mirror of https://gitlab.com/QEF/q-e.git
141 lines
3.3 KiB
Fortran
141 lines
3.3 KiB
Fortran
!
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! Copyright (C) 2001 PWSCF group
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!-----------------------------------------------------------------------
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subroutine ylmr2 (lmax2, ng, g, gg, ylm)
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!-----------------------------------------------------------------------
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!
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! Real spherical harmonics ylm(G) up to l=lmax
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! lmax2 = (lmax+1)^2 is the total number of spherical harmonics
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! Numerical recursive algorithm as given in Numerical Recipes
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!
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USE kinds
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implicit none
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!
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! Input
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!
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integer :: lmax2, ng
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real(kind=DP) :: g (3, ng), gg (ng)
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!
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! Output
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!
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real(kind=DP) :: ylm (ng,lmax2)
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!
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! local variables
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!
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real(kind=DP), parameter :: pi = 3.14159265358979d0, fpi = 4.d0 * pi, &
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eps = 1.0d-9
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real(kind=DP), allocatable :: cost (:), phi (:), P(:,:,:)
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real(kind=DP) :: c, gmod
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integer :: lmax, ig, l, m, lm
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integer, external:: fact, semifact
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!
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if (ng < 1 .or. lmax2 < 1) return
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do lmax = 0, 6
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if ((lmax+1)**2 == lmax2) go to 10
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end do
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call errore (' ylmr', 'l > 6 or wrong number of Ylm required',lmax2)
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10 continue
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!
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if (lmax == 0) then
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ylm (:,1) = sqrt (1.d0 / fpi)
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return
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end if
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!
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! theta and phi are polar angles, cost = cos(theta)
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!
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allocate(cost(ng), phi(ng), P(ng,0:lmax,0:lmax) )
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do ig = 1, ng
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gmod = sqrt (gg (ig) )
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if (gmod < eps) then
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cost(ig) = 0.d0
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else
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cost(ig) = g(3,ig)/gmod
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endif
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!
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! beware the arc tan, it is defined modulo pi
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!
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if (g(1,ig) > eps) then
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phi (ig) = atan( g(2,ig)/g(1,ig) )
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else if (g(1,ig) < -1.d-9) then
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phi (ig) = atan( g(2,ig)/g(1,ig) ) + pi
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else
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phi (ig) = sign( pi/2.d0,g(2,ig) )
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end if
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enddo
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!
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! P(:,l,m), are the Legendre Polynomials (0 <= m <= l)
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!
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lm = 0
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do l = 0, lmax
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c = sqrt (dble(2*l+1) / fpi)
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if ( l == 0 ) then
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P (:,0,0) = 1.d0
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else if ( l == 1 ) then
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P (:,1,0) = cost(:)
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P (:,1,1) = -sqrt(max(0d0,1.d0-cost(:)**2))
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else
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!
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! recursion on l for P(:,l,m)
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!
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do m = 0, l - 2
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P(:,l,m) = (cost(:)*(2*l-1)*P(:,l-1,m) - (l+m-1)*P(:,l-2,m))/(l-m)
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end do
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P(:,l,l-1) = cost(:) * (2*l-1) * P(:,l-1,l-1)
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P(:,l,l) = (-1)**l * semifact(2*l-1) * (max(0.d0,1.d0-cost(:)**2))**(dble(l)/2)
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end if
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!
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! Y_lm, m = 0
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!
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lm = lm + 1
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ylm (:, lm) = c * P(:,l,0)
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!
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do m = 1, l
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!
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! Y_lm, m > 0
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!
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lm = lm + 1
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ylm (:, lm) = c * sqrt(dble(fact(l-m))/dble(fact(l+m))) * &
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sqrt(2.d0) * P(:,l,m) * cos (m*phi(:))
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!
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! Y_lm, m < 0
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!
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lm = lm + 1
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ylm (:, lm) = c * sqrt(dble(fact(l-m))/dble(fact(l+m))) * &
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sqrt(2.d0) * P(:,l,m) * sin (m*phi(:))
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end do
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end do
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!
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deallocate(cost, phi, P)
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!
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return
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end subroutine ylmr2
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integer function fact(n)
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! fact(n) = n!
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implicit none
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integer :: n, i
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fact = 1
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do i = n, 2, -1
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fact = i*fact
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end do
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return
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end function fact
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integer function semifact(n)
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! semifact(n) = n!!
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implicit none
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integer :: n, i
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semifact = 1
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do i = n, 1, -2
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semifact = i*semifact
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end do
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return
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end function semifact
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