# Owen-calculator.R
#
# This script works through the Owen calculator chapter with some extra
#  discussion.
#
#      modified from:  Owen, W. J., 2007. The R Guide, version 2.3.
#
#  created 9-7-10 by M. Dillon
#
#  last modified: 29 Aug 2011
#
#####################################################################

2+3
3/2
2^3
# beware of order of operations here
4^2-3*2
(56-14)/6 - 4*7*10/(5^2-5)

sqrt(2)
abs(2-4)
cos(4*pi)
log(0)
factorial(6)
choose(52,5)
# I don't understand how this works, so I look at the help file:
?choose

# Vector arithmetic
#  Here we use the "concatenate" function c() to create "vectors", which
#   are lists of numbers.  We assign them to "variables" using the
#   assignment operator "<-" (a less than sign followed by a dash).
#   The quick way to type this is _ (underscore).  
#   
x <- c(1, 2, 3, 4)  # note spaces after commas for legibility/readability
y <- c(5, 6, 7, 8)
x*y
# How did it perform this calculation?
#  The simple * does "element-wise" multiplication--
#  each element in one vector is multiplied by the
#  corresponding element in the other.  What happens if
#  vectors aren't the same length?
z <- c(1, 2, 3)
x*z

# This element-wise effect applies for all the other
#  simple mathematical operators as well
y/x
y-x
x^y
cos(x*pi) + cos(y*pi)

# Note that pi is a special variable that is already
#  assigned a value by R:
pi

# Also notice the distinction here between a scalar
#  (like pi), which is simply a number, and a vector
#  which is a list of numbers.  Of course, a scalar
#  can operate on a vector of any length--it
#  operates on every element of the vector:
pi*x
pi*z
pi*pi

s <- c(1, 1, 3, 4, 7, 11)
length(s)
sum(s)
prod(s)
cumsum(s)
diff(s)
diff(s, lag = 2)
# what is this lag thing?
?diff
# try the examples for diff listed in the help file.


# Matrices
#
#  Like scalars and vectors, a matrix (plural matrices)
#   is another way to store data.  As you'll find out,
#   it is a very powerful way to store data, particularly
#   if you are a "mathy" type and know how to manipulate
#   them (I am not and don't).
a <- c(1,2,3,4,5,6,7,8,9,10)
A <- matrix(a, nrow = 5, ncol = 2)
#  Note that variable names are case sensitive:
#    a does not equal A!
A
#  Why did it fill down the columns first?
?matrix
#  If you look at the help file, you'll see that one
#   of the arguments to the function "byrow" has a
#   preset value of "FALSE".  Many functions will
#   have arguments with preset values: if you don't tell
#   it differently, it will use this preset value.
#
#   We can also specify the arguments to change the way the
#    function works:
B <- matrix(a, nrow = 5, ncol = 2, byrow=TRUE)
B
#  Now it filled the matrix "by row"
#  Also notice that we don't have to specify "data=a", which
#   you might think was necessary after reading the help file.
#   R assumes that the first argument we send is "data".
#
#!!!!  These preset arguments are a really important reason
#      to read the help file for a function when you first
#      start using it.  Not only does it enlighten you as
#      to all the options, but it also makes you aware of
#      "hidden" switches that are controlling the behavior
#      of the function.
C <- matrix(a, nrow = 2, ncol = 5, byrow = TRUE)
C
#  More matrix manipulations
t(C)
B%*%C
#  This is very different from *!
#  matrix multiplication instead of element-wise multiplication
#  Matrix dimensions matter:
B%*%B
#  You can assign calculations to new variables:
D <- C%*%B
D
det(D)
solve(D)