;;; PLT Scheme Science Collection
;;; random-distributions/lognormal.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.
;;;
;;; -------------------------------------------------------------------
;;;
;;; Yhis module implements the lognormal distribution.  It is based on
;;; the Random Number Distributions in the GNU Scientific Library.
;;;
;;; Version  Date      Description
;;; 1.0.0    09/23/04  Marked as ready for Release 1.0  Added
;;;                    contracts for functions.  (Doug Williams)

(module lognormal mzscheme
  
  (require (lib "contract.ss"))
  
  (provide/contract
   (random-lognormal
    (case-> (-> random-source? real? (>=/c 0.0) real?)
            (-> real? (>=/c 0.0) real?)))
   (lognormal-pdf
    (-> real? real? (>=/c 0.0) (>=/c 0.0)))
   (lognormal-cdf
    (-> real? real? (>=/c 0.0) (real-in 0.0 1.0))))
  
  (require "../math.ss")
  (require "../random-source.ss")
  (require "../special-functions/error.ss")
  
  ;; random-lognormal: random-source x real x real -> real
  ;; random-lognormal: real x real -> real
  ;;
  ;; This function returns a random variate from the lognormal
  ;; distribution with parameters mu and sigma.
  (define random-lognormal
    (case-lambda
      ((r mu sigma)
       (let ((u 0.0)
             (v 0.0)
             (r2 0.0)
             (normal 0.0))
         (let loop ()
           (set! u (+ -1.0 (* 2.0 (random-uniform r))))
           (set! v (+ -1.0 (* 2.0 (random-uniform r))))
           (set! r2 (+ (* u u) (* v v)))
           (if (> r2 1.0)
               (loop)))
         (set! normal (* u (sqrt (/ (* -2.0 (log r2)) r2))))
         (exp (+ (* sigma normal) mu))))
      ((mu sigma)
       (random-lognormal (current-random-source) mu sigma))))
  
  ;; lognormal-pdf: real x real x real -> real
  ;;
  ;; This function computes the probability density p(x) at x for a
  ;; lognormal distribution with parameters mu and sigma.
  (define (lognormal-pdf x mu sigma)
    (if (not (real? x))
        (raise-type-error 'lognormal-pdf
                          "real" x))
    (if (not (real? mu))
        (raise-type-error 'lognormal-pdf
                          "real" mu))
    (if (not (real? sigma))
        (raise-type-error 'lognormal-pdf
                          "real" sigma))
    (if (<= x 0.0)
        0.0
        (let* ((u (/ (- (log x) mu) sigma))
               (p (* (/ 1.0 (* x (abs sigma) (sqrt (* 2.0 pi))))
                     (exp (/ (- (* u u)) 2.0)))))
          p)))
  
  ;; lognormal-cdf: real x real x real -> real
  ;;
  ;; This function computes the cummulative density d(x) at x for a
  ;; lognormal distribution with parameters mu and sigma.
  (define (lognormal-cdf x mu sigma)
    (if (<= x 0.0)
        0.0
        (* 0.5 (+ 1.0 (erf (/ (- (log x) mu) (* sigma sqrt2)))))))
  
)