,1)*b(k+1,3)*dcdpsi(k+1,k)-dbdpsi(k+1,k,2)dRdpsi(k+1,k,3,2) = h(k+1)*b(k+1,2)*dbdpsi(k+1,k,3)+h(k+1)*b(k+1,3)*dbdpsi(k+1,k,2) & -h(k+1)*h(k+1)*b(k+1,2)*b(k+1,3)*dcdpsi(k+1,k)+dbdpsi(k+1,k,1) dRdpsi(k+1,k,3,3) = (1d0-h(k+1)*h(k+1)*b(k+1,3)*b(k+1,3))*dcdpsi(k+1,k)+2d0*h(k+1)*b(k+1,3)*dbdpsi(k+1,k,3) enddo !define the derivative of R_{k} wrt th(k) for k=1,...,n ...