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removed stupid stuffs in spher_harm
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@ -2,3 +2,6 @@
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spher_harm
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==========
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Routines for spherical Harmonics evaluation in real space.
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The main routine is "spher_harm_func_r3(r,l,m,re_ylm, im_ylm)".
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The test routine is "test_spher_harm" where everything is explained in details.
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@ -1,10 +1,93 @@
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subroutine test_spher_harm
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implicit none
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BEGIN_DOC
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! routine to test the generic spherical harmonics routine "spher_harm_func_r3" from R^3 --> C
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!
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! We test <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2
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!
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! The test is done through the integration on a sphere with the Lebedev grid.
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END_DOC
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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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double precision :: theta,phi,r_abs
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lmax = 5 ! Maximum angular momentum until which we are going to test orthogonality conditions
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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 ! accumulator for the REAL part of <Y_l1,m1|Y_l2,m2>
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accu_im = 0.d0 ! accumulator for the IMAGINARY part of <Y_l1,m1|Y_l2,m2>
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accu = 0.d0 ! accumulator for the weights ==> should be \int dOmega == 4 pi
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! <l1,m1|l2,m2> = \int dOmega Y_l1,m1^* Y_l2,m2
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! \approx \sum_i W_i Y_l1,m1^*(r_i) Y_l2,m2(r_i) WITH r_i being on the spher of radius 1
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do i = 1, n_points_integration_angular
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r(1:3) = angular_quadrature_points(i,1:3) ! ith Lebedev point (x,y,z) on the sphere of radius 1
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weight = weights_angular_points(i) ! associated Lebdev weight not necessarily positive
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!!!!!!!!!!! Test of the Cartesian --> Spherical coordinates
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! theta MUST belong to [0,pi] and phi to [0,2pi]
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! gets the cartesian to spherical change of coordinates
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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, it should be in [0,pi]',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, it should be in [0,2 pi]',phi/pi
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print*,r
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endif
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!!!!!!!!!!! Routines returning the Spherical harmonics on the grid point
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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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!!!!!!!!!!! Integration of Y_l1,m1^*(r) Y_l2,m2(r)
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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_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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enddo
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! Test that the sum of the weights is 4 pi
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if(dabs(accu - dfour_pi).gt.1.d-6)then
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print*,'Problem !! The sum of the Lebedev weight is not 4 pi ..'
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print*,accu
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stop
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endif
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! Test for the delta l1,l2 and delta m1,m2
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!
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! Test for the off-diagonal part of the Kronecker delta
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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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! Test for the diagonal part of the Kronecker delta
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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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end
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subroutine test_cart
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implicit none
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BEGIN_DOC
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! test for the cartesian --> spherical change of coordinates
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!
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! simple test such that the polar angle theta ranges in [0,pi]
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! test the routine "cartesian_to_spherical" such that the polar angle theta ranges in [0,pi]
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!
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! and the asymuthal angle phi ranges in [0,2pi]
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END_DOC
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@ -40,97 +123,18 @@ subroutine test_cart
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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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BEGIN_DOC
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! routine to test the spherical harmonics integration on a sphere with the grid.
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!
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! We test <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2
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END_DOC
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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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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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! Test for the delta l1,l2 and delta m1,m2
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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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BEGIN_DOC
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! test for the <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2 using a two dimentional integration
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! Test for the <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2 using the following two dimentional integration
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!
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! \int_0^2pi d Phi \int_-1^+1 d(cos(Theta)) Y_l1,m1^*(Theta,Phi) Y_l2,m2(Theta,Phi)
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!
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!= \int_0^2pi d Phi \int_0^pi dTheta sin(Theta) Y_l1,m1^*(Theta,Phi) Y_l2,m2(Theta,Phi)
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!
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! Allows to test for the general functions spher_harm_func_m_pos with spher_harm_func_expl
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! Allows to test for the general functions "spher_harm_func_m_pos" with "spher_harm_func_expl"
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END_DOC
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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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@ -147,7 +151,7 @@ subroutine test_brutal_spheric
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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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lmax = 2
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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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@ -196,7 +200,7 @@ 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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! Test for the associated Legendre Polynoms. The test is done through the orthogonality condition.
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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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program spher_harm
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implicit none
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call test_spher_harm
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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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call test_brutal_spheric
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end
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