added spherical harmonics
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IRPF90_temp/
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IRPF90_man/
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ezfio_interface.irp.f
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aux_quantities
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becke_numerical_grid
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bitmask
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cis
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cisd
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perturbation
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pseudo
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psiref_cas
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psiref_utils
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scf_utils
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selectors_cassd
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selectors_full
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selectors_utils
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single_ref_method
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tools
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dft_utils_in_r
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==========
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spher_harm
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==========
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double precision function plgndr(l,m,x)
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integer, intent(in) :: l,m
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double precision, intent(in) :: x
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BEGIN_DOC
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! associated Legenre polynom P_l,m(x). Used for the Y_lm(theta,phi)
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! Taken from https://iate.oac.uncor.edu/~mario/materia/nr/numrec/f6-8.pdf
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END_DOC
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integer :: i,ll
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double precision :: fact,pll,pmm,pmmp1,somx2
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if(m.lt.0.or.m.gt.l.or.dabs(x).gt.1.d0)then
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print*,'bad arguments in plgndr'
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pause
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endif
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pmm=1.d0
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if(m.gt.0) then
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somx2=dsqrt((1.d0-x)*(1.d0+x))
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fact=1.d0
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do i=1,m
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pmm=-pmm*fact*somx2
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fact=fact+2.d0
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enddo
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endif ! m > 0
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if(l.eq.m) then
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plgndr=pmm
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else
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pmmp1=x*(2*m+1)*pmm ! Compute P_m+1^m
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if(l.eq.m+1) then
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plgndr=pmmp1
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else ! Compute P_l^m, l> m+1
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do ll=m+2,l
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pll=(x*dble(2*ll-1)*pmmp1-dble(ll+m-1)*pmm)/(ll-m)
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pmm=pmmp1
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pmmp1=pll
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enddo
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plgndr=pll
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endif ! l.eq.m+1
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endif ! l.eq.m
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return
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end
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double precision function ortho_assoc_gaus_pol(l1,m1,l2)
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implicit none
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integer, intent(in) :: l1,m1,l2
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double precision :: fact
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if(l1.ne.l2)then
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ortho_assoc_gaus_pol= 0.d0
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else
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ortho_assoc_gaus_pol = 2.d0*fact(l1+m1) / (dble(2*l1+1)*fact(l1-m1))
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endif
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end
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@ -0,0 +1,217 @@
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program spher_harm
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implicit none
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call test_spher_harm
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! call test_cart
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! call test_brutal_spheric
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end
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subroutine test_cart
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implicit none
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include 'constants.include.F'
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double precision :: r(3),theta,phi,r_abs
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print*,''
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r = 0.d0
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r(1) = 1.d0
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r(2) = 1.d0
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call cartesian_to_spherical(r,theta,phi,r_abs)
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print*,r
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print*,phi/pi
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print*,''
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r = 0.d0
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r(1) =-1.d0
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r(2) = 1.d0
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call cartesian_to_spherical(r,theta,phi,r_abs)
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print*,r
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print*,phi/pi
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print*,''
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r = 0.d0
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r(1) =-1.d0
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r(2) =-1.d0
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call cartesian_to_spherical(r,theta,phi,r_abs)
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print*,r
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print*,phi/pi
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print*,''
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r = 0.d0
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r(1) = 1.d0
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r(2) =-1.d0
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call cartesian_to_spherical(r,theta,phi,r_abs)
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print*,r
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print*,phi/pi
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end
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subroutine test_spher_harm
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implicit none
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include 'constants.include.F'
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integer :: l1,m1,i,l2,m2,lmax
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double precision :: r(3),weight,accu_re, accu_im,accu
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double precision :: re_ylm_1, im_ylm_1,re_ylm_2, im_ylm_2
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l1 = 0
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m1 = 0
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l2 = 0
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m2 = 0
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lmax = 5
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do l1 = 0,lmax
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do m1 = -l1 ,l1
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do l2 = 0,lmax
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do m2 = -l2 ,l2
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accu_re = 0.d0
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accu_im = 0.d0
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! <l1,m1|l2,m2> = \int dOmega Y_l1,m1^* Y_l2,m2
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! = \int dOmega (re_ylm_1 -i im_ylm_1) * (re_ylm_2 +i im_ylm_2)
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! = \int dOmega (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2) +i (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
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accu = 0.d0
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do i = 1, n_points_integration_angular
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double precision :: theta,phi,r_abs
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r(1:3) = angular_quadrature_points(i,1:3)
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weight = weights_angular_points(i)
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call cartesian_to_spherical(r,theta,phi,r_abs)
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if(theta.gt.pi.or.theta.lt.0.d0)then
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print*,'pb with theta',theta
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print*,r
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endif
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if(phi.gt.2.d0*pi.or.phi.lt.0.d0)then
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print*,'pb with phi',phi/pi
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print*,r
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endif
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call spher_harm_func_r3(r,l1,m1,re_ylm_1, im_ylm_1)
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call spher_harm_func_r3(r,l2,m2,re_ylm_2, im_ylm_2)
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! call spher_harm_func_m_pos(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
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! call spher_harm_func_m_pos(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
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! call spher_harm_func_expl(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
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! call spher_harm_func_expl(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
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! call spher_harm_func_expl(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
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! call spher_harm_func_expl(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
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accu_re += weight * (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2)
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accu_im += weight * (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
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accu += weight
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write(33,'(10(F16.10,X))')phi/pi
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enddo
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if(l1.ne.l2.or.m1.ne.m2)then
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if(dabs(accu_re).gt.1.d-6.or.dabs(accu_im).gt.1.d-6)then
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print*,'pb OFF DIAG !!!!! '
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print*,'l1,m1,l2,m2',l1,m1,l2,m2
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print*,'accu_re = ',accu_re
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print*,'accu_im = ',accu_im
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endif
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endif
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if(l1==l2.and.m1==m2)then
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if(dabs(accu_re-1.d0).gt.1.d-5.or.dabs(accu_im).gt.1.d-6)then
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print*,'pb DIAG !!!!! '
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print*,'l1,m1,l2,m2',l1,m1,l2,m2
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print*,'accu_re = ',accu_re
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print*,'accu_im = ',accu_im
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endif
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endif
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enddo
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enddo
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enddo
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enddo
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double precision :: x,dx,xmax,xmin
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integer:: nx
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nx = 10000
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xmin = -5.d0
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xmax = 5.d0
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dx = (xmax - xmin)/dble(nx)
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x = xmin
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do i = 1, nx
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write(34,*)x,datan(x),dacos(x)
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x += dx
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enddo
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end
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subroutine test_brutal_spheric
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implicit none
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include 'constants.include.F'
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integer :: itheta, iphi,ntheta,nphi
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double precision :: theta_min, theta_max, dtheta,theta
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double precision :: phi_min, phi_max, dphi,phi
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double precision :: accu_re, accu_im,weight
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double precision :: re_ylm_1, im_ylm_1 ,re_ylm_2, im_ylm_2,accu
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integer :: l1,m1,i,l2,m2,lmax
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phi_min = 0.d0
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phi_max = 2.D0 * pi
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theta_min = 0.d0
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theta_max = 1.D0 * pi
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ntheta = 1000
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nphi = 1000
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dphi = (phi_max - phi_min)/dble(nphi)
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dtheta = (theta_max - theta_min)/dble(ntheta)
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lmax = 3
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do l1 = 0,lmax
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do m1 = 0 ,l1
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do l2 = 0,lmax
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do m2 = 0 ,l2
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accu_re = 0.d0
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accu_im = 0.d0
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accu = 0.d0
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theta = theta_min
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do itheta = 1, ntheta
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phi = phi_min
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do iphi = 1, nphi
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! call spher_harm_func_expl(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
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! call spher_harm_func_expl(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
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call spher_harm_func_m_pos(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
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call spher_harm_func_m_pos(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
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weight = dtheta * dphi * dsin(theta)
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accu_re += weight * (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2)
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accu_im += weight * (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
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accu += weight
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phi += dphi
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enddo
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theta += dtheta
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enddo
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print*,'l1,m1,l2,m2',l1,m1,l2,m2
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print*,'accu_re = ',accu_re
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print*,'accu_im = ',accu_im
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print*,'accu = ',accu
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if(l1.ne.l2.or.m1.ne.m2)then
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if(dabs(accu_re).gt.1.d-6.or.dabs(accu_im).gt.1.d-6)then
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print*,'pb OFF DIAG !!!!! '
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endif
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endif
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if(l1==l2.and.m1==m2)then
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if(dabs(accu_re-1.d0).gt.1.d-5.or.dabs(accu_im).gt.1.d-6)then
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print*,'pb DIAG !!!!! '
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endif
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endif
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enddo
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enddo
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enddo
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enddo
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end
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subroutine test_assoc_leg_pol
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implicit none
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BEGIN_DOC
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! TODO : Put the documentation of the program here
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END_DOC
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print *, 'Hello world'
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integer :: l1,m1,ngrid,i,l2,m2
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l1 = 0
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m1 = 0
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l2 = 2
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m2 = 0
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double precision :: x, dx,xmax,accu,xmin
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double precision :: plgndr,func_1,func_2,ortho_assoc_gaus_pol
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ngrid = 100000
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xmax = 1.d0
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xmin = -1.d0
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dx = (xmax-xmin)/dble(ngrid)
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do l2 = 0,10
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x = xmin
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accu = 0.d0
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do i = 1, ngrid
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func_1 = plgndr(l1,m1,x)
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func_2 = plgndr(l2,m2,x)
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write(33,*)x, func_1,func_2
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accu += func_1 * func_2 * dx
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x += dx
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enddo
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print*,'l2 = ',l2
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print*,'accu = ',accu
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print*,ortho_assoc_gaus_pol(l1,m1,l2)
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enddo
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end
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@ -0,0 +1,151 @@
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subroutine spher_harm_func_r3(r,l,m,re_ylm, im_ylm)
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implicit none
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integer, intent(in) :: l,m
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double precision, intent(in) :: r(3)
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double precision, intent(out) :: re_ylm, im_ylm
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double precision :: theta, phi,r_abs
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call cartesian_to_spherical(r,theta,phi,r_abs)
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call spher_harm_func(l,m,theta,phi,re_ylm, im_ylm)
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end
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subroutine spher_harm_func_m_pos(l,m,theta,phi,re_ylm, im_ylm)
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include 'constants.include.F'
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implicit none
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BEGIN_DOC
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! Y_lm(theta,phi) with m >0
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!
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END_DOC
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double precision, intent(in) :: theta, phi
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integer, intent(in) :: l,m
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double precision, intent(out):: re_ylm,im_ylm
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double precision :: prefact,fact,cos_theta,plgndr,p_lm
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double precision :: tmp
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prefact = dble(2*l+1)*fact(l-m)/(dfour_pi * fact(l+m))
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prefact = dsqrt(prefact)
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cos_theta = dcos(theta)
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p_lm = plgndr(l,m,cos_theta)
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tmp = prefact * p_lm
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re_ylm = dcos(dble(m)*phi) * tmp
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im_ylm = dsin(dble(m)*phi) * tmp
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end
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subroutine spher_harm_func(l,m,theta,phi,re_ylm, im_ylm)
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implicit none
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BEGIN_DOC
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! Y_lm(theta,phi) with -l<m<+l
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!
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END_DOC
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double precision, intent(in) :: theta, phi
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integer, intent(in) :: l,m
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double precision, intent(out):: re_ylm,im_ylm
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double precision :: re_ylm_pos,im_ylm_pos,tmp
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integer :: minus_m
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if(abs(m).gt.l)then
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print*,'|m| > l in spher_harm_func !! stopping ...'
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stop
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endif
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if(m.ge.0)then
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call spher_harm_func_m_pos(l,m,theta,phi,re_ylm_pos, im_ylm_pos)
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re_ylm = re_ylm_pos
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im_ylm = im_ylm_pos
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else
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minus_m = -m !> 0
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call spher_harm_func_m_pos(l,minus_m,theta,phi,re_ylm_pos, im_ylm_pos)
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tmp = (-1)**minus_m
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re_ylm = tmp * re_ylm_pos
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im_ylm = -tmp * im_ylm_pos ! complex conjugate
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endif
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end
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subroutine cartesian_to_spherical(r,theta,phi,r_abs)
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implicit none
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double precision, intent(in) :: r(3)
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double precision, intent(out):: theta, phi,r_abs
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double precision :: r_2,x_2_y_2,tmp
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include 'constants.include.F'
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x_2_y_2 = r(1)*r(1) + r(2)*r(2)
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r_2 = x_2_y_2 + r(3)*r(3)
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r_abs = dsqrt(r_2)
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if(r_abs.gt.1.d-20)then
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theta = dacos(r(3)/r_abs)
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else
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theta = 0.d0
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endif
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if(.true.)then
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if(dabs(r(1)).gt.0.d0)then
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tmp = datan(r(2)/r(1))
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! phi = datan2(r(2),r(1))
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endif
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! From Wikipedia on Spherical Harmonics
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if(r(1).gt.0.d0)then
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phi = tmp
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else if(r(1).lt.0.d0.and.r(2).ge.0.d0)then
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phi = tmp + pi
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else if(r(1).lt.0.d0.and.r(2).lt.0.d0)then
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phi = tmp - pi
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else if(r(1)==0.d0.and.r(2).gt.0.d0)then
|
||||
phi = 0.5d0*pi
|
||||
else if(r(1)==0.d0.and.r(2).lt.0.d0)then
|
||||
phi =-0.5d0*pi
|
||||
else if(r(1)==0.d0.and.r(2)==0.d0)then
|
||||
phi = 0.d0
|
||||
endif
|
||||
if(r(2).lt.0.d0.and.r(1).le.0.d0)then
|
||||
tmp = pi - dabs(phi)
|
||||
phi = pi + tmp
|
||||
else if(r(2).lt.0.d0.and.r(1).gt.0.d0)then
|
||||
phi = dtwo_pi + phi
|
||||
endif
|
||||
endif
|
||||
|
||||
if(.false.)then
|
||||
x_2_y_2 = dsqrt(x_2_y_2)
|
||||
if(dabs(x_2_y_2).gt.1.d-20.and.dabs(r(2)).gt.1.d-20)then
|
||||
phi = dabs(r(2))/r(2) * dacos(r(1)/x_2_y_2)
|
||||
else
|
||||
phi = 0.d0
|
||||
endif
|
||||
endif
|
||||
end
|
||||
|
||||
|
||||
subroutine spher_harm_func_expl(l,m,theta,phi,re_ylm, im_ylm)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Y_lm(theta,phi) with -l<m<+l and 0<= l <=2
|
||||
!
|
||||
END_DOC
|
||||
double precision, intent(in) :: theta, phi
|
||||
integer, intent(in) :: l,m
|
||||
double precision, intent(out):: re_ylm,im_ylm
|
||||
double precision :: tmp
|
||||
include 'constants.include.F'
|
||||
if(l==0.and.m==0)then
|
||||
re_ylm = 0.5d0 * inv_sq_pi
|
||||
im_ylm = 0.d0
|
||||
else if(l==1.and.m==1)then
|
||||
tmp = - inv_sq_pi * dsqrt(3.d0/8.d0) * dsin(theta)
|
||||
re_ylm = tmp * dcos(phi)
|
||||
im_ylm = tmp * dsin(phi)
|
||||
else if(l==1.and.m==0)then
|
||||
tmp = inv_sq_pi * dsqrt(3.d0/4.d0) * dcos(theta)
|
||||
re_ylm = tmp
|
||||
im_ylm = 0.d0
|
||||
else if(l==2.and.m==2)then
|
||||
tmp = 0.25d0 * inv_sq_pi * dsqrt(0.5d0*15.d0) * dsin(theta)*dsin(theta)
|
||||
re_ylm = tmp * dcos(2.d0*phi)
|
||||
im_ylm = tmp * dsin(2.d0*phi)
|
||||
else if(l==2.and.m==1)then
|
||||
tmp = - inv_sq_pi * dsqrt(15.d0/8.d0) * dsin(theta) * dcos(theta)
|
||||
re_ylm = tmp * dcos(phi)
|
||||
im_ylm = tmp * dsin(phi)
|
||||
else if(l==2.and.m==0)then
|
||||
tmp = dsqrt(5.d0/4.d0) * inv_sq_pi* (1.5d0*dcos(theta)*dcos(theta)-0.5d0)
|
||||
re_ylm = tmp
|
||||
im_ylm = 0.d0
|
||||
endif
|
||||
end
|
||||
Loading…
Reference in New Issue