Subsetting matrices
The biggest advantage of using matrices is that we can find and access elements based on the margins of the matrix. Let’s take a look at this matrix:
mat<- matrix(11:22, ncol=4, nrow=3)
mat
[,1] [,2] [,3] [,4]
[1,] 11 14 17 20
[2,] 12 15 18 21
[3,] 13 16 19 22
The show() method which prints out the content of the matrix gives us a hint about the dimensions and element indices of the matrix.
Subsetting entire rows
Let’s examine what happens if we use one of the subscripts above, such as [,1]:
mat[1,]
[1] 11 14 17 20
This subsetting returns the first row of the matrix. The 1 before the comma indicates that the first column should be returned. There is nothing after the comma, which indicates that all columns need to be included in the subset.
Subsetting entire columns
A similar pattern exists if columns are to be returned. The subscript [,2] returns the second column:
mat[2,]
[1] 14 15 16
Subscript blueprint
There is a comma in the square brackets, which possibly separates two integer values that represent rows and columns. The structure of a subscript is typically:
object[<row>, <column>]
Accessing individual elements happens with the specification of a row and column index. For instance, the value in the second row and the third columns:
mat[2,3]
[1] 18
Other subscript values
The examples above work if the row- and column-subscript values fall between 1 and the number of rows for the rows (the first value of the dim attribute), and between 1 and the number of columns (the second value of the dim attribute) for the number of columns.
Subscripts that are higher than the number of columns/rows
If a subset if defined that does not exist because the subscript are higher than the highest available row or column indices, matrices and arrays work differently from vectors:
a <- 1:4
a[5]
[1] NA
which results in missing values. Matrices (and arrays), on the other hand, return the iconic ‘Out of bounds’ error - either if the desired row, or column (or both) indices are defined:
mat[4,5]
Error in mat[4, 5] : subscript out of bounds
This is an effective way to prevent accessing positions that are invalid.
0 subscript
0 subscripts behave similarly to those in vectors: they produce empty containers that do not contain any values, and they have not much practical use:
mat[0,3]
integer(0)
Negative subscripts
The negative subscripts of vectors indicate the omission of values:
vec <- 1:5
vec[-1]
[1] 2 3 4 5
They work similarly in matrices, they define the omission of entire rows:
mat[-1,]
[,1] [,2] [,3] [,4]
[1,] 12 15 18 21
[2,] 13 16 19 22
or columns:
mat[,-1]
[,1] [,2] [,3]
[1,] 14 17 20
[2,] 15 18 21
[3,] 16 19 22
or both:
mat[-2,-1]
[,1] [,2] [,3]
[1,] 14 17 20
[2,] 16 19 22
As the outputs show here, the results of this operation is a matrix - similar to the original object.
The drop argument of subsetting
When subsetting matrices, the default behavior is to simplify the output of the object. When an individual value, row or column subset is defined, the subsetting returns a vector class (numeric, logical, character. etc…):
sb <- mat[,2]
class(sb)
[1] "integer"
which looses its matrix class:
# the original object
is.matrix(mat)
[1] TRUE
# the subset
is.matrix(sb)
[1] FALSE
This is because subsetting by implicitly involves the drop argument, which is by default set to drop=TRUE, forcing the results of subsetting to drop the matrix class, whenever possible.
When subsetting is applied in a programmatic context and subscripts change during the process, the result of subsetting can sometimes be either easilly simplified to a single vector (row or column) and sometimes cannot (and has to stay a matrix). If the result is sometimes simplied to a matrix and sometimes not, then further subsetting can cause issues. Consider this case:
sa <- -1
partial <- mat[sa, ]
partial
[,1] [,2] [,3] [,4]
[1,] 12 15 18 21
[2,] 13 16 19 22
This can be further subsetted, with matrix rules:
partial[,2]
[1] 15 16
Contrast the case above with this scenario, when sa is set to 1:
sa <- 1
partial <- mat[sa, ]
partial
[1] 11 14 17 20
We will encounter the error with the same chunk of code:
partial[,2]
Error in partial[, 2] : incorrect number of dimensions
This issue can be easilly evaded, with the drop=FALSE argumentation, that forces the output of the subsetting to conserve its matrix class.
sa <- 1
partial <- mat[sa, , drop=FALSE]
partial
[,1] [,2] [,3] [,4]
[1,] 11 14 17 20
This result is a simple row-matrix, where the matrix-style subsetting will not cause any error:
partial[,2]
[1] 14