Basic MATLAB Scientific Computing, Bridging course Scientific Computing and Matlab n Matlab is a tool and programming environment used in computational science but also in other areas. n A simple environment to quickly test ideas and to study the results n Also available in other tools, such as Freemat, Maple, Mathematica, Comsol Multiphysics, and other programming languages like C/C++, Fortran, Java. Informationsteknologi Institutionen för informationsteknologi | www.it.uu.se 1 What is MATLAB? n Developed by MathWorks, Inc. http://www.mathworks.com n First version already in late 70s n Originally MATrix LABoratory. n Matemathical environment for ® Numerical computations ® Graphics ® Programming n Many powerful predefined functions with the ability to define your own. n Own object oriented programming language. Informationsteknologi Collaboration with C++, Java and Fortran possible. Institutionen för informationsteknologi | www.it.uu.se What is MATLAB? n Over 25 plug-in (toolboxes) are available for special applications, eg: ® Signal analysis ® Image analysis ® Statistics ® Symbolic mathematics ® Finacial mathematics ® Parallel computing ® … n Run under UNIX/Linux, Windows or Macintosh. Informationsteknologi Institutionen för informationsteknologi | www.it.uu.se 2 Application areas Wherever there are computational problems n Education: mathematics (specifically linear algebra), computational science, physics, chemistry, engineering, economics, etc. n Research: lab environment to test the solution methods, study, analyze problems, perform calculations and visualize the results. n Industry:used in the same manner as in research, for example on development Informationsteknologi departments in biotechnology, electronics, automotive, etc. Institutionen för informationsteknologi | www.it.uu.se MATLAB environment n The development environment (MATLAB desktop) has a plurality of windows, Command window, Current folder, Workspace and Command History. Task: Start Matlab on your computer and change to a Informationsteknologi prefered folder by clicking it in Current folder window. Institutionen för informationsteknologi | www.it.uu.se 3 MATLAB environment n MATLAB is usually controlled from the command window (Command Window), but also from the menus. n Commands are given by »-prompter and executed when return key is pressed. n Example: >> 42 + 19 ans = 61 Informationsteknologi >> exit n Exit matlab: Institutionen för informationsteknologi | www.it.uu.se MATLAB environment n In the command window, >> a = 75 you can work interactively as an advanced calculator. a = 75 The semicolon suppresses printing. >> b = 34; >> c = a*b If no variable names specified, the variable is c = ans (= answer) 2550 >> a+b Task: Compute the sum and Informationsteknologi product of a,b,c and store the ans = results in new variables. Note 109 the use of semicolon. Institutionen för informationsteknologi | www.it.uu.se 4 MATLAB environment n Help is available through the Help menu n But even writing demo in the command window provides information on how to use Matlab. Informationsteknologi Task: How do you perform square root in Matlab? Institutionen för informationsteknologi | www.it.uu.se MATLAB environment Help for individual commands can be done directly in the command window >> help command Ex) What does the command exit ? >> help exit EXIT Exit from MATLAB. EXIT terminates MATLAB. Informationsteknologi Institutionen för informationsteknologi | www.it.uu.se 5 Variables in MATLAB A variable in MATLAB n can be viewed as containers of a value of a certain type (integer, float, char, ...) n always have a name. Must begin with a letter. Do not use å, ä, ö, space, hyphen (minus), plus signs etc in the name n can be assigned a value n created when needed, >> a = 3 without special "declaration” a = (is of type "matrix"). 3 n Can be predefined, >> pi Informationsteknologi e.g. pi,eps,realmax ans = 3.1416 Institutionen för informationsteknologi | www.it.uu.se Variables in MATLAB n The variables are displayed in Workspace- window n The issued commands are displayed in Command History Informationsteknologi Institutionen för informationsteknologi | www.it.uu.se 6 Variables in MATLAB n Can also list the variables in the , command window using who whos >> who Your variables are: a ans >> whos Name Size Bytes Class a 1x1 8 double array ans 1x1 8 double array Grand total is 2 elements using 16 bytes Informationsteknologi Institutionen för informationsteknologi | www.it.uu.se Variables in MATLAB n Variables can be displayed in various formats >> y = sin(2*pi/3); >> format short e; y >> y y = y = 8.6603e-001 0.8660 >> format short; y >> format long; y y = y = 0.8660 0.86602540378444 % Standardformat >> format long e; y e-001 equals to 10-1 y = 8.660254037844387e- Informationsteknologi 001 Task: Display pi in different formats (note the accuracy is not changed only the format). Institutionen för informationsteknologi | www.it.uu.se 7 Variables in MATLAB n Variables can be saved to file and loaded up on another MATLAB session later. n In the menu use the buttons Save Load n Variables will be saved as so-called MAT-files, files with the extension.mat n MAT-files are called binary and is not readable or editable. Informationsteknologi n Can also use save and load command directly in the command window Institutionen för informationsteknologi | www.it.uu.se Save and load variables n The button Import Data can be used to load other formats such as spreadsheets (Excel), audio files, video files, etc. n Select a file format in the window that opens after clicking the button Informationsteknologi Institutionen för informationsteknologi | www.it.uu.se 8 Functions There are lots of predefined functions, such as for n Elementary mathematics n Linear algebra n Graphics in 2D and 3D n Integrals and differential equations n Statistics n Curve fitting Example: abs(x),sqrt(x),sin(x),log(x),log10(x),… (Help -> Documentation -> Matlab -> Mathematics) Informationsteknologi There are lot of Toolboxes with specilized functions. You can also create your own functions. Institutionen för informationsteknologi | www.it.uu.se Matrices n Matrix is the basic data type. n A two-dimensional matrix is a table with rows and columns. n A matrix with m rows and n columns, has the size mxn (m times n). n Vectors are special cases of the matrices, then the number of rows or number of columns is 1. Example: row vector, 1xn, and column vector, mx1. n A matrix of size 1x1 called scalar. n Each value in the matrix are called elements. Informationsteknologi Institutionen för informationsteknologi | www.it.uu.se 9 Vectors Column vector and row vector in MATLAB >> vcol = [ 1; 2; 3; 4; 5 ] >> vrow = [5 6 7 8 ], x = 3 The vcol = % Column vector semicolon 1 into vectors 2 provide 3 new row 4 5 vrow = % Row vector 5 6 7 8 Informationsteknologi x = % Scalar 3 Institutionen för informationsteknologi | www.it.uu.se Vectors Change individual elements >> vrad(1) = -1.1; vrad(2) = 3.5; >> vrad vrad = -1.1000 3.5000 >> vkol = vrad' %transpose vkol = -1.1000 3.5000 Informationsteknologi vrad(1) indicates that the index 1 (position 1) to be assigned. The ’ means transpose. Institutionen för informationsteknologi | www.it.uu.se 10 Generate vectors n Colon notation is often used to create vectors start:stride:stop if stride = 1 it can be omitted >> vektor = 0:5 vektor = 0 1 2 3 4 5 >> vektor2 = 0.0:0.05:2.0 vektor2 = Informationsteknologi 0 0.0500 0.1000 0.1500 ... 1.9500 2.0000 Institutionen för informationsteknologi | www.it.uu.se Generate vectors The command linspace also create vectors linspace(start,stop,elements) >> v = linspace(0,2,10) v = 0 0.2222 0.4444 0.6667 0.8889 1.1111 1.3333 1.5556 1.7778 2.0000 These two methods are used, for example, when creating the x-axis at the graphics Informationsteknologi Task: Create a vector in two different ways with equally spaced elements using stride 2*pi/100 in the interval [-pi, pi]. Institutionen för informationsteknologi | www.it.uu.se 11 Generate Matrices >> A = [1 7; 5 3]; ⎡1 7⎤ Create A = ⎢ ⎥ >> A ⎣5 3⎦ A = Semicolon or return 1 7 in the matrix gives a 5 3 new row >> A = [1 7 Semicolon in the end suppresses printing 5 3] A = Task: Create a 3x4 Informationsteknologi matrix and then 1 7 transpose it. 5 3 Institutionen för informationsteknologi | www.it.uu.se Creating a Matrix elementwise ⎡1 7⎤ A = ⎢ ⎥ ⎣5 3⎦ >> A(1,1)=1; A(1,2)=7; >> A(2,1)=5; A(2,2)=3; >> A A = 1 7 Informationsteknologi 5 3 Institutionen för informationsteknologi | www.it.uu.se 12 Special matrix commands n Available built-in >> B = ones(2,3) features to create the B = usual (and unusual) 1 1 1 matrices n Can create more 1 1 1 advanced matrices by >> eye(2) combinations of these ans = 1 0 eye(n) identity-matrix 0 1 ones(m,n) one-matrix zeros(m,n) zero-matrix >> C = zeros(2,2) rand(m,n) rand-matrix C = Informationsteknologi 0 0 + numerous other 0 0 commands Institutionen för informationsteknologi | www.it.uu.se Extending a matrix ⎡1 7⎤ Given A = ⎢ ⎥ >> A = [A; 2 1]; ⎣5 3⎦ alternative ⎡1 7⎤ create A ⎢5 3⎥ >> temp = [2 1]; = ⎢ ⎥ ⎣⎢2 1⎦⎥ >> A = [A; temp]; Separate row and column vectors! >> temp2 = [2;1]; >> A = [A; temp2]; ??? Error using ==> vertcat Informationsteknologi All rows in the bracketed expression must have the same number of columns. Institutionen för informationsteknologi | www.it.uu.se 13 Elements, rows and columns n One can work with individual elements, rows, columns, submatrices >> A(2,1) ans = 5 >> A(2,:) ans = 5 3 >> A(2,:) = [0 0] Colon (:) denotes the whole range (all rows A = or all columns) Informationsteknologi 1 7 0 0 2 1 Institutionen för informationsteknologi | www.it.uu.se Submatrices, colon notation Submatrices of the matrix A, mxn can be created quickly with colon notation n A(:,j) j:th column of A n A(i,:) i:th row of A n A(i:k,j:m) submatrix, rows i-k and cols j-m A = 1 7 6 0 0 5 Example, 2 1 3 Picking out this submatrix >> B = A(2:3,1:2) B = Informationsteknologi 0 0 2 1 Institutionen för informationsteknologi | www.it.uu.se 14 Workspace and Array Editor n If you double-click on a variable in Workspace a new window is opened, Array Editor Double- click on a variable in the Workspace Informationsteknologi n Here you can change the variable value but also size.