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INFINITY -数学とかプログラミングとか-

統計とプログラムを使って役に立たせたい

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2次元版、勾配降下法1(最急降下法)


#loss function


x=seq(-3,3,length=50)
y=seq(-3,3,length=50)
lossfunc1=function(x,y){
	return(x^2+y^2)
}




z=matrix(0,50,50)
for(i in 1:50){
	for(j in 1:50){
		z[i,j]=pdf(x[i],y[j])
	}
}


persp(x,y,z,theta = 0, phi = 20, expand = 0.5,col = "lightblue",xlim=c(-3,3),ylim=c(-3,3),zlim=c(-0.5,3))

f:id:infinity_th4:20120616060420j:image:w360

dffunc1=function(vecw){
	x=vecw[1];y=vecw[2]
	return(matrix(c(2*x,2*y),2,1))
}

vecw_list=c()
cntlist=c()
errorlist=c()

grad201=function(vecw,alpha,times){
	cnt=1
	for(i in 1:times){
		vecw_before=vecw
		vecw=vecw-alpha*dffunc1(vecw)
		#if(cnt==1||0==cnt%%1000000){
			vecw_list<<-c(vecw_list,vecw)
			cntlist<<-c(cntlist,cnt)
			errorlist<<-c(errorlist,abs(vecw-vecw_before))
			printf("cnt:%d;vecw=(%.8f,%.8f),error=%.8f\n",cnt,vecw[1],vecw[2],c(vecw-vecw_before)%*%c(vecw-vecw_before))

		#}
		if(c(vecw-vecw_before)%*%c(vecw-vecw_before)<=1.0e-8){
			break
		}
		cnt=cnt+1
	}

}


実行結果:

> vecw=matrix(c(1,2),2,1)
> grad201(vecw,0.1,1e+3)
cnt:1;vecw=(0.80000000,1.60000000),error=0.20000000
cnt:2;vecw=(0.64000000,1.28000000),error=0.12800000
cnt:3;vecw=(0.51200000,1.02400000),error=0.08192000
cnt:4;vecw=(0.40960000,0.81920000),error=0.05242880
cnt:5;vecw=(0.32768000,0.65536000),error=0.03355443
cnt:6;vecw=(0.26214400,0.52428800),error=0.02147484
cnt:7;vecw=(0.20971520,0.41943040),error=0.01374390
cnt:8;vecw=(0.16777216,0.33554432),error=0.00879609
cnt:9;vecw=(0.13421773,0.26843546),error=0.00562950
cnt:10;vecw=(0.10737418,0.21474836),error=0.00360288
cnt:11;vecw=(0.08589935,0.17179869),error=0.00230584
cnt:12;vecw=(0.06871948,0.13743895),error=0.00147574
cnt:13;vecw=(0.05497558,0.10995116),error=0.00094447
cnt:14;vecw=(0.04398047,0.08796093),error=0.00060446
cnt:15;vecw=(0.03518437,0.07036874),error=0.00038686
cnt:16;vecw=(0.02814750,0.05629500),error=0.00024759
cnt:17;vecw=(0.02251800,0.04503600),error=0.00015846
cnt:18;vecw=(0.01801440,0.03602880),error=0.00010141
cnt:19;vecw=(0.01441152,0.02882304),error=0.00006490
cnt:20;vecw=(0.01152922,0.02305843),error=0.00004154
cnt:21;vecw=(0.00922337,0.01844674),error=0.00002658
cnt:22;vecw=(0.00737870,0.01475740),error=0.00001701
cnt:23;vecw=(0.00590296,0.01180592),error=0.00001089
cnt:24;vecw=(0.00472237,0.00944473),error=0.00000697
cnt:25;vecw=(0.00377789,0.00755579),error=0.00000446
cnt:26;vecw=(0.00302231,0.00604463),error=0.00000285
cnt:27;vecw=(0.00241785,0.00483570),error=0.00000183
cnt:28;vecw=(0.00193428,0.00386856),error=0.00000117
cnt:29;vecw=(0.00154743,0.00309485),error=0.00000075
cnt:30;vecw=(0.00123794,0.00247588),error=0.00000048
cnt:31;vecw=(0.00099035,0.00198070),error=0.00000031
cnt:32;vecw=(0.00079228,0.00158456),error=0.00000020
cnt:33;vecw=(0.00063383,0.00126765),error=0.00000013
cnt:34;vecw=(0.00050706,0.00101412),error=0.00000008
cnt:35;vecw=(0.00040565,0.00081130),error=0.00000005
cnt:36;vecw=(0.00032452,0.00064904),error=0.00000003
cnt:37;vecw=(0.00025961,0.00051923),error=0.00000002
cnt:38;vecw=(0.00020769,0.00041538),error=0.00000001
cnt:39;vecw=(0.00016615,0.00033231),error=0.00000001
>