An Introduction to Matlab: Part 3 - Creating and Manipulating Vectors, Study notes of Mathematics

Download An Introduction to Matlab: Part 3 - Creating and Manipulating Vectors and more Study notes Mathematics in PDF only on Docsity! An Introduction to Matlab: Part 3 This lecture assumes that you have already worked through part 1 and part 2. You should be able to use many basic Matlab commands and use Matlab as a calculator on scalar variables. You should be able to create and execute a script le. This lecture covers • Creating row/column vectors • Vector operations • Applying functions to vectors • Component wise arithmetic Creating vectors This section goes through creating row and column vectors by typing each element, by using patterns, and by using a few built in functions. 1. Typing in vectors explicitly: Here we learn how to type vectors. (a) Open Matlab. If you already have it open, type clear all; in the Command Window. You may do everything here in a script le or on the Command Window. I would suggest simply using the Command Window for now so you don't have to rerun you le everytime we make a change. (b) Let us create a row vector consisting of the elements 1, 3, 5 and 7. To do this, we use the bracket notation []. We assign this vector to the variable u. u=[1,3,5,7] Instead of using commas, try simply inserting a space between each element. Type u=[1 3 5 7] Note that they are the same thing. Also note that this is a row vector (Matlab prints out the numbers in a row). (c) Let us create a column vector consisting of the same elements 1, 3, 5 and 7. For a row vector, we put either spaces or commas in between elements. For a column vector, we put a semicolon between each element. Note that a semicolon is also used to supress output, but Matlab is smart enough to know that a semicolon within brackets [] means to change rows. Type v=[1;3;5;7] Note that Matlab displays the elements of v as a column. 2. Typing in vectors using a pattern: We create vectors which are large and correspond to a distinct pattern. (a) Suppose we want to create a row vector, u, that contains elements 1 through 100 (ie u = [1, 2, . . . , 99, 100]). How can we do this? Well, you can type in each element, but that seems awfully silly. Matlab has a nice way to do this. Type u=[1:1:100] This notation means u goes from 1 by 1 to 100. Create the vector u = [1, 3, 5, 7, 9, 11] using this notation. How do you think you would create the vector u = [15, 12, 9, 6, 3, 0]? Well, it goes from 15 by −3 to 0. So we type u=[15:-3:0] We can also use negative numbers. Create a vector that goes from −15 to 0 by 3. (b) Note that using the notation above (u=[15:-3:0]) created a row vector. Let us say we want a column vector instead. The easiest way to do this is to use the transpose operator, which is the single quote: '. Type: u=[15:-3:0] v=u' What happened? Well, u is created as a row vector, then v is the transpose of u, which is a column vector. We could have simply done this on one line also by typing v = [15:-3:0]' Try to create a column vector that goes from 2 to 16 by 2. 1 3. Creating a zero vector, one vector, or random vector: Here we discuss how to create a vector of all zeros, all ones, or of completely random entries (between 0 and 1) (a) To create a vector of all zeros, we use the zeros function. It takes two (for now) arguments. These represent the size of the vector you wish to create. Type: u = zeros(5,1) You get a column vector with 5 zeros. Try to create a row vector with 10 entries. (b) To create a vector of all ones, we use the ones function. It has the same structure as the zeros function: v = ones(1,6) (c) You can also create a vector with random entries (these random entries are randomly drawn from between 0 and 1) using the rand function: u = rand(4,1) Vector operations This section goes through basic vector arithmetic and how to create new vectors using parts of old vectors. 1. Vector addition and scalar multiplication: We learn how to add vectors and scale vectors. (a) Type clear all; Create three row vectors, u, v and w by doing the following: u = [1 3 5 7] v = [0 1 2 4] w = [2 4 6 8 10] Add vectors u and v by typing: u+v Note that your result is another vector. We could assign it a varible by typing r=u+v . Now add v and w. What happens? We get an error because they are not the same size. Recall that we can only add vectors of the same size. Create a new vector, v1, that is the transpose of v , again by typing : v1=v'; Try adding v1 and v. What happens? An error again. Why? Because row vectors and column vectors cannot be added together. (b) How do you suppose we multiply a vector by a scalar? Well, exactly how you would expect! Let us multiply w by 2 by typing: 2*w Find πu and e2v by doing the same. 2. New vectors from old vectors: Here we'll learn how to incorporate an old vector as part of a new vector, or how to extract part of an old vector. (a) We'll use the same u, v, and w from above, so recreate the vectors if need be. Let us say that I only want to look at the 2nd element (component) of vector v. How might I do this? Well, vectors are indexed from 1 until their size (4 in this case) and are accessed using parenthesis. So typing: v(2) returns the 2nd element of v. Use this idea to nd the 1st and 4th components of v. (b) Let us say that I want more than one element of v. Say I want to get a new vector that is the same as v, but without the 2nd element. So I want a new vector, call it v1, that is size 3 an contains the 1st, 3rd and 4th components of v. I could type: v1=[v(1) v(3) v(4)] but for very large vectors, this will not be feasible. Another way I could do this is by typing: 2