bmb splus notes for week 1 Feb, 3 Feb


Splus
-----

Object Oriented Statistical Programming Language
 - apply procedures to objects
 - flexible/extensible
 - interpreted so can be a bit slow (avoid loops at all costs)

Main Data Object types
----------------------

Data frame - used to store related data.
           - matrix like
           - usually rows are observations and columns are measurements of various variables
	   - can mix different scalar types together. ie numbers, strings, logical values may be mixed together
	   - usually created by reading in data with read.data() command

Matrix - stores information all of the same type in a 2 dimesional array
      - can not mix types in same matrix ie must be all numeric or all logical or .... etc
      - matrix algebra is supported
      - created with the matrix() command

Vector - one dimensional version of the matrix

List - collection of itmes of different types that are stored together because the are some what related. eg a student record ..

Scalar - a plain old number, or character string or single logical value

Indexing
--------

We can index information stored in these data structures in a number of different ways. Assume we have the following datafile which we will read into Splus

eg

name	age	height	weeight	gender
Fred	22	185	80	M
Bob	35	172	78	M
Jane	27	167	63	F
Mary	19	163	57	F


this can be read in using the following command

> data <- read.table("data",header=T)

the first parameter is the name of the datafile, the second parameter specifies that the first row of the file contains the column names.

To index a single cell we can use data[i,j] to return the jth element of the ith row. for example

> data[3,4]
 
returns 63

You can however also index an entire row with data[i,] to get the ith row. so 

> data[2,]

would return

Bob	35	172	78	M

or index an entire column, so data[,j] would return the jth column of data. so

> data[,4] 

would return

weight
80
78
63
57


we can also refer to columns by name so

data$gender refers to the column

M
M
F
F

Even more powerful we may use logical indexing. do for example

> data[data$age > 25,] would return

name	age ....
Bob	35  ....
Jane	27  ....


or 

>data[data$gender ="m",] would return

name	.....
Fred	.....
Bob	.....


Note that all of the above indexing methods work equally well with matrices. We can create a matrix withthe call

> matrix(data, nrows, ncols)

Vectors have only 1 dimension so we may use only one index. one simple way to create a vector is to use the concatenate function c(). For example

> avec <- c(3.1,8.0,5.8,-4.2)
> avec[1]

returns 

3.1.

the colon (:) is used as the range operator in format lowerlimit:upperlimit and will in fact return a vector containing the ordered elements (lowerlimit, lowerlimit+1, ..... ,upperlimit)

>avec[2:3]

would thus return

8.0 5.8

or you could use

> avec[c(1,4)]   

to get

3.1 -4.2

logical operators would also work. note that you can use the range operator (or any other suitable vector) to index both data frames and matrices also. 

to create a list that is say a student record

> alist <- list(name="john", major="Statistics",age=23,courses=c(200,248))

indexing works slightly differently from above. name indexing works as might be expected. so

> alist$name 

would return

john

or we could use

> alist[[1]] to do the same thing

note the last item of our list is a vector. this introcudes slightly more complexity to the situation

alist$courses or alist[[4]]

would return

200 248

to index say the first element of the vector we would use

alist$courses[1] or alist[[4]][1]

to get 200

Some useful functions for dealing with data objects
---------------------------------------------------

dim() - get dimensions
names() - column names
row.names() - row names
length() - lenght of a vector
cbind(), rbind() - join dataframes or matrices together by columns or rows
nrows(),ncols() - number of rows or columns

Operators
---------

+,-,*,/		arthemetical
<-		assignment operator
<,>,<=,>=	logical comparison
==		equal to
!=		not equal
!		logical not
&		logical and
|		logical or


Special data items
------------------
F = 0  (false)
T = 1  (true)
NA     missing data marker

Matrix operations
-----------------

t(X)		transpose matrix X
solve(X)	invert a square matrix X
solve(A,B)	solve linear system AX = B for X  


%*% - matrix multiplication