MATLAB Functions and M-Files

• Functions perform a task and are defined in separate MATLAB files, called m-files.
• The function and file names should match.
• Functions operate on variables within its local workspace.
• The base workspace is accessed at the MATLAB command prompt.
• Functions can accept multiple input arguments and also return multiple output arguments.
• Types include user-defined, anonymous, and recursive functions.

Basic m-file Functions

• Function name must match the m-file name.
• Functions can have multiple input and output parameters.
• Input parameters take values from the calling function.
• Output parameters return values to the calling function.
• Variables within a function have their own workspace (memory).
• Variables in a function are separate from the command window, even if the variable names are same.
• Values are shared only through input and output parameters.

User-Defined Functions

• They are Matlab programs created by the user and saved as function files and work like built-in functions.
• Functions can have input arguments (parameters) and output variables (parameters) that can be scalars, vectors, or matrices of any size.
• Functions can have any number of input and output parameters, including zero.
• The calculation results are transferred out of the function by the output parameters.

Basic Parts of an m-file

• Consists of the function definition line, H1 line, help text, the function body, and comments.
• The function definition line informs MATLAB that the M-file contains a function.
• The function definition line specifies the argument calling sequence. Its syntax follows:function [out1, out2, ...] = functionName(in_1, in2, ...)
• "functionName" is the name of the function.
• in1, in2, ... are the input parameters.
• out1, out2, ... are the output parameters.
• function is a keyword.
• Parentheses are necessary even when there are no parameters: function [out1, out2, ...] = functionName()
• Brackets for an output parameter can be omitted if there is only one: function out = functionName(in1, in2, ...)
• If there is no output parameter, they are called void functions.
• Example of a void function: function functionName(in1, in2, ...)
• The first comment line in the function is the H1 line.
• It should contain important keywords that describe the function.
• The lookfor command searches the H1 lines of all functions.
• User-defined functions are used like built-in functions.
• User-defined functions can be called from the command line, script file, or another function (including itself, called recursive).

Anonymous Functions

• Anonymous functions are simple, single-line, user-defined functions.
• They are defined and written within the computer code.
• Only one-line executable statement.
• These functions do not have"function" or "end" statements.
• They use a special @(x) syntax.
• Syntax: functionName = @(var1, var2, ...) expression
• functionName is the name of the anonymous function.
• var1, var2... are the comma separated list of arguments.
• expression is a single mathematical expression involving those variables.
• Anonymous functions can be defined in any part of MATLAB: command window, script files, and regular user-defined functions.

Nested Functions

• Functions contained within the body of another function.
• They are defined within the scope of another function and can access the containing function's workspace.

Program Decomposition/Linear Solving

• Decomposition creates reusable matrix decompositions and solves linear systems, such as Ax = b or xA = b.
• After dA = decomposition(A), then dA\b returns the same vector, but faster.
• Decomposition objects are well-suited to require repeated solutions.
• dA can be used with the same operators as A.
• Including:
• Complex conjugate transpose dA'
• Negation -dA
• Multiply or divide by a scalar using c*dA or dA/c.
• Solve a linear system Ax = b using x = dA\b.
• Solve a linear system xA = b using x = b/dA.