chez-scmutils/scmutils/numerics/statistics/gauss.scm

#| -*-Scheme-*-

Copyright (C) 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994,
    1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
    2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Massachusetts
    Institute of Technology

This file is part of MIT/GNU Scheme.

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it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at
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WITHOUT ANY WARRANTY; without even the implied warranty of
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General Public License for more details.

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|#

(declare (usual-integrations))

;;; UNIFORM-RANDOM produces an inexact number x,    0 <= x < 1

#|
(define uniform-random
  (let* ((random-max (expt 2 23))
	 (frandom-max (exact->inexact random-max)))
    (lambda ()
      (/ (random random-max)
	 frandom-max))))
|#

(define (uniform-random) (random 1.))

(define (nonzero-uniform-random)
  (let ((x (uniform-random)))
    (if (= x 0.)
	(nonzero-uniform-random)
	x)))

;;; Given uniform random numbers, we can produce pairs of
;;; gaussian-distributed numbers, with zero mean and unit
;;; standard deviation, by the following trick:

(define* (gaussian-random-pair #:optional continue)
  ;; continue = (lambda (y1 y2) ...)
  (let ((continue (if (default-object? continue) cons continue))
	(x1 (uniform-random))
	(x2 (uniform-random)))
    (let ((r (sqrt (* -2.0 (log x1)))))
      (continue (* r (cos (* 2pi x2)))
		(* r (sin (* 2pi x2)))))))

(define (gaussian-random)
  (gaussian-random-pair (lambda (x y) x)))

(define (gaussian-random-list d)
  (let lp ((j d) (t '()))
    (if (fix:= j 0)
	t
	(gaussian-random-pair
	 (lambda (x1 x2)
	   (if (fix:= j 1)
	       (cons x1 t)
	       (lp (fix:- j 2) (cons x1 (cons x2 t)))))))))


;;; Makes a list of n 2-vectors of gaussian-distributed random numbers  

(define (gaussian-random-pairs n)
  (if (fix:= n 0) 
      '()
      (cons (gaussian-random-pair vector)
	    (gaussian-random-pairs (fix:- n 1)))))


;;; Makes a list of n d-vectors of gaussian-distributed random numbers  

(define (gaussian-random-tuples d n)
  (if (fix:= n 0) 
      '()
      (cons (list->vector (gaussian-random-list d))
	    (gaussian-random-tuples d (fix:- n 1)))))


;;; For adding zero-mean noise with a given standard deviation to a vector.

(define* ((add-noise sigma) v)
  (list->vector (map (lambda (signal noise)
		       (+ signal (* sigma noise)))
		     (vector->list v)
		     (gaussian-random-list (vector-length v)))))