2.1 R, ( ), Download R for Windows base. R ( ) R win.exe, 2.,.,.,. R > 3*5 # [1] 15 > c(19,76)+c(11,13)

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Download "2.1 R, ( ), Download R for Windows base. R ( ) R win.exe, 2.,.,.,. R > 3*5 # [1] 15 > c(19,76)+c(11,13)"

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1 3 ( ) R , 2016/4/7( ), 4/14( ), 4/21( ) R, ( ) ggm , ( ) ( ) ,,.,,.,,. 2.,, 2 (p. 10). 1, 6 356, matsui@mist.i.u-tokyo.ac.jp; TA. jikken3.html 1

$2.1 R, ( ), http://cran.md.tsukuba.ac.jp/, Download R for Windows base. R (2014-4-17 ) R-3.1.0-win.exe, 2.,.,.,. R > 3*5 # [1] 15 > c(19,76)+c(11,13) # [1] 30 89 > x <- c(3,1,4,1,5,9) # > 1:4 # [1] 1 2 3 4 > 1:4+1 # (1:4)+1 [1] 2 3 4 5 > f <- function(x,y){ sqrt(x^2+y^2) } # > f(3,4) [1] 5 R,.$

2 2.1 R, ( ), Download R for Windows base. R ( ) R win.exe, 2.,.,.,. R > 3*5 # [1] 15 > c(19,76)+c(11,13) # [1] > x <- c(3,1,4,1,5,9) # > 1:4 # [1] > 1:4+1 # (1:4)+1 [1] > f <- function(x,y){ sqrt(x^2+y^2) } # > f(3,4) [1] 5 R, ,. 2. R...,., browser()., R, URL. 2 PC R 2

3 1. R R web 3 sum, prod, cumsum abs, log, sqrt mean, sd, min, median, max scale combine, c list, matrix, array %*% t rbind, cbind diag cor det or apply solve read.table, write.table plot, pairs EPS dev.copy2eps which pnorm, rnorm ls, rm browser for, while, repeat 2.2 ggm, ggm (Graphical Gaussian Models). 1. R ( Japan (Tsukuba) ). 2. ggm. 3. package ggm successfully unpacked and MD5 sums checked. graph RBGL graph R : graph > source(" > bioclite("graph") RBGL 3 3

4 RBGL > source(" > bioclite("rbgl").,., R 1.,,,. > library(ggm) 2.3,,.,,,.., ggm marks,.. > data(marks) > marks mechanics vectors algebra analysis statistics ( ) , 5, 88.,., (X t,i ) 1 t n,1 i p (n = 88, p = 5). X 2,3 = 80. summary (min), 1 (1st Qu.), = 2 (median), (mean), 3 (3rd Qu.), (max)., X i = 1 n 4 n t=1 X t,i

5 , 25%, 50%, 75%. > summary(marks) mechanics vectors algebra analysis statistics Min. : 0.00 Min. : 9.00 Min. :15.00 Min. : 9.00 Min. : st Qu.: st Qu.: st Qu.: st Qu.: st Qu.:31.00 Median :41.50 Median :51.00 Median :50.00 Median :49.00 Median :40.00 Mean :38.97 Mean :50.59 Mean :50.60 Mean :46.68 Mean : rd Qu.: rd Qu.: rd Qu.: rd Qu.: rd Qu.:51.50 Max. :77.00 Max. :82.00 Max. :80.00 Max. :70.00 Max. : (r i,j ) r i,j = s i,j si,i s j,j, s i,j = 1 n (X t,i n X i )(X t,j X j ) t=1 > cor(marks) mechanics vectors algebra analysis statistics mechanics vectors algebra analysis statistics > round(cor(marks),3) # 3 mechanics vectors algebra analysis statistics mechanics vectors algebra analysis statistics i j,,. R,., ( ) 1. marks,, mechanics statistics., 2,., vectors mechanics statistics,. 4,. 5

6 mechanics vectors algebra analysis statistics :. > pairs(marks), 2,.,,,.,, G, V E V V., (= G = (V, E)). V = {a, b, c, d}, E = {(a, b), (a, c), (b, d)} ggm., drawgraph adjust TRUE,.. > amat <- UG(~ a*b + a*c + b*d) > amat a b c d a b c d > drawgraph(amat,adjust=false) d a c b 6

7 2.5 1 ( ),, ( ),,., web (1997),., R = (r i,j ), R 1 = (r i,j )., p i,j = r i,j r i,i r j,j (i j), 1 (i = j) (1), i j. P = (p i,j )., ( ) 1.,.,, ( )., S1 = mechanics, S2 = vectors, S3 = algebra, S4 = analysis, S5 = statistics. 1: ( ) ( ). S1 S2 S3 S4 S5 S S S S1 S2 S3 S4 S5 S S S S , R, P. I cor2par <- function(r){ X <- solve(r) p <- nrow(r) P <- matrix(0,p,p) dimnames(p) <- dimnames(r) for(i in (1:p)){ for(j in (1:p)){ if(i!= j) P[i,j] <- -X[i,j]/sqrt(X[i,i]*X[j,j]) if(i == j) P[i,j] <- 1 }} P } 7

8 II cor2par <- function(r){ X <- solve(r) d <- sqrt(diag(x)) P <- -X / (d %*% t(d)) diag(p) <- 1 P } 2.6, 4 8.,,,, StatLib web. : "math" "phys" "chem" "eng" "1" "2" "3" "4" "5" "6" mark4.txt R...,, : > X <- read.table("mark4.txt") 3., ( Word ) ( ) i j p i,j, 8

9 i j, i j.. 1 ( ).., i j,, p i,j., i j p i,j = 0., p i,j = 0, i j,.,, analysis mechanics (p 41 = 0.001) 0.,, vectors, algebra, statistics, analysis mechanics.,, 5., ,, 10 4.,, 2.., ,,. 2: ( ) ( ) S1 S2 S3 S4 S5 S S S S1 S2 S3 S4 S5 S S S S ,. (1997) ( [2]). 2 ( )., a, b, s, a b s (a b s, )., s, a b. 5,.,. 9

10 2:., a = {vectors}, b = {statistics}, s = {algebra}, 2 2., algebra, vectors statistics (mechanics analysis )., a = {mechanics,vectors}, b = {analysis,statistics}, s = {algebra}, 2., mechanics vectors algebra. 4. a = {mechanics}, b = {statistics}, s = {vectors,analysis} a b s (, 1 2 )., web.,,,., R, n ( n = 88). AIC ( ) G, G M = M(G), P = P (G),.., G, G,,., AIC (Akaike s Information Criterion) ( ), AIC = 2 ( ) 2 ( ) + ( ) 10

11 ., AIC 0 ( web )., ggm fitcongraph. 2, AIC. fitcongraph, AIC > options(digits=3) # 3 > X <- marks # > n <- nrow(x); p <- ncol(x) # > R <- cor(x) # > amat <- matrix(1,p,p)-diag(p); #, # amat <- UG(~a*b*c*d*e). > dimnames(amat) <- dimnames(r) # > amat[4,1] <- amat[1,4] <- 0 # (4,1) > amat[4,2] <- amat[2,4] <- 0 # (4,2) > amat[5,1] <- amat[1,5] <- 0 # (5,1) > amat[5,2] <- amat[2,5] <- 0 # (5,2) > amat # mechanics vectors algebra analysis statistics mechanics vectors algebra analysis statistics > f <- fitcongraph(amat,r,n) # > f # $Shat # mechanics vectors algebra analysis statistics mechanics vectors algebra analysis statistics $dev # [1] 0.9 $df # [1] 4 $it # [1] 2 > f$dev # [1] 0.9 > aic <- f$dev - 2*f$df # AIC > aic [1]

12 . 1. G ( ). M = R. AIC 0 AIC. 2. M (R ) P = (p i,j ) ( 2 ). 3. G (i, j), p i,j (i, j), G. 4. G M = M(G) AIC = AIC(G) (fitcongraph fitcongraph M R ). 5. AIC 2. AIC, G (i, j), p ij (i, j),. G amat., select.ij <- function(p,amat){ p <- nrow(p); minabsp <- Inf for(i in (2:p)){ for(j in (1:(i-1))){ if(amat[i,j] == 1 && abs(p[i,j]) < minabsp){ minabsp <- abs(p[i,j]); i0 <- i; j0 <- j }}} c(i0,j0) },. 1,. M 0, P 0. M 0 S1 S2 S3 S4 S5 S S S P 0 S1 S2 S3 S4 S5 S S S S P 0 AIC 0 AIC 0 = 0. P 0, (4,1) (4,1). fitcongraph, AIC, 12

13 M 1 S1 S2 S3 S4 S5 S S S P 1 S1 S2 S3 S4 S5 S S S S AIC 1 AIC 0. AIC 1 = 2 P 1, (5,2) 0.02 (P 0 P 1 )., (5,2), M 2 S1 S2 S3 S4 S5 S S S P 2 S1 S2 S3 S4 S5 S S S S AIC 2 = AIC 2 AIC 1,., P 2 (5, 1) (0.032), M 3 S1 S2 S3 S4 S5 S S S P 3 S1 S2 S3 S4 S5 S S S S AIC 3 = 5.86 P 3 (4, 2) (0.085), M 4 S1 S2 S3 S4 S5 S S S P 4 S1 S2 S3 S4 S5 S S S S AIC 4 = 7.1 P 4 (3, 1) (0.235), M 5 S1 S2 S3 S4 S5 S S S P 5 S1 S2 S3 S4 S5 S S S S AIC 5 =

14 . AIC 5 > AIC 4, P ,,, P 0 P 1,. web.) 2.9 3, 2.3, 2.8. ( ) 3 4 (zip )., PDF, or Word. (2.3 ). (2.3 ). (2.8 ), AIC..... matsui@mist.i.u-tokyo.ac.jp 2016/4/28( ).,. 3,. [1] (2004), The R Book R,. [2] (1997),,. 14

1 R Windows R 1.1 R The R project web R web Download [CRAN] CRAN Mirrors Japan Download and Install R [Windows 9

1 R Windows R 1.1 R The R project web R web Download [CRAN] CRAN Mirrors Japan Download and Install R [Windows 9 1 R 2007 8 19 1 Windows R 1.1 R The R project web http://www.r-project.org/ R web Download [CRAN] CRAN Mirrors Japan Download and Install R [Windows 95 and later ] [base] 2.5.1 R - 2.5.1 for Windows R