Source file gsl_complex.ml

(* gsl-ocaml - OCaml interface to GSL                       *)
(* Copyright (©) 2002-2012, 2003 - Olivier Andrieu, Paul Pelzl   *)
(* Distributed under the terms of the GPL version 3         *)

let () = Error.init ()

type complex = Complex.t = { re : float; im : float }

let complex ~re ~im = { re; im }

type complex_array = float array

let set a i c =
  a.(2 * i) <- c.re;
  a.((2 * i) + 1) <- c.im

let get a i = { re = a.(2 * i); im = a.((2 * i) + 1) }

let unpack ca =
  let len = Array.length ca in
  if len mod 2 <> 0 then invalid_arg "unpack_complex_array";
  Array.init (len / 2) (get ca)

let pack a =
  let len = Array.length a in
  let ca = Array.make (2 * len) 0. in
  for i = 0 to pred len do
    ca.(2 * i) <- a.(i).re;
    ca.((2 * i) + 1) <- a.(i).im
  done;
  ca

let mult a b =
  if Array.length a mod 2 <> 0 then invalid_arg "mult: not a complex array";
  let len = Array.length a / 2 in
  for i = 0 to pred len do
    let re = (a.(2 * i) *. b.(2 * i)) -. (a.((2 * i) + 1) *. b.((2 * i) + 1)) in
    let im = (a.(2 * i) *. b.((2 * i) + 1)) +. (a.((2 * i) + 1) *. b.(2 * i)) in
    a.(2 * i) <- re;
    a.((2 * i) + 1) <- im
  done

(* added by Paul Pelzl, 2003/12/25 *)
let rect x y = { re = x; im = y }
let polar = Complex.polar
let arg = Complex.arg
let abs = Complex.norm
let abs2 = Complex.norm2

external logabs : complex -> float = "ml_gsl_complex_logabs"

let add = Complex.add
let sub = Complex.sub
let mul = Complex.mul
let div = Complex.div
let add_real a x = { re = a.re +. x; im = a.im }
let sub_real a x = { re = a.re -. x; im = a.im }
let mul_real a x = { re = a.re *. x; im = a.im *. x }
let div_real a x = { re = a.re /. x; im = a.im /. x }
let add_imag a y = { re = a.re; im = a.im +. y }
let sub_imag a y = { re = a.re; im = a.im -. y }
let mul_imag a y = { re = a.im *. ~-.y; im = a.re *. y }
let div_imag a y = { re = a.im /. y; im = a.re /. ~-.y }
let conjugate = Complex.conj
let inverse = Complex.inv
let negative = Complex.neg

(* elementary complex functions *)
external sqrt : complex -> complex = "ml_gsl_complex_sqrt"
external sqrt_real : float -> complex = "ml_gsl_complex_sqrt_real"
external pow : complex -> complex -> complex = "ml_gsl_complex_pow"
external pow_real : complex -> float -> complex = "ml_gsl_complex_pow_real"
external exp : complex -> complex = "ml_gsl_complex_exp"
external log : complex -> complex = "ml_gsl_complex_log"
external log10 : complex -> complex = "ml_gsl_complex_log10"
external log_b : complex -> complex -> complex = "ml_gsl_complex_log_b"

(* complex trigonometric functions *)
external sin : complex -> complex = "ml_gsl_complex_sin"
external cos : complex -> complex = "ml_gsl_complex_cos"
external tan : complex -> complex = "ml_gsl_complex_tan"
external sec : complex -> complex = "ml_gsl_complex_sec"
external csc : complex -> complex = "ml_gsl_complex_csc"
external cot : complex -> complex = "ml_gsl_complex_cot"

(* inverse complex trigonometric functions *)
external arcsin : complex -> complex = "ml_gsl_complex_arcsin"
external arcsin_real : float -> complex = "ml_gsl_complex_arcsin_real"
external arccos : complex -> complex = "ml_gsl_complex_arccos"
external arccos_real : float -> complex = "ml_gsl_complex_arccos_real"
external arctan : complex -> complex = "ml_gsl_complex_arctan"
external arcsec : complex -> complex = "ml_gsl_complex_arcsec"
external arcsec_real : float -> complex = "ml_gsl_complex_arcsec_real"
external arccsc : complex -> complex = "ml_gsl_complex_arccsc"
external arccsc_real : float -> complex = "ml_gsl_complex_arccsc_real"
external arccot : complex -> complex = "ml_gsl_complex_arccot"

(* complex hyperbolic functions *)
external sinh : complex -> complex = "ml_gsl_complex_sinh"
external cosh : complex -> complex = "ml_gsl_complex_cosh"
external tanh : complex -> complex = "ml_gsl_complex_tanh"
external sech : complex -> complex = "ml_gsl_complex_sech"
external csch : complex -> complex = "ml_gsl_complex_csch"
external coth : complex -> complex = "ml_gsl_complex_coth"

(* inverse complex hyperbolic functions *)
external arcsinh : complex -> complex = "ml_gsl_complex_arcsinh"
external arccosh : complex -> complex = "ml_gsl_complex_arccosh"
external arccosh_real : float -> complex = "ml_gsl_complex_arccosh_real"
external arctanh : complex -> complex = "ml_gsl_complex_arctanh"
external arctanh_real : float -> complex = "ml_gsl_complex_arctanh_real"
external arcsech : complex -> complex = "ml_gsl_complex_arcsech"
external arccsch : complex -> complex = "ml_gsl_complex_arccsch"
external arccoth : complex -> complex = "ml_gsl_complex_arccoth"