ylmrot.f90

Go to the documentation of this file.

 
! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross
! This file is distributed under the terms of the GNU Lesser General Public
! License. See the file COPYING for license details.
 
!BOP
! !ROUTINE: ylmrot
! !INTERFACE:
subroutine ylmrot(p,ang,lmax,ld,d)
! !INPUT/OUTPUT PARAMETERS:
!   p    : if p=-1 then the rotation matrix is improper (in,integer)
!   ang  : Euler angles; alpha, beta, gamma (in,real(3))
!   lmax : maximum angular momentum (in,integer)
!   ld   : leading dimension (in,integer)
!   d    : complex spherical harmonic rotation matrix (out,complex(ld,*))
! !DESCRIPTION:
!   Returns the rotation matrix in the basis of complex spherical harmonics
!   given the three Euler angles, $(\alpha,\beta,\gamma)$, and the parity, $p$,
!   of the rotation. The matrix is given by the formula
!   $$ D^l_{m_1m_2}(\alpha,\beta,\gamma)=d^l_{m_1m_2}(\beta)
!    e^{-i(m_1\alpha+m_2\gamma)}, $$
!   where $d$ is the rotation matrix about the $y$-axis. For improper rotations,
!   i.e. those which are a combination of a rotation and inversion, $D$ is
!   modified with $D^l_{m_1m_2}\rightarrow(-1)^l D^l_{m_1m_2}$. See the routines
!   {\tt roteuler} and {\tt ylmroty}.
!
! !REVISION HISTORY:
!   Created December 2008 (JKD)
!EOP
!BOC
implicit none
! arguments
integer, intent(in) :: p
real(8), intent(in) :: ang(3)
integer, intent(in) :: lmax,ld
complex(8), intent(out) :: d(ld,*)
! local variables
integer l,m1,m2,lm1,lm2,n
real(8) t1
! automatic arrays
real(8) dy(ld,ld)
! generate the rotation matrix about the y-axis
call ylmroty(ang(2),lmax,ld,dy)
! apply inversion if required
if (p == -1) then
  do l=1,lmax,2
    lm1=l**2+1
    lm2=lm1+2*l
    dy(lm1:lm2,lm1:lm2)=-dy(lm1:lm2,lm1:lm2)
  end do
end if
! rotation by alpha and gamma
do l=0,lmax
  n=l*(l+1)+1
  do m1=-l,l
    lm1=n+m1
    do m2=-l,l
      lm2=n+m2
      t1=-dble(m1)*ang(1)-dble(m2)*ang(3)
      d(lm1,lm2)=dy(lm1,lm2)*cmplx(cos(t1),sin(t1),8)
    end do
  end do
end do
end subroutine
!EOC