LECTURE 1. What Is Matlab? Matlab Windows. Help

Transcription

1 LECTURE 1 What Is Matlab? Matlab ("MATrix LABoratory") is a software package (and accompanying programming language) that simplifies many operations in numerical methods, matrix manipulation/linear algebra, and other tasks engineers will often want to accomplish. The Matlab language shares common ideas (i.e. for loops, if statements) with other languages like Java, C++, and Python. Matlab was chosen for this class because of its use in industry, elaborate Matrix manipulation functionality, tools for efficient graphing/plotting, implementation of numerical algorithms, and specialized toolkits. Matlab Windows When you open Matlab, you see something like this: There are 4 types of windows: Command Window : This is where you type and execute commands Workspace Window: This shows you the current variables Current Directory Window: This shows you the current directory and all the files in that directory. It also allows you to navigate to a different directory. History Window: This shows you previously executed commands Viewing of all these windows can be turned on or off. The most important window is the command window. Help The help functionality within matlab is very well developed. The most important commands to know are the following. You can type these into the command window and press enter: >> help This command shows you all the help topics >> help topic This tells you how the topic is used in matlab. In most cases, it gives you examples as well. Type in: >> help sin This gives you information about how the sine function can be used in matlab. >> helpwin This brings up a window with the help topics. You can conveniently search for topics in this and see examples of usage of different operators and functions.

2 Matlab as a Calculator (Immediate Mode) Let us now type in the following basic math operations: Scalar Variables >> >> >> sin(3) >> clear >> clc From the previous exercise, we can observe that matlab creates a special variable ans every time you type in a command. This special variable stores the answer to the last command. We can access this variable by using its name: >> 3/ >> ans* Some other Special Variables: >> nan NaN >> inf Inf >> pi We can also define variables of our choice and apply operators and functions to these variables:

3 Vectors Matlab can also be used to define and manipulate vectors. Elementwise Definition: Interval Representation: >> x = 5 x = 5 >> y = 10 y = 10 >> x+y 15 >> sin(pi) e-016 >> x = [ ] x = >> x = [1,2,3,4,5] x = >> y = [1;2;3;4;5] y = >> x = 1:5 x = >> y = 100:104 y = >> z = 300:0.1:300.5 >> p = 75:-5:40

4 We can also use mathematical operators to apply to every element on the vector: >> exp(x) >> Z = exp(x-y) Z = 1.0e-042 * >> x.*y We can also apply functions to vectors: Matrices >> a = [1 2 3] >> b = [4 5 6] >> c = cross(a,b) c = >>d = dot(a,b) d = 32 Special matrices >> eye(3) >> magic(3) >> ones(3,4) >> zeros(2,3) >> rand(2,2)

5 Elementwise Matrix Definition >> mat = [1,2,3;4,5,6] mat = Accessing matrix elements >> a = mat(2,2) a = 5 >> mat(1,1) = 0 mat = >> mat(2,3) = -1 mat = Operators: Matrix addition, multiplication, transpose, dotmultiplication, slashes >> a = [1,2;3,4] a = >> b = [5,6;7,8] b = >> a+b >> a-b >> a*b Elementwise functions: Exp, sin >> a.*b >> a/b >> a./b >> a\b

6 Matrix functions >> exp(a) >> sin(a) >> inv(a) >> det(a) -2 >> diag(a) 1 4 Matrix manipulation functions: fliplr, flipud, rot90 >> fliplr(a) >> flipud(a) >> rot90(a) True And False (Relational Operators) In just about all computer languages, you'll run into the concept of TRUE and FALSE. A statement can be True ( i.e. 5 > 3 ), or a statement can be False ( i.e. 5 < 3 ). In Matlab and basically all programming languages: 0 means False and 1 means True.

7 Example: >> 5>3 1 >> 5<3 0 Relational operators are the tests you can use to compare the relationships between two quantities > greater than < less than >= greater than or equal to <= less than or equal to == (2 equals signs!) is equal to ~= NOT equal to IMPORTANT: If you only have a single equal sign, you're not comparing two numbers, you're setting a variable! Therefore, to test (True/False) whether X equals 15, you'd say x==5 Logical Operators Negation Operator: ~ means NOT. This operator switches true and false. >> x = 7 x = 7 >> x > 5 1 >> ~(x > 5) 0 Sometimes, you want to test the truth of two statements at once. You can do this using logical operators. For example, if you want to know if a variable x is between 5 and 10, you would have to test for x > 5 and x < 10. & is used to test if both statements are true is used to test if one of the statements are true >> (x>5)&(x<10) >> (x>5) (x<6)

8 Displaying Results: The semicolon operator In MATLAB, a semicolon at the of the command doesn t display the result on the command window. >> a = 1:5 a = >> a = 1:5; In the rest of our notes, we will use the semicolon. However, if you would like to see the results of the command, do not type the semicolon. Saving and loading workspaces Remember a workspace stores all your current variable names and values associated with them. Saving workspaces is useful when they are result of long computations, so that they can simply be loaded the next time you start matlab. It is also a useful way of sharing data. >> save myworkspace; >> save('myworkspace'); >> save('myworkspace','a') >> load myworkspace >> load('myworkspace') Some Special Commands/Functions >> who >> whos >> which >> what Writing Scripts Scripts are an easy way of running multiple commands. A script file or an m-file is saved with an extension.m. In matlab, navigate to File -> New -> M-file and it opens up the matlab text editor. (or you can also type in edit in the command prompt). The MATLAB text editor is similar to other text editors, but it is especially suited for creating MATLAB-specific files, M- files. There are a number of different features that the MATLAB text editor offer: One features that it offers is syntax highlighting (i.e., comments are green, command lines are black, and other constructs will use other colors), making easier to read the script. Another is that it automatically app the ".m" suffix when saving files, so you don't need to app it yourself. The MATLAB text editor also offers extensive debugging functionality as well (i.e., finding and fixing errors in scripts). Now, to save the last few commands in a file called myscripts.m, you would type:

9 a = 1:5; b = 101:105; c = a+b and then save the file as myscripts.m. Paths Matlab keeps a list of directories in a variable called path. Matlab can only find scripts that are in a directory in the path OR in the current directory. To see the list of directories in its path, type in : >> path; If you want to run myscript.m which you have created in the previous section, make sure that either you have saved the script in the current directory, or add the directory that contains myscript.m to your path. To add this directory to your path, navigate to: File -> Set Path Click on Add Folder and select the folder that contains your script. Now, all you have to do to run your script is to type in the following in the command window: >> myscript NOTE : THIS IS VERY IMPORTANT. If you have saved your script and run into the following error, then the first thing you should do is to check your path. >> myscript??? Undefined function or variable 'myscript'. EXERCISES: 1. Define a random vector a of size Use the mean and median function to find the mean and median 3. Use the sort function to sort values in the vector in ascing order. 4. Use the following functions to find the : Minimum value min Maximum value - max Standard Deviation std Sum sum Built In functions: mean, median, sort, min, max, std, var, abs, sum, floor, ceil, round, rem, sign, complex numbers: imag, real, angle IS s: isnan, isreal, ininf, isempty, isequal

10 Problem Statement For the rest of this class, we will think about writing a program to solve the following problem using different methods: There are 5 passengers sitting in a bus. They have the following ages: 7, 33, 65, 2,16. Write a program that tells you which passengers are children and which ones are adults, given that anyone less than the age of 12 is a child. Input: We will first define a vector variable called ages to hold all the values. ages = [7, 33, 65, 2, 16] Expected output: What we would like to produce is an output which is a vector which has 1 s if the age is a child s age and a 0 if the age is an adult s age: output = [1,0,0,1,0] Conditional Statements A very important part of computer programming is the ability to make decisions based on whether things are True or False. To do this, you'll use "If Statements," which are a crucial piece in just about every programming language. If statements In Matlab, If Statements are implemented as follows: if(condition) statements Example: Write a script that asks for your age and displays You are not a child if you are older than 12 yrs. age = input( How old are you? ); if(age>12) disp('you are not a child'); If- statements Sometimes, you'll want to take one action if the condition is true and a different action if the condition is false. Matlab lets you use If-Else Statements to say "If the condition is true, let's only do the other set of actions; however, if the condition is false, let's only execute the second set of actions."

11 if(condition) statements statements Example: Write a script that asks for your age and displays You are a child if you are less than or equal to 12 yrs and You are not a child if you are older than 12 yrs. age = input( How old are you? ); if(age>12) disp('you are not a child'); disp('you are a child'); If-if- statements Sometimes, you'll want your program to choose one from several courses of action. In these instances, use If-Elseif-Else statements. if(condition) statements if (condition) statements statements Example: Write a script that asks for your age and displays You are a child if you are less than or equal to 12 yrs, You are a teenager if you are between 12 and 19 and You are an adult otherwise. age = input('how old are you: '); if(age>19) disp('you are an adult.'); if(age>12) disp('you are a teenager.'); disp('you are a child.');

12 Solving the bus problem ages = input('please enter the ages of passengers in the bus: '); if ages(1) < 12 output(1) = 1; if ages(2) < 12 output(2) = 1; if ages(4) < 12 output(4) = 1; if ages(5) < 12 output(5) = 1; disp(output) if ages(3) < 12 Switch output(3) Case statements = 1; These are useful for writing cleaner code where the condition you are checking for is equality. If (a==1) disp('one'); if (a==2) (a == 22) (a == 222) disp('two'); if (a==3) (a == 33) disp('three'); disp('something '); versus: switch a case 1 disp('one'); case {2,22,222} disp('two'); case {3,33} disp('three'); otherwise disp('something '); This is also very useful for comparing strings. You do not need to use the strcmp function: switch a case 'One' disp('this is One'); case {'Two','Twenty-Two'} disp('this is Two'); case {'Three', 'Thirty Three'} disp('this is Three'); otherwise disp('something ');

13 Functions Functions are useful for modular processing, ie: where a set of lines of code conduct a task that can be defined using a higher level idea. A function typically takes in a set of inputs and returns a set of outputs. (In some cases it may not take in an input, for example a function that returns the current time.) In matlab a function can be written as : function [output1, output2...] = function_name (input1, input2 ) statements Functions in MATlab can be saved as M-files with the name of the function, function_name.m. The function can then be called by scripts and other functions by passing inputs and receiving outputs as follows: [outputs] = function_name(inputs) Function Workspaces Workspaces contain variables that can be accessed by the program. We have seen the MATLAB workspace and we have learned that we can access variables in the matlab workspace from the command line and a script. When you define a function however, you define a new workspace. This is called the function workspace. The only variables that can be accessed in this workspace are variables that are input to the function or variables that are created in the function. If you would like for a variable that is created or modified in your function to be accessed outside your function, you will have to return it as an output. Every time a function is called, this workspace is generated and when the function has terminated its execution, the workspace is deleted from memory. This separation of workspaces is useful because it allows you to rename variables within functions and also get rid of intermediate variables from the memory once the function has finished its execution. Example Function with one input and no output. Write a function called plusone that takes in a number, adds one to it and then displays it. (save this as plusone.m) function plusone(num) result = num+1; disp(result); Function with one input and one output. Write a function called plustwo that takes in a number, adds two to it, displays the result and then returns the result. (save this as plustwo.m) function result = plustwo(num) result = num+2; disp(result);

14 Function with many inputs and many outputs. Write a function called plusany that takes in two numbers, adds them, displays the result and then returns the sum value and the mean value. (save this as plusany.m) function [sumvalue, meanvalue] = plusany(num1, num2) sumvalue = num1+num2; meanvalue = sumvalue / 2; disp(sumvalue); disp(meanvalue); Special Variables Nargin number of input arguments used to call the function Nargout number of output arguments used to call the function Return The return command causes a return to the invoking function. What this means is that it stops execution of the function after this line and the value of the output variables that the function outputs will be what it is as that line. For example, if we modify the above function to: function [sumvalue, meanvalue] = plusany(num1, num2) sumvalue = 0; meanvalue = 0; sumvalue = num1+num2; if sumvalue < 0 return meanvalue = sumvalue / 2; disp(sumvalue); disp(meanvalue) Normally functions return when the of the function is reached. Exercise: Write a function called isodd that takes in a number and returns the character O if the value is odd and E if the value is even. (hint: use the rem function). Call this function from the command line script with different values. Solving the bus problem categorize_age.m function category = categorize_age(age) if age < 12 category = 1; category = 0;

15 myscript.m ages = input('please enter the ages of passengers in the bus: '); output(1) = categorize_age(ages(1)); output(2) = categorize_age(ages(2)); output(3) = categorize_age(ages(3)); output(4) = categorize_age(ages(4)); output(5) = categorize_age(ages(5)); Loops disp(output) In programming, loops are used to provide a more efficient way of processing through indexed data or for repeatedly executing a sequence of statements until a certain condition is reached. For loops For loops provide a nice way of processing through indexed data such as vectors. The syntax is as follows: for index = first : last Statements For example, if we have a vector and we would like to display all the elements in the vector: vector = [ ]; for i = 1:length(vector) disp(vector(i)); Note: Try to avoid overwriting your index variable. While loops While loops are used to test for conditions and execute code until a condition is satisfied. The syntax is as follows: while (conditional statement) statements Example: Take in an input value. If the value is less than 100, add 10 to it. Stop only when the value is greater than or equal to 100. number = input( Please input a value: ) while (number < 100) number = number + 10

16 Break This allows you to leave the loop and not execute the statements after the break statement. Continue The continue statement causes the program to return back to the beginning of the loop it is presently in, and to recheck the condition to see if it should continue executing loop code or not. The code in the loop after the "continue" statement is not executed in the same pass. Solving the bus problem myscript.m ages = input('please enter the ages of passengers in the bus: '); for i = 1:5 output(i) = categorize_age(ages(i)); disp(output) Doing it all in one line All in one line Matlab is specially designed to handle matrices efficiently: Exercises output = ages < 12 1) Write a function called 'operate' which takes in two numeric inputs and one character input which is an operator ( '+' or '-') and returns the sum of the two numbers if the character input was '+' and the difference if the character input was '-'. Use a Switch case statement. 2) Write a function called 'add' which takes in either one, or two numeric inputs. If there is only one input, add 2 to the number and return this value. If there are two inputs, add them together and return the value.

17 Script files: myscript.m categorize_age.m ages = input('please enter the ages of passengers in the bus: '); function category = categorize_age(age) %part 1: if statements if ages(1) < 12 output(1) = 1; if age < 12 category = 1; category = 0; if ages(2) < 12 output(2) = 1; if ages(3) < 12 output(3) = 1; if ages(4) < 12 output(4) = 1; if ages(5) < 12 output(5) = 1; disp(output) %part 2: functions output(1) = categorize_age(ages(1)); output(2) = categorize_age(ages(2)); output(3) = categorize_age(ages(3)); output(4) = categorize_age(ages(4)); output(5) = categorize_age(ages(5)); disp(output) % part 3: loops for i = 1:5 output(i) = categorize_age(ages(i)); disp(output)