= Indexing =
<<TableOfContents(3)>>

== Indexing with Positive Integers ==
   * there are circumstances where we want to select only some of the elements of a vector/array/dataframe/list
   * this selection is done using subscripts (also known as indices)
   * subscripts have square brackets [2] while functions have round brackets (2)
   * Subscripts on vectors, matrices, arrays and dataframes have one set of square brackets [6], [3,4] or [2,3,2,1]
   * when a subscript appears as a blank it is understood to mean ''all of'' thus
      * [,4] means all rows in column 4 of an object
      * [2,] means all columns in row 2 of an object.
      * subscripts on lists have (usually) double square brackets [ [2] ] or [ [i,j] ]
   * ''A vector of positive integers as index'':The index vector can be of any length and the result is of the same length as the index vector. For example,
{{{#!highlight r
> letters[1:3]
[1] "a" "b" "c"
> letters[c(1:3,1:3)]
[1] "a" "b" "c" "a" "b" "c"
}}}
   * ''A logical vector as index'': Values corresponding to T values in the index vector are selected and those corresponding to F or NA are omitted. For example,
{{{#!highlight r
> x<-c(1,2,3,NA)
> x[!is.na(x)]
[1] 1 2 3
}}}
creates a vector without missing values. Also
{{{#!highlight r
> x[is.na(x)] <- 0
> x
[1] 1 2 3 0
}}}
replaces the missing value by zeros.
A common operation is to select rows or columns of data frame that meet some criteria. For example, to select those rows of painters data frame with Colour >= 17:
{{{#!highlight r
> library(MASS)
> painters[painters$Colour >= 17,]
Composition Drawing Colour Expression School
Bassano          6       8     17          0      D
Giorgione        8       9     18          4      D
Pordenone        8      14     17          5      D
}}}
We may want to select on more than one criterion. We can combine logical indices by the 'and', 'or' and 'not' operators. For example,
{{{#!highlight r
> painters[painters$Colour >= 17 &  Composition Drawing Colour
Titian             12      15     18
Rembrandt          15       6     17
Rubens             18      13     17
Van Dyck           15      10     17
}}}
== List of Logical Operations ==
||'''Operation''' ||'''Description'''||
||! || logical NOT ||
||&brvbar; | logical OR ||
||&lt; || less than ||
||&lt;= || less than or equal to ||
||&gt; || greater than ||
||&gt;= || greater than or equal to ||
||== || logical equals (double =) ||
||!= || not equal ||
||&brvbar;&brvbar; || OR with IF ||
||xor(x,y) ||exclusive OR ||
||isTRUE(x) ||an abbreviation of identical(TRUE,x)||


If we want to select a subgroup, for example those with schools A, B, and D. We can generate
a logical vector using the  <latex> \mathtt{\%in\%}</latex> operator as follows:
{{{#!highlight r
> painters[painters$School %in% c("A","C","D"),]
Da Udine           10       8     16        3      A
Da Vinci           15      16      4       14      A
Del Piombo          8      13     16        7      A
}}}

Sometimes we are interested in the indices of rows satisfying a certain condition. To extract these indices we use the which() command.
{{{#!highlight r
> which(painters$School %in% c("A","C","D"))
[1]  1  2  3  4  5  6  7  8  9 10 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
[26] 32
}}}
== Indexing with Character Vectors ==
A vector character strings with variable names can be used to extract those variables relevant for analysis. This is very useful when we have a large number of variables and we need to work with a few ones. For example,
{{{#!highlight r
> names(painters)
[1] "Composition" "Drawing" "Colour" "Expression" "School"
> painters[1:3,c("Drawing","Expression")]
Drawing Expression
Da Udine         8          3
Da Vinci        16         14
Del Piombo      13          7
}}}

   * ''a vector of character strings'' could a index on a vector when the vector has names:
{{{#!highlight r
> x <- c(1:3,NA)
> names(x)<-letters[1:4]
> x
a  b  c  d
1  2  3 NA
> x[c("a","c")]
a c
1 3
}}}

== Trimming Vectors Using Negative Indices ==
   * an extremely useful facility is to use negative indices to drop terms from a vector
   * suppose we wanted a new vector, z, to contain everything but the first element of x
{{{#!highlight r
> x<- c(5,8,6,7,1,5,3)
> (z <- x[-1])
[1] 8 6 7 1 5 3
}}}