;;; PLT Scheme Science Collection
;;; random-distributions/logarithmic.ss
;;; 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 module implements the logarithmic distribution.  It is based
;;; on the Random Number Distributions in the GNU Scientific Library.
;;;
;;; Version  Date      Description
;;; 1.0.0    09/28/04  Marked as ready for Release 1.0.  Added
;;;                    contracts for functions.  (Doug Williams)

(module logarithmic mzscheme
  
  (require (lib "contract.ss"))
  
  (provide/contract
   (random-logarithmic
    (case-> (-> random-source? (real-in 0.0 1.0) integer?)
            (-> (real-in 0.0 1.0) integer?)))
   (logarithmic-pdf
    (-> integer? (real-in 0.0 1.0) (>=/c 0.0))))
  
  (require "../random-source.ss")
  
  ;; random-logarithmic: random-source x real -> integer
  ;; random-logarithmic: real -> integer
  ;;
  ;; This function returns a random variate from a logarithmic
  ;; distribution with probability p.
  (define random-logarithmic
    (case-lambda
      ((r p)
       (let ((c (log (- 1.0 p)))
             (v (random-uniform r)))
         (if (>= v p)
             1
             (let* ((u (random-uniform r))
                    (q (- 1.0 (exp (* c u)))))
               (cond ((<= v (* q q))
                      (inexact->exact
                       (truncate
                        (+ 1.0 (/ (log v) (log q))))))
                     ((<= v q)
                      2)
                     (else
                      1))))))
      ((p)
       (random-logarithmic (current-random-source) p))))
  
  ;; logarithmic-pdf: integer x real -> real
  ;;
  ;; This function computes the probability density p(x) at x for a
  ;; logarithmic distribution with probability p.
  (define (logarithmic-pdf k p)
    (if (= k 0)
        0.0
        (/ (expt p (exact->inexact k))
           (exact->inexact k)
           (log (/ 1.0 (- 1.0 p))))))
  
)