Matlab Chapter 3 - Mars at UMHBmars.umhb.edu/~wgt/engr1320/MATLab/Matlab Chapter 3 - Handout fr… · Example – complex functions ... C = 2pir; 50.2655 C = 25.1327 A = 28.2743 50.2655

Matlab - Chapter 3 3/30/2009

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MATLAB Ch 3 – Functions & FilesMATLAB Ch 3 – Functions & Files

EGR1302

Outline

IntroductionElementary mathematical operationsElementary mathematical operationsUser-defined functionsWorking with data files


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Introduction

Review from Ch 1MATLAB mathematical functions

Pair of parentheses after function name encloses function’s argumentCan be part of mathematical expression

Users can define functionsMATLAB has commands and functions for managing the work session

Introduction

MATLAB has many built-in functionsUsers may define functionsUsers may define functions

Convenient use Advanced function capability

Function handlesAnonymous functionsSubfunctionsSubfunctionsNested functions

MATLAB allows input/output of data files


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Section 3.1

ELEMENTARY MATHEMATICAL FUNCTIONS

Finding relevant functionsCommand – lookfor

Seeks the word in the help descriptions p pof the MATLAB help system

If user does not know the name of function>> lookfor imaginaryi - Imaginary unit.j - Imaginary unit.complex Construct complex resultcomplex - Construct complex result

from real and imaginary parts.

imag - Complex imaginary part.


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Finding relevant functions

Finding relevant functionsCommand – disp help

If user knows correct spelling of a p gMATLAB function

Same output as selecting complexhyperlink after using lookfor command

>> disp help complex


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Tables 3.1-1, 3.1-2, 3.1-3

List of some common mathematical functions (pp. 142, 146, 148)(pp , , )

Exponential & logarithmicComplex number NumericTrigonometricH b liHyperbolic

Example – complex functions

>> x=-3+4i;>> y=6-8i;y ;>> mag_x = abs(x)mag_x =

5>> mag_y = abs(y)mag_y =

10>> mag_product = abs(x*y)mag_product =

50


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>> angle_x = angle(x)angle x =

Example – complex functions

angle_x =2.2143

>> angle_y = angle(y)angle_y =

-0.9273>> sum_angles = angle_x + angle_ysum angles =_ g

1.2870>> angle_product = angle(x*y)angle_product =

1.2870

Section 3.2

USER-DEFINED FUNCTIONS


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Functions files

Differences between script & functions M-files

All functions variables are localValues available only within functionUseful when repeating a set of commands multiple times

Building blocks of larger programs

First line in function function definition line

List of inputs and outputs

Function definition line

Distinguishes function from scriptfunction[output vars]=func name(input vars)

function – must be lower caseOutput variables must be enclosed in square bracketsInput variables must be enclosed in parentheses

function[output vars] func_name(input vars)

parenthesesfunc_name must be same as name of M-file

Use exist function before naming a function


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Simple function examplefunction z = fun(x,y)u = 3*x;z = u + 6*y ^2;

>> z = fun(3,7)z =

303

>> fun(3,7)ans =

303

z = u + 6 y. 2; 303

>> y = [3 4 5];>> z = fun(y,7)z =

303 306 309

>> z??? Undefined function or variable 'z'.>> u??? Undefined function or variable 'u'.

Functions

Suppress output of function by putting semicolon after the function p gcallOnly order of arguments is important, not names of argumentsArrays can be used as input argumentsMay have more than one output


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2nd simple function examplefunction [A, C] = circle(r)A = pi*r.^2;C = 2*pi*r;

>> [A, C] = circle(4)A =

50 2655

>> r = [3 4 5];>> [A, C] = circle(r)A =

C = 2 pi r; 50.2655C =

25.1327

A =28.2743 50.2655 78.5398

C =18.8496 25.1327 31.4159

Variations in function lineOne input, one output:

Brackets are optional

Two inputs, one output

One inp t t o o tp ts

function [area_square] = square(side)OR

function area_square = square(side)

function [volume_box] = box(height,width,length)

One input, two outputs

No named output: function sqplot(side)function [area_circle,circumf] = circle(radius)

function sqplot(side)


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Comments in functions

Comment lines, starting with %, may be placed anywhere in function filep yIf user types help to obtain information about function

All comment lines immediately following function definition line up to first blank or executable line is displayedor executable line is displayed

If user types lookfor commandFirst comment line is displayed

Local variables

Names of input variables given in function are local to the function

Other variable names can be used when calling the function

All variables inside a function are erased after the function finishes executingexecuting

Except when the same variable names appear in the output variable list used in the function call


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Global variables

global command declares certain variables globalg

Their values are available to the basic workspace and to other functions that declare these variables global.

Any assignment to those variables in

global a x q

Any assignment to those variables, in any function or in the base workspace, is available to all the other functions declaring them global.

Finding the zeros of a function

function is a string containing the fzero(‘function’, x0)

g gname of the functionx0 is a user-supplied guess for the zero Returns a value of x that is near x0Identifies only points where the function crosses the x-axiscrosses the x axis

Not points where the function just touches the axis. >> fzero('cos',2)

ans =1.5708


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Using fzero with user-defined functions

To find the zeros of more complicated functions, it is more convenient to ,define the function in a function filefunction y = f1(x)y = x + 2*exp(-x) - 3;

>> x = fzero('f1',-1)x =x =

-0.5831>> x = fzero('f1',2)x =

2.8887

Finding the minimum of a function

function is a string containing thefminbnd(‘function’, x1,x2)

function is a string containing the name of the function

Returns a value of x that minimizes the function in the interval x1 ≤ x ≤ x2

>> fminbnd('cos', 0,4)ans =

3.1416


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Finding the minimum of a function

For functions of more than one variable

function is a string containing the name of the functionVector x0 is a guess that must be supplied by the user

fminsearch(‘function’, x0)

supplied by the user.

>> fminsearch('f4',[0,0])ans =

-0.7071 0.0000

function f = f4(x)f = x(1).*exp(-x(1).^2-x(2).^2);

Design optimization example

Example 3.2-2, p. 161


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Section 3.4

WORKING WITH DATA FILES

Importing data files

Typical ASCII fileHeader lines

One or more lines of textContain comments, creation date, column headings

DataArranged in rows & columnsEach number in a row may be separated

SpacesCommasTab


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Importing an externally generated file in ASCII format

Matlab can not import data that is separated (i.e., delimited) by commasTo import a comma-delimited ASCII file, some pre-processing is required

First, open data file in a text editor (e.g., st, ope data e a te t ed to (e g ,Notepad)Second, delete the text header linesThird, replace each comma with at least one space (i.e., use Replace function)


Importing an externally generated file in ASCII format

Matrix is generatedName of matrix is filename with extension stipped off

load filename

load tensile test txtThis command creates a matrix named “tensile_test”

load tensile_test.txt


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Excel spreadsheets may be imported into Matlab

Save Excel file in 2003 format (i.e., .xlsextension)

Imports file into array A

A = xlsread(‘filename’)

[A, B] = xlsread(‘filename’)Imports all numeric data into array A and all text data into array B

[ , ] ( )

Import Wizard

Allows for importing a variety of ASCII file formats

Space-delimited filesMixed text and numeric filesFiles with text headersFiles with non-space delimiters

CommasCommasSemi-colonsTabs


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Import Wizard

What you must know before you may import the data filep

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?descriptive text header?What character is used as the delimiter that separates items in each row into columns?

Import Wizard

CautionImport Wizard overwrites any existing p y gvariable in the workspace with no warning message!

Dialog boxes ask you to:Specify the name of the file you want to importimportSpecify the delimiter used in the fileSelect the variables that you want to import


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Import Wizard

End of Chapter 3


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Slides that I do not plan to use

Outline

IntroductionElementary mathematical operationsElementary mathematical operationsUser-defined functionsAdvanced function programmingWorking with data files


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Section 3.3

ADVANCED FUNCTION PROGRAMMING

Function handles

Create a function handle to any function by using the at sign, @, before the function name.

Name the handleUse the handle to reference the function

i i l t d f

>>sine_handle = @sin;sine_handle is a user-selected name for the handle


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Function handles

A common usePass the function as an argument to ganother functionExample - plot sin x over 0 ≤ x ≤ 6 as follows:

Cumbersome way to plot the sine function

>>plot([0:0.01:6],sine_handle,[0:0.01:6])

Cumbersome way to plot the sine functionHowever, the concept can be extended to create a general purpose plotting function that accepts a function as an input

Function handles

function x = gen_plot(fun_handle, _ _interval)plot(interval, fun_handle, interval)

You may call this function to plot the sin x over 0 ≤ x ≤ 6 as follows:>>gen_plot(sine_handle,[0:0.01:6])

Documents

Matlab Chapter 3 - Mars at UMHBmars.umhb.edu/~wgt/engr1320/MATLab/Matlab Chapter 3 - Handout fr… · Example – complex functions ... C = 2pir; 50.2655 C = 25.1327 A = 28.2743 50.2655