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<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN"><!-- This collection of hypertext pages is Copyright 1995-2005 by Steve Summit. --><!-- Content from the book "C Programming FAQs: Frequently Asked Questions" --><!-- (Addison-Wesley, 1995, ISBN 0-201-84519-9) is made available here by --><!-- permission of the author and the publisher as a service to the community. --><!-- It is intended to complement the use of the published text --><!-- and is protected by international copyright laws. --><!-- The on-line content may be accessed freely for personal use --><!-- but may not be published or retransmitted without explicit permission. --><!-- --><!-- this page built Sat Dec 24 21:47:46 2005 by faqproc version 2.7 --><!-- from source file librand.sgml dated Sat Jul 3 13:09:31 2004 --><!-- corresponding to FAQ list version 4.0 --><html><!-- Mirrored from c-faq.com/lib/gaussian.html by HTTrack Website Copier/3.x [XR&CO'2008], Sat, 14 Mar 2009 07:58:59 GMT --><head><meta name=GENERATOR content="faqproc"><title>Question 13.20</title><link href="fprand.html" rev=precedes><link href="rand48.html" rel=precedes><link href="index.html" rev=subdocument></head><body bgcolor="#ffffff"><a href="fprand.html" rev=precedes><img src="../images/buttonleft.gif" alt="prev"></a><a href="index.html" rev=subdocument><img src="../images/buttonup.gif" alt="up"></a><a href="rand48.html" rel=precedes><img src="../images/buttonright.gif" alt="next"></a> <a href="../index-2.html"><img src="../images/buttontop.gif" alt="top/contents"></a><a href="../search.html"><img src="../images/buttonsrch.gif" alt="search"></a><hr><p><!-- qbegin --><h1>comp.lang.c FAQ list<font color=blue>·</font><!-- qtag -->Question 13.20</h1><p><font face=Helvetica size=8 color=blue><b>Q:</b></font>How can I generate random numbers with anormal orGaussian distribution?</p><p><hr><p><font face=Helvetica size=8 color=blue><b>A:</b></font>There are a number of ways of doing this.</p><OL><li>ExploittheCentral Limit Theorem(``law of large numbers'')and add up several uniformly-distributed random numbers:<pre>#include <stdlib.h>#include <math.h>#define NSUM 25double gaussrand(){ double x = 0; int i; for(i = 0; i < NSUM; i++) x += (double)rand() / RAND_MAX; x -= NSUM / 2.0; x /= sqrt(NSUM / 12.0); return x;}</pre>(Don't overlook the <TT>sqrt(NSUM / 12.)</TT> correction,thoughit's easy to do so accidentally,especially when <TT>NSUM</TT> is 12.)<li>Use a method described byAbramowitzandStegun:<pre>#include <stdlib.h>#include <math.h>#define PI 3.141592654double gaussrand(){ static double U, V; static int phase = 0; double Z; if(phase == 0) { U = (rand() + 1.) / (RAND_MAX + 2.); V = rand() / (RAND_MAX + 1.); Z = sqrt(-2 * log(U)) * sin(2 * PI * V); } else Z = sqrt(-2 * log(U)) * cos(2 * PI * V); phase = 1 - phase; return Z;}</pre><li>Use amethoddiscussedinKnuthand due originallyto Marsaglia:<pre>#include <stdlib.h>#include <math.h>double gaussrand(){ static double V1, V2, S; static int phase = 0; double X; if(phase == 0) { do { double U1 = (double)rand() / RAND_MAX; double U2 = (double)rand() / RAND_MAX; V1 = 2 * U1 - 1; V2 = 2 * U2 - 1; S = V1 * V1 + V2 * V2; } while(S >= 1 || S == 0); X = V1 * sqrt(-2 * log(S) / S); } else X = V2 * sqrt(-2 * log(S) / S); phase = 1 - phase; return X;}</pre></OL>Thesemethodsallgenerate numbers with mean 0and standard deviation1.(To adjust to someother distribution,multiply bythe standard deviationand add the mean.)Method 1 is poor ``in the tails''(especially if <TT>NSUM</TT> is small),but methods 2 and 3 performquitewell.See the references for more information.<p><a href="sd16.html" rel=subdocument>Additional links</a></p><p>References:Knuth Sec. 3.4.1 p. 117<br>Box and Muller, ``A Note on the Generation of Random Normal Deviates''<br>Marsaglia and Bray, ``A Convenient Method for Generating Normal Variables''<br>Abramowitz and Stegun, <I>Handbook of Mathematical Functions</I><br>Press et al., <I>Numerical Recipes in C</I> Sec. 7.2 pp. 288-290<br></p><!-- aend --><p><hr><a href="fprand.html" rev=precedes><img src="../images/buttonleft.gif" alt="prev"></a><a href="index.html" rev=subdocument><img src="../images/buttonup.gif" alt="up"></a><a href="rand48.html" rel=precedes><img src="../images/buttonright.gif" alt="next"></a> <a href="../questions.html"><img src="../images/buttontop.gif" alt="contents"></a><a href="../search.html"><img src="../images/buttonsrch.gif" alt="search"></a><br><!-- lastfooter --><a href="../about.html">about this FAQ list</a> <a href="../eskimo.html">about eskimo</a> <a href="../search.html">search</a> <a href="../feedback.html">feedback</a> <a href="copyright.html">copyright</a><p>Hosted by<a href="http://www.eskimo.com/"><img src="../../www.eskimo.com/img/link/eskitiny.gif" alt="Eskimo North"></a></body><!-- Mirrored from c-faq.com/lib/gaussian.html by HTTrack Website Copier/3.x [XR&CO'2008], Sat, 14 Mar 2009 07:58:59 GMT --></html>⌨️ 快捷键说明
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