Assignment:	Looping, Matrices
Due:		Just run the examples.  There is nothing due  

Discussion: There are often functions in R to do what you want.
            Often the task may take a short sequence of function.
            You may know what you want to do but not know the
            name of the R functions or the syntax for branching, etc. 
             
            Below are descriptions or at least clues to many
            useful functions

		1. Sequences 
		2. Looping
		3. apply functions to an array
		4. scaling matrix columns

		5. sweeping arrays
		6. tapply: apply a function to table cells  
            7. processing lists
		8. tabling

		9.  matrix subscripts
		10. matrix operations
		11. data.frames, missing data and merging
		12. branching

		13. text and formatting functions 
		14. sampling
		15. lattice construction

1. Sequences______________________________________________
	
##Run
1:10
seq(1,10)
seq(1,10,by=3)
##

##Run
seq(0,2*pi,length=101)
## 

2. Looping___________________________________________

Explicit looping is slow in R.  Some of the
R functions below have internally coded
looping that runs much faster.  
 
Still, sometimes it is more convenient to code
using loops.

R has for() and while() statements for explicit looping.
	next to skip a cycle 
	break to get out of the current loop    
	
2.1  Simple for() loop 

##Run
mysum = 0
for (i in 1:10)mysum = mysum+i
mysum
## 

##Run
mysum = 0
for (i in 1:10){
   if(i==5)next
   mysum = mysum+i
}
mysum
## 

2.2  Nested loops

##Run

iBegin = 1		# constant
iEnd = 5      # constant
k = 0          # initial values
mat = matrix(0,nrow=iEnd,ncol=iEnd)  # define a matrix
for (i in iBegin:(iEnd-1)){
    for (j in (i+1):iEnd){
        k = k+1
	  mat[i,j] = k
    }  
}
mat
## 

2.3 Looping through a list

The syntax is 
for (i in listObject){}
The index i will refer to each component of the
listObject in turn and can be used in computations.
  
3. apply()______________________________________________

The first argument to apply is an array.
The second argument controls array subsetting
	1 means compute on the reduced array for
        as the first subscript steps through it values.
	      For a matrix this mean compute on each row. 
      2 does the same for each value of the second subscript
	      For a matrix this mean compute on each column. 
The third argument is the function to apply to the reduce array at
      each step.  This can be an analyst written function.
Additional arguments pass through as argument to function specified in the
	third argmument.   For example the argument na.rm=T might be
      supplied to remove missing data.  

The function range()below returns the min and max of a vector.
The returned object below, mat.r, is a matrix with two rows.
	The first row has the minimum of each column.
	The second row has the maximum of each column.

##Run
mat = matrix(rnorm(49),ncol=7)
mat.r = apply(mat,2,range)
round(mat.r,2)
## 

We can find the midpoint of the range for
each column by using the mean() and the
max - min by using diff()

##Run
cen = apply(mat.r,2,mean)
round(cen,2)
sc = apply(mat.r,2,diff)
round(sc,2)
## 

4. scale()_________________________________________

The following scales all columns in mat into values [-1,1].  
The first argument is the input matrix
The second is a vector whose elements are to subtracted
    from the respective columns.  
The third is a vector whose respective elements divide into
    corresponding columns.

##Run
mat.sc1 = scale(mat, center=cen, scale=sc/2)
round(mat.sc1,2)
## 

5. sweep()___________________________________________

Provides a more general array capability
             
    The first two arguments are like those in apply().  
    The third argument is additional data to use.
    The forth gives the operation which is "-" by default.  

##Run
mat.sc2 = sweep(mat,2,apply(mat.r,2,mean)) #subtract the means from colums
mat.sc2
mat.sc2 = sweep(mat.sc2,2,apply(mat.r,2,diff)/2,"/") #standardize               
mat.sc2

range(mat.sc2-mat.sc1)  # a quick comparison of the two matrices
##

6.  tapply()________________________________________

Applies a function to cells of a categorical table. 

##Run
# make a list of the classification factors
Sex = c("M","F","M","M","F","F")
Eyes = c("Brown","Blue","Blue","Brown","Brown","Brown")
cellIndices = list(Sex,Eyes)

# construct a dependent variable 
Weight = c(160,120,150,200,105,110)

# compute the mean for each cell.
weight.ave = tapply(Weight,cellIndices,mean,na.rm=T)
weight.ave

# The values might have been stored in a data frame
people = data.frame(Weight,Sex,Eyes)

# Then same results can be obtained using  
cellIndices = list(people$Sex,people$Eyes)
weight.ave = tapply(people$Weight,cellIndices,mean,na.rm=T)
weight.ave
##

7. Lists and processing lists______________________________________

7.1  Creating lists

##Run:  make list with a vector, a character string, and a matrix
myList = list(x=c(1:4), lab ="A character string", mat=matrix(1:4,ncol=2))
myList$x
myList$lab
myList$mat
##

split()
split(data,group) creates list element using data for each
      unique element in group.    
      If data is vector, the list elements are vectors
      If data is a matrix the list element are matrices
      whose rows have the same group membership.


7.2  processing lists sapply() and lapply()

sapply() and lapply() apply a function to each top level
element of a list.  The result of lapply() is a list.  
The result of sapply may simplify to a vector or a matrix.  

##Run
weightByEye = split(people$Weight,people$Eye)
weightByEye 
sapply(weightByEye,mean)
## 

8. table()_____________________________________________________

Counting cases in the table cells.

##Run
table(people$Sex,people$Eyes)
## 

9.  Matrix subscripts________________________________________

# logical subscripts

##Run
i.end = 3
j.end = 4
mat2 = matrix(0,nrow=i.end,ncol=j.end)  # define a matrix
col(mat2)       # returns matrix with column numbers
row(mat2)       # returns matrix with row numbers 
subs.logical = col(mat2) > row(mat2)
subs.logical
##

##Run
mat2[subs.logical] = 1:6  # Insert in the TRUE locations
mat2        # R increase the row subscript fastest
##                 

10. Matrices and a few matrix operations__________________________

10.1  Access the dimension attribute

##Run
dim(mat)
nrow(mat)
ncol(mat)
## 

10.2  Row and column names

The dimnames are a list structure composed of two vectors
whose elements are character strings.

##Run
dimnames(mat) = list(paste("Row",1:nrow(mat),sep=''),
                      paste("Col",1:ncol(mat),sep=''))
dimnames(mat)
dimnames(mat)[[1]]   # row names
dimnames(mat)[[2]]   # column names
##

10.3  Construction from vectors

##Run
v1 = rnorm(10)
v2 = rnorm(10)
v3 = rnorm(10)
cbind(v1,v2,v3)   # column binding
##

##Run             # row binding
rbind(v1,v2,v3)[,1:4]
##

10.3  Matrix Multiplication

%*% is the matrix multiple operator.
The example below sums the elements of each row.

##Run  Sum rows of a matrix with matrix multiplication 
one = rep(1,ncol(mat))  #  A vector of 1s
tmp = mat %*% one
tmp 
## 

R treats vectors as either rows or columns. 
If the situation is not clear, as in x %*% x, 
R will use the inner product.

To produce the outer product use x %o% x.

10.4  Removing rows with missing data

## Run
mat[1,2] = NA
tmp = mat %*% one
tmp
mat = mat[!is.na(tmp),]  
mat
##

11. Data.frames, missing data and merging______________________

11.1  Data.frames have convenient options for handling missing
data, na.omit() omits rows.

A package contains na.gam.replace() that replaces the missing values
with the average of the available data in missing items column.  


##Run
nmat = as.data.frame(matrix(rnorm(12),ncol=3))
nmat[1,2] = NA

na.omit(nmat)
#  na.gam.replace(nmat) # must install package first
##


11.2  Merging data.frames

##Run  
nam = c('George','Henry','Sue','Sarah')
score1 = c(94,95,91,99)
score2 = c(15,NA,18,20)
IQ = c(115,125,121,136) 
datFrame1 = data.frame(score1,row.names=nam)
datFrame2 = data.frame(score2,IQ,row.names=nam)

frameNew = merge(datFrame1,datFrame2,by="row.names")
datFrame1       
frameNew      # the row.names become a column
##

##Run
?merge       # there are many data frame merging options
##

12. Branching___________________________________________

12.1 The if() syntax is pretty common

if ( ) statement

if ( ) {
	multiple lines
}

if ( ) statement else statement  

if ( ) {
	multiple lines
} else {
	multiple lines
}

##Run
k = 5
m = 13
if(k <=7 & m <15) x = 1:5 else x = 6:10 
x	
##

12.2 ifelse 

ifelse () works on three vectors,
a logical vector and two vectors of values. 

If the item is T for the logical vector
   the result comes from the corresponding value
                          in the second column
   otherwise it comes from the third column.

##Run   
tst = c(1,3,9,16)
result1 = c(1,2,3,4)
result2 = c(11,12,13,14)
ifelse(tst>3,result1,result2)
##

To evalate one of several expression see switch

##Run
?switch 	
##

13. Some text and formatting functions__________________________ 
 
paste()
nchar()
substring()
lowerCase()
upperCase()
format()
round()
cat()

##Run
strings  = paste('s',1:1000,sep='')
n = nchar(strings)
good = substring(strings,n-1,n)=="23"
strings[good]
##

##Run
for(i in 1:5)cat(i,fill=T)  # print values from inside a loop
##	

14. Sampling_________________________________________________	

##Run
dat = rnorm(1000,mean=100,sd=16) # simulated IQ values
samp1 = sample(dat,50,replace=T)  # bootstrap sample
samp2 = sample(dat,50,replace=T)
cbind(samp1,samp2)
##

##Run
scramble = sample(1:10,10,replace=F)
scramble
##

15. Lattice construction___________________________________

##Run
mylist = list(x=1:4,y=1:3,z=1:4)
ans = expand.grid(mylist)
ans
##