R scripts - 1. Data
Structures –
a. Matrices –
Matrices are
the R objects in which the elements are arranged in a two-dimensional
rectangular layout. They contain elements of the same atomic types. Though we
can create a matrix containing only characters or only logical values, they are
not of much use. We use matrices containing numeric elements to be used in
mathematical calculations.
A Matrix is
created using the matrix() function.
Syntax
The basic
syntax for creating a matrix in R is –
matrix(data, nrow, ncol, byrow,
dimnames)
Following is
the description of the parameters used −
•
data is the input vector which
becomes the data elements of the matrix.
•
nrow is the number of rows to be
created.
•
ncol is the number of columns to be
created.
•
byrow is a logical clue. If TRUE
then the input vector elements are arranged by row. dimname
is the names assigned to the rows and columns.
Example –
Create a
matrix taking a vector of numbers as input.
# Elements
are arranged sequentially by row.
M
<- matrix(c(3:14), nrow = 4, byrow =
TRUE) print(M)
# Elements
are arranged sequentially by column.
N
<- matrix(c(3:14), nrow = 4, byrow =
FALSE) print(N)
# Define the
column and row names.
rownames = c("row1",
"row2", "row3", "row4") colnames =
c("col1", "col2", "col3")
P <- matrix(c(3:14), nrow = 4, byrow
= TRUE, dimnames = list(rownames, colnames)) print(P)
When we
execute the above code, it produces the following result –
[,1] [,2] [,3]
[1,]
3 4 5
[2,]
6 7 8
[3,]
9 10 11
[4,]
12 13 14
[,1] [,2] [,3]
[1,]
3 7 11
[2,]
4 8 12
[3,]
5 9 13 [4,]
6 10 14
col1 col2 col3 row1 3 4
5 row2 6 7 8 row3
9 10 11 row4
12 13 14
Accessing Elements of a Matrix –
Elements of
a matrix can be accessed by using the column and row index of the element. We
consider the matrix P above to find the specific elements below.
# Define the
column and row names.
rownames = c("row1",
"row2", "row3", "row4")
colnames = c("col1",
"col2", "col3")
# Create the
matrix.
P <- matrix(c(3:14), nrow = 4, byrow
= TRUE, dimnames = list(rownames, colnames))
#
Access the element at 3rd column and 1st row. print(P[1,3])
#
Access the element at 2nd column and 4th row. print(P[4,2])
#
Access only the 2nd row. print(P[2,])
#
Access only the 3rd column. print(P[,3])
When we
execute the above code, it produces the following result –
[1] 5 [1] 13 col1 col2 col3 6
7 8 row1 row2 row3 row4
5 8 11
14
Matrix Computations –
Various
mathematical operations are performed on the matrices using the R operators.
The result of the operation is also a matrix.
The
dimensions (number of rows and columns) should be same for the matrices
involved in the operation.
Matrix
Addition & Subtraction – # Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2,
6), nrow = 2) print(matrix1)
matrix2 <- matrix(c(5, 2, 0, 9, 3,
4), nrow = 2) print(matrix2)
# Add the
matrices.
result <- matrix1 + matrix2
cat("Result of addition","\n") print(result)
# Subtract
the matrices
result <- matrix1 - matrix2
cat("Result of subtraction","\n") print(result)
Matrix Multiplication & Division – #
Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2,
6), nrow = 2) print(matrix1)
matrix2 <- matrix(c(5, 2, 0, 9, 3,
4), nrow = 2) print(matrix2)
#
Multiply the matrices. result <- matrix1 * matrix2 cat("Result of
multiplication","\n")
print(result)
# Divide the
matrices
result <- matrix1 / matrix2 cat("Result of division","\n") print(result)
b. Arrays –
Arrays are
the R data objects which can store data in more than two dimensions. For
example − If we create an array of dimension (2, 3, 4) then it creates 4
rectangular matrices each with 2 rows and 3 columns. Arrays can store only data
type.
An array is
created using the array() function. It takes vectors as input and uses the
values in the dim parameter to create an array.
An array of
two 3x3 matrices each with 3 rows and 3 columns.
# Create two
vectors of different lengths.
vector1 <- c(5,9,3)
vector2 <- c(10,11,12,13,14,15)
# Take these
vectors as input to the array.
result <-
array(c(vector1,vector2),dim = c(3,3,2)) print(result)
When we
execute the above code, it produces the following result –
, , 1
[,1] [,2] [,3]
[1,]
5 10 13
[2,]
9 11 14
[3,]
3 12 15
, , 2
[,1] [,2] [,3]
[1,]
5 10 13
[2,]
9 11 14
[3,]
3 12 15
Naming Columns and Rows –
We can give
names to the rows, columns and matrices in the array by using the dimnames
parameter.
# Create two
vectors of different lengths.
vector1 <- c(5,9,3) vector2 <-
c(10,11,12,13,14,15) column.names <- c("COL1","COL2","COL3")
row.names <- c("ROW1","ROW2","ROW3")
matrix.names <-
c("Matrix1","Matrix2")
# Take these
vectors as input to the array.
result <-
array(c(vector1,vector2),dim = c(3,3,2),dimnames =
list(row.names,column.names,matrix.names)) print(result)
When we
execute the above code, it produces the following result –
, , Matrix1
COL1 COL2 COL3
ROW1
5 10 13
ROW2
9 11 14
ROW3
3 12 15
, , Matrix2
COL1 COL2 COL3
ROW1
5 10 13
ROW2
9 11 14
ROW3
3 12 15
Accessing Array Elements –
# Create two
vectors of different lengths.
vector1 <- c(5,9,3) vector2 <-
c(10,11,12,13,14,15) column.names <-
c("COL1","COL2","COL3") row.names <-
c("ROW1","ROW2","ROW3")
matrix.names <-
c("Matrix1","Matrix2")
# Take these
vectors as input to the array.
result <-
array(c(vector1,vector2),dim = c(3,3,2),dimnames = list(row.names, column.names, matrix.names))
#
Print the third row of the second matrix of the array. print(result[3,,2])
# Print the
element in the 1st row and 3rd column of the 1st matrix. print(result[1,3,1])
# Print the
2nd Matrix.
print(result[,,2])
When we
execute the above code, it produces the following result –
COL1 COL2 COL3
3 12 15
[1] 13
COL1 COL2 COL3
ROW1
5 10 13
ROW2
9 11 14
ROW3
3 12 15
Manipulating Array Elements –
As array is
made up matrices in multiple dimensions, the operations on elements of array
are carried out by accessing elements of the matrices.
#
Create two vectors of different lengths. vector1 <- c(5,9,3)
vector2 <- c(10,11,12,13,14,15)
# Take these
vectors as input to the array.
array1 <-
array(c(vector1,vector2),dim = c(3,3,2))
# Create two
vectors of different lengths.
vector3 <- c(9,1,0) vector4 <-
c(6,0,11,3,14,1,2,6,9) array2 <- array(c(vector1,vector2),dim = c(3,3,2))
# create
matrices from these arrays.
matrix1 <- array1[,,2] matrix2 <-
array2[,,2]
# Add the
matrices.
result <- matrix1+matrix2
print(result)
When we
execute the above code, it produces the following result –
[,1] [,2] [,3]
[1,]
10 20 26
[2,]
18 22 28
[3,]
6 24 30
Calculations Across Array Elements –
We can do
calculations across the elements in an array using the apply() function.
Syntax
apply(x, margin, fun)
Following is
the description of the parameters used −
x is an
array.
margin is
the name of the data set used.
fun is the
function to be applied across the elements of the array.
Example
We use the
apply() function below to calculate the sum of the elements in the rows of an
array across all the matrices.
#
Create two vectors of different lengths. vector1 <- c(5,9,3)
vector2 <- c(10,11,12,13,14,15)
# Take these
vectors as input to the array.
new.array <-
array(c(vector1,vector2),dim = c(3,3,2)) print(new.array)
# Use apply
to calculate the sum of the rows across all the matrices.
result <- apply(new.array, c(1), sum)
print(result)
When we
execute the above code, it produces the following result –
, , 1
[,1] [,2] [,3]
[1,]
5 10 13
[2,]
9 11 14
[3,]
3 12 15
, , 2
[,1] [,2] [,3]
[1,]
5 10 13
[2,]
9 11 14
[3,]
3 12 15
[1] 56 68 60