Chapter 1: Introduction to MATLAB Part I – COMPUTING SYSTEM ENIAC Computing System • Computing system: a system of one or more computers and associated software with common storage. • Components: hardware, software, data and user. Hardware Hardware refers to the physical parts of the computing system that have mass (i.e. the parts you can see and touch): – Computer – Display – Mouse – Printer –… Hardware Von Neumann architecture -- Input device(s) -- Output device(s) -- CPU (Central Processing Unit) consisting of: • Control Unit • ALU (Arithmetic Logic Unit) From Wiki Hardware Harvard architecture a computer architecture with physically signal pathways for instructions and data From Wiki Moore’s Law Gordon Moore (1965): The observation that the number of transistors in a dense integrated circuit doubles approximately every two years. Software Interface to Computer Hardware Copyright © 2012 Pearson Education, Inc. Software Computer software refers to programs that reside and execute electronically on the hardware. – Compilers System Software – Translate source code – Operating systems – Provide the HCI (Human Computer Interface) – Application programs – Provide problem solutions Key Terms • Source Program – printable/Readable Program file • Object Program – nonprintable machine readable file • Executable Program – nonprintable executable code Chapter 1: Introduction to MATLAB Part II – DATA Base: number of unique identifiers to represent distinct digits. Humans Computers (Decimal System) Base 10: { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } (Binary System) Base 2: { 0, 1 } (Octal System) Base 8: { 0, 1, 2, 3, 4, 5, 6, 7 } (Hexadecimal System) Base 16: { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F } Each of these base systems is just another way of writing down the same number. When you convert a number between different bases, it should still have the same value. Base ten number system It's generally easiest to understand the concept of different bases by looking at base 10. When we have a number in base 10, each digit can be referred to as the ones digit, the tens digit, the hundreds digit, the thousands digit, or so forth. For instance, in the number 432, - 4 is the hundreds digit, - 3 is the tens digit, - 2 is the ones digit. Base ten number system Another way to think about this is to rewrite 43210 as: 4 x 102 + 3 x 101 + 2 x 100 To evaluate a number in a base system, multiply successive values by increasing powers of the base. Base two (binary) number system • Two binary digits (0,1) • Each digit multiplies a power of two – Example: 101102 = 1*24 + = = = 0*23 + 1*22 + 1*21 + 0*20 1*16 + 0*8 + 1*4 + 1*2 + 0*1 16 + 0 + 4 + 2 + 0 2210 Base eight number system • Eight octal digits (0,1,2,3,4,5,6,7) • Each digit multiplies a power of eight – Example: 2458 = 2*82 + 4*81 + 5*80 = 2*64 + 4*8 + 5*1 = 128 + 32 + 5 = 16510 Base sixteen number system • Sixteen hex digits (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) • Each digit multiplies a power of sixteen – Example: 2FB16 = 2*162 + F*161 + B*160 = 2*256 + F*16 + B*1 = 512 + 240 + 11 = 76310 Base systems are different ways to represent a quantity. Base: B = 10 Number of digits: N = 3 0123456789 100 101 102 12310 = 1*100 + 2*10 + 3*1 = 1*102 + 2*101 + 3*100 Base systems can be expressed as: BN-1 … B3 B2 B1 B0 Exercises: Convert 10112 , 10118 and 101116 to Base 10 systems. To go other way, e.g. 1317810, how to convert it to base 16? 1. Find the next highest power of base: 160 = 1, 161 = 16, 162 = 256, 163 = 4096, 164 = 65536 164 163 13178 = 4096 3.2 2. Since 13178 < = 65536, use = 4096, There are “3” units of 4096 in this number, so record this and remove that component: 13178 – 3*(4096) = 890 . 890 3. Since 162 = 256, 256 = 3.47 There are “3” units of 256 in this number, so record this and remove that component: 890– 3*(256) = 122 . 4. Since 161 = 16, 122 = 7.625, 122 – 7*(16) = 10 16 10 5. Since 160 = 1, 1 = 10, Symbol of 10 in base 16 is A The number 1317810 is written as 337A16 in basis 16. Convert a number from Base 10 to Base N: 1. Find largest value of Bj that is less than the number 32110 Base 5 4 3 2 1 0 625 125 25 5 1 2. Remove as many as that value that you can − 321 250 (= 2 ∗ 125) 71 3. Repeat to next lower value. 71 − 50 (= 2 ∗ 25) 21 − 20 (= 4 ∗ 5) 1 (= 1 ∗ 1) 32110 = 22415 Question? Exercises: Convert 33810 to Base 8 systems. Memory Storage The most fundamental unit of computer memory is the bit. 1 bit (Binary digit) = 0 or 1 0 1 1 bit 1 bit 0110 01101011 4 bits 8 bits A collection of 8 bits is called a byte. A collection of 4 bytes, or 32 bits, is called a word. 1 byte 8 bits 2 bytes 16 bits 4 bytes 32 bits (word) 8 bytes 64 bits The number of bytes and words used for an individual data value depends on the storage format, the operating system, and even the computer hardware. • A single letter or character of text takes up one byte; - The text “hello” would take up 5 bytes of storage, one per character. - The text “12345” would also require 5 bytes. • An integer, or whole number, takes up one word. - The integer 12,345 would take up 4 bytes (1 word), • A real or decimal number takes up one or two words depending on how it is stored. - The real number 123.45 would take up 4 or 8 bytes. Unsigned Integer: either positive or zero. An unsigned integer containing n bits can have a value between 0 and (which is 2n different values). An 8 bit unsigned integer: 0~28–1, or 255. (Short) integers (16 bits): 0~216-1, or 65,535. Long integers (32 bits): 0~232-1, or 4,294,967,295. Double integers (64 bits): 0~264–1, or 18,446,744,073,709,551,615. Signed Integer: Negative values allowed. In computers, the left most bit of a signed integer is called the "sign bit". If a signed integer has n bits, it can contain a number between -2n-1 and +(2n-11). An 8 bit signed integer: -128 (-28-1) to 127 (28-1–1) Signed short integer: -32,768 to +32,767 Signed long integer: -2,147,483,648 to +2,147,483,647 Signed double integer: -9,223,372,036,854,775,808 to +9,223,372,036,854,775,807 How to represent a negative integer? One sign bit is allocated to represent number's sign: - Sign bit = 0 : a positive number or zero, - Sign bit = 1 : a negative number. - The remaining bits in the number indicate the magnitude (or absolute value). Negative integers are often represented in their two’s complement form. The two’s complement of an integer is formed by negating all of the bits and adding one. Two’s complement • The two's complement of an N-bit number is defined as its complement with respect to 2N. • Form the two’s complement representation for the value -12710 12710 = 011111112 Negate bits: 10000000 Add 1: 10000001 • two’s complement is 1000 00012 Two’s complement Add 12710 to -12710 011111112 + 100000012 = 000000002 12710 + -12710 = 010 Eight-bit two's complement Binary value Two's complement interpretation Unsigned interpretation 00000000 0 0 00000001 1 1 … … … 01111110 126 126 01111111 127 127 10000000 −128 128 10000001 −127 129 10000010 −126 130 ⋮ ⋮ ⋮ 11111110 −2 25 11111111 −1 255 Exercise: Form the 2’s complement representation for the value -210 Signed types: - Enable you to work with negative integers as well as positive; - But cannot represent as wide a range of numbers as the unsigned types (one bit is used to designate a positive or negative sign for number). Unsigned types: - Give you a wider range of numbers; - But these numbers can only be zero or positive. Here are the eight integer classes, the range of values, and the MATLAB conversion function required to create that type: Class Range of Values Conversion Function Signed 8-bit integer -27 to 27-1 int8 Signed 16-bit integer -215 to 215-1 int16 Signed 32-bit integer -231 to 231-1 int32 Signed 64-bit integer -263 to 263-1 int64 Unsigned 8-bit integer 0 to 28-1 uint8 Unsigned 16-bit integer 0 to 216-1 uint16 Unsigned 32-bit integer 0 to 232-1 uint32 Unsigned 64-bit integer 0 to 264-1 uint64 >> A = uint8(3) A = 3 B = uint16(3) >> B = 3 C = uint32(3) >> C = 3 >> whos Name Size A B C 1x1 1x1 1x1 Bytes 1 2 4 Class uint8 uint16 uint32 Floating Point Numbers Floating point number: a real number (that is, a number that can contain a fractional part). i.e. 3.14. In decimal system, very large/small floating point numbers can be shown with a mantissa and an exponent. i.e. 0.12*108, 0.45*10-6 Here the 0.12/0.45 is the mantissa and the 108/10-6 is the exponent. The mantissa holds the main digits, and the exponent defines where the decimal point should be placed. Matlab represents floating-point numbers in either single-precision format or double-precision format (default). Single precision: 4 bytes (32 bits) Double precision: 8 bytes (64 bits) single double sign 1 bit 1 bit exponent 8 bits 11 bits mantissa 23 bits 52 bits Total 32 bits (4 bytes) 64 bits (8 bytes) Single precision: Floating points numbers have finite precision. single double Mantissa 23 bits 52 bits Number of decimal precision 7 15 Finite precision is the fundamental limit of digital computers. >> A = single(101239.216); >> B = single(101239.215); >> A - B ans = 0 Other Pitfalls 1. Integer arithmetic: >> i = int8(2); >> j = int8(3); >> k = int8(5); >> i/j ans = 1 >> i/k ans = 0 >> x = 2 / 3 x = 0.6667 >> y = 2 / 5 y = 0.4000 >> class(x) ans = double >> class(y) ans = double >> 2./3. ans = 0.6667 >> 2./5. ans = 0.4000 Other Pitfalls 2. Division by difference of two small numbers: >> A = single(101239.216) A = 1.0124e+05 >> B = single(101239.215) B = 1.0124e+05 >> 1/(A - B) ans = Inf >> C = double(101239.216) C = 1.0124e+05 >> D = double(101239.215) D = 1.0124e+05 >> 1/(C -D) ans = 1.0000e+03 Other Pitfalls 3. Round off error The decimal number 4/3 is not exactly representable as a binary fraction. For this reason, the following calculation does not give zero. >> e = 1 - 3*(4/3 - 1) e = 2.2204e-16 Part II: Data • • • • • Base System; Memory Storage; Data Type; Negative Integer; Finite Precision. Chapter 1: Introduction to MATLAB Part III -- MATLAB What is MATLAB? • MATLAB stands for Matrix Laboratory. As the name suggests, MATLAB is especially designed for matrix computations: solving systems of linear equations, computing eigenvalues and eigenvectors, factoring matrices, and so forth. • It is an interactive software system for numerical computations, programming and graphics. What is MATLAB? • Matlab is a computer language/application designed for scientific computation. It can be used in two ways, interactively (like a calculator) or non-interactively (as a programming language). As a command-line calculator, Matlab can do: – Simple arithmetic operators • +-*/^ – Basic mathematic functions • sin(), log(), log10(), exp(), rem() What is MATLAB? For example, >> x = 1.5+2*3^2/4 x= 6 will result in x being given the value 6. >> sin(pi/6)+cos(pi/3) ans = 1 Exercises: 1. 12−3 5+1 2. 32 + 5 3. 32+5 The MATLAB System MATLAB system consists of five main parts: 1. Desktop Tools and Development Environment 2. Mathematical Function Library 3. The Language 4. External Interfaces 5. Graphics The MATLAB System 1. Desktop Tools and Development Environment – Includes the Command Window, an editor and debugger, a code analyzer, browsers for viewing help, the workspace, and other 2. Mathematical Function Library – Vast collection of computational algorithms ranging from elementary functions, like sine, cosine, and complex arithmetic, more sophisticated functions like matrix inverse, matrix eigenvalues, and fast Fourier transforms. – https://www.mathworks.com/help/matlab/functionlist.html#r onsive_offcanvas The MATLAB System 3. The Language The MATLAB language is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features. 4. External Interfaces – The external interfaces library allows you to write C and programs that interact with MATLAB. – http://www.unc.edu/depts/case/BMELIB/apiextMATLAB6p1. pdf The MATLAB System 5. Graphics – MATLAB has extensive facilities for displaying data as graphs, as well as editing and printing these graphs. It also includes that allow you to customize the appearance of graphics as well as build complete graphical user interfaces on your MATLAB applications. – http://courses.washington.edu/css485/graphg.pdf Why MATLAB? 1. It is very easy to use Matlab. - The grammar is simple. -Many program development tools are provided to make the program easy to use, including editor/debugger, online documentation, workspace browser, and so forth. Why MATLAB? 2. Matlab has many predefined functions to use in various applications. - More than 1000 functions in the basic Matlab; - These functions solve very complex problems, such as differential equations, matrix and vector formulas, and so on; - The functions are efficient, robust. Why MATLAB? Why MATLAB? Suppose we want to multiply two matrices A and B A11 A21 AIxJ = … … AI1 A12 … … … … … … Aij … ... … … … … … A1J … … … AIJ B11 B21 BJxK = … … BJ1 B12 … … … … Bjk … … … ... … … … … … B1K … … … BJK C = A·B is a new matrix where Cik = AB ik = J j=1 AijBjk = A 𝑖1B1j + A𝑖2B2j+ … + A𝑖𝑗Bjk C11 C21 C = A·B = … … CI1 C12 … … … … C ik … … … ... … … … … … C1K … … … CIK Why MATLAB? - Comparison with C++ C++ Code for matrix multiplication (O(I*K+I*J*K)) C11 C12 C21 … … 𝐂= … … … CI1 … … … Cij … ... … … … … … C1K … … … CIK If I =20, J= 20, K= 30 I*K+I*J*K = 12600 ! Why MATLAB? - Comparison with C Matlab Code for matrix multiplication: Why MATLAB? 3. Toolboxes extend functions’ capacity with many more functions in various specialties. - Signal Processing, - Image Processing; - Parallel Computation, - Curve Fitting, - Control Theory, - Simulation, - Optimization. https://www.mathworks.com/search/site_search.html?c%5B%5D=enti re_site&q=toolbox Why MATLAB? 4. Matlab offers a variety of ways to visually display data. It is easy to make the visualization of results immediately available. https://www.mathworks.com/help/matlab/ref/plot.html 6. Matlab has interfaces to C/C++, Java, .NET, Python, SQL, Hadoop, and Microsoft Excel. Disadvantage: 1. A full copy of Matlab is much more expensive than a conventional Fortran or C compiler. 2. Matlab is an interpreted language and therefore it executes more slowly than compile language. Source code compiler Interpreter (line by line) Object code Machine code execute Machine code execute MATLAB is an interpreted language Advantages Disadvantages •easy to learn •easy to debug •No compiler •run quite slowly •use a lager RAM. What types of companies use MATLAB? • MATLAB is used in many industries. - Large aerospace and defense companies. - Major car manufacturers. - Computer vision-related companies. - Robotics. • Some financial companies. MATLAB Desktop •Command Window •Command History Window •Editor Window •Figure Window •Current Folder Browser •Workspace •Toolstrip •Help Browser Current Folder Browser Details Window MATLAB file path Command Window Workspace Line Numbers * means the file is not saved Help files Comments Debugging Tools Editor Window Command Window: As you work in MATLAB, you issue commands that create variables and call functions. For example, create a variable named a by typing this statement at the command line: a=1 MATLAB adds variable a to the workspace and displays the result in the Command Window. a=1 Create a few more variables. b = 2*a c = a + b^2 Command History Window: The Command History window displays a log of statements that you ran in the current and previous Matlab sessions. You can recall previous commands by pressing the up- and down-arrow keys, ↑ and ↓. Press the arrow keys after you type the first few characters of a command. For example, to recall the command b = 2, type b, and then press the up-arrow key. Editor Window: You can write a program or script called a m-file (has a .m extension) in the Editor Window. The Editor Window is a word processor specifically designed for Matlab commands so it automatically formats certain things for you. Figure Editor : • MATLAB ﬁgures include the ability to ﬁne-tune the appearance of the plot, zoom, etc. • The ﬁgures can be saved in a wide variety of formats. - .fig file is preferred. Current Directory : The directory that MATLAB is currently working in. This is where anything you save will go by default, and it will also inﬂuence what ﬁles MATLAB can see. Variable Editor or Array Editor: Opens variables in an Excel-like format, and is useful for checking what data is in which column/row, checking that value is where you meant it to be, etc. Data can also be edited or created in this window. Double-clicking on a variable in the Workspace will open it for editing. Workspace: Work space shows the all the variables that we have currently deﬁned and some basic information about each variable, including its dimensions and values. Managing the workspace: In order to display a list of the variables currently in the memory, type >> who If you want to know more details about size, space allocation, and class of the variables. >> whos Managing the workspace: - The contents of the workspace persist between the executions of separate commands. - The results of one problem to have an eﬀect on the next one. - To avoid this possibility, it is a good idea to issue a clear command at the start of each new independent calculation. >> clear The command clear frees up system memory. Toolstrip: The Toolstrip organizes MATLAB functionality in a series of tabs. Toolstrip - Home: The Home tab is where you do general purpose operations: • Creating new files, • Importing data, • Managing your workspace, • Setting your Desktop layout. Toolstrip - Plots: The Plots tab can be used to create MATLAB Plots. Toolstrip - Apps: The Apps tab is the place you go to run interactive MATLAB applications. Getting help: To view the online documentation, select MATLAB Help from Help menu or MATLAB Help directly in the Command Window. Information about any command is available by typing: >> help Use on-line help to request info on a speciﬁc function >> help sqrt The help command searches for an exact function name match. Getting help: Another way to get help is to use the lookfor command. The lookfor command searches the quick summary information in each function for a match. >> help inverse >> lookfor inverse Questions?