auc.b <-
function(x=dat.sin,xt=dat.sin,label1=TRUE,T=5,lambda=0.001){
        N=T	
	probs=1:30/30
	y=x[,dim(x)[2]]==label1   # training data xのラベル y=Tがpresent(kyphosis(後彎症)あり)，y=Fがabsent
	x=x[,1:2]
	
	n0=sum(y==F)   # y=Fのサンプル数
	n1=sum(y==TRUE)　#y=Tのサンプル数　　
	n = dim(x)[1]　　#n=n0+n1
	m = dim(x)[2]  #マーカーの数(3つ)
	sd.n=1
	
	T.auc=0
	F0=rep(0,n0)
        F1=rep(0,n1)
	
	B=list()
	Z=list()
	Fz=list()
	for(i in 1:m){
		B[[i]]=quantile(x[,i],probs=probs)
		Z[[i]]=c(min(x[,i]),min(x[,i]),B[[i]],max(x[,i]))
		Fz[[i]]=rep(0,length(Z[[i]]))
	}
	nb=unlist(lapply(B,length))
	M=NULL
	for(i in 1:m){
		Md=matrix(x[,i],n,nb[i])
		Md=t(t(Md)>=B[[i]])
		M=cbind(M,Md)
	}
	M0=M[y==F,]
	M1=M[y==TRUE,]
	a=numeric(0)
	b=numeric(0)
	p=numeric(0)
	alpha=numeric(0)


	ff=function(x){
		nb=length(x)-3
		2*(x[1:nb]-3*x[2:(nb+1)]+3*x[3:(nb+2)]-x[4:(nb+3)])
	}

	nn=100
	eps=0.1
	grid1=seq(min(x[,1])-eps,max(x[,1])+eps,length=nn)
	grid2=seq(min(x[,2])-eps,max(x[,2])+eps,length=nn)
	Grid=expand.grid(grid1,grid2)

windows(width=12,height=8)

	xx=-100:800/100
	for(k in 1:N){#N:ブースティングの繰り返し数
		T.auc=T.auc+1
		w1=unlist(lapply(Fz,ff))
		d=0
		for(i in 1:n0) # 弱判別機f_tの選択のための計算(p969のstep a.)
			d=d+apply(1/(n0*n1)*dnorm(F1-F0[i],sd=sd.n)*(t(t(M1)-M0[i,])),2,sum)
		d=d-lambda*w1

		maxd=d[order(d)[length(d)]]
		mind=d[order(d)[1]]
		if(maxd>=-mind){
			a[k]=1
			l=order(d)[length(d)]
		}
		else{
			a[k]=-1
			l=order(d)[1]
		}
		ii=0
		ld=l
		while(ld>0){
			ii=ii+1
			ld=ld-nb[ii]
		}
		p[k]=ii  #選ばれたf_tに対応するマーカーのid
		ld=ld+nb[ii]
		b[k]=B[[p[k]]][ld] #選ばれたf_t(stump)
		if(k<4)
			al=1/sd.n
		else 
			al=median(alpha[(k-3):(k-1)])/sd.n
		al0=0
		nz=length(Fz[[p[k]]])

		AA=0
		while(abs(al-al0)>0.000001&AA<5){#弱判別機の係数\alphaの更新
			AA=AA+1
			al0=al
			d1=0
			d2=0
			for(i in 1:n0){
				d1=d1+sum(1/(n0*n1)*dnorm(F1-F0[i]+al0*a[k]*(M1[,l]-M0[i,l]),sd=sd.n)*a[k]*(M1[,l]-M0[i,l]))
				d2=d2-sum(1/(n0*n1)*(F1-F0[i]+al0*a[k]*(M1[,l]-M0[i,l]))*dnorm(F1-F0[i]+al0*a[k]*(M1[,l]-M0[i,l]),sd=sd.n)/sd.n^2*(M1[,l]-M0[i,l])^2)
			}

			dw1=2*(a[k]*(Fz[[p[k]]][ld]-3*Fz[[p[k]]][ld+1]+3*Fz[[p[k]]][ld+2]
				-Fz[[p[k]]][ld+3])+2*al0)
			dw2=4
			al=al0-(d1-lambda*dw1)/(d2-lambda*dw2)
		}

		alpha[k]=al

		if(a[k]==1){
			F0=F0+al*M0[,l]
			F1=F1+al*M1[,l]
			Fz[[p[k]]][(ld+2):nz]=Fz[[p[k]]][(ld+2):nz]+al
		}
		else{
			F0=F0+al*(!M0[,l])
			F1=F1+al*(!M1[,l])
			Fz[[p[k]]][1:(ld+1)]=Fz[[p[k]]][1:(ld+1)]+al
		}
		max.fz=0
		for(i in 1:m){
			if(max.fz<max(Fz[[i]]-min(Fz[[i]])))
			max.fz=max(Fz[[i]]-min(Fz[[i]]))
		}

		n.p=length(unique(p))
		n.row=round(sqrt(n.p))
		n.col=ceiling(n.p/n.row)
		par(mfcol=c(n.row,n.col+1))
		for(i in sort(unique(p))){
			plot(Z[[i]],Fz[[i]]-min(Fz[[i]]),xlab=names(x)[i],ylab="score",type="s",ylim=c(0,max.fz))
			rug(x[y==F,i],side=1)
			rug(x[y==T,i],side=3,col=2)
			title(paste("T=",T.auc))
		}
		
		Fs=data.frame(a,b,p,alpha)
		
        	val=apply(x[,1:m],1,F.v.auc,Fs=Fs)
		

		q=quantile(val,probs=1:100/100)
		err=apply(y!=t(t(matrix(val,n,length(q)))>=q),2,mean)
		ord=order(err)[1]
		thres=q[ord]

		plot(x)
		points(x[y,],col="red")
		valG=apply(Grid,1,F.v.auc,Fs=Fs)
		A=matrix(valG,nn,nn)
		contour(grid1,grid2,A,add=T,lty=1,drawlabels=F,levels=thres,lwd=2,col="blue")
		title(paste("T=",T.auc))
		points(xx,sin(xx),type="l",col="gray")
print(paste("T=",k,", 誤判別率=",min(err)))
	}





		
}
F.v.auc <-
function (x, Fs) 
{
    a = Fs[, 1]
    b = Fs[, 2]
    p = Fs[, 3]
    alpha = Fs[, 4]
    return((a * ((x[p] - b) >= 0)) %*% alpha)
}
dat.sin <-
structure(list(x1 = c(1.19925745746754, 2.08237121792183, 3.74505056248484, 
6.52285342195077, 0.670568807893061, 6.44152823864612, 6.82492030496778, 
4.47351056574375, 4.21106820496354, -0.488212872277646, 0.706125572458451, 
0.462452298431516, 4.69073754913244, 2.18160227514107, 5.37673913899031, 
3.1225350494347, 4.944167083816, 7.21614199080174, 2.14790181450192, 
5.4397228343731, 6.74233663684036, 0.757215815316545, 4.39793456431693, 
0.0399961261083075, 1.2134383169786, 2.19825457825313, -0.889085389119998, 
2.16739030764483, 6.20381043506038, 1.81917380867671, 2.99315892935312, 
3.96631483584809, 3.08809410303343, 0.542474899946189, 5.85328651623781, 
4.53703386413326, 5.57883594474627, -0.105882944042022, 4.99463187488545, 
2.40666231284192, 5.80005028140399, 4.35971949030998, 5.48517715310525, 
3.5809022509243, 3.38776544361898, 5.53838394046072, -0.806743327629891, 
2.95298506285523, 5.06589040039875, 4.73802385047643, 2.95621183649373, 
6.13355768490113, 2.6288395216771, 1.02770120834461, -0.414552355163502, 
-0.176103363496777, 1.61973715801276, 3.29594370868211, 4.48351072226139, 
2.36984982903658, 6.56152044310365, 1.43197114338497, 2.80252647878427, 
1.75328668141486, 4.3912806897154, 1.1372008070433, 2.96387896933725, 
5.34749328782912, -0.302167196730748, 6.25044878002311, 1.8086039768143, 
5.95323997493045, 1.87164358364151, 1.76471960268688, 2.94570563425036, 
6.39024414656158, 6.15948400354204, 2.23035565645211, 5.43869139155627, 
6.95697688036778, 2.6003650579052, 4.90189111788019, 2.31322747940842, 
1.69495216409659, 5.27109314079584, 0.678937509695653, 4.89034886158672, 
0.00799673225642983, 1.03342685191128, 0.18701673010003, 0.984894850297149, 
-0.511835632079996, 4.32019266604674, 6.25830026769685, 5.45189461175767, 
5.60425675187793, 2.77112266495522, 2.39680244311599, 5.71658848094791, 
4.01077454184357, 4.42319962130752, 1.92559845343322, 1.23861486953348, 
7.22258603018245, 4.24734210019492, 0.76604249300416, 0.0716151327516601, 
2.9603402769149, 6.65428007125802, 3.95964804555054, 7.08580275747029, 
5.06157298234261, 1.95483511684231, 2.57397653400473, 0.227663821759987, 
-0.891676018925848, 4.92716632498399, -0.14530585452041, 2.6966559592371, 
4.30207557219134, 7.21558308464415, 3.10509344243102, 3.01195686379656, 
0.436654999821654, 5.25232175710454, 2.75970044729868, 3.23411404240643, 
0.719134632932118, 0.894017768248455, 3.93439285517199, 3.76177294631392, 
-0.361661457536796, -0.705610793369912, 4.32439417648295, 6.69189177763866, 
3.95411036518611, 3.64604483469305, 3.35718511389367, 7.15972628459555, 
3.20489128405457, 4.6556601811831, 3.98267737569606, 0.978593521932405, 
1.13843621062821, 5.04100675662091, 2.74872806113651, 0.450607475035545, 
5.18504013581726, -0.130367919607525, 6.16118601919036, 4.09121819851987, 
3.61505570592798, 1.72332345851526, 2.75337173117835, 3.14524531155265, 
0.498149585075293, 3.38702842737115, -0.376477049160404, 1.30070386030511, 
0.76182953259225, 1.35897232763724, 6.41423032207403, 2.69624987370851, 
5.46075937888777, 6.29433065085451, 2.42198438219304, -0.47146253176207, 
1.77890506185973, 4.9947561274683, 1.79653036990523, 4.22183699678772, 
5.96296612274884, 6.09149722613806, 2.24170144643692, 2.15170136271223, 
6.41714039598042, 4.33698686052853, 5.13849177451062, 4.01384061467776, 
6.48039233553873, 1.43302130499314, 0.584242932077063, 6.34263742911305, 
3.16925423273015, 6.26483015393091, 0.567125833623345, 5.27950806486011, 
5.00115858282071, 6.81704754892077, 3.53625816309848, 4.89550634760057, 
2.22137300876538, -0.164449203314144, 6.68101503551301, 1.34606728509171, 
3.89182691189978, -0.0858626586388305, 5.96207549901162, 1.63375211919813, 
5.48450269225775, 1.21582005271036, 0.811079411232576, 3.28072396203787, 
1.22776759224339, 0.500650827156082, 3.29546224270041, 3.66163534493478, 
0.0698301592618791, 1.12354037081715, 4.94679092954428, 6.96353665958202, 
-0.170514811065808, 5.32191496783485, 6.8521809806723, 5.78090282280763, 
1.55364250403959, 4.38058704305765, 6.89681986519099, 6.89994427369387, 
1.81611074249775, 1.17412169243768, 0.370485588326501, 1.66857771303975, 
3.22546161572174, 6.65340206621559, 3.23237386595817, 1.13392464248723, 
-0.615155863844506, 2.46118081959642, 6.07385269594201, 1.87617604793992, 
0.0887610981813369, 2.10194409412635, 4.23017075851793, 2.23109609207116, 
4.71231526458885, 4.71053904877797, 3.59634468869943, 2.55865858217055, 
2.74996417251004, 1.53832629949833, 3.79061289130441, 6.54076592824981, 
0.181216037795897, 2.43791639176895, 0.747137078832619, 2.55141877237161, 
0.0990956530039224, 2.81106412028221, 6.81068805845949, 5.31157069490084, 
6.72746498720031, 2.8987172154896, 3.99963181390884, 3.01725939633599, 
-0.0987371177727665, 1.0519672631519, 3.12928823623071, 2.08852403796103, 
6.74222182465351, 3.34027378135831, 1.62696808477515, 1.30244413125375, 
5.52334396248497, 4.81862716266701, 0.366954511864072, -0.466086261919139, 
5.25136651631564, 4.13897127007079, 0.404635782102467, -0.484669476050224, 
-0.0968903641715566, 2.16182727610462, 0.402433680038649, 1.47379434831437, 
0.592107196589114, 1.13018694188863, 0.50117677196372, 2.95367790692126, 
5.38415774931091, -0.769834115926421, 3.36781288028025, 6.29184597719906, 
2.0901530414517, -0.602745625335581, 0.148283456460177, 1.66297880799474, 
0.282498927960454, 0.0952704527594561, 0.833118008943111, 0.875154084677248, 
0.0885475022307507, 7.13047203254263, 1.70871529717401, 3.19907379382415, 
4.64451462595102, -0.178563941481621, -0.0151080766997569, -0.582198953480076, 
6.69718241470055, 4.58048326839892, -0.214274805324139, 3.08026495023732, 
2.82311942497309, 2.1079880555032, 7.20945849322114, 0.460745640692653, 
5.73783456753934, -0.433043820988381, 2.31699945857669, 0.169124605027743, 
0.601221411960229, 5.96907217859556, 4.96318097093401, 1.21336720061445, 
3.10019035146426, -0.311552182716351, 1.93128874228294, 7.02813613611535, 
4.17462339710012, 4.50515612121066, 1.58840973135526, 2.36040223943616, 
7.25069344865787, 6.08280561072065, 6.89841806348344, 5.72847360586691, 
5.47895940937025, 1.21888418153655, 5.31304235138673, 7.1698016634228, 
1.43198916981631, 2.30789922154882, 5.72703590587793, -0.360938427346529, 
2.01256807168457, 2.66607542122521, 0.298092199927839, 3.82251413975232, 
7.03603310547629, 7.19621048176395, 0.46158491600424, 3.49056676603338, 
2.18326035196569, 4.60079213098989, 1.23061027965814, 2.88689251103358, 
0.423051917617288, 2.05806473044813, 5.00866629543663, 3.02686311793619, 
-0.471512345038529, 5.49854180504253, 2.46503562739132, 7.12595458609175, 
1.34318022685148, 6.02316496302636, -0.318797211251065, 6.34270209823637, 
2.90908969582543, -0.0962965025129453, 1.7606033046014, 5.93647662228989, 
1.29319854105619, 3.86252085820508, 5.93080844267403, -0.410618033969895, 
4.82124656109127, 4.78849313899297, 2.84308637744248, 2.6191813543528, 
3.65661450841195, 6.69079861835352, 0.90899601625584, 0.837324431470968, 
2.48072611325883, 1.76261463738002, 6.16336119442907, 0.467735174890041, 
3.0862504448021, 2.55939544606062, 3.67390197370975, 4.43511405098999, 
7.1055446350847, 0.923033813749487, 0.994687075101798, 5.60034094311766, 
5.88889093021361, -0.0597946337718063, 6.97929193993052, 0.220302877891025, 
0.189688582025904, 6.66385100508041, 3.19986985352929, 0.282659669264919, 
1.88505044060964, 4.4654198262281, 1.58246835111492, 1.91214769814154, 
0.224633387143907), x2 = c(0.381306261755526, -0.755832085199654, 
1.09050752855837, 0.954836380854249, 1.06487293057144, 0.536857802979648, 
-0.31114304177463, 0.674442096613348, -1.17324117925018, 1.05674090925604, 
1.18499814290553, -0.342226211540401, 0.594324152357876, 0.702981657162309, 
0.49406161531806, -0.0580199070274829, -0.0128291375935077, -0.460674122907221, 
0.468029391020536, 0.774703933484852, -0.156677662208676, 0.0353583667427302, 
0.391226322390139, -0.856400192342698, -0.373230255022645, -0.226167402416468, 
-0.995253586024046, 1.03817262779921, 0.812121760100126, 0.910639910772443, 
1.04570992235094, -1.02609447967261, -0.290977342799306, 0.0908758146688342, 
-0.947879667207599, 0.724050493352115, 0.575140189938247, -1.07484236788005, 
-0.0427930243313313, 1.00924281757325, -1.10033177062869, -0.494419682398438, 
0.00204116944223642, 0.263397444225848, -0.565802280977368, -0.184563337080181, 
-0.320247320830822, 1.06201277375221, -0.903063443675637, -1.03192156981677, 
1.11436089109629, -0.137975740246475, -0.311346287280321, -0.791415407694876, 
-1.06994296945631, 0.378787366300821, 0.187588600069284, 1.16904423348606, 
0.24910176359117, -1.04412019494921, -0.810938203521073, -0.059044990874827, 
-1.19536119662225, -0.14049805663526, -0.573768630623817, 1.052192989178, 
0.517999880947173, -0.80859485194087, -0.0571487557142973, 0.456616135127842, 
-0.093851569108665, 1.0923521719873, 0.510096293874085, -0.246844960190356, 
-0.917470530979335, -0.623720944672823, 0.872713359631598, -0.153656635992229, 
-0.0051166752353311, 0.460626413114369, 0.624751876294613, -0.827037065662444, 
0.838697023317218, 1.07236276566982, 0.212206056900322, 0.00540195666253562, 
-0.744528197497129, -1.1955915402621, 0.906187349371612, -0.878132789209485, 
-1.14542106203735, 1.05392809454352, -0.496923065185547, -0.805616221390665, 
-0.242153866030276, -0.0970190109685063, -0.158325963467359, 
0.040823583304882, 0.830989806354046, -1.06760571263731, 0.130024946853518, 
0.451860570162535, 0.379338128864765, 0.392022540606558, -0.0666379138827324, 
1.12686759866774, -0.234727049432695, 0.838925049081445, 0.61594777777791, 
0.0782429264858364, 0.897959185950458, -0.0789237225428223, -1.18049170710146, 
0.546640811115503, 0.519814749062061, -0.750176709517837, 0.350561464391649, 
0.100750271603465, -0.395230176486075, 0.330980935692787, 0.790082553215325, 
0.50154047627002, -0.363479157909751, -0.892013100162149, -0.268611626699567, 
1.02762611601502, 0.730537851154804, 0.620872336998582, 1.09739973340183, 
1.18539330884814, 0.255458387173712, -1.12949480284005, -0.392531141079962, 
-0.533620591834188, -0.91872587967664, -1.09627617839724, -0.311256514303386, 
-0.391492058895528, -0.783233871683478, 0.292255870811641, -0.245175294019282, 
1.09362184479833, 0.368038663454354, -0.411015079915524, -0.726847887597978, 
-0.92317842040211, 1.19031714890152, -0.289735859446228, 0.148771422542632, 
0.558523242361844, 0.889933327026665, 0.173208623193204, -1.17351342961192, 
0.975156627036631, 0.649568715691566, -0.281988903880119, -0.97428986672312, 
-1.08083139862865, 0.770789563469589, 0.790378330461681, 0.371358901821077, 
-0.881213248707354, -0.379656237177551, 0.555291789583862, 0.977499398589134, 
0.47087279856205, -0.620209866575897, 0.345857348665595, -0.526199487224221, 
1.09832764975727, -0.819849703833461, -0.195986419916153, -0.595176486298442, 
-0.973463357426226, 0.786522647179663, 0.0607332089915871, 0.402594305947423, 
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