MATLAB 입문
CHAPTER 3
Functions and Files
• Note: Class presentation slides from 2016 MATLAB Course
• Provided by Prof. Poogyun Park, EE Department, POSTECH
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MATLAB 입문 : Chapter 1. An Overview of MATLAB
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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
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Exponential and Logarithmic Functions
Complex

Some common mathematical
functions
Exponential
exp(x)
Exponential;
sqrt(x)
Square root;
e
x
abs(x)
Absolute value; x
angle(x)
Angle of a complex number x
conj(x)
Complex conjugate
imag(x)
Imaginary part of a complex
number x
real(x)
Real part of a complex number x
Numeric
ceil(x)
Round to the nearest integer
toward
fix(x)
Round to the nearest integer
toward zero.
floor(x)
Round to the nearest integer
toward
round(x)
Round toward nearest integer
sign(x)
Signum function:
+1 if x> 0; if x = 0; -1 if x < 0
x
Logarithmic
log(x)
Natural logarithm; ln x
log10(x)
Common(base10) logarithm;
log(x) means ln x.


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Complex Number Functions(1/2)

rectangular representation


a + ib
polar representation
Mθ

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 ∞  ans = 3, 3, 4



e.g.



z = [-2.6 , -2.3 , 5.7]
floor(z) : rounds to the nearest integer toward - ∞  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
Trigonometric
Inverse
trigonometric
acos(x)
Inverse cosine;
1
arccos x = cos x
acot(x)
Inverse cotangent;
1
arccot x = cot x
acsc(x)
Inverse cosecant;
1
arccsc x = csc x
asec(x)
Inverse secant;1
arcsec x = sec x
asin(x)
Inverse sine; arcsin x
= si n1x
atan(x)
Inverse tangent;
arctan x = tan1x
atan2(y,x)
four-quadrant
inverse tangent.
*angle : radian
cos(x)
Cosine; cos x.
cot(x)
Cotangent; cot x.
csc(x)
Cosecant; csc x.
sec(x)
Secant; sec x.
sin(x)
Sine; sin x.
tan(x)
Tangent; tan x.
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Hyperbolic Functions(1/2)

Hyperbolic functions
Hyperbolic
(ex  e  x )/2
cosh(x)
Hyperbolic cosine; cosh x =
coth(x)
Hyperbolic cotangent; cosh x / sinh x
csch(x)
Hyperbolic cosecant; 1 / sinh x
sech(x)
Hyperbolic secant; 1 / cosh x
sinh(x)
Hyperbolic sine; sinh x =
tanh(x)
Hyperbolic tangent; sinh x / cosh x
(ex  e  x )/2
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Hyperbolic Functions(2/2)

Hyperbolic functions
Inverse hyperbolic
acosh (x)
Inverse hyperbolic cosine;
acoth (x)
Inverse hyperbolic cotangent; coth1x  1 l n(x  1), x  1 o r x  1
cosh1x  l n(x x 2  1), x  1
2
acsch (x)
Inverse hyperbolic cosecant;
asech (x)
Inverse hyperbolic secant;
asinh (x)
Inverse hyperbolic sine;
atanh (x)
Inverse hyperbolic tangent;
x -1
1
1
csch1x  l n ( 
 1), x  0
x
x2
1
1
se ch1x  l n ( 
 1), 0  x  1
x
x2
si nh1x  l n(x x 2  1), -   x  
tanh1x 
1 1 x
l n(
),  1  x  1
2 1- x
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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
Function definition line
File name
1. function [area_square] = square(side);
square.m
2. function area_square = square(side);
square.m
3. function [volume_box] = box(height,width,length);
box.m
4. function [area_circle, circumf] = circle(radius);
circle.m
5. function sqplot(side);
sqplot.m
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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
Function
Description
fminbnd(‘function’,x1,x2)
Returns a value of x in the interval x1≤x ≤x2 that corresponds to
a minimum of the single-variable function described by the string
‘function’.
fminsearch(‘function’,x0)
Uses the starting vector x0 to find a minimum of the multivariable
function described by the string ‘function’.
fzero(‘function’,x0)
Uses the starting value x0 to find a zero of the single-variable
function described by the string ‘function’.
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Advanced Function Programming

Function Handles

using the at sign : @
 e.g.
>> sine_handle = @sin;
>> plot([0:0.01:6], sine_handle(0: 0.01: 6))
function x = gen_plot(fun_handle, interval)
 plot(interval, fun_handle, interval)
>>gen_plot(sine_handle, [0: 0.01: 6])
or
>>gen_plot(@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;
>>[x, value] = fzero(‘fun1’,[0,3])


2. As a function handle.
>>[x, value] = fzero(@fun1,[0,3])

3. As an “inline” function object, or
>>fun1 = ‘x.^2-4’;
>>fun_inline = inline(fun1);
>>[x, value] = fzero(fun_inline, [0,3])

4. As a string expression.
 >>fun1 = ‘x.^2-4’;
 >>[x, value] = fzero(fun1, [0,3])
 >>[x, value] = fzero(‘x.^2-4’, [0,3])
or as
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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 = @(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 = @(x) x.^2;
>>sq(5)
>>ans = 25
>>sq([5,7])
>>ans = 25
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
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 = @(x) x.^3;
as variables specified in the body of the expression
 e.g.

plane = @(x, y) A*x + B*y;
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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 as 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)
primary function
y = a – mean(a);
subfunction
%
function w = mean(x)
w = sqrt(sum(x.^2))/length(x);
a sample session follows.
>> y =subfun_demo([4,-4])
y=
1.1716 -6.8284
if had used the MATLAB M-function mean  different answer
>> a= [4, -4];
>> 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 =@p;
function y = p(x)
y = a*x^2 + b*x + c;
end
end
In the command window type
>>f = parabola(4, -50, 5);
>>fminbnd(f, -10, 10)
ans =
6.2500
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.
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