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# Inline Function in Matlab

Inline Functions in Matlab have two categories one is inbuilt functions and the second is used defined functions that are created by the user.

## Inbuilt Functions:

Matlab has many built-in functions square root, sin, cos, tan, exponential, log, etc. It also has more complex and special mathematical functions like gamma functions and Bessel functions. It also has some built-in constants pi, I (complex numbers) and infinity.

## Example:

``sin ( pi / 2 )``

It gives output as 1.

in this example we did not even mention the value of pi, automatically pi takes the value 3.14.

``sqrt (3)``

It gives output 1.73.

And if write program statement sqrt   ( -1 ) it will give ans as 0.00 + i

## User Defined Functions

The keyword is used to define our own function is “ inline ”, now let see how to use it

Let us assume I want to create one function fun = x ^ 2 – 6

#### Matlab commands will be

`Fun = inline ( ‘ x ^ 2 – 6 ’ , ’ x ’ )  . . . . . . . . . . (1)   function declaration and definationFun =inline function :`

Fun= – 6. . . . . . . output of (1)

`Fun ( 1 ) (2) giving value x=1`

Ans =

-5. . . .output of(2)

`Fun ( 2 ) ....(3) giving value x=2`

Ans =

-2 . . . output of(3)

`Fun ( 3 )                  .  . . . . . . . . . . . . . . .  . . . . (2)  giving value x=3`

Ans=

3. . . . . . . output of(3)

• Matlab functions operate on scalar as well as vectors
• To make inline function victories, the ‘ vectorize ’ keyword is used inside the function definition.
• In the above example suppose I want to create vector function ‘fun’ then commands will be
``Fun  = inline ( vectorize ( ‘ x ^ 2  –  5 ’ , ’ x ’ )``

It will create vector fun.

``````Fun ( 1 : 5 )
And evolution will take values of x as  1 , 2 , 3 , 4 and 5``````

Output for this program will be

-4 -1 4 11 and 20

In this first value is for x = 1 , second value is for x = 2 , third value is for x = 3 , forth value is for  x = 4 and fifth value is for x = 5.

## Syntax of Inline Function

It is categorized into three parts:

1. Function Definition: In this, we write the function string and define the independent variable.

``````Function name = inline ( ‘ function ’ , ’ independent variable ’ )
Fun = inline ( ‘ x ^ 2 – 5 ’ , ’ x ’ )``````

2. Function Evolution: In this, we evaluate function by giving any value to the independent variable.

``````Function name (variable value )
Fun ( 1 )``````

3. Vectorize function: This function creates a vector of given function.

``````Function name = inline ( vectorize( ‘ function string ’ ) , ’ independent variable ’ )
Y = inline ( vectorize ( ‘ x ^ 2 – 1 ’ ) , ’ x ’ )``````

## Examples:

The following examples are as follows

## Example 1:

Let us consider one function

``Z = x3 - 56``

To solve the above equation in Matlab, we need to create an inline function for z and need to assign one independent variable.

## Matlab code:

``````>>
z =
Inline function :
Z ( x ) = x . ^ 3 - 56
>> z ( 0 )

Ans = 4

>> z ( 1 0 )

Ans = 996

z ( -1 )

Ans = 5
``````

## Example 2:

``Z = x ^ 3 + 23 x - 9``

## Matlab code for example 2

``````Z = inline ( vectorize ( ' x .^3 + 23*x – 9 ' ) ,' x ' )
z =
Inline function :
Z ( x ) = x . ^ 3 + 23 * x - 9
>> z ( 1 : 10 )``````

Ans = Columns 1 through 3

15          45          87

Columns 4 through 6

147         231         345

Columns 7 through 9

495         687         927

Column 10

1221

`>> z ( 1 : 0.5 : 5 )`

Ans = Columns 1 through 4

15.0000   28.8750   45.0000   64.1250

Columns 5 through 8

87.0000 114.3750 147.0000  185.6250

Column 9

231.0000