Introduction to Matlab Programming with Applications

Transcription

1 Introduction to Matlab Programming with Applications Zheng-Liang Lu Department of Computer Science and Information Engineering National Taiwan University Matlab 289 Summer 2017

2 Class Information ˆ The course page is d /matlab.html. ˆ Lecture notes will be uploaded right before class and be modified after class if necessary. ˆ Note that most of the lecture notes are organized in English. ˆ You can contact me by sending messages to ˆ ˆ facebook. Zheng-Liang Lu 1 / 54

3 Prerequisites ˆ No programming experience required. ˆ It would be helpful if you have some. ˆ Linear algebra is strongly recommended. ˆ Matlab refers to Matrix laboratory. ˆ A beautiful and complete theory, widely used in Computer Science. ˆ I promise to keep everything simple in this class. 1 1 Simple is not easy.... Easy is a minimum amount of effort to produce a result.... Simple is very hard. Simple is the removal of everything except what matters.... Read this article. Zheng-Liang Lu 2 / 54

4 Grading Policy ˆ To acquire the certificate, you need at least 70 points in the final score. ˆ For summer/winter short courses: final exam ˆ For regular night courses: final project ˆ Do not worry about these figures. Zheng-Liang Lu 3 / 54

5 Final Project ˆ Topic: no restriction ˆ Requirement: ˆ define your problem ˆ organize algorithms in need ˆ write codes in Matlab (at least) ˆ present your result with a few slides ˆ Goals: ˆ solve a problem by formulating the problem, organizing an algorithm, writing codes, and debugging ˆ get familiar with programming concepts ˆ expand your horizon by asking questions in others work Zheng-Liang Lu 4 / 54

6 Final Exam ˆ On-site programming ˆ 5 questions (more or less) ˆ Open everything 2 2 You should learn how to integrate the tools you use, even if the tools you have are not made on your own. Zheng-Liang Lu 5 / 54

7 1 >> Lecture 0 2 >> 3 >> -- Introduction 4 >> Zheng-Liang Lu 6 / 54

8 What Is Programming? ˆ Programming is the activity of writing a sequence of instructions to tell a machine to perform a specific task. ˆ A sequence of instructions program ˆ A set of well-defined notations is used to write a program programming language ˆ The person who writes a program programmer designer 3 3 Writing codes is not what the CS people work for. We are writing codes to make a better world. Zheng-Liang Lu 7 / 54

9 In Practice ˆ Programming is to provide a solution to a real-world problem using computational models supported by programming languages. ˆ The solution is a program. Zheng-Liang Lu 8 / 54

10 Programs ˆ A program is a sequence of instructions, written in an artificial language, to perform a specified task by a machine. ˆ They are almost everywhere. 4 ˆ For example, ˆ Computer virus ˆ Video games ˆ Operating systems 5 ˆ ATM, traffic light, Google search engine, recommendation system... ˆ Differences: goal, functionality, algorithms, and resources. 4 See 5 For desktops and laptops, you may know Windows, Unix, Linux, and Mac OS. For mobile devices, Windows, Android, and ios are popular. Zheng-Liang Lu 9 / 54

11 How and Where The Programs Run 8 ˆ The programs are activated from the disk into the main memory. ˆ We now call them the processes. 6 ˆ CPUs contain the arithmetic and logic units (ALUs) and the registers (REGs). 7 ˆ ALUs provide the computational power. ˆ REGs supply operands to the ALU and store the results of ALU operations temporarily. ˆ The output is written back to the main memory and further stored into the disk if necessary. 6 The process is a formal terminology used in OS. 7 See Herein ALUs include control units. 8 You may refer to any class for an introduction to computer system. For example, Introduction to Computer Science & Programming in C. Zheng-Liang Lu 10 / 54

12 Memory Hierarchy 9 9 See Figure 1-9 in Bryant, p. 14. Zheng-Liang Lu 11 / 54

13 Programming Languages ˆ A programming language is an artificial language to communicate with machines. ˆ Programming languages syntax and semantics ˆ Recall how you learned the 2nd human language. ˆ How many programming languages in the world? ˆ Top 20 programming languages are listed in TIOBE. ˆ Matlab: top 20. ˆ Note that every language originates from reasons. Zheng-Liang Lu 12 / 54

14 Short History ˆ 1st generation: machine code ˆ 2nd generation: assembly code ˆ 3rd generation: high-level programming languages ˆ Post-3rd generations ˆ Matlab is one of 4th programming languages. Zheng-Liang Lu 13 / 54

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16 1st-Generation Programming Languages ˆ Computers understand instructions only in binary, which is a sequence of 0s and 1s. (Why?) ˆ Each computer has its own set of instructions. 10 ˆ So the programs at the very early stage were machine-dependent. ˆ These are so-called the machine language, aka machine code. ˆ Pros: ˆ Cons: ˆ Most efficient for machines ˆ Hard to program for human ˆ Not portable ˆ Still widely used in programming lower level functions of the system, such as drivers, interfaces with firmware and hardware. 10 For example, X86 and ARM. Zheng-Liang Lu 15 / 54

17 2nd-Generation Programming Languages ˆ An assembly language uses mnemonics which are easier to recognize and memorize, to represent instructions as opposed to the machine codes. ˆ Hence, the code can be read and written by human programmers. ˆ Yet, it is still machine-dependent. Zheng-Liang Lu 16 / 54

18 ˆ To run on a computer, it must be converted into a machine readable form, a process called assembly. ˆ More often find use in extremely intensive processing such as games, video editing, graphic manipulation/rendering. ˆ Note that machine languages and assembly languages are also known as low-level languages. Zheng-Liang Lu 17 / 54

19 3rd-Generation Programming Languages ˆ The high-level programming languages use English-like words, mathematical notation, and punctuation to write programs. ˆ They are much closer to human languages. ˆ Pros: ˆ Portable, machine-independent ˆ Human-friendly ˆ For example, C 11, C++ 12, and Java Dennis Ritchie (1973). FYI, C is the cornerstone of modern programming languages. If possible, taking C programming course gives you an insight of computer science. 12 Bjarne Stroustrup (1983). 13 James Gosling (1995). Zheng-Liang Lu 18 / 54

20 ˆ Note that the machines understand and execute only the machine codes as before. ˆ The translation is accomplished by a compiler, an interpreter, or a combination of both. Zheng-Liang Lu 19 / 54

21 What Can A Program Do? ˆ A program is an implementation of an algorithm expressed in a specific programming language. Zheng-Liang Lu 20 / 54

22 Algorithms In A Nutshell ˆ Simply put, an algorithm is a procedure that solves a particular class of problems, such as a cookbook. ˆ An algorithm is a well-defined computational procedure that takes a set of values as input and produces a set of values as output. ˆ Note that an algorithm is not necessarily expressed in a specific programming language. ˆ Could be human languages, flow charts, or pseudo codes. Zheng-Liang Lu 21 / 54

23 Properties of Algorithms 14 ˆ An algorithm must possess the following properties: ˆ Input and output ˆ Correctness ˆ Definiteness: basic instructions provided by a machine, e.g. +. ˆ Effectiveness: actions which can be completed by combination of basic instructions. ˆ Finiteness: resource requirement, especially time and space. 14 Donald E. Knuth (1938 ). Zheng-Liang Lu 22 / 54

24 Example ˆ Organize an algorithm that finds the greatest element in the input list, say A. Input: A (a list of n numbers) Output: max (the greatest element in A) ˆ Can you provide a procedure to determine the greatest element? ˆ For all situations? Zheng-Liang Lu 23 / 54

25 Optimal Solution ˆ The first element of A can be fetched by calling A(1). ˆ Let be the assignment operator in the following pseudo code. 1 max <- A(1) 2 for i <- 2 ~ n 3 if A(i) > max 4 max <- A(i) 5 end 6 end 7 return max ˆ How to find the minimal element? ˆ How to find the location of the greatest element? ˆ Why not max 0? Zheng-Liang Lu 24 / 54

26 Computers are good at following instructions, but not at reading your mind. Donald Knuth (1938-) Computer science is no more about computers than astronomy is about telescopes. Edsger Wybe Dijkstra ( ) Zheng-Liang Lu 25 / 54

27 Steps of Developing A Program ˆ Problem formulation: state the problem concisely. ˆ Input: specify the data to be used. ˆ Output: specify the information to be returned. ˆ Modeling and algorithm: work through the solution steps by hands; use a simpler set of data if necessary. ˆ Programming: write and debug the program. ˆ Verification: check the outputs by trying various inputs; a unit test could be necessary. 15 ˆ Generalization: generalize your solution for the purpose of reuse. 15 As to unit test, you may spend as much time as you write the program. Zheng-Liang Lu 26 / 54

28 Alan Turing ( ) Zheng-Liang Lu 27 / 54

29 Alan Turing ˆ Provided a formalization of the concepts of algorithm and universal computation model for general-purpose computers. ˆ The central subject of study in computing theory is Turing machine: ˆ Toy example from Google ˆ Also proved that there exist problems which are undecidable by Turing machines. 16 ˆ Father of computing theory and artificial intelligence 17 ˆ Turing Award of ACM 18 ˆ The Imitation Game (2014) 16 See Halting problem. 17 See Turing test. 18 Association for Computing Machinery Zheng-Liang Lu 28 / 54

30 What is Matlab? ˆ Matlab is a powerful and easy-to-use integrated programming environment, especially for numerical computing. ˆ programmable, matrix computation, fruitful toolboxes 19 available, good memory management, easy to draw graphs... ˆ The only thing you need to provide is Zheng-Liang Lu 29 / 54

31 Algorithms! A screenshot of The Social Network (2010) Zheng-Liang Lu 30 / 54

32 Summary ˆ Program design data structures + algorithms ˆ Data structures: organize your data in an efficient way ˆ Algorithms: process your data so that you can derive the solution ˆ In some sense, we can say that programming languages are less important than the two above. ˆ Here we will learn Matlab programming and classical algorithms. ˆ Additionally, I wish you could capture computational thinking. Zheng-Liang Lu 31 / 54

33 Fathers of Matlab 21 Prof. Cleve Moler Zheng-Liang Lu 32 / 54

34 Jack Little Zheng-Liang Lu 33 / 54

35 MATLAB: An Overview Zheng-Liang Lu 34 / 54

36 Command Window ˆ Let s try a greeting, Hello, Matlab. 1 >> disp('hello, Matlab.'); ˆ disp takes the string as input in the parenthesis, and outputs ˆ A string is single-quoted in Matlab. ˆ The convention in the slides is as follows: ˆ Boxes are the listings for sample programs. ˆ Words and sentences highlighted in red are important. ˆ Words in blue are reserved words. ˆ Bold words in black are functions. Zheng-Liang Lu 35 / 54

37 Errors ˆ Matlab interrupts your program if an error occurs somewhere. ˆ Don t be frustrated by red lines. ˆ Most of these errors which are detected by Matlab are syntax errors and runtime errors, which can be avoided by more practices. ˆ The others are logic errors 22, which cannot be found by the machine itself! 22 Aka semantic errors. Zheng-Liang Lu 36 / 54

38 Why do we fall sir? So that we can learn to pick ourselves up. Alfred Pennyworth, Batman Begins (2005) Zheng-Liang Lu 37 / 54

39 Helpers ˆ The function help followed by the command name shows the usage of that command, for example, 1 >> help disp 2... ˆ The reference page also provides the detail of commands with fruitful examples. ˆ Google is your best friend (when you learn by yourself). Zheng-Liang Lu 38 / 54

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41 m Files ˆ A script is a complete program which contains the input data and can be executed directly. ˆ A function is a subroutine which may need input data when being called in other programs and functions. ˆ Reuse your code. ˆ Lower the program complexity: abstraction. Zheng-Liang Lu 40 / 54

42 Debut: Your First Matlab Program 1 % This is my first Matlab program. 2 clear; % Clear all variables stored in Workspace. 3 clc; % Clear the screen. 4 % main program 5 disp('hello, world.'); ˆ The lines which begin with % are regarded as the comments which will not be executed. ˆ The function clear is used to release all the variables in the workspace. 23 ˆ The function clc cleans the command window. 23 You may release the variable x by calling clear x. Zheng-Liang Lu 41 / 54

43 ˆ Then we need to save 24 to the script, for example, helloworld.m. ˆ Click the Run button. 25 ˆ If this script is not at the current folder when you execute it, Matlab will offer two options: 1. Change folder 2. Add to Path Pool 26 ˆ You can run this program later, simply by calling helloworld. 1 >> helloworld 2 3 Hello, world. 24 Press ctrl + s. 25 Alternatively, press F5 for saving the file and executing the program. 26 Path Pool is a list of directories where the functions could be. Zheng-Liang Lu 42 / 54

44 Block Comments ˆ Press ctrl + r to comment lines. ˆ Press ctrl + t to de-comment lines which begin with %. ˆ Note that the contiguous comment lines starting from the top of file are regarded as the program document. 1 >> help helloworld 2 3 This is my first Matlab program. ˆ We can easily organize the program by these two hot keys during the trial-and-error stage. Zheng-Liang Lu 43 / 54

45 1 >> Lecture 1 2 >> 3 >> -- Variables, Date Types, and Vectorization 4 >> Zheng-Liang Lu 44 / 54

46 Data Types ˆ Binary digit, aka bit, is a digit whose value is either 0 or ˆ Everything in the machine is encoded in binary. ˆ How many bits do you need to store a zero in the memory? ˆ Not depending on the value itself, but on the type of the variable! 28 ˆ The types determine the size of a variable. ˆ We have two different numeric types: integers and real numbers (more precisely, floating points 29 ). ˆ An int value takes 32 bits. ˆ A double value takes 64 bits FYI, 1 byte contains 8 bits. 28 Use class(x) to check the type of x. 29 IEEE 754 Standard (1985). 30 The type double refers to double-precision floating point. Zheng-Liang Lu 45 / 54

47 Computational Limits ˆ It is a common convention to use e to identify a power of 10, e.g. 1e5 = 100, 000 and 1.2e 5 = Zheng-Liang Lu 46 / 54

48 ˆ The types further determine the possible states. ˆ For example, consider 2 bits for nonnegative integers. ˆ There are 2 2 = 4 possible states, and the greatest value is 3. ˆ By default, Matlab takes every numeric data as double values. ˆ However, the floating points approximate real numbers. ˆ For example, =? (Why?) Zheng-Liang Lu 47 / 54

49 Causes of Numerical Errors 32 ˆ Finite precision of computations involving floating-points 31 ˆ Truncation because simplifications are made to the mathematical equations to make them more amenable to calculation, e.g. the truncation to an infinite series ˆ Loss of significance ˆ For example, is the expression e20 1e20 equal to the expression (1e20 1e20)? (Why?) 31 Read 32 See by Prof. C.-J. Lin. Zheng-Liang Lu 48 / 54

50 Variables and Assignments ˆ A variable is used to keep a value or values. ˆ A box which contains something. ˆ In most languages, a statement looks like var = expression, where var is a variable and expression is any arithmetic operation. 33 ˆ For example, suppose x = 0. ˆ Then run y = x + 1 and so y = 1. (Trivial.) ˆ How about x = x + 1? ˆ Actually, the assignment operator (=) is defined to assign a value to the variable, from right to left. 33 To the best of my knowledge, 1 = x is not allowed because the left-hand side of the assignment should be a space. Zheng-Liang Lu 49 / 54

51 ˆ For example, 1 >> a = 10; 2 >> b = 20; 3 >> a + b 4 5 ans = ˆ The variable ans is used by default if you don t assign one for the immediate result. ˆ If you drop the semicolon (;) in Line 2, then the immediate result will appear in the command window Note that you may not drop semicolons in other programming languages. For example, the semicolon is used as the end symbol of a statement in C, C++, and Java. Zheng-Liang Lu 50 / 54

52 Variable Naming ˆ Cannot begin with a number, e.g. 1x is wrong. ˆ Cannot have blanks, e.g. x 1 is wrong. ˆ Cannot contain +-*\%, e.g. x%1 ˆ Cannot be any of key words, e.g. for ˆ Cannot be the same name as any m-file ˆ Matlab is case-sensitive, e.g. A and a are two distinct letters. Zheng-Liang Lu 51 / 54

53 ˆ Variable names should always be mnemonic. 35 ˆ May use underscores ( ) or use CamelCase. 36 ˆ We avoid to use names of reserved words 37 and built-in functions. ˆ i = 1 and j = 1 by default. ˆ If you set i = 1, then i = 1 until you clear i. ˆ pi and sin are also the names which are not to be overloaded. 35 The length of name is limited to 63 characters. The function namelengthmax returns the maximum length in this machine. 36 See 37 Try iskeyword. Zheng-Liang Lu 52 / 54

54 Scalar Variables ˆ The variable x is said to be a scalar variable if x R 1 or C 1. ˆ The complex field, denoted by C, contains all the complex numbers a + bi, where i = 1, and a, b R. 38 ˆ Try x = 1 + i in the command window. ˆ Usually used for parameters of the problems. ˆ For example, pi is a default variable to store the ratio of a circle s circumference to its diameter. 38 In math, C 1 is equivalent to R 2. So x contains two double values. However, Matlab treats a complex number as an entity. Zheng-Liang Lu 53 / 54

55 Scalar Arithmetic Operators See Table 2.1 Arithmetic Operations Between Two Scalars in Moore, p. 21. Zheng-Liang Lu 54 / 54