R Studio Interface
Instructor: Dr. Bob Batzinger
Academic year: 2021/2022
Semester: 1
Begins June 2021
## a = 14.92 Output: 14.92
## round(a,1) Output: 14.9
## as.integer(a) Output: 14
## is.numeric(a) Output: TRUE
## is.integer(a) Output: FALSE
## a * 2 Output: 29.84
## a / 2 Output: 7.46
## a + 2 Output: 16.92
## a - 2 Output: 12.92
## a ^ 2 Output: 222.6064
## a %% 2 Output: 0.92## s = "PYU CS Dept" Output: PYU CS Dept
## substr(s,start=5,stop=6) Output: CS
## grep("/PYU/",s) Output:
## gsub("PYU","Payap",s) Output: Payap CS Dept
## strsplit(s, " ") Output: PYU CS Dept
## paste("a","=",a) Output: a = 14.92
## toupper(s) Output: PYU CS DEPT
## tolower(s) Output: pyu cs dept
## nchar(s) Output: 11## vector: x 2 13 5 17 11 3
## reversed: rev(x) 3 11 17 5 13 2
## selected entries: x[c(1,3,5)] 2 5 11
## number of elements: length(x) 6
## order map: order(x) 1 6 3 5 2 4
## sorted list: x[order(x)] 2 3 5 11 13 17
## scaled value: 3 * x 6 39 15 51 33 9
## offset value: 3 + x 5 16 8 20 14 6
## squared values: x * x 4 169 25 289 121 9
## sequence: 5:10 5 6 7 8 9 10
## average: mean(x) 8.5
## std dev: sd(x) 6.058052
## sum: sum(x) 51
## sequence: seq(0,3,.5) 0 0.5 1 1.5 2 2.5 3
## repeated num: rep(a,3) 14.92 14.92 14.92
## vector of Labels: LETTERS[1:8] A B C D E F G H
## vector of labels: letters[1:8] a b c d e f g h## mtxa=rbind(c(1,2,3),
## c(6,5,4),c(7,9,8))## mtxa -------------## [,1] [,2] [,3]
## [1,] 1 2 3
## [2,] 6 5 4
## [3,] 7 9 8## t(mtxa) ----------## [,1] [,2] [,3]
## [1,] 1 6 7
## [2,] 2 5 9
## [3,] 3 4 8## colMeans(mtxa) ------## [1] 4.666667 5.333333 5.000000## rowSums(mtxa) ------## [1] 6 15 24## diag(3) ---------## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] 0 1 0
## [3,] 0 0 1## det(mtxa) -------## [1] 21## mtxa * mtxa -----## [,1] [,2] [,3]
## [1,] 1 4 9
## [2,] 36 25 16
## [3,] 49 81 64\[\begin{pmatrix} 1 & 2 & 3\\ 6 & 5 & 4\\ 7 & 9 & 8\\ \end{pmatrix}\begin{pmatrix} 10\\ 12\\ 20\\ \end{pmatrix} = \begin{pmatrix} 1 \cdot 10 + 2 \cdot 12 + 3 \cdot 20\\ 6 \cdot 10 + 5 \cdot 12 + 4 \cdot 20\\ 7 \cdot 10 + 9 \cdot 12 + 8 \cdot 20\\ \end{pmatrix} = \begin{pmatrix} 94\\ 200\\ 358\\ \end{pmatrix}\]
## mtxa = rbind(c(1,2,3),c(6,5,4),c(7,9,8))## mtxb = c(10,12,20)## mmprod = mtxa %*% mtxb## [,1]
## [1,] 94
## [2,] 200
## [3,] 338Algebraic Equations
\[\begin{eqnarray} x + 2y + 3z & = & 10\\ 6x + 5y + 4z & = & 12\\ 7x + 9y + 8z & = & 20\\ \end{eqnarray}\]
Rendering in R
## result = solve(mtxa,mtxb)## [1] 1.523810 -3.619048 5.238095Matrix version
\[\begin{pmatrix} 1 & 2 & 3 \\ 6 & 5 & 4 \\ 7 & 9 & 8 \\ \end{pmatrix}\begin{pmatrix} x\\ y\\ z\\ \end{pmatrix} = \begin{pmatrix} 10\\ 12\\ 20\\ \end{pmatrix}\]
\[\begin{pmatrix} 1 & 2 & 3\\ 0 & 1 & 2\\ 0 & 0 & 1\\ \end{pmatrix} = \begin{pmatrix} 10.00000\\ 6.85714\\ 5.23809\\ \end{pmatrix}\]
\[\begin{pmatrix} x\\ y\\ z\\ \end{pmatrix} = \begin{pmatrix} 1.523810\\ -3.619048\\ 5.238095\\ \end{pmatrix} \]
Transition map \[\begin{matrix} From/To & Fresh &Soph & Jr& Sr & Grad & Resign\\ Fresh &0.08& 0.72& 0& 0& 0 &0.2\\ Soph &0 & 0.08& 0.72& 0.1 &0 & 0.1\\ Jr & 0 & 0 & 0.08 & 0.82 & 0 & 0.1\\ Sr & 0 & 0 & 0& 0.1& 0.85 & 0.5\\ Grad & 0 & 0 & 0& 0 & 1 & 0\\ Resign & 0 & 0 &0 & 0 & 0 & 1\\ \end{matrix}\]
dat = data.frame(rbind(
c(14, 2963,6.6),
c(14,10110,6.5),
c(11.1,1402112,7.0),
c(13,3214,2.2),
c(17.4,1380004,3.7),
c(6,51780,2.7)))
rownames(dat) = c("AR","AZ","CN",
"GE","IN","KR")
colnames(dat) = c('birthrate',
'population', 'diff.100')
unmatched = round(
(dat[,1] * dat[,2] * dat[,3]) /
10000, 3)
dat = cbind(dat,unmatched)| birthrate | population | diff.100 | unmatched | |
|---|---|---|---|---|
| AR | 14.0 | 2963 | 6.6 | 27.378 |
| AZ | 14.0 | 10110 | 6.5 | 92.001 |
| CN | 11.1 | 1402112 | 7.0 | 10894.410 |
| GE | 13.0 | 3214 | 2.2 | 9.192 |
| IN | 17.4 | 1380004 | 3.7 | 8884.466 |
| KR | 6.0 | 51780 | 2.7 | 83.884 |
## dim(dat) ========## [1] 6 4## colnames(dat) ====## [1] "birthrate" "population" "diff.100" "unmatched"## rownames(dat) ====## [1] "AR" "AZ" "CN" "GE" "IN" "KR"## head(dat,2) ======## birthrate population diff.100 unmatched
## AR 14 2963 6.6 27.378
## AZ 14 10110 6.5 92.001## tail(dat,2) ======## birthrate population diff.100 unmatched
## IN 17.4 1380004 3.7 8884.466
## KR 6.0 51780 2.7 83.884## str(data) ======## 'data.frame': 6 obs. of 4 variables:
## $ birthrate : num 14 14 11.1 13 17.4 6
## $ population: num 2963 10110 1402112 3214 1380004 ...
## $ diff.100 : num 6.6 6.5 7 2.2 3.7 2.7
## $ unmatched : num 27.38 92 10894.41 9.19 8884.47 ...##
## summary(dat) =====## birthrate population diff.100 unmatched
## Min. : 6.00 Min. : 2963 Min. :2.200 Min. : 9.192
## 1st Qu.:11.57 1st Qu.: 4938 1st Qu.:2.950 1st Qu.: 41.505
## Median :13.50 Median : 30945 Median :5.100 Median : 87.942
## Mean :12.58 Mean : 475030 Mean :4.783 Mean : 3331.889
## 3rd Qu.:14.00 3rd Qu.:1047948 3rd Qu.:6.575 3rd Qu.: 6686.350
## Max. :17.40 Max. :1402112 Max. :7.000 Max. :10894.410doStat <- function(n=10000) {
total = 0; sq = 0; cnt = 0; x = 1:n
for (i in x) {total = total + i
sq = sq + i * i; cnt = cnt + 1
}
mn = round(total / n,5); msq = mn * mn
doStat = paste("mean=",mn,", std.dev=",
round(sqrt((sq - msq*cnt)/(cnt-1)),5),"\n")
}
doStat2 <- function(n=10000) { x = 1:n
doStat2 = paste("mean=",mean(x),", std.dev=",sd(x),"\n")
}doStat()
## time= 0.03611 +/- 0.00215
## mean= 5000.5 , std.dev= 2886.89568
## mean() and sd()
## time= 0.00289 +/- 0.00127
## mean= 5000.5 , std.dev= 2886.89567990717
## 
Titles: K-Z