SEVERAL Log Lines for Classes 3 and 4, STAT 705 Fall 2017
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> A = (1:20) %o% rep(1,20)
> B = outer(1:20,1:20, function(x,y) x <= y)
> C = c(A)[c(B)]

###--------------------------------------------

## We considered the following code for an R function to 
##   examine the columns of an input data-frame   infram , 
##   decide which ones are numeric, and to calculate and output 
##   the numbers of missing elements in those columns.

> framfix = function(infram) {
       numcols = which( sapply(infram, 
                    function(col) is.numeric(col)) )
       newfram = sapply( infram[,numcols], 
                    function(col) sum(is.na(col)) )
       list(numcols=numcols, newfram=newfram)      }

##  Here is a little test of the function code just given:

> toyfram = cbind.data.frame(letcol = letters[1:23], 
               numcol1 = c(1:10,rep(NA,3),11:20),
               numcol2 = c(1,replace(1:22,(0:21) %% 2 ==1, NA)), 
               bool1 = c(as.logical(rbinom(20,1,0.4)),NA,NA,NA) )

> toyfram
   letcol numcol1 numcol2 bool1
1       a       1       1  TRUE
2       b       2       1  TRUE
3       c       3      NA FALSE
4       d       4       3 FALSE
5       e       5      NA FALSE
6       f       6       5  TRUE
7       g       7      NA FALSE
8       h       8       7 FALSE
9       i       9      NA  TRUE
10      j      10       9 FALSE
11      k      NA      NA  TRUE
12      l      NA      11 FALSE
13      m      NA      NA FALSE
14      n      11      13 FALSE
15      o      12      NA FALSE
16      p      13      15 FALSE
17      q      14      NA FALSE
18      r      15      17 FALSE
19      s      16      NA  TRUE
20      t      17      19  TRUE
21      u      18      NA    NA
22      v      19      21    NA
23      w      20      NA    NA

> framfix(toyfram)
$numcols
numcol1 numcol2 
      2       3 

$newfram
numcol1 numcol2 
      3      11 

## -----------------------Done as part of solution to HW2:

> summary(diff(nepali$id))
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
     0.0      0.0      0.0    400.5      0.0 239319.0 
        #### shows that the id's are in sorted increasing numerical order
> tmp = c(0,as.numeric(substr(nepali$id,1,5)))		
  newind = which(tmp[-1] > tmp[-1001])   ### 113 indices at which new households begin

### ------------------------------- alt solution to HW2 (e)

> aux = rle(as.numeric(substr(nepali$id,1,5)))
> length(aux)
[1] 2
> names(aux)
[1] "lengths" "values" 

> sapply(aux,length)
lengths  values 
    113     113 

> aux$lengths
  [1] 10 15  5 15 10 10 10  5 10  5 15 10 10 10 10 10  5 10 10  5  5 10 10  5 10
 [26] 10 10 10 20 10 10 10  5 20 15 15  5  5 10 10  5 15  5 10  5 10 15 10 10  5
 [51] 10 20  5 10  5 10  5 10  5 15  5 10  5  5 15 10 10 15  5 10 10 10  5 10  5
 [76]  5  5  5 10  5  5 10  5  5 20  5 10  5  5  5 10 10  5  5 15 10  5  5  5 10
[101]  5  5 10 10 10 10  5 10  5 15 10  5  5
> aux$values
  [1] 12001 12002 12003 12005 12006 12007 12008 12009 12011 12012 12013 12014
 [13] 12015 12016 12019 12021 12023 12024 12025 12026 12027 12029 12032 12033
 [25] 12034 12035 12036 12037 12038 12039 12040 12041 12043 12044 12045 12047
 [37] 12054 12056 12057 12058 12059 12060 12061 12063 12065 12067 12068 12069
 [49] 36001 36002 36005 36011 36012 36013 36014 36016 36018 36019 36021 36022
 [61] 36025 36030 36033 36034 36035 36036 36037 36039 36041 36043 36047 36048
 [73] 36049 36050 36051 36053 36054 36055 36056 36057 36058 36059 36061 36062
 [85] 36067 36069 36070 36071 36072 36074 36075 36078 36079 36080 36081 36084
 [97] 36087 36088 36090 36091 36092 36094 36095 36099 36100 52002 52003 52004
[109] 52005 52006 52007 52008 52009

## still another way:

> HHdat2 = aggregate.data.frame(nepali[,c("mage","lit","died","alive")], 
         by=list(substr(nepali$id,1,5)), function(col) var(col)  )  

### -----------------------------------------
## calling function within standard function "integrate"

> integrate(function(x) sin(x)^2, 0,6)
3.134143 with absolute error < 5.6e-10
> tmp = integrate(function(x) sin(x)^2, 0,6)

> unlist(tmp)
$value
[1] 3.134143

$abs.error
[1] 5.598301e-10

$subdivisions
[1] 1

$message
[1] "OK"

$call
integrate(f = function(x) sin(x)^2, lower = 0, upper = 6)

> unlist(tmp[1:3])
       value    abs.error subdivisions 
3.134143e+00 5.598301e-10 1.000000e+00