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(***************************************************************************)
(* Copyright (C) 2000-2013 LexiFi SAS. All rights reserved. *)
(* *)
(* This program is free software: you can redistribute it and/or modify *)
(* it under the terms of the GNU General Public License as published *)
(* by the Free Software Foundation, either version 3 of the License, *)
(* or (at your option) any later version. *)
(* *)
(* This program is distributed in the hope that it will be useful, *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *)
(* GNU General Public License for more details. *)
(* *)
(* You should have received a copy of the GNU General Public License *)
(* along with this program. If not, see <http://www.gnu.org/licenses/>. *)
(***************************************************************************)
val ugaussian_P : float -> float
(** The cumulative distribution function for a normal variate with mean 0 and
variance 1. [ugaussian_P x] returns the probability that a variate takes a
value less than or equal to [x]. *)
module Rootfinder: sig
type error =
| NotbracketedBelow (** The function is below zero on both the given brackets. *)
| NotbracketedAbove (** The function is above zero on both the given brackets. *)
val string_of_error: error -> string
(** Pretty-printing of error. *)
exception Rootfinder of error
val brent: float -> float -> (float -> float) -> float -> float
(** [brent xlo xhi f eps] finds a root of function [f] given that
it is bracketed by [xlo, xhi]. [eps] is the absolute error on the
returned root. Raises {!Rootfinder.Rootfinder} exception when an error is encountered.
The root is found using brent's method (http://en.wikipedia.org/wiki/Brent's_method).
Requires [xlo < xhi]. *)
end
module Gaussian_quadrature:
sig
val gauss_hermite_coefficients: float array * float array
(** [gauss_hermite_coefficients nb_points] returns two arrays [x] and [w] such that
for all [f], the integral of [f] over \]-infty; infty\[ is approximated by \sum w_i f(x_i).
the approximation is good if [f(x)] is close to [exp(-x^2) * P(x)] with [P] a polynomial, and is exact
if [P] is a polynomial of degree less or equal to [2 * nb_points - 1]
*)
end
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