/*
**??????Author:?Tapas?Kanungo?kanungo@cfar.umd.edu
**??????Date:???15?December?1997
**??????File:???backward.c
**??????Purpose:?Backward?algorithm?for?computing?the?probabilty
**??????????????of?observing?a?sequence?given?a?HMM?model?parameter.
**??????Organization:?University?of?Maryland
**
**??????$Id:?backward.cv?1.3?1998/02/23?07:56:05?kanungo?Exp?kanungo?$
*/

#include?
#include?“hmm.h“
static?char?rcsid[]?=?“$Id:?backward.cv?1.3?1998/02/23?07:56:05?kanungo?Exp?kanungo?$“;

void?Backward（HMM?*phmm?int?T?int?*O?double?**beta?double?*pprob）
{
????????int?????i?j;???/*?state?indices?*/
????????int?????t;??????/*?time?index?*/
????????double?sum;
?
?
????????/*?1.?Initialization?*/
?
????????for?（i?=?1;?i?<=?phmm->N;?i++）
????????????????beta[T][i]?=?1.0;
?
????????/*?2.?Induction?*/
?
????????for?（t?=?T?-?1;?t?>=?1;?t--）?{
????????????????for?（i?=?1;?i?<=?phmm->N;?i++）?{
????????????????????????sum?=?0.0;
????????????????????????for?（j?=?1;?j?<=?phmm->N;?j++）
????????????????????????????????sum?+=?phmm->A[i][j]?*
????????????????????????????????????????（phmm->B[j][O[t+1]]）*beta[t+1][j];
????????????????????????beta[t][i]?=?sum;
?
????????????????}
????????}
?
????????/*?3.?Termination?*/
????????*pprob?=?0.0;
????????for?（i?=?1;?i?<=?phmm->N;?i++）
????????????????*pprob?+=?beta[1][i];
?
}

void?BackwardWithScale（HMM?*phmm?int?T?int?*O?double?**beta?
	double?*scale?double?*pprob）
{
????????int?????i?j;???/*?state?indices?*/
????????int?????t;??????/*?time?index?*/
	double?sum;
?
?
????????/*?1.?Initialization?*/
?
????????for?（i?=?1;?i?<=?phmm->N;?i++）
????????????????beta[T][i]?=?1.0/scale[T];?
?
????????/*?2.?Induction?*/
?
????????for?（t?=?T?-?1;?t?>=?1;?t--）?{
????????????????for?（i?=?1;?i?<=?phmm->N;?i++）?{
			sum?=?0.0;
????????????????????????for?（j?=?1;?j?<=?phmm->N;?j++）
????????????????????????	sum?+=?phmm->A[i][j]?*?
					（phmm->B[j][O[t+1]]）*beta[t+1][j];
????????????????????????beta[t][i]?=?sum/scale[t];
?
????????????????}
????????}
?
}

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????2012??1999-05-06?00:51??UmdHmm-v1.02\backward.c

?????文件???????3563??2012-11-01?10:59??UmdHmm-v1.02\backward.o

?????文件???????3968??1999-05-06?00:51??UmdHmm-v1.02\baum.c

?????文件???????6703??2012-11-01?10:59??UmdHmm-v1.02\baum.o

?????文件???????1773??1999-05-06?02:01??UmdHmm-v1.02\CHANGES

?????文件??????17976??1999-05-06?00:51??UmdHmm-v1.02\COPYING

????....SH.????????78??2012-07-25?17:14??UmdHmm-v1.02\Desktop.ini

?????文件??????71068??1999-05-06?02:05??UmdHmm-v1.02\esthmm

?????文件???????5365??2012-10-30?20:31??UmdHmm-v1.02\esthmm.c

?????文件??????11373??2012-11-01?10:59??UmdHmm-v1.02\esthmm.o

?????文件???????2215??2012-10-30?18:02??UmdHmm-v1.02\forward.c

?????文件???????4016??2012-11-01?10:59??UmdHmm-v1.02\forward.o

?????文件??????47120??1999-05-06?02:04??UmdHmm-v1.02\genseq

?????文件???????2640??1999-05-06?00:52??UmdHmm-v1.02\genseq.c

?????文件???????8567??2012-11-01?10:59??UmdHmm-v1.02\genseq.o

?????文件???????2539??1999-05-06?00:51??UmdHmm-v1.02\hmm.h

?????文件????????718??1999-05-06?00:51??UmdHmm-v1.02\hmmrand.c

?????文件???????2624??2012-11-01?10:59??UmdHmm-v1.02\hmmrand.o

?????文件?????180218??1999-05-06?02:00??UmdHmm-v1.02\hmmtut.pdf

?????文件?????254653??1999-05-06?01:57??UmdHmm-v1.02\hmmtut.ps

?????文件???????3954??1999-05-06?00:51??UmdHmm-v1.02\hmmutils.c

?????文件??????10618??2012-11-01?10:59??UmdHmm-v1.02\hmmutils.o

?????文件???????1143??1999-05-06?00:53??UmdHmm-v1.02\Makefile

?????文件???????3980??1999-05-06?00:51??UmdHmm-v1.02\nrutil.c

?????文件????????764??1999-05-06?00:51??UmdHmm-v1.02\nrutil.h

?????文件???????9746??2012-11-01?10:59??UmdHmm-v1.02\nrutil.o

?????文件???????3097??1999-05-06?01:49??UmdHmm-v1.02\README

?????文件???????2852??1999-05-06?00:51??UmdHmm-v1.02\sequence.c

?????文件???????8868??2012-11-01?10:59??UmdHmm-v1.02\sequence.o

?????文件????????213??1999-05-06?00:51??UmdHmm-v1.02\t2.100.seq

............此處省略39個文件信息