;;; PLT Scheme Science Collection
;;; random-distributions/triangular.ss; version 0.9.0
;;; Copyright (c) 2004 M. Douglas Williams
;;;
;;; This library is free software; you can redistribute it and/or
;;; modify it under the terms of the GNU Lesser General Public
;;; License as published by the Free Software Foundation; either
;;; version 2.1 of the License, or (at your option) any later version.
;;;
;;; This library 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
;;; Lesser General Public License for more details.
;;;
;;; You should have received a copy of the GNU Lesser General Public
;;; License along with this library; if not, write to the Free
;;; Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
;;; 02111-1307 USA.
;;;
;;; -------------------------------------------------------------------
;;;
;;; This code implements a triangular distribution.
;;;
;;; Version  Date      Description
;;; 0.9.0    08/06/04  This is the initial release of the triangular
;;;                    distribution routines. (Doug Williams)
;;; 1.0.0    09/28/04  Marked as ready for Release 1.0.  Added
;;;                    contracts for functions.  (Doug Williams)

(module triangular mzscheme
  
  (require (lib "contract.ss"))
  
  (provide/contract
   (random-triangular
    (case-> (->r ((r random-source?)
                  (a real?)
                  (b (>/c a))
                  (c (and/c (>=/c a)
                            (<=/c b))))
                 real?)
            (->r ((a real?)
                  (b (>/c a))
                  (c (and/c (>=/c a)
                            (<=/c b))))
                 real?)))
   (triangular-pdf
    (->r ((x real?)
          (a real?)
          (b (>/c a))
          (c (and/c (>=/c a)
                    (<=/c b))))
         (>=/c 0.0)))
   (triangular-cdf
    (->r ((x real?)
          (a real?)
          (b (>/c a))
          (c (and/c (>=/c a)
                    (<=/c b))))
         (real-in 0.0 1.0))))
  
  (require "../random-source.ss")
  
  ;; random-triangular: random-source x real x real x real -> real
  ;; random-triangular: real x real x real -> real
  ;;
  ;; This function returns a random variate from a triangular
  ;; distribution with min, a, max, b, and mode, c.
  (define random-triangular
    (case-lambda
      ((r a b c)
       (let ((u (random-uniform r)))
         (if (<= u (/ (- c a) (- b a)))
             (+ a (sqrt (* u (- b a) (- c a))))
             (- b (sqrt (* (- 1.0 u) (- b a) (- b c)))))))
      ((a b c)
       (random-triangular (current-random-source) a b c))))
  
  ;; triangular-pdf: real x real x real x real -> real
  ;;
  ;; This function computes the probability density p(x) at x of a
  ;; triangular distribution with min, a, max, b, and mode, c.
  (define (triangular-pdf x a b c)
    (if (< x a)
        ;; x < a
        0.0
        (if (<= x c)
            ;; a <= x <= c
            (/ (* 2.0 (- x a)) (* (- b a) (- c a)))
            (if (<= x b)
                ;; x <= x <= b
                (/ (* 2.0 (- b x)) (* (- b a) (- b c)))
                ;; x > b
                0))))
  
  ;; triangular-cdf: real x real x real x real -> real
  ;;
  ;; This function computes the cummulative density d(x) at a for a
  ;; triangular distribution with min, a, max, b, and mode, c.
  (define (triangular-cdf x a b c)
    (if (< x a)
        0.0
        (if (<= x c)
            (/ (* (- x a) (- x a))
               (* (- b a) (- c a)))
            (if (<= x b)
                (- 1.0 (/ (* (- b x) (- b x))
                          (* (- b a) (- b c))))
                1.0))))
  
)