Lab1

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Apr 3, 2024

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x=Lab 1: Introduction to Matlab 1. Creating vectors (a) Generate the following vectors: A = [1 0 4 5 3 9 0 2] a = [4 5 0 2 0 0 7 1] Be aware that Matlab are case sensitive. Vector A and a have different values. (b) Generate the following vectors: B = [A a] B=[ 1 0 4 5 3 9 0 2 4 5 0 3 0 0 7 1] C = [a,A] C=[4 5 0 2 0 0 7 1 1 0 4 5 3 9 0 2] Concatenation is the process of joining small matrices to make bigger ones. In fact, you made your first matrix by concatenating its individual elements. The pair of square brackets, [], is the concatenation operator. (c) Generate the following vectors using function zeros and ones: D = [0 0 0 . . . 0] with fifty 0’s. D=zeros(1,50) E = [1 1 1 . . . 1] with a hundred 1’s. E=ones(1,100) (d) Generate the following vectors using the colon operator F = [1 2 3 4 . . . 30] F=[1:30] G = [25 22 19 16 13 10 7 4 1] G=[25:-3:1] H = [0 0.2 0.4 0.6 . . . 2.0] H=[0,0.2,2.0] The colon, :, is one of Matlab’s most important operators. 2. Operate with the vectors V1 = [1 2 3 4 5 6 7 8 9 0] V2 = [0.3 1.2 0.5 2.1 0.1 0.4 3.6 4.2 1.7 0.9] V3 = [4 4 4 4 3 3 2 2 2 1] (a) Calculate, respectively, the sum of all the elements in vectors V1, V2, and V3.

sum(V1)=45 sum(V2)=15 sum(V3)=29 (b) How to get the value of the fifth element of each vector? V1(5)=5 V2(5)=0.1 V3(5)=3 What happens if we execute the command V1(0) and V1(11)? Remember if a vector has N elements, their subscripts are from 1 to N. 1 (c) Generate a new vector V4 from V2, which is composed of the first five elements of V2. V4=V2(1:5) Generate a new vector V5 from V2, which is composed of the last five elements of V2. V5=V2(1,5:end) (d) Derive a new vector V6 from V2, with its 6th element omitted. V6=V2 V6(6)=[] Derive a new vector V7 from V2, with its 7th element changed to 1.4. V7=V2 V7(7)=[1.4] Derive a new vector V8 from V2, whose elements are the 1st, 3rd, 5th, 7th, and 9th elements of V2 V8=[V2(1,1) V2(1,3) V2(1,5) V2(1,7) V2(1,9)] (e) What are the results of 9-V1 9-V1= [8 7 6 5 4 3 2 1 0 9] V1*5 V1*5= [ 5 10 15 20 25 30 35 40 45 0] V1+V2 V1+V2= [1.3 3.2 3.5 6.1 5.1 6.4 10.6 12.2 10.7 0.9]

V1-V3 V1.*V2 V1*V2 V1.^2 V1.^V3 V1^V3 V1 == V3 V1>6 V1>V3 V3-(V1>2) (V1>2) & (V1<6) (V1>2) | (V1<6) any(V1) all(V1) 2 3. Using Matlab help system, click on Help -> MATLAB help or type helpdesk to can open the help files. For description of a single function or command, type help command_name on the command line, or use ’search’ in the help window. For example, type help plot on the command line.

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4. Flow control What are the results of these sets of commands? Think them over and run them with Matlab to see if you are right. (a) A = zeros(1,5); for n = 1:4 for m = 1:3 A = A + n*m; end end A (b) B = [1 0]; if (all(B)) B = B + 1; elseif (any(B)) B = B + 2; else B = B + 3; end B 3 (c) C = 7:2:22 num = 0; while (all( C>0)) C = C - 3; num = num + 1; end C num (b) Situations under which loops can be avoided. Does the set of commands: for i = 1:20 H(i) = i * 5; end have the same result as:

H = 1:20; H = H*5; Does the set of commands: for n = 1:100000 x(n) = sin(n*pi/10); end have the same result as: n = 1:100000; x = sin(n*pi/10); 5. Compare a script and a function (a) Write a script: In the main menu of Matlab, select file -> new -> M-file A new window will pop up. Input the following commands: 4 x = 1:5; y = 6:10; g = x+y; and then save the file as myscript.m under the default path matlab/work (b) Write a function: Create a new m file following the procedure of above. Type in the commands: function g = myfunction(x,y) g = x + y; and then save it as myfunction.m (c) Compare their usage (1) run the commands one by one: myscript x y

g z = myscript (error?) (2) Run command clear to remove all variables from memory (3) Run the commands one by one: x = 1:5; y = 6:10; myfunction (error?) z = myfunction(x,y) g (error?) a = 1:10; b = 2:11; myfunction(a,b) Can you explain what is going on here? 5

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Lab1

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