## MATLAB MODULE 1

MATLAB Window Environment and the Base Program

## Developing user-defined Functions

Suppose you want to write a function to generate and plot N data points of the exponentially-decaying sinusoid of amplitude A, frequency f, and exponential time-constant . A MATLAB function   which can take all these parameters as arguments and provide decaying sinusoid as an output is shown in Fig. M1.20.

Generate an M-file with the code given in Fig.M1.20. When you attempt to save the file, editor will automatically assign a function name decaying_sin to your M-file. Save the function to the current working directory or include your personal directory into MATLAB search path by using addpath command. We must avoid duplicating function names with built-in MATLAB functions or keywords.

A function file begins with a function definition line, which contains the keyword function, a well-defined list of input and output arguments, and function name. Some examples of function definition are given below (execute help function for details):

function [ph, mag] =   complex (z)

function [r,theta] =   polar_form(a, b)

function decaying_sin( )

function sys_response( )

The first commented line just after the function definition is called the H1 line.   This line is automatically catalogued in the contents.m file of the directory in which function file resides. This allows the line to be searched by the lookfor command. Very carefully chosen keywords related to your function should come in the H1 line. Note that if there is any blank space before the % sign in the H1 line, then it is no longer H1 line !!

All comment lines immediately following the function definition line and immediately before the first executable statement of the function are displayed by MATLAB if help is asked on the function. Type

>> help decaying_sin

and see what MATLAB displays.

Input-argument names used in the function are local to the function; so arbitrary variable names   can be used to call the function. The name of another function can also be passed as an input variable. The following are examples of legal function calls:

Fig. M1.20 DECAYING_SIN Function

>> Yt = decaying_sin (time_span, time_const, mag, freq, pts)

In this case, input variables time_span, time_const, mag, freq, and pts must be defined before the function call.

>> res = decaying_sin ([0 10], tau, 3, 50, 1000)

Here the input variable tau must be defined beforehand; all other inputs have been defined in the function call.

>> sig = decaying_sin ([0,10], 2, 3, 50, 100)

Here all the inputs have been specified in the call statement.

>> decaying_sin ([0,10], 3, 0.5, 60, 100)

In this case, the output is assigned to generic variable ans.

#### Exercise M1.12

1. Execute decaying_sin function with less than four and greater than five arbitrary arguments and interpret the messages. Study nargin and nargout commands through online help.

2. Execute decaying_sin function with tspan = [-1 10] and tspan=[3 0] and interpret the messages.

3. Execute the function as Yt = decaying_sin([0 5], 3, 0.5, 50). What is the length of the vector Yt ?

4. In some applications we don't want to generate the plot every time.   We may need only output given by the function. Modify the above function with one more input argument ‘str' to provide control over whether we want to generate the plot or not? If str = ‘Y' or ‘y', then it should generate the plot. If str = ‘N' or ‘n', then it should not. If any other character is passed, then it should give the error message ‘Unrecognized user input' and terminate the program. You also need to modify processing with the nargin command.

Exercise   M1.13

Write a function named specifications with the following input and output arguments:

Input arguments:

1.          vector tspan of initial and final times.

2.          Scalars y0 0, zeta , wn, and theta.

3.          Character argument str controlling whether to plot the final result or not.

4.         Scalar N of number of data points required to be generated.

Output arguments:

1.          Yt calculated by

2.          Tau calculated by

3.          Tr calculated by

4.          Tp calculated by

5.          Mp calculated by