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Functions are used to simplify a series of calculations.

For instance, let us suppose that there exists an array of numbers which we wish to add to another variable. Instead of carrying out separate calculations for each number in the array, it would be much easier to simply create a function that does this for us automatically.

A function in R generally works by:

(a) Defining the variables to include in the function and the calculation. e.g. to add two numbers together, our function is:

function(number1,number2) {(number1+number2)}

(b) Using sapply to define the list of numbers and typically an associated sequence:

sapply(c(20,40,60), number1addnumber2, seq(2,20,by=2))

Here's a few examples below that you can try out for yourself!

1. Add an array of numbers to a sequence

> number1addnumber2<-function(number1,number2) {(number1+number2)}
> result1<-sapply(c(20,40,60),number1addnumber2,seq(2,20,by=2))
> result1df<-data.frame(result1)
> result1df

X1 X2 X3
22 42 62
24 44 64
26 46 66
28 48 68
30 50 70
32 52 72
34 54 74
36 56 76
38 58 78
140 60 80

2. Subtract an array of numbers from a sequence

> number1minusnumber2<-function(number1,number2) {(number1-number2)}

> result2<-sapply(c(20,40,60),number1minusnumber2,seq(2,20,by=2))
> result2df<-data.frame(result2)
> result2df

X1 X2 X3
18 38 58
16 36 56
14 34 54
12 32 52
10 30 50
8 28 48
6 26 46
4 24 44
2 22 42
0 20 40

3. Multiply an array of numbers by a sequence

> multiplynumber1bynumber2 <-function(number1,number2) {(number1*number2)}

> result3<-sapply(c(20,40,60), multiplynumber1bynumber2, seq(2,20, by=2))
> result3df=data.frame(result3)
> result3df

X1 X2 X3
40 80 120
80 160 240
120 240 360
160 320 480
200 400 600
240 480 720
280 560 840
320 640 960
360 720 1080
400 800 1200

4. Divide an array of numbers by a sequence

> dividenumber1bynumber2<-function(number1,number2) {(number1/number2)}

> result4<-sapply(c(20,40,60), dividenumber1bynumber2, seq(2, 20, by=2))
> result4df<-data.frame(result4)
> result4df

X1 X2 X3
10.000000 20.000000 30.000000
5.000000 10.000000 15.000000
3.333333 6.666667 10.000000
2.500000 5.000000 7.500000
2.000000 4.000000 6.000000
1.666667 3.333333 5.000000
1.428571 2.857143 4.285714
1.250000 2.500000 3.750000
1.111111 2.222222 3.333333
1.000000 2.000000 3.000000

5. Raise number to a power

> raisenumber1bypower<-function(number1,power) {(number1^power)}
> result5<-sapply(c(20,40,60),raisenumber1bypower,seq(0.5,2.5,by=0.5))
> result5df<-data.frame(result5)
> result5df

X1 X2 X3
4.472136 6.324555 7.745967
20.000000 40.000000 60.000000
89.442719 252.982213 464.758002
400.000000 1600.000000 3600.000000
1788.854382 10119.288513 27885.480093

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