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‫‪1‬‬
Basic Matlab
2
Basic calculations in MATLAB
Matlab can be used as an interactive calculator
 All commands from the command line are executed immediately
 Any variables defined on the command line are stored in memory
 By default – all variables are of type double
(64 bits: 53 for the mantissa, 11 for the exponent)
 Angles are always in radians
Basic math:
 + - * / ^
 sin, cos, tan, log, log10, log2, exp
 Complex numbers: 1+2j, 1+2i
 Constants: pi, i, j
Precedence:
 Left to right, with ^ before * and / , before + and –
 Parentheses may be used.
3
Some examples:
>> 3*4+5*6
ans=
42
>> 3*(4+5)*6
ans=
162
>> log10(4)
ans =
0.6021
>> log2(4)
>> 1+2j
ans=
1.0000 + 2.0000i
>> 1+2j*2
ans=
1.0000 + 4.0000i
>> (1+2j)*2
ans=
2.0000 + 4.0000i
>> sin(pi/4)
ans=
0.7071
>> exp(1)
ans=
2.7183
ans =
2
4
Output precision:
The format command
controls how many digits are
present on the display line:
 format short: 5
digits
 format long: 15
digits
 NOTE: this does not
affect the internal
representation!
Other options of this
command exist for scientific
notation etc.
>> format short
>> sin(pi/4)
ans=
0.7071
>> format long
>> sin(pi/4)
ans=
0.70710678118655
5
Variables:
Variables can be any name we wish
Some variables have predefined
values (next slide)
 These can be overridden,
e.g: pi=2;
 Don’t do this!
The ‘=‘ sign is used to define
variables:
 e.g. students=20
 Such an expression will cause the
variable to be displayed
 RULE: to avoid displaying a
result – use a semicolon ‘;’:
Naming rules:
 Names are case sensitive
 Up to 31 characters
 Start with a letter
>> erasers=4;
>> pads=6;
>> tape=2;
>> items=erasers+pads+tape
items =
12
>> pi
pi =
3.1416
>> pi=2
pi =
2
>> clear pi
>> pi
pi =
3.1416
6
More examples:
>> 1/2/3
>> sqrt(3^2+4^2)
ans =
0.16667
ans =
5
>> (3^2+4^2)^1/2
ans =
12.5
>> (3^2+4^2)^(1/2)
ans =
5
>> 1/(2/3)
ans =
1.5
>> radius=2;
>> 2*pi*radius
ans =
12.566
>> sin(pi/6)
ans=
0.5
7
Special variables:
Reserved words:
 for end if while
function return
elseif case
otherwise switch
continue else
try catch global
persistent break
Special variables:
Special
variables
ans
Description
Default for result
beep
Make a beep sound
pi
Pi
eps
Smallest detectable difference
inf
Infinity - 1/0
NaN, nan
Not a number – 0/0
i, j
Sqrt(-1)
nargin
Number of input args.
nargout
Number of output args
realmin
Smallest real number
realmax
Largest real number
bitmax
Largest integer
varargin
Variable number of input args
varargout
Variable number of output args
8
The workspace:
Where do variables go?
 They’re stored in the workspace
 who and whos commands give
their names and details
Workspaces can be loaded and
stored as entire entities, including all
the variables, in one file.
 The save command creates a
*.mat file
 More about this - later
Useful keys:
 Up arrow – command recall
 Down arrow – scrolls forward
through commands
 Tab – variable name completion
 Escape – all of current
command is deleted
>> who
Your variables are:
a b c d
>> whos
Name
a
b
c
d
Size
1x1
1x3
2x2
1x5
Bytes Class
8
24
32
10
Attributes
double
double
double
char
9
Comments and punctuation:
Comments: anything after the
percent (%) sign
Multiple commands: separated
by a comma or semicolon
Continued lines: ellipses (…)
Not in the middle of a name!
Comments can’t be continued
Interrupting execution:
Ctrl-C
 This is useful for stopping a
program that’s taking too
long to finish (e.g. in an
infinite loop)
>> cost=2, items=10
cost =
2
items =
10
>> price=cost/items
price =
0.2000
>> price=cost... %comment
/items
price =
0.2000
>> price=cost/item... %another comment
s
??? s
|
Error: Unexpected MATLAB expression.
10
Dealing with complex numbers:
MATLAB deals with complex
numbers like any other number
We can interchange:
i, j, sqrt(-1)
Transforming between polar
and cartesian forms:
 real, imag, abs,
angle
Complex conjugate (change the
sign of the imaginary part):
 conj()
>> c1=1-2i;
>> c2=1+2j;
>> c3=1+2*sqrt(-1);
>> c4=1+sin(pi/6)*1j
ans =
1.0000 + 0.5000i
>> abs(c1)
ans =
2.2361
>> angle(c1)
ans =
1.1071
>> real(c1)
ans =
1
>> imag(c1)
ans =
-2
11
Precision issues in floating point:
calculations are normally in
double-precision floating point
largest positive number:
realmax
smallest positive number:
realmin
smallest number that can be
added to 1 to give a result larger
than 1: eps (useful for
numerical errors estimation)
the largest integer that has an
exact representation is bitmax,
which is: 253-1
>> realmax
ans =
1.797693134862316e+308
>> realmin
ans =
2.225073858507201e-308
>> eps
ans =
2.220446049250313e-016
>> 0.42-0.5+.08
ans =
-1.387778780781446e-017
>> 0.08-0.5+0.42
ans =
0
>> sin(0)
ans =
0
>> sin(pi)
ans =
1.224646799147353e-016
>> bitmax
ans =
9.007199254740991e+015
12
Precision problems:
Limited precision leads to results such as these:
>> sin(pi)
ans =
1.224646799147353e-016
>> 1+sin(pi)
ans =
1.00000000000000
The reason for this “error” is that sin(pi) is smaller
than eps


Therefore – adding it to 1 gives a number that isn’t 1,
but
Matlab cannot represent such a small difference!
13
Math functions
Exp. Functs.
^
Description
exp
Exponential
log
Natural logarithm
log10
Base 10 logarithm
log2
Base 2 logarithm
pow2
Base 2 power
sqrt
Square root
Power
Complex
Functs.
abs
Description
Magnitude
angle
Phase angle [radians]
conj
Complex conjugate
imag
Imaginary part
real
Real part
isreal
True for real values
14
Math functions
Trig functions
Description
acos
Inverse cosine
coth
Hyperbolic cotangent
acosh
Inverse hyperbolic cosine
csc
Cosecant
acot
Inverse cotangent
csch
Hyperbolic cosecant
acoth
Inverse hyperbolic cotangent
sec
Secant
acsc
Inverse cosecant
sech
Hyperbolic secant
acsch
Inverse hyperbolic cosecant
sin
Sine
asec
Inverse secant
sinh
Hyperbolic sine
asech
Inverse hyperbolic secant
tan
Tangent
asin
Inverse sine
tanh
Hyperbolic tangent
atan
Inverse tangent
atan2
Four quadrant inverse tangent
atanh
Inverse hyperbolic tangent
cos
Cosine
cosh
Hyperbolic cosing
cot
cotangent
Trig functions
Description
15
Math functions
Round and
remainder
Description
Number
theory.
Description
fix
Round towards zero
factor
Prime factors
floor
Round towards negative inf.
isprime
True for prime numbers
ceil
Round towards positive inf.
gcd
Greatest common divisor
round
Round toward neaest int.
lcm
Least common multiple
mod
Modulus – signed remainder
rat
Rational approximation
rem
Remainder after division
rats
Rational output
sign
Signum
perms
All possible combinations
nchoosek
All combinations of N elements
taken K at a time
Coordinate
transforms
Description
cart2sph
Cartesian to spherical
cart2pol
Cartesian to cylindrical or polar
pol2cart
Cylindrical or polar to cartesian
sph2cart
Spherical to cartesian
16
Example – roots of quadratic equation
>> a=input('Input first coeff : ')
Input first coeff: 3
a=
3
>> b=input('Input second coeff : ')
Input second coeff: -4
b=
-4
>> c=input('Input third coeff : ')
Input third coeff: 7
c=
7
>> d = b^2 - 4*a*c;
>> r = sqrt(d);
>> x1 = (-b+r) / (2*a);
>> x2 = (-b-r) / (2*a);
>> disp(x1)
0.6667 + 1.3744i
>> disp(x2)
0.6667 - 1.3744i
>> a=input('Input first coeff: ')
Input first coeff: 2
a=
2
>> b=input('Input second coeff: ')
Input second coeff: 15
b=
15
>> c=input('Input third coeff: ')
Input third coeff: -25
c=
-25
>> x1 = ( -b + sqrt(b^2 - 4*a*c) ) / (2*a)
x1 =
1.4039
>> x2 = ( -b - sqrt(b^2 - 4*a*c) ) / (2*a)
x2 =
-8.9039
17
Getting help
18
Help Features in MATLAB
How do we find the syntax for using the
following functions?

COS, ACOS, EXP, SIN, ASIN
In order to obtain assistance in MATLAB type
any of the following options at the MATLAB
Command Line:
help function_name
helpwin function_name
doc function_name
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Using Help Features in MATLAB
20
Using Help Features in MATLAB
21
Contents of the MATLAB Desktop
As we have just seen, the main panels of the Matlab
Desktop are:
 Current directory
 Workspace (variables)
 Command history
 The command window
Some properties:
 All of the above can be docked and undocked
 Right clicking on any of them opens a context
sensitive menu
22
Contents of the MATLAB Desktop –
Current directory
23
Contents of the MATLAB DesktopWorkspace
24
Contents of the MATLAB Desktop Command history
25