MATLAB Basics. Mohamed Taha. Communication Engineering Department Princess Sumaya University Page 1 of 32. Full Screen.

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1 Mohamed Taha Communication Engineering Department Princess Sumaya University Page 1 of 32

2 1 What is It is an abbreviation to MATrix LABoratory Front end for a matrix library It is an interpreted language It contains huge amount of built in functions and accept user defined functions Compatible with almost all programming languages (C ++, JAVA,.net applications), etc. Memory allocations and de-allocations are done automatically Page 2 of 32

3 data structures and data types Basic data structure is matrix calls matrices arrays Basic data type is double Page 3 of 32

4 Layout Page 4 of 32

5 Interactive computing with Using as a calculator ans is a default variable used if a variable is not specified to hold the result At the command prompt >> 2+6-4*sin(4) ans = If we assign the variable x the last statement >> x = 2+6-4*sin(4) x = ans disappeared Page 5 of 32

6 % sign is used to write a comment % This is my first command The last statement is totaly ignored by ; is used to suppress the result, useful when the result is a huge matrix (image) >>a=1; To display the result >> a or disp(a) Page 6 of 32

7 vectors Row vector A = [1 0 1] is entered in as A=[1 0-1] spaces are used between the elements commas can be used as well >> A=[1 0-1] A = The size and data structure can be checked by typing >> whose A Name Size Bytes Class A 1x3 24 double Page 7 of 32

8 Column vector A = >> A=[1;0;-1] A = To convert a row vector to a column vector, use transpose operator A = >> B=A B = Page 8 of 32

9 Matrices Matrices are collection of column or row vectors m n matrix, contains m rows and n columns [ ] The matrix A = is entered as 1 j 2 >> A=[1 1/2 0;-1 j 2] A = i Size of the matrix or vector can be returned as >> [m,n]=size(a) m = 2 n = 3 Page 9 of 32

10 Accessing the elements of a matrix/vector For a vector (column or row), elements can be accessed by specifying the number of the element First element is a number 1 and not 0 in the array A = [1 0-1] >> A(1) ans = 1 >> A(2) ans = 0 >> A(3) ans = -1 >> A(end) ans = -1 Page 10 of 32

11 For matrix, elements are accessed by specifying their locations in the row and column A = j j /2 >> A=[1-1 5 ; -j 0 2+3*j ; 1 2-7/2]; Page 11 of 32

12 Elements of A are accessed as Page 12 of 32 Colon operator : is used to specify range of columns and rows 1:3, produces [1 2 3]

13 Creating vectors automatically It is much efficient to create matrices and vectors automatically Functions used to create matrices can be used to create vectors, opposite is not always possible. For vectors: x = linspace(startval, EndVal, N); Creates a row vector of N linearly spaced numbers between StartVal and EndVal Increment = difference between any two consecutive numbers = EndV al StartV al N 1 Creates 10 elements between 1 and 5 >> x=linspace(-1,5,10); Page 13 of 32

14 The increment can be checked by subtracting any two consecutive numbers in x >> x(2)-x(1) >> ans = Exactly equals to 5 ( 1) 10 1 = x = StartVal : Increment : EndVal Exactly the same as linspace x=-1:0.667:5 Produces the same x produced previously by linspace Page 14 of 32

15 Creating matrices automatically Several functions Function eye(m,n) zeros(m,n) ones(m,n) diag(m) diag(m) rand(m,n) randn(m,n) hilb(m) magic(m) Operation m n identity matrix m n matrix of zeros m n matrix of ones m m diagonal matrix extract diagonals m n randomly generated matrix m n randomly generated matrix m m Hilbert matrix m m magic square Page 15 of 32

16 Matrix algebra A±B, A and B are vectors or matrices of the same size >> A=[1 0-1; 1/2 j -3]; >> B=ones(2,3); >> C=A-B; A B, columns {A} = rows {B} >> A=[1 0-1; 1/2 j -3]; >> B=ones(2,3); >> C=A*B ; A. B, multiply the corresponding elements of A and B, A and B must be of the same size Page 16 of 32

17 >> A=[1 0-1; 1/2 j -3]; >> B=ones(2,3); >> C=A.*B C = i A./B, divide the corresponding elements in A and B, A and B must be of the same size >> A=[1 0-1; 1/2 j -3]; >> B=ones(2,3); >> C=A./B C = i Page 17 of 32

18 Inverse of a matrix A, A is a square, full rank matrix >> A=randn(3); >> B=inv(A) B = Page 18 of 32

19 Matrix functions Page 19 of 32

20 built in variables has several built in variables These variables name should not be used for user defined variables Page 20 of 32

21 User defined variables Should starts with characters a-z or A-Z Can have any remaining characters Maximum length 31 Should not have the name of a built in variable/function or a user defined function A is different from a, case sensitive Page 21 of 32

22 Polynomials Most engineering problems based on polynomial manipulations Some functions Page 22 of 32 The polynomial f(x) = x 2 + 2x + 1 is entered as f=[1 2 1]; The polynomial g(x) = x is entered as g=[1 0 1]; The value of g( 0.5) polyval(g,-0.5)

23 c(x) = f(x)g(x) is computed as >> f=[1 2 1]; >> g=[1 0 1]; >> c=conv(f,g) c = The result is interpreted from right to left as c(x) = 1 + 2x + 2x 2 + 2x 3 + x 4 Page 23 of 32

24 Vectorization Transforming any problem to matrix-vector manipulation Useful in engineering problems In this case loops are avoided. Consider the C-loop pi=3.14; N=5; for (i=0; i < N ; i++) { x[i]=pi*i/4; } version x=0:pi/4:pi Uses 1 5 of the time required for the C-loop Page 24 of 32

25 2 (x,y) data Two dimensional plots are created with the plot function. plot(x,y) plot(xdata,ydata,symbol) plot(x1,y1,x2,y2,...) plot(x1,y1,symbol1,x2,y2,symbol2,...) x and y must have the same size, x1 and y1 must have the same size, x2 and y2 must have the same size, etc. Page 25 of 32

26 Different axis scaling Name loglog plot semilogx semilogy Axis scaling log 10 (y) versus log 10 (x) linear y versus x linear y versus log 10 (x) log 10 (y) versus linear x Page 26 of 32

27 Linear Scale >>x=-10:0.1:10; >>y=x.ˆ2; >>plot(x,y) >>grid Page 27 of 32

28 Log Scale >>x=linspace(0,1,10); >>y=exp(2*x); >>semilogy(x,y) Page 28 of 32

29 Practice 1. Use colon operator to create a 100 elements vector between 3 and 10 with uniform spacing between elements. 2. For the vector created in (1), square all elements. 3. Create 4 4 normal random matrix, A. Find a new matrix, B such that its columns are the diagonal of the matrix A. Ans. diag(a)*ones(1,4) Page 29 of Create a 3 3 uniform random matrix, X. Find the eigen value decomposition of the matrix, X = V ΛV 1.

30 5. Create random vector with zero mean and unity variance. Check the values of the mean and the variance using commands. 6. You need to use the randn, mean, var functions. To find help about these functions, at the command prompt, type, help FunctionName. 7. Create the matrix Write commands to: Page 30 of 32

31 Extract the elements of the second row Interchange column 3 and column 1 Subtract row 1 from row 2 and store the result in the second row Multiply all elements in row 1 and all elements in column 2 and store the result in row 1 [ ] 8. Given the vectors x = 1 3 7, y = [ ] [ ] 3 1 6, A =, and B = Determine which of the following statements will correctly execute (and if not, state why). For the correctly executed statements give the final result Page 31 of 32

32 using. 1. x + y 2.[x; y ] 3.B A 4.B./x 5.x + A 6.[x; y] 7.B A 8.B./x 9.A [x, y ] 10.ones(1, 3) A 11.[x; y] + A Page 32 of 32