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removed GSL dependency

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This commit is contained in:
Anthony Scemama 2018-02-01 22:53:00 +01:00
parent d93729deff
commit 91f1dacaf4
1 changed files with 46 additions and 1 deletions
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47
Utils/Util.ml
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@ -8,6 +8,48 @@ include Constants
let factmax = 150
(*reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
(New Algorithm handbook in C language) (Gijyutsu hyouron
sha, Tokyo, 1991) p.227 [in Japanese] *)
(* Incomplete gamma function
1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt *)
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 could 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.
(* Incomplete gamma function
1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt *)
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 could not converge."
else if prev = res then res
else
let la, lb =
lb, ((k -. 1. -. a) *. (lb -. la) +. (k +. x) *. lb) /. k
in
let w = w *. (k -. 1. -. a) /. k 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
(** Generalized Boys function. Uses GSL's incomplete Gamma function.
maxm : Maximum total angular momentum
*)
@ -25,7 +67,10 @@ let rec boys_function ~maxm t =
Array.init (maxm+1) (fun m -> 1. /. float_of_int (m+m+1))
else
let incomplete_gamma ~alpha x =
(gamma_float alpha) *. ( Gsl.Sf.gamma_inc_P alpha x )
(* (gamma_float alpha) *. ( Gsl.Sf.gamma_inc_P alpha x )
*)
let gf = gamma_float alpha in
gf *. p_gamma alpha x (log gf)
in
let t_inv =
1. /. t