SOLUTION TO HOMEWORK 3.

###  ----------- Part (a) 
> matcols = function(xvec, outcols) {
    outmat = cbind(rep(1,length(xvec)), xvec)
    if(outcols > 1) for(i in 2:outcols) 
	   outmat = cbind(outmat, xvec^i)
    outmat 
}
> matcols(c(0,1,1,0,2.2,4,7),4)
       xvec
[1,] 1  0.0  0.00   0.000    0.0000
[2,] 1  1.0  1.00   1.000    1.0000
[3,] 1  1.0  1.00   1.000    1.0000
[4,] 1  0.0  0.00   0.000    0.0000
[5,] 1  2.2  4.84  10.648   23.4256
[6,] 1  4.0 16.00  64.000  256.0000
[7,] 1  7.0 49.00 343.000 2401.0000
> matcols(2:5,1)
       xvec 
[1,] 1    2
[2,] 1    3
[3,] 1    4
[4,] 1    5

## Here is another function that does the same thing:

> matcol2 = function(xvec, outcols) outer(xvec, 0:outcols,
              function(x,y) ifelse(y==0, 1, x^y))


###  ------------ Part (b) 

> convtype = function(infram, charac=NULL, numer=NULL, bool=NULL){
    tmpfram = infram
    charcols = unlist(lapply(tmpfram, is.character))
    numcols = unlist(lapply(tmpfram, is.numeric))
    boolcols = unlist(lapply(tmpfram, is.logical))
    if(!is.null(charac) && charac == "factor" && sum(charcols)) 
       for(i in (1:ncol(tmpfram))[charcols]) 
              tmpfram[,i] = factor(tmpfram[,i]) 
    if(!is.null(numer) && numer == "charac" && sum(numcols))
       for(i in (1:ncol(tmpfram))[numcols]) 
              tmpfram[,i] = as.character(tmpfram[,i]) 
    if(!is.null(bool) && (bool=="charac" | bool=="numer") && sum(boolcols)) 
          if(bool=="charac") 
              for(i in (1:ncol(tmpfram))[boolcols]) 
                  tmpfram[,i] = as.character(tmpfram[,i])
          else  for(i in (1:ncol(tmpfram))[boolcols]) 
                  tmpfram[,i] = as.numeric(tmpfram[,i]) 
      tmpfram
   }

> auxfram = cbind.data.frame(numfac = as.character(11:20), 
     numlab = rep(c(3,5),5), TF = rep(c(3,5),5) < 4, 
     Lett = rep("",10))
 
> unlist(lapply(auxfram,class))
   numfac    numlab        TF      Lett
 "factor" "numeric" "logical"  "factor"

>  auxfram$Lett = as.character(1:10)
   unlist(lapply(auxfram,class))
     numfac      numlab          TF        Lett
   "factor"   "numeric"   "logical" "character"

> auxfram
   numfac numlab    TF Lett
1      11      3  TRUE    1
2      12      5 FALSE    2
3      13      3  TRUE    3
4      14      5 FALSE    4
5      15      3  TRUE    5
6      16      5 FALSE    6
7      17      3  TRUE    7
8      18      5 FALSE    8
9      19      3  TRUE    9
10     20      5 FALSE   10

> unlist(lapply(convtype(auxfram, numer="charac"),class))
     numfac      numlab          TF        Lett
   "factor" "character"   "logical" "character"
> unlist(lapply(convtype(auxfram, bool="numer",
     numer="charac"),class))
     numfac      numlab          TF        Lett
   "factor" "character"   "numeric" "character"

### Note that in this last case, it would be INCORRECT for the TF
##    numeric column to have been converted to "character"