1. A Brief Introduction to Matlab Laila Guessous Dept. of Mechanical Engineering Oakland University

2. What is Matlab MATLAB® is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. 1 1 Matlab Help

3. Matlab as a calculator Matlab incorporates simple arithmetic operators + - * / ^ Matlab includes basic functions such as: sin(), log(), log10(), exp(), cosh() Matlab also includes predefined constants: pi, e Values may be assigned to variables: >>U=6; (semicolon suppresses screen output) >>V=5; (Matlab is case- sensitive) >>U*V ans= 30(If no name is specified, “ans” is used by default) >>W=log(U);

4. Some Basic Commands Who:Lists all variables in workspace Whos:Provides more detailed information on variables in workspace Clear:Clears variables and functions from memory… Clear a, bClears only a and b cd:Change directory ls:Lists files in current directory load filename:Loads file into memory

5. Matrices You can enter matrices into MATLAB in several different ways: Enter an explicit list of elements. Load matrices from external data files. Generate matrices using built-in functions. Create matrices with your own functions in M-files. An NxM matrix has N rows and M columns Rows may be separated by “enter” >>A=[1 2 3 4] gives A = 1 2 3 4 Rows may also be separated by semi- colons: >>A=[1 2;3 4]; Columns are separated by a space or comma >>A= [1,2;3,4]

6. Matrix elements The element located in the i th row and j th column of matrix A can be accessed as: >>A(i,j) The value of an element can easily be changed >>A(2,1)=5; This changes the previous matrix to A= 1 2 5 4 Formulas can be used >>A(2,2)=cos(pi)+sin(pi) A = 1.0000 2.0000 5.0000 -1.0000 The elements of an entire row or column can be accessed or changed: >>A(:,2)=6; This changes A to: A= 1 6 5 6

7. Matrix elements (Contd) A column can be deleted using: >>A(:,2)=[ ] (This erases the 2 nd column) A row can be deleted in a similar way: >>A(4,:)=[ ] The transpose of a matrix can be obtained using ‘: If A is 1 2 5 4 Then, A’ is 1 5 2 4 Special arrays: Zeros: creates a matrix of all zeros; >>zeros(2,2) yields 0 Ones: creates an array of all ones; >>ones(2,1) yields 1 Eye: creates the identity matrix; >>eye(2,2) yields 1 0 0 1

8. For-Loops For loops allow you to repeat statements a certain number of times, and are especially useful for assigning values to array elements. Each for loop ends with an “end” statement For i=1:N For j=1:M A(i,j)=sin(x(i))+b*cos(pi*y(j)) end

9. Matrix operations If A and B are arrays of the same size: C=A+B; generates an array of the same size as A and B whose elements are the sum of the elements of A and B Alternatively, use For i=1:N For j=1:M C(i,j)=A(i,j)+B(i,j); end Inv(A) generates the matrix inverse of A, i.e., inv(A)*A yields the identity matrix C=A*B; product of matrices A and B

10. If-statement If (i==2) A(i)=1; end If ((i>2) & (i<=6)) A(i)=3*i; else A(i)=0; end If ((i~=2) & (i<5))Note: ~= means “not equal to” A(i)=3 elseif (i>6) A(i)=1; end

11. While statement While repeats a statement until the expression between parentheses is no longer true. i=1 While(i<10) i=i+1; End At the end of this while loop, i will be equal to 10

12. Basic Plotting Suppose x, U and V are 1-D arrays plot(x,U) plots U vs. x plot(x,U,’o’) plots U vs. x and uses an ‘o’ marker xlabel(‘this is my x title’) ylabel(‘this is my y title’) title(‘This is my title’) plot(x,U,’o’,x,V,’+’) Plots U vs x and V vs x on same plot legend(‘this is my U legend’,’this is my V legend’) Figure(1) opens the first figure window

13. Basic plotting (cont’d) You can also use the GUI to input titles, legends, etc.

14. More plotting If x, y, and T are NxM arrays where x and y arrays hold the x and y coordinate info: contour(x,y,T) generates a contour plot of T in the x-y plane colorbar inserts a colorbar showing the scale used for the contour plot If x, y, U and V are NxM arrays and U and V represent the x and y components of velocity: quiver(x,y,U,V) generates a velocity vector plot in the x-y plane

15. A few more tricks Suppose x and A are NxM arrays and you want to plot the data in the k’th row plot(x(k,:),A(k,:)) the colon indicates that you want to go over the entire j-index range If you wish to have 4 plots on the same page, use the “subplot” command If you save a figure in a.fig format, you can open it again in Matlab at a later time and edit it. To copy and paste Matlab plot in Word, either use “edit – copy figure” in Matlab, then paste in document or save figure in Matlab as.jpg file.