mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-12-22 12:23:31 +01:00
143 lines
3.8 KiB
OCaml
143 lines
3.8 KiB
OCaml
(** Functions from libm *)
|
|
external erf_float : float -> float = "erf_float_bytecode" "erf_float" [@@unboxed] [@@noalloc]
|
|
external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float" [@@unboxed] [@@noalloc]
|
|
external gamma_float : float -> float = "gamma_float_bytecode" "gamma_float" [@@unboxed] [@@noalloc]
|
|
|
|
open Constants
|
|
|
|
let factmax = 150
|
|
|
|
|
|
|
|
|
|
|
|
(* Incomplete gamma function : Int_0^x exp(-t) t^(a-1) dt
|
|
p: 1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt
|
|
q: 1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt
|
|
|
|
reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
|
|
(New Algorithm handbook in C language) (Gijyutsu hyouron
|
|
sha, Tokyo, 1991) p.227 [in Japanese] *)
|
|
|
|
let incomplete_gamma ~alpha x =
|
|
let rec p_gamma a x loggamma_a =
|
|
if x >= 1. +. a then 1. -. q_gamma a x loggamma_a
|
|
else if x = 0. then 0.
|
|
else
|
|
let rec pg_loop prev res term k =
|
|
if k > 1000. then failwith "p_gamma did not converge."
|
|
else if prev = res then res
|
|
else
|
|
let term = term *. x /. (a +. k) in
|
|
pg_loop res (res +. term) term (k +. 1.)
|
|
in
|
|
let r0 = exp (a *. log x -. x -. loggamma_a) /. a in
|
|
pg_loop min_float r0 r0 1.
|
|
|
|
and q_gamma a x loggamma_a =
|
|
if x < 1. +. a then 1. -. p_gamma a x loggamma_a
|
|
else
|
|
let rec qg_loop prev res la lb w k =
|
|
if k > 1000. then failwith "q_gamma did not converge."
|
|
else if prev = res then res
|
|
else
|
|
let k_inv = 1. /. k in
|
|
let la, lb =
|
|
lb, ((k -. 1. -. a) *. (lb -. la) +. (k +. x) *. lb) *. k_inv
|
|
in
|
|
let w = w *. (k -. 1. -. a) *. k_inv in
|
|
let prev, res = res, res +. w /. (la *. lb) in
|
|
qg_loop prev res la lb w (k +. 1.)
|
|
in
|
|
let w = exp (a *. log x -. x -. loggamma_a) in
|
|
let lb = (1. +. x -. a) in
|
|
qg_loop min_float (w /. lb) 1. lb w 2.0
|
|
in
|
|
let gf = gamma_float alpha in
|
|
gf *. p_gamma alpha x (log gf)
|
|
|
|
|
|
|
|
|
|
|
|
let fact_memo =
|
|
let rec aux accu_l accu = function
|
|
| 0 -> aux [1.] 1. 1
|
|
| i when (i = factmax) ->
|
|
let x = (float_of_int factmax) *. accu in
|
|
List.rev (x::accu_l)
|
|
| i -> let x = (float_of_int i) *. accu in
|
|
aux (x::accu_l) x (i+1)
|
|
in
|
|
aux [] 0. 0
|
|
|> Array.of_list
|
|
|
|
|
|
|
|
(** Factorial function.
|
|
@raise Invalid_argument for negative or arguments >100. *)
|
|
let fact = function
|
|
| i when (i < 0) ->
|
|
raise (Invalid_argument "Argument of factorial should be non-negative")
|
|
| i when (i > 150) ->
|
|
raise (Invalid_argument "Result of factorial is infinite")
|
|
| i -> fact_memo.(i)
|
|
|
|
|
|
|
|
(** Integer powers of floats *)
|
|
let rec pow a = function
|
|
| 0 -> 1.
|
|
| 1 -> a
|
|
| 2 -> a *. a
|
|
| 3 -> a *. a *. a
|
|
| -1 -> 1. /. a
|
|
| n when (n<0) -> pow (1./.a) (-n)
|
|
| n ->
|
|
let b = pow a (n / 2) in
|
|
b *. b *. (if n mod 2 = 0 then 1. else a)
|
|
;;
|
|
|
|
|
|
(** In chop f g, evaluate g only if f is non zero, and return f *. (g ()) *)
|
|
let chop f g =
|
|
if (abs_float f) < cutoff then 0.
|
|
else f *. (g ())
|
|
|
|
|
|
|
|
(** Generalized Boys function.
|
|
maxm : Maximum total angular momentum
|
|
*)
|
|
let boys_function ~maxm t =
|
|
match maxm with
|
|
| 0 ->
|
|
begin
|
|
if t = 0. then [| 1. |] else
|
|
let sq_t = sqrt t in
|
|
[| (sq_pi_over_two /. sq_t) *. erf_float sq_t |]
|
|
end
|
|
| _ ->
|
|
begin
|
|
let result =
|
|
Array.init (maxm+1) (fun m -> 1. /. float_of_int (2*m+1))
|
|
in
|
|
if t <> 0. then
|
|
begin
|
|
let fmax =
|
|
let t_inv = sqrt (1. /. t) in
|
|
let n = float_of_int maxm in
|
|
let dm = 0.5 +. n in
|
|
let f = (pow t_inv (maxm+maxm+1) ) in
|
|
(incomplete_gamma dm t) *. 0.5 *. f
|
|
in
|
|
let emt = exp (-. t) in
|
|
result.(maxm) <- fmax;
|
|
for n=maxm-1 downto 0 do
|
|
result.(n) <- ( (t+.t) *. result.(n+1) +. emt) *. result.(n)
|
|
done
|
|
end;
|
|
result
|
|
end
|
|
|