;;; -*- syntax: common-lisp; base: 10; mode: lisp -*-
;;; Some probability distributions
;;; Uniform
(defun uniform ()
(random 1.0))
;;; Linear
(defun linear ()
(let* ((ua (random 1.0))
(ub (random 1.0)))
(if (< ua ub) ua ub)))
;;; Triangular
(defun triangular ()
(let* ((ua (random 1.0))
(ub (random 1.0)))
(* 0.5 (+ ua ub))))
;;; Exponential
;;; delta controls the horizontal scale of the density function
(defun exponential (delta)
(/ (- (log (random 1.0))) delta))
;;; Bilateral exponential
(defun biexp (delta)
(let* ((val (random 2.0)))
(if (> val 1.0)
(/ (- (log val)) delta)
(- (/ (- (log (- 2.0 val))) delta)))))
;;; Gaussian
;;; mu = center of the distribution (between 0 and 1)
;;; sigma = standard deviation (% of span) 68.26% of results fall into
;;; mu+-sigma
(defun gaussian (sigma mu &optional (n 12))
(let* ((novr (/ n 2))
(scale (/ (sqrt (/ n 12))))
(sum (loop repeat n sum (random 1.0))))
(+ (* sigma scale (- sum novr)) mu)))
;;; a function we can use to plot the distribution of the
;;; probability function, first argument is number of slots
;;; in which we split the 0..1 range, second argument is the
;;; number of trials (the bigger, the more we average the
;;; random variations) and the last is the distribution
;;; we want to plot with an optional argument list. A key
;;; argument lets you select the range over which values
;;; are counted (compile and load "plot.lisp" before
;;; trying to run this example)
(defun plot-distribution (slots times dist &optional (dist-args nil)
&key (range '(0.0 1.0)))
(let* ((limits (make-array (+ slots 1) :initial-contents
(loop
for l from (first range)
by (* (- (second range)(first range))(/ slots))
repeat (+ slots 1) collect l)))
(bins (make-array slots :initial-element 0)))
(loop repeat times
for each = (apply dist dist-args)
do
(loop
for i from 0 below slots
for low = (aref limits i)
for high = (aref limits (+ i 1))
do
(if (< low each high)
(progn
(incf (aref bins i))
(loop-finish)))))
(loop
for i from 0
for bin across bins
collect (/ bin times 1.0) into data
finally (plot-data data))))
;;; Silly example
(with-sound()
(loop
repeat 60
for time from 0 by 0.1
for freq = 440.0 then (+ 440 (- (* (triangular) 100) 50))
do
(fm-violin time 0.17 freq 0.1)))
(with-sound()
(loop
repeat 60
for time from 0 by 0.1
for freq = 440.0 then (+ 440 (- (* (exponential 10) 100) 50))
do
(fm-violin time 0.17 freq 0.1)))
(defparameter distribs (new cycle :of '(uniform triangular linear)))
(with-sound()
(let* ((time 0))
(loop
repeat 4
for dist = (next distribs)
do
(format t "~s...~%" dist)
(fm-violin time 0.1 3000 0.1)
(loop
repeat 70
for freq = 440.0 then (+ 440 (- (* (funcall dist) 400) 200))
do
(fm-violin time 0.1 freq 0.1)
(incf time 0.02)))))