SOLUTION  TO HW1, STAT 705 FALL 2017

## (a)

> LongI = NULL
  for (k in 1:20) LongI = c(LongI, rep(1:k,k))
  
## (b) 
> c(length(LongI), sum((1:20)^2))
[1] 2870 2870
> LongI[c(777,1200)]
[1] 10  5

### entry 777 is the 127th after the 650 entries obtained by repetitions of 1, ..., 1:12,
###   then 117 entries later we have the 9th completed cycle 1:13, so the 127th entry is a 10
### entry 1200 is the 185th after the 1015 obtained be repetitions up to 1:14, then
###   180 entries later we have the 12th completed cycle 1:15, so 5 entries later is a 5.

## (c) 

> digits = as.numeric(strsplit(paste(LongI,collapse=""),"")[[1]])
> length(digits)
[1] 3970
> table(digits)
digits
   0    1    2    3    4    5    6    7    8    9 
 185 1445  373  339  323  305  285  263  239  213 
> hist(digits, breaks=seq(-0.5,9.5, by=1), plot=F)$count
 [1]  185 1445  373  339  323  305  285  263  239  213

> nams = c("John","James","Henry","Doug","Richard")
> abs(sin(100*(1:10)))
 [1] 0.50636564 0.87329730 0.99975584 0.85091936 0.46777181 0.04418245 0.54397052 0.89396965 0.99780327
[10] 0.82687954
> nums = substr(as.character(abs(sin(100*(1:10)))),3,5)
> CMAT = outer(nams,nums,paste0)
  CMAT 
     [,1]         [,2]         [,3]         [,4]         [,5]         [,6]         [,7]        
[1,] "John506"    "John873"    "John999"    "John850"    "John467"    "John044"    "John543"   
[2,] "James506"   "James873"   "James999"   "James850"   "James467"   "James044"   "James543"  
[3,] "Henry506"   "Henry873"   "Henry999"   "Henry850"   "Henry467"   "Henry044"   "Henry543"  
[4,] "Doug506"    "Doug873"    "Doug999"    "Doug850"    "Doug467"    "Doug044"    "Doug543"   
[5,] "Richard506" "Richard873" "Richard999" "Richard850" "Richard467" "Richard044" "Richard543"
     [,8]         [,9]         [,10]       
[1,] "John893"    "John997"    "John826"   
[2,] "James893"   "James997"   "James826"  
[3,] "Henry893"   "Henry997"   "Henry826"  
[4,] "Doug893"    "Doug997"    "Doug826"   
[5,] "Richard893" "Richard997" "Richard826"
  
  
## (e) 

> LongStr = paste(CMAT,collapse="")
> CharVec = strsplit(LongStr,"")[[1]]
  c(nchar(LongStr), length(CharVec))
[1] 400 400


##(f) 

> CombList = list(longI = LongI, tabl = table(digits), matr = CMAT, chv = CharVec)
  sapply(CombList, class)
      longI        tabl        matr         chv 
  "integer"     "table"    "matrix" "character" 

  ### In the case of long vectors, "class" tells the underlying data type
  ## but a "table" and "matrix" have additional structure that is reflected in their "class".