Basic of Calculations _Functions_Matrices in R Language

Function :-

Function are a bunch of commands grouped together in a sensible unit.

Functions take input arguments, do calculations (or make some graphics, call other functions) and produce some output and return a result in a variable. The returned variable can be a complex construct, like a list.

Syntax 

Name <- function(Argument1, Argument2, ...)
                {
                   expression
                                     }
Where expression is a single command or a group of commands

• Function arguments can be given a meaningful name
• Function arguments can be set to default values
• Functions can have the special argument '...'

Functions (Single variable)

The sign <- is furthermore used for defining functions:
> abc <- function(x) {
                    x^2
                         }

> abc (3)
  [1]  9

>abc (6)
  [1]  36

> abc (-2)
  [1]   4

Function (Two variables)

>abc  <- function (x,y) {
               x^2+y^2
                      }
> abc (2,3)
   [1]  13
> abc (3,4)
    [1]  25
> abc  (-2,-1)
   [1]  5

Matrix

• Matrices are important objects in any calculation.
• A matrix is a rectangular array with p rows and n columns.
• An element in the i-th row and j-th column is denoted by xij (book version) or x[i,j] ("program version"), i = 1,2,.....,n, j = 1,2,...,p. 
• An element of a matrix can also be an object, for example a string. However, in mathematics, we are mostly interested in numerical matrices, whose element are generally real numbers

In R, a 4⤫2-matrix x can be created with a following command:

>x <- matrix (nrow = 4 , ncol = 2, data = c(1,2,3,4,5,6,7,8) )

We see:

• The parameter nrow defines the row number of a matrix.
• The parameter ncol defines the column number of a matrix.
• The parameter data assigns specified values to the matrix element.
• The value from the parameters are written column-wise in matrix.

>  x
              [,1]          [,2]
[1,]           1             5
[2,]           2             6
[3,]           3             7
[4,]           4             8

• One can access a single element of a matrix with x[i,j] :

> x [3,2]
 [1]   7