mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-07 22:13:38 +01:00
228 lines
5.9 KiB
Fortran
228 lines
5.9 KiB
Fortran
|
|
||
|
|
subroutine test_cart
|
||
|
|
implicit none
|
||
|
|
BEGIN_DOC
|
||
|
|
! test for the cartesian --> spherical change of coordinates
|
||
|
|
!
|
||
|
|
! simple test such that the polar angle theta ranges in [0,pi]
|
||
|
|
!
|
||
|
|
! and the asymuthal angle phi ranges in [0,2pi]
|
||
|
|
END_DOC
|
||
|
|
include 'constants.include.F'
|
||
|
|
double precision :: r(3),theta,phi,r_abs
|
||
|
|
print*,''
|
||
|
|
r = 0.d0
|
||
|
|
r(1) = 1.d0
|
||
|
|
r(2) = 1.d0
|
||
|
|
call cartesian_to_spherical(r,theta,phi,r_abs)
|
||
|
|
print*,r
|
||
|
|
print*,phi/pi
|
||
|
|
print*,''
|
||
|
|
r = 0.d0
|
||
|
|
r(1) =-1.d0
|
||
|
|
r(2) = 1.d0
|
||
|
|
call cartesian_to_spherical(r,theta,phi,r_abs)
|
||
|
|
print*,r
|
||
|
|
print*,phi/pi
|
||
|
|
print*,''
|
||
|
|
r = 0.d0
|
||
|
|
r(1) =-1.d0
|
||
|
|
r(2) =-1.d0
|
||
|
|
call cartesian_to_spherical(r,theta,phi,r_abs)
|
||
|
|
print*,r
|
||
|
|
print*,phi/pi
|
||
|
|
print*,''
|
||
|
|
r = 0.d0
|
||
|
|
r(1) = 1.d0
|
||
|
|
r(2) =-1.d0
|
||
|
|
call cartesian_to_spherical(r,theta,phi,r_abs)
|
||
|
|
print*,r
|
||
|
|
print*,phi/pi
|
||
|
|
end
|
||
|
|
|
||
|
|
subroutine test_spher_harm
|
||
|
|
implicit none
|
||
|
|
BEGIN_DOC
|
||
|
|
! routine to test the spherical harmonics integration on a sphere with the grid.
|
||
|
|
!
|
||
|
|
! We test <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2
|
||
|
|
END_DOC
|
||
|
|
include 'constants.include.F'
|
||
|
|
integer :: l1,m1,i,l2,m2,lmax
|
||
|
|
double precision :: r(3),weight,accu_re, accu_im,accu
|
||
|
|
double precision :: re_ylm_1, im_ylm_1,re_ylm_2, im_ylm_2
|
||
|
|
l1 = 0
|
||
|
|
m1 = 0
|
||
|
|
l2 = 0
|
||
|
|
m2 = 0
|
||
|
|
lmax = 5
|
||
|
|
do l1 = 0,lmax
|
||
|
|
do m1 = -l1 ,l1
|
||
|
|
do l2 = 0,lmax
|
||
|
|
do m2 = -l2 ,l2
|
||
|
|
accu_re = 0.d0
|
||
|
|
accu_im = 0.d0
|
||
|
|
! <l1,m1|l2,m2> = \int dOmega Y_l1,m1^* Y_l2,m2
|
||
|
|
! = \int dOmega (re_ylm_1 -i im_ylm_1) * (re_ylm_2 +i im_ylm_2)
|
||
|
|
! = \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)
|
||
|
|
accu = 0.d0
|
||
|
|
do i = 1, n_points_integration_angular
|
||
|
|
double precision :: theta,phi,r_abs
|
||
|
|
r(1:3) = angular_quadrature_points(i,1:3)
|
||
|
|
weight = weights_angular_points(i)
|
||
|
|
call cartesian_to_spherical(r,theta,phi,r_abs)
|
||
|
|
if(theta.gt.pi.or.theta.lt.0.d0)then
|
||
|
|
print*,'pb with theta',theta
|
||
|
|
print*,r
|
||
|
|
endif
|
||
|
|
if(phi.gt.2.d0*pi.or.phi.lt.0.d0)then
|
||
|
|
print*,'pb with phi',phi/pi
|
||
|
|
print*,r
|
||
|
|
endif
|
||
|
|
call spher_harm_func_r3(r,l1,m1,re_ylm_1, im_ylm_1)
|
||
|
|
call spher_harm_func_r3(r,l2,m2,re_ylm_2, im_ylm_2)
|
||
|
|
accu_re += weight * (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2)
|
||
|
|
accu_im += weight * (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
|
||
|
|
accu += weight
|
||
|
|
write(33,'(10(F16.10,X))')phi/pi
|
||
|
|
enddo
|
||
|
|
! Test for the delta l1,l2 and delta m1,m2
|
||
|
|
if(l1.ne.l2.or.m1.ne.m2)then
|
||
|
|
if(dabs(accu_re).gt.1.d-6.or.dabs(accu_im).gt.1.d-6)then
|
||
|
|
print*,'pb OFF DIAG !!!!! '
|
||
|
|
print*,'l1,m1,l2,m2',l1,m1,l2,m2
|
||
|
|
print*,'accu_re = ',accu_re
|
||
|
|
print*,'accu_im = ',accu_im
|
||
|
|
endif
|
||
|
|
endif
|
||
|
|
if(l1==l2.and.m1==m2)then
|
||
|
|
if(dabs(accu_re-1.d0).gt.1.d-5.or.dabs(accu_im).gt.1.d-6)then
|
||
|
|
print*,'pb DIAG !!!!! '
|
||
|
|
print*,'l1,m1,l2,m2',l1,m1,l2,m2
|
||
|
|
print*,'accu_re = ',accu_re
|
||
|
|
print*,'accu_im = ',accu_im
|
||
|
|
endif
|
||
|
|
endif
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
double precision :: x,dx,xmax,xmin
|
||
|
|
integer:: nx
|
||
|
|
nx = 10000
|
||
|
|
xmin = -5.d0
|
||
|
|
xmax = 5.d0
|
||
|
|
dx = (xmax - xmin)/dble(nx)
|
||
|
|
x = xmin
|
||
|
|
do i = 1, nx
|
||
|
|
write(34,*)x,datan(x),dacos(x)
|
||
|
|
x += dx
|
||
|
|
enddo
|
||
|
|
end
|
||
|
|
|
||
|
|
subroutine test_brutal_spheric
|
||
|
|
implicit none
|
||
|
|
include 'constants.include.F'
|
||
|
|
BEGIN_DOC
|
||
|
|
! test for the <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2 using a two dimentional integration
|
||
|
|
!
|
||
|
|
! \int_0^2pi d Phi \int_-1^+1 d(cos(Theta)) Y_l1,m1^*(Theta,Phi) Y_l2,m2(Theta,Phi)
|
||
|
|
!
|
||
|
|
!= \int_0^2pi d Phi \int_0^pi dTheta sin(Theta) Y_l1,m1^*(Theta,Phi) Y_l2,m2(Theta,Phi)
|
||
|
|
!
|
||
|
|
! Allows to test for the general functions spher_harm_func_m_pos with spher_harm_func_expl
|
||
|
|
END_DOC
|
||
|
|
integer :: itheta, iphi,ntheta,nphi
|
||
|
|
double precision :: theta_min, theta_max, dtheta,theta
|
||
|
|
double precision :: phi_min, phi_max, dphi,phi
|
||
|
|
double precision :: accu_re, accu_im,weight
|
||
|
|
double precision :: re_ylm_1, im_ylm_1 ,re_ylm_2, im_ylm_2,accu
|
||
|
|
integer :: l1,m1,i,l2,m2,lmax
|
||
|
|
phi_min = 0.d0
|
||
|
|
phi_max = 2.D0 * pi
|
||
|
|
theta_min = 0.d0
|
||
|
|
theta_max = 1.D0 * pi
|
||
|
|
ntheta = 1000
|
||
|
|
nphi = 1000
|
||
|
|
dphi = (phi_max - phi_min)/dble(nphi)
|
||
|
|
dtheta = (theta_max - theta_min)/dble(ntheta)
|
||
|
|
|
||
|
|
lmax = 3
|
||
|
|
do l1 = 0,lmax
|
||
|
|
do m1 = 0 ,l1
|
||
|
|
do l2 = 0,lmax
|
||
|
|
do m2 = 0 ,l2
|
||
|
|
accu_re = 0.d0
|
||
|
|
accu_im = 0.d0
|
||
|
|
accu = 0.d0
|
||
|
|
theta = theta_min
|
||
|
|
do itheta = 1, ntheta
|
||
|
|
phi = phi_min
|
||
|
|
do iphi = 1, nphi
|
||
|
|
! call spher_harm_func_expl(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
|
||
|
|
! call spher_harm_func_expl(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
|
||
|
|
call spher_harm_func_m_pos(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
|
||
|
|
call spher_harm_func_m_pos(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
|
||
|
|
weight = dtheta * dphi * dsin(theta)
|
||
|
|
accu_re += weight * (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2)
|
||
|
|
accu_im += weight * (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
|
||
|
|
accu += weight
|
||
|
|
phi += dphi
|
||
|
|
enddo
|
||
|
|
theta += dtheta
|
||
|
|
enddo
|
||
|
|
print*,'l1,m1,l2,m2',l1,m1,l2,m2
|
||
|
|
print*,'accu_re = ',accu_re
|
||
|
|
print*,'accu_im = ',accu_im
|
||
|
|
print*,'accu = ',accu
|
||
|
|
if(l1.ne.l2.or.m1.ne.m2)then
|
||
|
|
if(dabs(accu_re).gt.1.d-6.or.dabs(accu_im).gt.1.d-6)then
|
||
|
|
print*,'pb OFF DIAG !!!!! '
|
||
|
|
endif
|
||
|
|
endif
|
||
|
|
if(l1==l2.and.m1==m2)then
|
||
|
|
if(dabs(accu_re-1.d0).gt.1.d-5.or.dabs(accu_im).gt.1.d-6)then
|
||
|
|
print*,'pb DIAG !!!!! '
|
||
|
|
endif
|
||
|
|
endif
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
|
||
|
|
|
||
|
|
end
|
||
|
|
|
||
|
|
subroutine test_assoc_leg_pol
|
||
|
|
implicit none
|
||
|
|
BEGIN_DOC
|
||
|
|
! TODO : Put the documentation of the program here
|
||
|
|
END_DOC
|
||
|
|
print *, 'Hello world'
|
||
|
|
integer :: l1,m1,ngrid,i,l2,m2
|
||
|
|
l1 = 0
|
||
|
|
m1 = 0
|
||
|
|
l2 = 2
|
||
|
|
m2 = 0
|
||
|
|
double precision :: x, dx,xmax,accu,xmin
|
||
|
|
double precision :: plgndr,func_1,func_2,ortho_assoc_gaus_pol
|
||
|
|
ngrid = 100000
|
||
|
|
xmax = 1.d0
|
||
|
|
xmin = -1.d0
|
||
|
|
dx = (xmax-xmin)/dble(ngrid)
|
||
|
|
do l2 = 0,10
|
||
|
|
x = xmin
|
||
|
|
accu = 0.d0
|
||
|
|
do i = 1, ngrid
|
||
|
|
func_1 = plgndr(l1,m1,x)
|
||
|
|
func_2 = plgndr(l2,m2,x)
|
||
|
|
write(33,*)x, func_1,func_2
|
||
|
|
accu += func_1 * func_2 * dx
|
||
|
|
x += dx
|
||
|
|
enddo
|
||
|
|
print*,'l2 = ',l2
|
||
|
|
print*,'accu = ',accu
|
||
|
|
print*,ortho_assoc_gaus_pol(l1,m1,l2)
|
||
|
|
enddo
|
||
|
|
end
|