mirror of https://gitlab.com/scemama/QCaml.git
74 lines
1.7 KiB
OCaml
74 lines
1.7 KiB
OCaml
(** Constants *)
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let pi = acos (-1.)
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let pi_inv = 1. /. pi
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let two_over_sq_pi = 2. /. (sqrt pi)
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let factmax = 150
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(** Generalized Boys function. Uses GSL's incomplete Gamma function.
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maxm : Maximum total angular momentum
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*)
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let boys_function ~maxm t =
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begin
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if t = 0. then
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Array.init (maxm+1) (fun m -> 1. /. float_of_int (m+m+1))
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else
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let incomplete_gamma ~alpha x =
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Gsl.Sf.gamma alpha *. ( Gsl.Sf.gamma_inc_P alpha x )
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in
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let t_inv =
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1. /. t
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in
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let factor =
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Array.make (maxm+1) (0.5, sqrt t_inv);
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in
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for i=1 to maxm
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do
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let (dm, f) = factor.(i-1) in
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factor.(i) <- (dm +. 1., f *. t_inv);
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done;
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Array.map (fun (dm, f) -> (incomplete_gamma dm t ) *. 0.5 *. f) factor
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end
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let fact_memo =
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let rec aux accu_l accu = function
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| 0 -> aux [1.] 1. 1
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| i when (i = factmax) ->
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let x = (float_of_int factmax) *. accu in
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List.rev (x::accu_l)
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| i -> let x = (float_of_int i) *. accu in
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aux (x::accu_l) x (i+1)
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in
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aux [] 0. 0
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|> Array.of_list
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(** Factorial function.
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@raise Invalid_argument for negative or arguments >100. *)
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let fact = function
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| i when (i < 0) ->
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raise (Invalid_argument "Argument of factorial should be non-negative")
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| i when (i > 150) ->
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raise (Invalid_argument "Result of factorial is infinite")
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| i -> fact_memo.(i)
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(** Integer powers of floats *)
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let rec pow a = function
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| 0 -> 1.
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| 1 -> a
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| 2 -> a *. a
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| 3 -> a *. a *. a
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| -1 -> 1. /. a
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| n when (n<0) -> pow (1./.a) (-n)
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| n ->
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let b = pow a (n / 2) in
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b *. b *. (if n mod 2 = 0 then 1. else a)
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;;
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