Commit 74156e8d authored by Luca's avatar Luca

init

parents
*
!/**/
!*.*
!makefile
*.out
*.mod
*.smod
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sup
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! Contains some functions that might be useful later
MODULE utils
implicit none
CONTAINS
FUNCTION dilog(x,n)
! Computes the dilog Li_2(x) using the series representation up to order n
integer :: n
complex :: x, dilog
integer :: i
integer :: j(n)
j = (/(i, i=1,n,1)/)
dilog = sum(x**j / j**2)
END FUNCTION dilog
FUNCTION polylog(m,x,n)
! Computes the classical polylogarithm Li_m(x) using series representation up to order n
integer :: m,n
complex :: x, polylog
integer :: i
integer :: j(n)
j = (/(i, i=1,n,1)/)
polylog = sum(x**j / j**m)
END FUNCTION polylog
recursive FUNCTION multiple_polylog(m, x, n) result(res)
! Computes the multiple polylogarithm Li_{m1,...,mk} (x1,...,xk) up to order n
integer :: m(:)
complex :: x(:)
complex :: res
integer :: n, i
! print*, 'm = ', m
! print*, 'x = ', x
! print*, 'n = ', n
if(size(m) /= size(x)) then
print*, 'Error: m and x must have the same length'
end if
if(size(m) == 1) then
! base case
! print*, 'landed in base case'
res = polylog(m(1),x(1), n)
else
! recursion step
! print*, 'landed in step'
res = 0
do i = 1, n
res = res + x(1)**i / i**m(1) * multiple_polylog(m(2:), x(2:), i - 1)
end do
! a nicer way to do it would be but problem is i
! i = (/(j, j=1,n, 1)/)
! res = sum( x(1)**i / i**m(1) * multiple_polylog(m(2:), x(2:), i(1) - 1) )
end if
END FUNCTION multiple_polylog
END MODULE utils
PROGRAM test
! Used to test the procedures defined in this module
use utils
implicit none
complex :: result
! print*, dilog((0.8,0),100) ! should be 1.07479 + 0i
! print*, dilog((0.2,0.5),100) ! should be 0.133909 + 0.537628i
! print*, polylog(2,(0.2,0.5),100) ! should be 0.133909 + 0.537628i
! print*, polylog(5,(0.2,0.5),100) ! should be 0.192872345 + 0.505898833i
result = multiple_polylog((/ 5 /),(/ (0.2,0.5) /), 100)
print*, 'result = ', result
result = multiple_polylog((/ 5, 5 /),(/ (0.8,0),(0.3,0.5) /), 100)
print*, 'result = ', result
END PROGRAM test
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