mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-11-07 14:43:41 +01:00
442 lines
11 KiB
OCaml
442 lines
11 KiB
OCaml
(** All utilities which should be included in all source files are defined here *)
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(** {1 Functions from libm} *)
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open Constants
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open Lacaml.D
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let factmax = 150
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external erf_float : float -> float = "erf_float_bytecode" "erf_float"
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[@@unboxed] [@@noalloc]
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external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float"
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[@@unboxed] [@@noalloc]
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external gamma_float : float -> float = "gamma_float_bytecode" "gamma_float"
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[@@unboxed] [@@noalloc]
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external popcnt : int64 -> int32 = "popcnt_bytecode" "popcnt"
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[@@unboxed] [@@noalloc]
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(** popcnt instruction *)
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let popcnt i = popcnt i |> Int32.to_int
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external trailz : int64 -> int32 = "trailz_bytecode" "trailz"
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[@@unboxed] [@@noalloc]
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(** ctz instruction *)
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let trailz i = trailz i |> Int32.to_int
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external leadz : int64 -> int32 = "leadz_bytecode" "leadz"
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[@@unboxed] [@@noalloc]
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(** bsf instruction *)
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let leadz i = leadz i |> Int32.to_int
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(* Incomplete gamma function : Int_0^x exp(-t) t^(a-1) dt
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p: 1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt
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q: 1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt
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reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
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(New Algorithm handbook in C language) (Gijyutsu hyouron
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sha, Tokyo, 1991) p.227 [in Japanese] *)
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let incomplete_gamma ~alpha x =
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let a = alpha in
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let a_inv = 1./. a in
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let gf = gamma_float alpha in
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let loggamma_a = log gf in
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let rec p_gamma x =
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if x >= 1. +. a then 1. -. q_gamma x
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else if x = 0. then 0.
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else
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let rec pg_loop prev res term k =
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if k > 1000. then failwith "p_gamma did not converge."
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else if prev = res then res
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else
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let term = term *. x /. (a +. k) in
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pg_loop res (res +. term) term (k +. 1.)
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in
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let r0 = exp (a *. log x -. x -. loggamma_a) *. a_inv in
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pg_loop min_float r0 r0 1.
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and q_gamma x =
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if x < 1. +. a then 1. -. p_gamma x
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else
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let rec qg_loop prev res la lb w k =
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if k > 1000. then failwith "q_gamma did not converge."
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else if prev = res then res
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else
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let k_inv = 1. /. k in
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let kma = (k -. 1. -. a) *. k_inv in
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let la, lb =
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lb, kma *. (lb -. la) +. (k +. x) *. lb *. k_inv
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in
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let w = w *. kma in
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let prev, res = res, res +. w /. (la *. lb) in
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qg_loop prev res la lb w (k +. 1.)
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in
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let w = exp (a *. log x -. x -. loggamma_a) in
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let lb = (1. +. x -. a) in
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qg_loop min_float (w /. lb) 1. lb w 2.0
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in
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gf *. p_gamma x
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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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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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let binom n k =
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(*TODO : slow function *)
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assert (n >= k);
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let rec aux n k =
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if k = 0 || k = n then
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1
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else
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aux (n-1) (k-1) + aux (n-1) k
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in aux n k
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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 ->
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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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| n when n < 0 -> pow (1./.a) (-n)
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| _ -> assert false
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let chop f g =
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if (abs_float f) < Constants.epsilon then 0.
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else f *. (g ())
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(** Generalized Boys 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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match maxm with
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| 0 ->
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begin
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if t = 0. then [| 1. |] else
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let sq_t = sqrt t in
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[| (sq_pi_over_two /. sq_t) *. erf_float sq_t |]
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end
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| _ ->
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begin
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let result =
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Array.init (maxm+1) (fun m -> 1. /. float_of_int (2*m+1))
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in
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(*
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assert (abs_float t > 1.e-10);
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*)
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if t <> 0. then
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begin
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let fmax =
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let t_inv = sqrt (1. /. t) in
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let n = float_of_int maxm in
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let dm = 0.5 +. n in
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let f = (pow t_inv (maxm+maxm+1) ) in
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match classify_float f with
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| FP_zero
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| FP_subnormal
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| FP_normal ->
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(incomplete_gamma dm t) *. 0.5 *. f
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| _ -> invalid_arg "zero_m overflow"
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in
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let emt = exp (-. t) in
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result.(maxm) <- fmax;
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for n=maxm-1 downto 0 do
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result.(n) <- ( (t+.t) *. result.(n+1) +. emt) *. result.(n)
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done
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end;
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result
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end
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let of_some = function
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| Some a -> a
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| None -> assert false
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(** {2 List functions} *)
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let list_some l =
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List.filter (function None -> false | _ -> true) l
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|> List.map (function Some x -> x | _ -> assert false)
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let list_range first last =
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if last < first then [] else
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let rec aux accu = function
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| 0 -> first :: accu
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| i -> aux ( (first+i)::accu ) (i-1)
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in
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aux [] (last-first)
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let list_pack n l =
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let rec aux i accu1 accu2 = function
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| [] -> if accu1 = [] then
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List.rev accu2
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else
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List.rev ((List.rev accu1) :: accu2)
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| a :: rest ->
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match i with
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| 0 -> aux (n-1) [] ((List.rev (a::accu1)) :: accu2) rest
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| _ -> aux (i-1) (a::accu1) accu2 rest
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in
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aux (n-1) [] [] l
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(** {2 Stream functions} *)
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let stream_range first last =
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Stream.from (fun i ->
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let result = i+first in
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if result <= last then
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Some result
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else None
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)
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let stream_to_list stream =
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let rec aux accu =
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try aux (Stream.next stream :: accu) with
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Stream.Failure -> List.rev accu
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in aux []
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(** {2 Linear algebra} *)
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let array_sum a =
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Array.fold_left ( +. ) 0. a
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let array_product a =
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Array.fold_left ( *. ) 0. a
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let diagonalize_symm m_H =
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let m_V = lacpy m_H in
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let result =
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syevd ~vectors:true m_V
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in
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m_V, result
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let xt_o_x ~o ~x =
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gemm o x
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|> gemm ~transa:`T x
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let x_o_xt ~o ~x =
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gemm o x ~transb:`T
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|> gemm x
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let canonical_ortho ?thresh:(thresh=1.e-6) ~overlap c =
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let d, u, _ = gesvd (lacpy overlap) in
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let d_sqrt = Vec.sqrt d in
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let n = (* Number of non-negligible singular vectors *)
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Vec.fold (fun accu x -> if x > thresh then accu + 1 else accu) 0 d
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in
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let d_inv_sq = (* D^{-1/2} *)
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Vec.map (fun x ->
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if x >= thresh then 1. /. x
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else 0. ) ~y:d d_sqrt
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in
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if n < Vec.dim d_sqrt then
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Printf.printf "Removed linear dependencies below %f\n" (1. /. d.{n})
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;
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Mat.scal_cols u d_inv_sq ;
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gemm c u
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let qr_ortho m =
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(** Performed twice for precision *)
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let result = lacpy m in
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let tau = geqrf result in
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orgqr ~tau result;
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let tau = geqrf result in
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orgqr ~tau result;
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result
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let normalize v =
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let result = copy v in
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scal (1. /. (nrm2 v)) result;
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result
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let normalize_mat m =
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Mat.to_col_vecs m
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|> Array.map (fun v -> normalize v)
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|> Mat.of_col_vecs
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(** {2 Bitstring functions} *)
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let bit_permtutations m n =
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let rec aux k u rest =
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if k=1 then
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List.rev (u :: rest)
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else
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let t = Z.(logor u (u-one)) in
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let t' = Z.(t+one) in
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let t'' = Z.(shift_right ((logand (lognot t) t') - one)) (Z.trailing_zeros u + 1) in
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aux (k-1) (Z.logor t' t'') (u :: rest)
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in
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aux (binom n m) Z.(shift_left one m - one) []
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(** {2 Printers} *)
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let pp_float_array_size ppf a =
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Format.fprintf ppf "@[<2>@[ %d:@[<2>" (Array.length a);
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Array.iter (fun f -> Format.fprintf ppf "@[%10f@]@ " f) a;
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Format.fprintf ppf "]@]@]"
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let pp_float_array ppf a =
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Format.fprintf ppf "@[<2>[@ ";
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Array.iter (fun f -> Format.fprintf ppf "@[%10f@]@ " f) a;
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Format.fprintf ppf "]@]"
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let pp_float_2darray ppf a =
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Format.fprintf ppf "@[<2>[@ ";
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Array.iter (fun f -> Format.fprintf ppf "@[%a@]@ " pp_float_array f) a;
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Format.fprintf ppf "]@]"
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let pp_float_2darray_size ppf a =
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Format.fprintf ppf "@[<2>@[ %d:@[" (Array.length a);
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Array.iter (fun f -> Format.fprintf ppf "@[%a@]@ " pp_float_array_size f) a;
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Format.fprintf ppf "]@]@]"
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let pp_matrix ppf m =
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let open Lacaml.Io in
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let rows = Mat.dim1 m
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and cols = Mat.dim2 m
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in
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let rec aux first last =
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if (first <= last) then begin
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Format.fprintf ppf "@[\n\n %a@]@ " (Lacaml.Io.pp_lfmat
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~row_labels:
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(Array.init rows (fun i -> Printf.sprintf "%d " (i + 1)))
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~col_labels:
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(Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) ))
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~print_right:false
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~print_foot:false
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() ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) m);
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aux (first+5) last
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end
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in
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aux 1 cols
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let pp_bitstring n ppf bs =
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String.init n (fun i -> if (Z.testbit bs i) then '+' else '-')
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|> Format.fprintf ppf "@[<h>%s@]"
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let string_of_matrix m =
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Format.asprintf "%a" pp_matrix m
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let debug_matrix name a =
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Format.printf "@[%s =\n@[%a@]@]@ " name pp_matrix a
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let matrix_of_file filename =
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let ic = Scanf.Scanning.open_in filename in
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let rec read_line accu =
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let result =
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try
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Some (Scanf.bscanf ic " %d %d %f" (fun i j v ->
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(i,j,v) :: accu))
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with End_of_file -> None
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in
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match result with
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| Some accu -> read_line accu
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| None -> List.rev accu
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in
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let data = read_line [] in
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Scanf.Scanning.close_in ic;
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let isize, jsize =
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List.fold_left (fun (accu_i,accu_j) (i,j,v) ->
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(max i accu_i, max j accu_j)) (0,0) data
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in
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let result =
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Lacaml.D.Mat.of_array
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(Array.make_matrix isize jsize 0.)
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in
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List.iter (fun (i,j,v) -> result.{i,j} <- v) data;
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result
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let sym_matrix_of_file filename =
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let result =
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matrix_of_file filename
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in
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for j=1 to Mat.dim1 result do
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for i=1 to j do
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result.{j,i} <- result.{i,j}
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done;
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done;
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result
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let test_case () =
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let test_external () =
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Alcotest.(check (float 1.e-15)) "erf" 0.842700792949715 (erf_float 1.0);
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Alcotest.(check (float 1.e-15)) "erf" 0.112462916018285 (erf_float 0.1);
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Alcotest.(check (float 1.e-15)) "erf" (-0.112462916018285) (erf_float (-0.1));
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Alcotest.(check (float 1.e-15)) "erfc" 0.157299207050285 (erfc_float 1.0);
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Alcotest.(check (float 1.e-15)) "erfc" 0.887537083981715 (erfc_float 0.1);
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Alcotest.(check (float 1.e-15)) "erfc" (1.112462916018285) (erfc_float (-0.1));
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Alcotest.(check (float 1.e-14)) "gamma" (1.77245385090552) (gamma_float 0.5);
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Alcotest.(check (float 1.e-14)) "gamma" (9.51350769866873) (gamma_float (0.1));
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Alcotest.(check (float 1.e-14)) "gamma" (-3.54490770181103) (gamma_float (-0.5));
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Alcotest.(check int) "popcnt" 6 (popcnt @@ Int64.of_int 63);
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Alcotest.(check int) "popcnt" 8 (popcnt @@ Int64.of_int 299605);
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Alcotest.(check int) "popcnt" 1 (popcnt @@ Int64.of_int 65536);
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Alcotest.(check int) "popcnt" 0 (popcnt @@ Int64.of_int 0);
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in
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[
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"External", `Quick, test_external;
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]
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