# The public domain program 'R' can be used as anything from
# a simple calculator to a sophisticated programming environment.
# We will be using it primarily as a platform for statistical
# analysis. Today, we saw a few simple procedures designed to show
# that R can be fairly simple and intuitive.

# Here is a simple calculation:

> 3 * 3
[1] 9

# While R can be used as a simple calculator, one must use caution
# when working with large numbers:

> 150000.30 + 150000.33
[1] 300000.6

# Functions in R tend to have short, intuitive names. For example,
# the function to calculate a square root is:

> sqrt(9)
[1] 3

# Functions can be applied to more complex expressions. Here,
# 3^2 means "three squared":

> sqrt( 3^2 )
[1] 3

# It is simple to create a variable in R. Here, we create a
# variable that we choose to name 'x' and stor the value 3 in it:

> x <- 3

# (The assignment operator '<-' represents an arrow and is read 'gets.'

# To see what value(s) a variable contains, simply type its name:

> x
[1] 3

# Basic operations can be performed on variables, just as we did
# before with numbers:

> x^2
[1] 9
> sqrt(x^2)
[1] 3

# Sometimes, we may have typed a complex expression and only then
# realized that we want to store it in a variable. In that case,
# we can type the arrow in the left-to-right direction and still
# save the result:

> 3^2 -> y
> y
[1] 9

# To find out what variables or other objects you have in your
# workspace, use the 'ls()' function:

> ls()
[1] "x" "y"

# Variables can hold more than one value. (Variables with more than
# one value are called vectors. At least for now; things can get more
# complex than that.) Here, we create a variable x that contains the
# integers from 1 to 10:

> x <- 1:10
> x
 [1]  1  2  3  4  5  6  7  8  9 10

# We can perform operations on that vector, just as we could on
# a single-valued variable (often called a scalar):

> x^2
 [1]   1   4   9  16  25  36  49  64  81 100
> sqrt(x)
 [1] 1.000000 1.414214 1.732051 2.000000 2.236068 2.449490 2.645751 2.828427
 [9] 3.000000 3.162278

# We can use the c() function to 'collect' a set of values:

> x <- c( 2.2, 3.141592654, pi, 99, 3811)
> x
[1]    2.200000    3.141593    3.141593   99.000000 3811.000000

# To get rid of a variable, remove it, using the rm() function:

> rm(x)

# Notice that x is now gone:

> ls()
[1] "y"

# We can get a set of integers in descending order this way:

> x <- 10:1
> x
 [1] 10  9  8  7  6  5  4  3  2  1

# If we wanted them back in ascending order, we could use the
# rev() function to "reverse" them:

> rev(x)
 [1]  1  2  3  4  5  6  7  8  9 10

# Statistical functions also tend to have short and intuitive
# names. For example, we can use the mean() function to calculate
# the mean, which is just the arithmetic average:

> mean(x)
[1] 5.5

# The median is the centermost value or the average of the two central
# value if there is not a unique central one. Not surprisingly, the
# function to get it is median():

> median(x)
[1] 5.5

# Sometimes, though, what seems like a natural, intuitive function
# name does something else. For example, we might be interested in the
# most frequently occurring value, also called the mode. But the
# mode() function in R just tells us what kind of variable we have:

> mode(x)
[1] "numeric"

# It is often beneficial to have a special workspace in R for
# different projects. For example, my home R workspace looks like
# this:


> ls()
 [1] "anscombe"          "bben"              "Benford"          
 [4] "bet"               "Bexp"              "bias"             
 [7] "Checkouts"         "cites"             "classdots"        
[10] "classdotsoriginal" "culleddots"        "d2ldm2"           
[13] "d2ldvc2"           "d2ldvcdm"          "degrees"          
[16] "digits"            "dldm"              "dldvc"            
[19] "expect"            "Eysenck"           "Eysenck2"         
[22] "fusion"            "gatb"              "glass2"           
[25] "gradient"          "guesses"           "hessian"          
[28] "i"                 "j"                 "justangles"       
[31] "justculledangles"  "library"           "meanangles"       
[34] "names"             "no"                "NYjobs"           
[37] "order"             "pars"              "pulse"            
[40] "pulse1"            "pulse2"            "q1a"              
[43] "q1m"               "radians"           "radius"           
[46] "rich"              "rmse"              "spaces"           
[49] "Statlab"           "tbias"             "temp0"            
[52] "temp1"             "temp2"             "theta"            
[55] "tmeanangle"        "tmeanangles"       "tmeanradii"       
[58] "trained"           "trmse"             "trueangle"        
[61] "trueradii"         "Uexp"              "untrained"        
[64] "utbias"            "utmeanangles"      "utmeanradii"      
[67] "utrmse"            "V"                 "winnings"         
[70] "words"             "x"                 "xx"               
[73] "xxx"               "y"                 "yes"              
[76] "yy"                "yyy"               "Z"                
> 

# But if I want to have a workspace that contains just things that
# are relevant to this class, I can specify a special working
# directory for my R session:

> setwd("c:/users/jvevea/desktop/Classes/202a")

# I now remove everything in my workspace:

> rm(list=ls())

# Note that all of that stuff is now gone:

> ls()
character(0)

# When I quit, using the q() function, R will ask me if I want
# to save my workspace. If I tell it yes, it will do so, creating
# a little file that appears as an "R" in the folder that I specified
# with my "setwd()" command. 

> q()

# If I start R up again by double clicking on that icon, all 
# of the things I deleted from my workspace are still gone (and 
# any variable I created after the deletion would still be there):

> ls()
character(0)

# But if I quit again and start R from my toolbar, all of
# the variables in my home workspace are still there:


> ls()
 [1] "anscombe"          "bben"              "Benford"          
 [4] "bet"               "Bexp"              "bias"             
 [7] "Checkouts"         "cites"             "classdots"        
[10] "classdotsoriginal" "culleddots"        "d2ldm2"           
[13] "d2ldvc2"           "d2ldvcdm"          "degrees"          
[16] "digits"            "dldm"              "dldvc"            
[19] "expect"            "Eysenck"           "Eysenck2"         
[22] "fusion"            "gatb"              "glass2"           
[25] "gradient"          "guesses"           "hessian"          
[28] "i"                 "j"                 "justangles"       
[31] "justculledangles"  "library"           "meanangles"       
[34] "names"             "no"                "NYjobs"           
[37] "order"             "pars"              "pulse"            
[40] "pulse1"            "pulse2"            "q1a"              
[43] "q1m"               "radians"           "radius"           
[46] "rich"              "rmse"              "spaces"           
[49] "Statlab"           "tbias"             "temp0"            
[52] "temp1"             "temp2"             "theta"            
[55] "tmeanangle"        "tmeanangles"       "tmeanradii"       
[58] "trained"           "trmse"             "trueangle"        
[61] "trueradii"         "Uexp"              "untrained"        
[64] "utbias"            "utmeanangles"      "utmeanradii"      
[67] "utrmse"            "V"                 "winnings"         
[70] "words"             "x"                 "xx"               
[73] "xxx"               "y"                 "yes"              
[76] "yy"                "yyy"               "Z"                
>