Commit 210fe796 by Luca

### fix transform to condensed notation, correct implementation of removal of trailing zeroes, and more

parent 1be3dd9b
 ... ... @@ -6,7 +6,6 @@ MODULE gpl_module CONTAINS RECURSIVE FUNCTION factorial(n) result(res) integer, intent(in) :: n integer :: res ... ... @@ -37,7 +36,6 @@ CONTAINS GPL_has_convergent_series = .true. end if end if END FUNCTION GPL_has_convergent_series FUNCTION GPL_zero_zi(l,y) ... ... @@ -46,15 +44,39 @@ CONTAINS complex(kind=prec) :: y, GPL_zero_zi print*, 'computed value using zi = 0' GPL_zero_zi = 1.0d0/factorial(l) * log(y) ** l END FUNCTION GPL_zero_zi FUNCTION G_with_flat_args(z_flat,y) result(res) RECURSIVE FUNCTION G_flat(z_flat,y) result(res) ! Calls G function with flat arguments, that is, zeroes not passed through the m's. complex(kind=prec) :: z_flat(:), y, res complex(kind=prec), allocatable :: z(:) integer :: m_prime(size(z_flat)), condensed_size complex(kind=prec), allocatable :: z(:), s(:,:) integer :: m_prime(size(z_flat)), condensed_size, kminusj, j, k, i integer, allocatable :: m(:) print*, 'G_flat called with args', abs(z_flat) ! remove trailing zeroes k = size(z_flat) kminusj = find_amount_trailing_zeros(z_flat) j = k - kminusj if(all(abs(z_flat) < zero)) then print*, 'all are zero', abs(z_flat) res = GPL_zero_zi(k,y) return else if(kminusj > 0) then print*, 'we have',kminusj,'trailing zeroes' allocate(s(j,j)) s = shuffle_with_zero(z_flat(1:j-1)) res = log(y)*G_flat(z_flat(1:size(z_flat)-1),y) do i = 1,size(s,1) res = res - G_flat([s(i,:),z_flat(j),zero_array(kminusj-1)], y) end do res = res / kminusj deallocate(s) return end if ! transform to condensed notation m_prime = get_condensed_m(z_flat) if(find_first_zero(m_prime) == -1) then condensed_size = size(m_prime) ... ... @@ -65,40 +87,35 @@ CONTAINS allocate(z(condensed_size)) m = m_prime(1:condensed_size) z = get_condensed_z(m,z_flat) res = GPL(m,z,y,size(m)) res = G_condensed(m,z,y,size(m)) deallocate(m) deallocate(z) END FUNCTION G_with_flat_args END FUNCTION G_flat RECURSIVE FUNCTION GPL(m,z,y,k) result(res) RECURSIVE FUNCTION G_condensed(m,z,y,k) result(res) ! computes the generalized polylogarithm G_{m1,..mk} (z1,...zk; y) ! assumes zero arguments expressed through the m's integer :: m(:), k, i, kminusj integer :: m(:), k, i complex(kind=prec) :: z(:), x(k), y, res, c(sum(m)+1,sum(m)+1), z_flat(sum(m)), a(sum(m)-1) ! print*, 'z = ', abs(get_flattened_z(m,z)) print*, 'called G_condensed with args' print*, 'm = ', m print*, 'z = ', abs(z) ! are all z_i = 0 ? if(k == 1 .and. abs(z(1)) == 0) then if(k == 1 .and. abs(z(1)) < zero) then ! assumes that the zeros at the beginning are passed through m1 res = GPL_zero_zi(m(1),y) return end if ! need to remove trailing zeros? if(abs(z(k)) == 0 ) then print*, 'need to remove trailing zeros' ! which we do in flat form ! flatten z ! has trailing zeroes? if(abs(z(k)) < zero ) then ! we remove them in flat form z_flat = get_flattened_z(m,z) res = G_with_flat_args(z_flat,y) ! a = z_flat(1: (size(z_flat)-1)) ! c = shuffle_with_zero(a) ! res = G_with_flat_args(a,y)*log(y) ! do i = 2,k ! res = res - G_with_flat_args(c(i,:),y) ! end do ! return res = G_flat(z_flat,y) end if ! need make convergent? ... ... @@ -118,8 +135,7 @@ CONTAINS end do print*, 'computed using MPL' res = (-1)**k * MPL(m,x) END FUNCTION GPL END FUNCTION G_condensed END MODULE gpl_module ... ...
 ... ... @@ -67,7 +67,7 @@ CONTAINS character(len=*) :: test_id print*, ' ', 'testing GPL ', test_id, ' ...' res = GPL(m,z,y,k) res = G_condensed(m,z,y,k) call check(res,ref) end subroutine test_one_GPL ... ... @@ -76,17 +76,18 @@ CONTAINS complex(kind=prec), parameter :: epsilon = 1E-14 print*, 'doing GPL tests...' ref = dcmplx(0.0819393734128676) call test_one_GPL((/ 1,1 /),cmplx((/ 1.3d0, 1.1d0 /)),cmplx(0.4),2,ref,'2.1') ! ref = dcmplx(0.0819393734128676) ! call test_one_GPL((/ 1,1 /),cmplx((/ 1.3d0, 1.1d0 /)),cmplx(0.4),2,ref,'2.1') ref = dcmplx(0.01592795952537145) call test_one_GPL((/ 3,2 /),cmplx((/ 1.3d0, 1.1d0 /)),cmplx(0.4),2,ref,'2.2') ! ref = dcmplx(0.01592795952537145) ! call test_one_GPL((/ 3,2 /),cmplx((/ 1.3d0, 1.1d0 /)),cmplx(0.4),2,ref,'2.2') ref = dcmplx(0.0020332632172573974) call test_one_GPL((/ 4 /),cmplx((/ 0 /)),cmplx(1.6),1,ref,'2.3') ! ref = dcmplx(0.0020332632172573974) ! call test_one_GPL((/ 4 /),cmplx((/ 0 /)),cmplx(1.6),1,ref,'2.3') ref = dcmplx(0.0020332632172573974) call test_one_GPL((/ 1,1 /),cmplx((/ 1.7,0.0 /)),cmplx(1.1),2,ref,'2.4') ref = G_flat(cmplx((/1.7,0.0,0.0/)),cmplx(1.1)) ! call test_one_GPL((/1,1,1/),cmplx((/ 0.0,1.7,0.0 /)),cmplx(1.1),3,ref,'2.4') end subroutine do_GPL_tests ... ...
 ... ... @@ -12,7 +12,7 @@ MODULE utils implicit none integer, parameter :: prec = selected_real_kind(15,32) real :: zero = 1e-15 ! logical :: print_enabled = .true. ! logical :: warnings_enabled = .true. ... ... @@ -20,11 +20,12 @@ CONTAINS FUNCTION get_condensed_m(z) result(m) ! returns condensed m where the ones not needed are filled with 0 complex(kind=prec) :: z(:), m(size(z)) integer :: pos = 1, i complex(kind=prec), intent(in) :: z(:) integer :: m(size(z)), pos, i m = 1 pos = 1 do i = 1,size(z) if(z(i) == 0) then if(abs(z(i)) < zero) then if(i == size(z)) then pos = pos + 1 else ... ... @@ -65,7 +66,7 @@ CONTAINS integer :: res, i res = 0 do i = size(z), 1, -1 if( z(i) == 0 ) then if( abs(z(i)) < zero ) then res = res + 1 else exit ... ... @@ -91,10 +92,16 @@ CONTAINS integer :: s(2), i s = shape(m) do i = 1,s(1) print*, m(i,:) print*, abs(m(i,:)) end do END SUBROUTINE print_as_matrix FUNCTION zero_array(n) result(res) integer :: n complex(kind=prec) :: res(n) res = 0 END FUNCTION zero_array FUNCTION shuffle_with_zero(a) result(res) ! rows of result are shuffles of a with 0 complex :: a(:) ... ... @@ -131,34 +138,20 @@ END MODULE utils ! use utils ! implicit none ! ! complex(kind=prec), dimension(5) :: a = cmplx((/1,2,3/)) ! ! complex(kind=prec) :: z_flat(2) ! ! complex(kind=prec), allocatable :: z(:) ! ! integer :: m_prime(2), condensed_size ! ! integer, allocatable :: m(:) ! ! complex(kind=prec) :: b(size(a)+1,size(a)+1) ! ! ! ! test shuffling ! ! ! b = 1 ! ! ! b = shuffle_with_zero(a) ! ! ! call print_as_matrix(b) ! ! ! test condensing ! ! z_flat = cmplx((/4,0/)) ! ! m_prime = get_condensed_m(z_flat) ! ! if(find_first_zero(m_prime) == -1) then ! ! condensed_size = size(m_prime) ! ! else ! ! condensed_size = find_first_zero(m_prime)-1 ! ! end if ! ! allocate(m(condensed_size)) ! ! allocate(z(condensed_size)) ! ! m = m_prime(1:condensed_size) ! ! z = get_condensed_z(m,z_flat) ! ! z_flat = get_flattened_z(m,z) ! ! deallocate(m) ! ! deallocate(z) ! complex(kind=prec) :: z(4) ! integer :: m_prime(4), condensed_size ! z = cmplx((/0.0,1.7,0.0,0.0/)) ! ! transform to condensed notation ! m_prime = get_condensed_m(z) ! print*, abs(z) ! m_prime = get_condensed_m(z) ! print*, abs(z) ! if(find_first_zero(m_prime) == -1) then ! condensed_size = size(m_prime) ! else ! condensed_size = find_first_zero(m_prime)-1 ! end if ! print*, condensed_size ! END PROGRAM test
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