utils.f90 2.14 KB
 Luca committed Apr 02, 2019 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 `````` ! 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 ``````