MATLAB Tutorial Chapter 6 Writing and calling functions In this chapter we discuss how to structure a program with multiple source code files First an explanation of how code files work in MATLAB is presented In compiled languages such as FORTRAN C or C code can be stored in one or more source files that are linked together to form a single executable at the time of compilation MATLAB being an interpreted language deals with multiple source files in a more open ended manner MATLAB code is organized into ASCII files carrying the extension m also known as m files MATLAB 6 has an integrated word processing and debugging utility that is the preferred mode of editing m files although other ASCII editors such as vi or emacs may also be used There are two different kinds of m files The simplest a script file is merely a collection of MATLAB commands When the script file is executed by typing its name at the interactive prompt MATLAB reads and executes the commands within the m file just as if one were entering them manually It is as if one were cutting and pasting the m file contents into the MATLAB command window The use of this type of m file is outlined in section 6 1 The second kind of m file discussed in section 6 2 contains a single function that has the same name as that of the m file This m file contains an independent section of code with a clearly defined input output interface that is it can be invoked by passing to it a list of dummy arguments arg1 arg2 and it returns as output the values out1 out2 The first non commented line of a function m file contains the function header which is of the form function out1 out2 filename arg1 arg2 The m file ends with the command return which returns the program execution to the place where the function was called The function code is executed whenever either at the interactive command prompt or within another m file it is invoked with the command outvar1 outvar2 filename var1 var2 with the mapping of input to dummy arguments arg1 var1 arg2 var2 etc Within the function body output values are assigned to the variables out1 out2 etc When return is encountered the current values of out1 out2 are mapped to the variables outvar1 outvar2 at the point where the function was called MATLAB allows much latitude in writing functions with variable length argument and output variable lists For example the function could also be invoked by the command outvar1 filename var1 var2 in which case only a single output variable is returned containing on exit the value of the function variable out1 The input and output arguments may be strings scalar numbers vectors matrices or more advanced data structures Why use functions As is well known from every computer science course splitting a large program into multiple procedures that perform each a single well defined and commented task results in programs that are easier to read easier to modify and that are more resistant to error In MATLAB one writes first a master file for the program either a script file or better yet a function m file that returns a single integer that might return 1 for program success 0 for incomplete program execution or a negative value to indicate a run time error that is the point of entry to the program This program file then calls upon code in other m files by invoking them as functions But if there is no compilation process to link all of the source code files together how does MATLAB know where to look for a function when it is called MATLAB s program memory contains a search path list the contents of which can be viewed with the command path that stores the names of the directories it has been told contain function m files Initially the path lists only the directories that hold the built in MATLAB functions such as sin exp etc As demonstrated in section 6 2 one uses the command addpath to add to this list the name of each directory that contains a m file for the present project Then when the MATLAB code interpreter encounters a function say with the name filename it starts at the top of the path list and works its way down searching in each directory for a file filename m When it finds it it executes the file s code in the manner described above For this reason it is imperative that the names of the m file and of the function agree in fact it is only the filename that counts 6 1 Writing and running m files While MATLAB can be run interactively from the command line you can write a MATLAB program by composing a text file that contains the commands you want MATLAB to perform in the order in which they appear in the file The standard file suffix for a text file containing a MATLAB program is m In the MATLAB command window selecting the pull down menu File New M file opens the integrated MATLAB text editor for writing a m file This utility is very similar to word processors so the use of writing and saving m files is not explained in detail here As an example use this secion as a file MATLAB tutorial c6s1 m that has only the following executable commands file name MATLAB tutorial c6s1 m disp Starting file name j 5 for i 1 5 j j 1 disp int2str i int2str j end disp Finished file name We can run this m file from the prompt by typing its name MATLAB tutorial c6s1 If we type whos now we see that the variables that are in the memory at the end of the program also remain in memory after the m file is done running This is because we have written the m file as a script file where we have simply collected together several commands in a file and then the code executes them one by one when the script is run as if we were merely typing them into the interactive session window A more common use for m files is to isolate a series of commands in an independent function as explained in the following section 6 2 Structured programming with functions Unstructured programming approach File unstructured m In this section let us demonstrate the use of subroutines to write structured well organized programs We do so for a particularly simple and familiar case the simple 1 D PDE problem that we encounted in section 4 1 First in this m file we solve the problem with a program the combines all of the commands into a single file This unstructured approach is fine for very small programs but rapidly becomes confusion as the size of the program grows num pts 100 of grid points x 1 num pts grid of x values We now set the values for the matrix discretizing the PDE with Dirichlet boundary conditions nzA 3 num pts