EGR 106 Lecture 9 Function Files

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EGR 106 Lecture 9Function Files

• Functions
• Concept
• Basic Structure
• Examples and Applications
• Textbook 6.1 - 6.7

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Function Concept

• So far
• Have used Matlabs built-in functions for
  example sin(x), exp(x), abs(x), . . .
• Have started writing scripts
• Function
• Reusable script
• Sometimes called a subprogram
• Useful as a building block for larger programs
• Computes an output from an input

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Building Block Concept
function 1 ------ ------ ------
Main Program ------ ------ ------ ------ functio
n 1 ------ ------ ------ function
2 ------ ------ ------ ------ ------ function
3 ------ ------ ------ ------ ------ ------ -----
-
function 2 ------ ------ ------
function 3 ------ ------ ------
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Function File Format
First line of the file must be of the form
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Example Convert Degrees to RadiansFunction
deg2rad
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Usage

• Syntax is just like a built-in functions
• Application is independent of the variable names
  within the function (x,y)
• Executed by typing name (input)

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Rules for Functions

• Again first line of the file must be of the form
  
• function outputs name(inputs)

List of any variables that the function needs
Identifies a function file
List of function result variables
Name of the function and the file (name.m)
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• inputs
• Used to transfer data into the function from the
  workspace
• Workspace variables are unavailable within the
  function
• Any necessary variables must be brought in
• For multiple inputs
• Separate them by commas
• Order is important
• Examples of built-in functions with inputs
• sum(x) plot(x,y)

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• outputs
• Used to transfer results back into the workspace
  from the function
• For multiple outputs
• Separate them by commas in brackets
• Order is important
• Output variables must be assigned
• Examples of built-in functions with outputs
• y sum(x)
• value,location max(x)

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• Note brackets on the left only make sense for
  functions
• value,location max(x) is okay
• value,location 1, 2 is not
• Default output is the first one
• value,location max(x)
• value max(x)

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• Comments are suggested in lines 2, 3
• Words in line 2 are searched when lookfor is
  employed
• Comments in lines 2, 3, are returned when help
  name is executed

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Variables Local vs Global

• Usually, once created, variables are available in
  the workspace until cleared
• Functions create their own workspace with their
  own local variables distinct from those in the
  original workspace
• Functions cannot modify variables within the
  original workspace except through outputs
• Exception variables can be declared global and
  will then span both workspaces and be
  manipulated in both.
• Format global variable_name

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Variables Local vs Global
function zfct2(x) Calcuate fct
2 z5x.2x - - -
function yfct1(x) Calcualte fct
1 y6x.310 - - -
Local variables x are not in general the same
Each workspace is different with different local
variables
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Example Functions

• Consider a script to compute the area of a
  triangle
• First as a script

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Now as a function
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• Usage doesnt depend on knowing parameter names
  internal to the program

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• Could add the perimeter calculation as a second,
  optional output

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• My plotting function

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• Can stack functions in one file (all must be
  functions)
• Useful for mailing and testing
• Must start
• m-file with
• function . . .that could be a main program
  used to call other functions

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Typical Errors
Too few inputs
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Too many inputs
Too many outputs
Wrong input type funny result
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Application f(x) 2e-xsin(x)e-x/2sin(2x)

• Find its minimum and the first root beyond zero

x ?
f(x) ?
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Solution using Matlab

• Construct a function m-file for f(x)

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• To find the root fzero('fun',a) (a nearby
  value)
• To find the minimum fminbnd('fun',a,b)
• (a,b range)