MATLAB CHAPTER 3 Functions and Files

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MATLAB ??CHAPTER 3 Functions and Files

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Elementary Mathematical Functions

• lookfor find functions that are relevant to
  your application
• help when you know the correct spelling of the
  function

3
Exponential and Logarithmic Functions

• Some common mathematical functions

4
Complex Number Functions(1/2)

• rectangular representation
• a ib
• polar representation
• .
• abs(x), angle(x)
• absolute value (magnitude)
• angle
• conj(x)
• complex conjugate

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Complex Number Functions(2/2)
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Numeric Functions

• MATLAB has been optimized to deal with arrays.
• round(y) rounds to the nearest integer ? ans
  2, 3, 4
• fix(y) truncates to the nearest integer toward
  zero ? ans 2, 2, 3
• ceil(y) rounds to the nearest integer toward 8
  ? ans 3, 3, 4
• e.g. z -2.6 , -2.3 , 5.7
• floor(z) rounds to the nearest integer toward
  - 8 ? ans -3, -3, 5
• fix(z) -2, -2, 5
• abs(z) 2.6 , 2.3, 5.7

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Trigonometric Functions

• Table 3.1-2
• Trigonometric functions

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Hyperbolic Functions(1/2)

• Hyperbolic functions

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Hyperbolic Functions(2/2)

• Hyperbolic functions

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User-Defined Functions(1/4)

• Function file when need to repeat a set of
  commands several times.
• variables local
• syntax
• function output variables function_name
  (input variables)
• function_name saved file name ( with the .m
  extension)
• ? function_name drop file name drop.m
• e.g.

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User-Defined Functions(2/4)

• e.g.

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User-Defined Functions(3/4)

• the order of arguments is important, not the
  names of the arguments
• use arrays as input arguments

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User-Defined Functions(4/4)

• more than one output

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Variations in the Function Line
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Local Variables, Global Variables

• Local variables
• variables created by a function file are local to
  that function.
• local their values are not available outside
  the function.
• Global variables
• their values are available to the basic workspace
  and to other functions that declare these
  variables global.
• variables in script file global

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Minimization and root-finding functions

• Table 3.2-1 Minimization and root-finding
  functions

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Advanced Function Programming

• Function Handles
• using the at sign _at_
• e.g.
• gtgt sine_handle _at_sin
• gtgt plot(00.016, sine_handle, 0 0.01 6)
• function x gen_plot(fun_handle, interval)
• plot(interval, fun_handle, interval)
• gtgtgen_plot(sine_handle, 0 0.01 6) or
• gtgtgen_plot(_at_sin, 0 0.01 6)
• advantages
• speed of execution and providing access to
  subfunctions.
• a standard MATLAB data type, and thus can be used
  in the same manner as other data types.

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Methods for Calling Functions

• four ways to invoke, or call, a function into
  action.
• 1. As a character string identifying the
  appropriate function M-file.
• function y fun1(x)
• y x.2-4
• gtgtx, value fzero(fun1,0,3)
• 2. As a function handle.
• gtgtx, value fzero(_at_fun1,0,3)
• 3. As an inline function object, or
• gtgtfun1 x.2-4
• gtgtfun_inline inline(fun1)
• gtgtx, value fzero(fun_inline, 0,3)
• 4. As a string expression.
• gtgtfun1 x.2-4
• gtgtx, value fzero(fun1, 0,3) or as
• gtgtx, value fzero(x.2-4, 0,3)

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Types of Functions(1/2)

• primary functions
• contains the main program.
• the only function that you can call from the
  MATLAB command line or from another M-file
  function
• anonymous functions
• create a simple function without needing to
  create an M-file for it.
• provide a quick way of making a function from any
  MATLAB expression
• subfunctions
• placed in the primary function
• use multiple functions within a single primary
  function M-file

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Types of Functions(2/2)

• nested functions
• defined within another function
• help to improve the readability of your program
• difference between nested functions and
  subfuntions subfunctions normally cannot be
  accessed outside of their primary function fle
• overloaded functions
• functions that respond differently to different
  types of input arguments.
• created to treat integer inputs differently than
  inputs of class double.
• private functions
• restrict access to a function
• called only from an M-file function in the parent
  directory

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Anonymous Functions

• create a simple function without needing to
  create an M-file for it.
• MATLAB command line
• from within another function or script
• syntax
• fhandle _at_(arglist) expr
• arglist a comma-separated list of input
  arguments to be passed to the function
• expr any single, valid MATLAB expression
• e.g.
• sq _at_(x) x.2
• gtgtsq(5)
• gtgtans 25
• gtgtsq(5,7)
• gtgtans 25 49
• be useful for more complicated functions
  involving numerous keystrokes.

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Variables and Anonymous Functions

• variables can appear in anonymous functions in
  two ways
• as variables specified in the argument list
• e.g.
• f _at_(x) x.3
• as variables specified in the body of the
  expression
• e.g.
• plane _at_(x, y) Ax By

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Subfunctions(1/2)

• all other functions in the primary function are
  called subfunctions.
• the order for checking functions in MATLAB
• 1. checks to see if the function is a built-in
  function such s sin.
• 2. checks to see if the function is subfunction
  in the file.
• 3. checks to see if the function is private
  function.
• may use subfunctions with the same name as
  another existing M-file.
• allow you to name subfunctions without being
  concerned about whether another function exists
  with the same name
• protects you from using another function
  unintentionally

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Subfunctions(2/2)

• e.g.
• function y subfun_demo(a)
• y a mean(a)
• function w mean(x)
• w sqrt(sum(x.2))/length(x)
• a sample session follows.
• gtgt y subfun_demo(4,-4)
• y
• 1.1716 -6.8284
• if had used the MATLAB M-function mean ?
  different answer
• gtgt a 4, -4
• gtgt b a mean(a)
• b
• 4 -4

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Nested Functions(1/2)

• Functions that are defined within the main
  function.
• contains the usual components of an M-file
  function.
• must always terminate with an end statement.
• e.g.
• function f parabola(a, b, c)
• f _at_p
• function y p(x)
• y ax2 bx c
• end
• end
• In the command window type
• gtgtf parabola(4, -50, 5)
• gtgtfminbnd(f, -10, 10)
• ans
• 6.2500

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Nested Functions(2/2)

• two unique properties
• 1. can access the workspace of all functions
  inside of which it is nested.
• 2. function handle
• stores the information needed to access the
  nested function
• stores the values of all variables shared between
  the nested function and those functions that
  contain it
• call a nested function
• 1. from the level immediately above it
• 2. from a function nested at the same level
  within the same parent function
• 3. from a function at any lower level

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Private Functions

• reside in subdirectories with the special name
  private.
• visible only to functions in the parent
  directory.
• invisible outside the parent directory.
• MATLAB looks for private functions before
  standard M-file functions.

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Working with Data Files

• header a comment that describe what the data
  represent, the date it was created, and who
  created the date.
• Importing data bring data created by other
  applications into the MATLAB workspace.
• Exporting data package workspace variables so
  that they can be used by other applications.
• Importing Wizard a graphical user interface

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Importing Data from Externally Generated Files

• ASCII file format
• if the file has a header or the data is separated
  by commas, MATLAB will produce an error message.
• to correct
• load the data file into a text editor
• remove header
• replace the commas with spaces
• type load filename to retrieve the data into
  MATLAB
• e.g. if the data file name is force.dat ? type
  load force.dat
• Importing Spreadsheet Files
• file format .wk1
• command M wk1read(filename)
• Microsoft Excel workbook file .xls
• A xlsread(filename)

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The Import Wizard(1/5)

• To import ASCII data
• How many data items are in each row?
• Are the data items numeric, text strings, or a
  mixture of both types?
• Does each row or column have a descriptive text
  header?
• What character is used as the delimiter, that is,
  the character used to separate the data items in
  each row? The delimiter is also called the column
  separator.
• The data format will usually fall into one of the
  following categories
• 1.Space-delimited ASCII data files,
• 2.Mixed text and numeric ASCII data files,
• 3.ASCII data files with text headers, or
• 4.ASCII data files with nonspace delimiters
  (usually semicolons).

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The Import Wizard(2/5)

• The import Wizard present a series of dialog
  boxes in which you
• 1. Specify the name of the file you want to
  import,
• 2. Specify the delimiter used in the file, and
• 3. Select the variables that you want to import
• Note
• when you use the Import Wizard to create a
  variable in the MATLAB workspace, it overwrites
  any existing variable in the workspace with the
  same name without issuing a warning.

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The Import Wizard(3/5)

• e.g.

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The Import Wizard(4/5)

• e.g.

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The Import Wizard(5/5)

• e.g.