1
• Programming in MATBLAB
• Presented by:
• Dr. Ebrahim Nemati-Kande
• Urmia University
• Fall 2023
2
• References
Programming with
MATLAB for Scientists
A Beginner’s Introduction
Eugeniy E. Mikhailov
http://physics.wm.edu/programmin
g_with_MATLAB_book.
3
4
1.2 Modern Computers
•
ENIAC (Electronic Numerical Integrator And Computer) 1946
•
Weight: 30 tons
•
Cost: $500,000 ($6,000,000 adjusted for inflation)
•
Power consumption: 150 kW (averaged consumption of 500 households)
•
ENIAC could do the following in 1 s:
•
5000 additions,
•
357 multiplications,
•
38 divisions.
•
Computing performance of: 100 FLOPS
•
Modern computer speed is measured in FLOPS
•
FLOPS (the number of floating-point operations per second)
5
1.2 Common features
of a modern computer
• CPU: Central processing Unit
• GPU: Graphical processing Unit
• Ram: Random-access memory
• Memory: which holds data and programs,
• (keyboards, hard drives, displays, printers,
...)
6
1.3 What Is Programming?
Generate a list of instructions suitable for execution by a computer.
• Coding
• Debugging
• Executing
7
1.4 Programming
Languages
low-level languages
• assembler
• C
• C++,
• Forth
• LISP
high-level languages​
•Fortran​
•Tcl
•Java​
•JavaScript​
•PHP​
•Perl​
• Python​
• MATLAB
8
1.5 Numbers Representation in Computers and Its Potential Problems
1.5.1 Discretization—the main weakness of computers
1/6 = 0.1666666666666666 · · ·
•
the computer has a finite memory size.
• So, the computer truncates every number to a specified number of significant digits.
1/6 = 0.1667c
“c” stands for computer representations.
"round-off error": 1/6 = 0.1667
All of the following numbers are equal:
1/6 = 1/5.999 = 0.1667123 = 0.1667321 = 0.1667222 = 0.1667
Paradox: 20 × (1/6 ) − 20/6 = 20 × 0.1667 − 3.333 = 3.334 − 3.333 = 10−4
9
bit
(binary digit)
single unit of information with a value of either 0 or 1 (off or on, false or true, low or high)
Byte
8 bits: 28 = 256
0 to 255
or −128 . . . 0 . . . 127
Example:
Hope
4 byte
4x8 = 32 bit
Other units:
Kilobyte (8000 bit)
Megabit (1x106 bit)
Gigabit (1x106 bit)
Terabit (1x106 bit)
10
processors (CPU)
16-bit CPU
capable of transferring 16 bits of data at a time
(decimal number up to 2^16-1 = 65535)
16-bit binary values
Bit #:
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Power:
215
214
213
212
211
210
29
28
27
26
25
24
23
22
21
20
Value:
326
78
162
84
819
2
409
6
204
8
102
4
512
256
128
64
32
16
8
4
2
1
11
32-bit CPU (x86)
capable of transferring 32 bits of data at a time
(decimal number up to 2^32-1 = 4,294,967,295)
12
64-bit CPU (x64 or x86-64)
capable of transferring 64 bits of data at a time
(decimal number up to 2^64-1 = 18,446,744,073,709,551,615 !!1.845E+019!!)
13
32-bit representation:
2^32= 4294967296
Int32: 32-bit (4-byte) integers: −2, 147, 483, 648 · · · 0 · · · 2, 147, 483, 647
>> intmin
• 1.5.2 Binary representation
ans =
int32
-2147483648
MATLAB code:
>> intmax
ans =
int32
2147483647
14
1.5.3 Floating-point number representation
floating-point numbers:
Numbers that have a decimal point
i.e., 2.443 or 31.2 × 103
−123.765 × 1012
sm: sign bit of the mantissa (1 in our case)
m: mantissa (1.23765)
b: base of the exponent (10)
se: the sign bit of the exponent (0 in our case)
q: is the exponent (14).
b=2
−1.23765 × 1014
15
>> realmax
ans =
MAX and MIN of the
numbers in MATLAB
1.79769313486232e+308
>> realmin
ans =
2.2250738585072e-308
• Institute of Electrical and Electronics
Engineers (IEEE) 754 standard:
mantissas take 52 bits + 1 bit for the sign
equivalent to about 17 decimal digits
The exponent takes 10 bits + 1 sign bit
equivalent to roughly 10 ±308
>> realmax*10
overflow error
ans =
Inf
>> realmin/1e17
underflow error ans =
0
>> 1.797693134862316 + 20
ans =
21.7976931348623
truncation error:
>> 1.797693134862316 + 100
ans =
101.797693134862
16
MATLAB
MATrix LABoratory
capabilities
•
matrix manipulations
•
plotting of functions and data
•
implementation of algorithms
•
creation of user interfaces
•
interfacing with programs written in other languages
Cleve Barry Moler
https://en.wikipedia.org/wiki/MATLAB
https://en.wikipedia.org/wiki/Cleve_Moler
17