Introduction to Matlab1 Lecture 1 Matlab Basics Laboratoire

Introduction to Matlab-1 Lecture 1 – Matlab Basics Laboratoire Mathématiques, Informatique et Applications

Introduction to Matlab 2 What is Matlab? § A software environment for interactive numerical computations § Examples: § Matrix computations and linear algebra § Solving nonlinear equations § Numerical solution of differential equations § Mathematical optimization § Statistics and data analysis § Signal processing § Modelling of dynamical systems § Solving partial differential equations § Simulation of engineering systems 2

Introduction to Matlab 3 Matlab used (on a daily basis) in many engineering companies 3

Introduction to Matlab 4 Matlab used in many courses Numerical analysis Chemical Process Control Signal and Systems I Control Project Course Signals and Systems II Signal Theory Modeling of Dynamical Systems Digital Signal Processing Automatic Control, Basic Course Adaptive Signal Processing Automatic Control, Advanced Course Signal Processing Project Nonlinear Control Communication theory Hybrid and Embedded Control Systems Advanced Communication Theory <and many, many more> 4

Introduction to Matlab 5 Today’s Lecture Matlab Basics § § Background to Matlab Interactive calculations Vectors and matrices Graphical illustrations Next lecture: Matlab programming 5

Introduction to Matlab 6 Matlab Background Matlab = Matrix Laboratory § Originally a user interface for numerical linear algebra routines § Commercialized 1984 by The Mathworks § Since then heavily extended (defacto-standard) Alternatives Matrix-X (symbolic) Octave (free; GNU) Lyme (free; Palm) Complements Maple Mathematica 6 (symbolic)

Introduction to Matlab 7 Construction Core functionality: compiled C-routines Most functionality is given as m-files, grouped into toolboxes § m-files contain source code, can be copied and altered § m-files are platform independent (PC, Unix/Linux, MAC) Simulation of dynamical systems is performed in Simulink Sig. Proc C-kernel Contr. Syst. m-files Simulink 7

Introduction to Matlab 8 Matlab Desktop Launch Pad Command Window History 8

Introduction to Matlab 9 Matlab Desktop – cont’d Workspace Command Window Current DIrectory 9

Introduction to Matlab 10 Matlab Help 10

Introduction to Matlab 11 MATLAB Demo § Demonstrations are invaluable since they give an indication of the MATLAB capabilities. § A comprehensive set are available by typing the command >>demo in MATLAB prompt. 11

Introduction to Matlab 12 Interactive Calculations Matlab is interactive, no need to declare variables >> 2+3*4/2 >> a=5 e-3; b=1; a+b Most elementary functions and constants are already defined >> cos(pi) >> abs(1+i) >> sin(pi) Last call gives answer 1. 2246 e-016 !? 12

Introduction to Matlab 13 Variable and Memory Management Matlab uses double precision (approx. 16 significant digits) >> format long >> format compact All variables are shown with >> whos Variables can be stored on file >> save filename >> clear >> load filename 13

Introduction to Matlab 14 The Help System Search for appropriate function >> lookfor keyword Rapid help with syntax and function definition >> help function An advanced hyperlinked help system is launched by >> helpdesk Complete manuals as PDF files 14

Introduction to Matlab 15 Variables § Don’t have to declare type § Don’t even have to initialise § Just assign in command window >> >> a=12; % variable a is assigned 12 Matlab prompt assign operator suppress command output comment operator Try the same line without the semicolon and comments 15

Introduction to Matlab 16 Variables (continued …) § View variable contents by simply typing the variable name at the command prompt >> a a = 12 >> >> a*2 a = 24 >> 16

Introduction to Matlab 17 Workspace § The workspace is Matlab’s memory § Can manipulate variables stored in the workspace >> b=10; >> c=a+b c = 22 >> 17

Introduction to Matlab 18 Workspace (continued …) Display contents of workspace >> whos Name Size Bytes Class a 1 x 1 8 double array b 1 x 1 8 double array c 1 x 1 8 double array Grand total is 3 elements using 24 bytes >> Delete variable(s) from workspace >> clear a b; % delete a and b from workspace >> whos >> clear all; % delete all variables from workspace >> whos 18

Introduction to Matlab 19 The : operator VERY important operator in Matlab Means ‘to’ >> 1: 10 ans = 1 2 3 4 5 6 7 8 9 10 >> 1: 2: 10 ans = 1 3 5 7 9 Try the following >> x=0: pi/12: 2*pi; >> y=sin(x) 19

Introduction to Matlab 20 The : operator and matrices >>A(3, 2: 3) ans = 1 >>A(: , 2) ans = 7 A= 3 5 2 2 1 1 1 0 7 2 1 1 What’ll happen if you type A(: , : ) ? 20

Introduction to Matlab 21 Vectors and Matrices Vectors (arrays) are defined as >> v = [1, 2, 4, 5] >> w = [1; 2; 4; 5] Matrices (2 D arrays) defined similarly >> A = [1, 2, 3; 4, -5, 6; 5, -6, 7] 21

Introduction to Matlab 22 Matrix Operators All common operators are overloaded >> v + 2 Common operators are available >> B = A’ >> A*B >> A+B Note: § Matlab is case-sensitive A and a are two different variables 22

Introduction to Matlab 23 Indexing Matrices Indexing using parentheses >> A(2, 3) Index submatrices using vectors of row and column indices >> A([2 3], [1 2]) Rows no. 2, 3 Column no. 1, 2 Ordering of indices is important! >> B=A([3 2], [2 1]) >> B=[A(3, 2), A(3, 1); A(2, 2), A(2, 1)] 23

Introduction to Matlab 24 Indexing Matrices Index complete row or column using the colon operator >> A(1, : ) Can also add limit index range >> A(1: 2, : ) >> A([1 2], : ) General notation for colon operator >> v=1: 5 >> w=1: 2: 5 24

Introduction to Matlab 25 Matrix Functions Many elementary matrices predefined >> help elmat; >> I=eye(3) Elementary functions are often overloaded >> help elmat >> sin(A) Specialized matrix functions and operators >> As=sqrtm(A) >> As^2 >> A. *A Note: in general, ”. <operator>” is elementwise operation 25

Introduction to Matlab Manipulating Matrices 26 A= 3 5 2 >> A ' % transpose >> B*A % matrix multiplication >> B. *A % element by element multiplication >> B/A % matrix division >> B. /A % element by element division >> [B A] % Join matrices (horizontally) >> [B; A] % Join matrices (vertically) B= 1 4 2 2 1 1 1 0 7 3 9 7 1 5 2 Enter matrix B into the Matlab workspace Create matrices A and B and try out the matrix operators in this slide 26

Introduction to Matlab 27 Numerical Linear Algebra Basic numerical linear algebra >> z=[1; 2; 3]; x=inv(A)*z >> x=Az Many standard functions predefined >> det(A) >> rank(A) >> eig(A) The number of input/output arguments can often be varied >> [V, D]=eig(A) 27

Introduction to Matlab 28 Matrix vs Element Math Matrix Math 28

Introduction to Matlab 29 Circuit Example + 10 V - 10 Ohms 3 u. F 0. 01 H I=V/R=10 / 29

Introduction to Matlab 30 RLC Series. m File %Example 4. m - RLC w=linspace(1, 40000, 1000); i=10. /(10+(1. /(j. *w. *3. *10^-6))+(j. *w. *0. 01)); plot(w, abs(v)); j is intrinsically unless its redefined 30

Introduction to Matlab 31 RLC series result 31

Introduction to Matlab 32 Graphics Visualization of vector data is available >> x=-pi: 0. 1: pi; y=sin(x); >> plot(x, y) >> plot(x, y, ’s-’) >> xlabel(’x’); >> ylabel(’y=sin(x)’); 32

Introduction to Matlab % print the cosine and sine u = 0: pi/20: 2*pi; w = sin(u); v = cos(u); figure(1); plot(u, w, 'ro-') ; hold on; plot(u, v, 'gs: '); xlabel('theta'); ylabel('y'); legend('Sin(theta)', 'Cos(theta)'); title('Sample Plots'); 33 33

Introduction to Matlab 34 Can change plot properties in Figure menu, or via ”handle” >> h=plot(x, y); set(h, ’Line. Width’, 4); Many other plot functions available >> v=1: 4; pie(v) 34

Introduction to Matlab 35 Graphics Three-dimensional graphics >> A = zeros(32); >> A(14: 16, 14: 16) = ones(3); >> F=abs(fft 2(A)); >> mesh(F) >> rotate 3 d on 35

Introduction to Matlab 36 Three-dimensional graphics >> A = zeros(32); >> A(14: 16, 14: 16) = ones(3); >> F=abs(fft 2(A)); >> mesh(F) >> rotate 3 d on 36

Introduction to Matlab 37 Graphics Three-dimensional graphics >> A = zeros(32); >> A(14: 16, 14: 16) = ones(3); >> F=abs(fft 2(A)); >> mesh(F) >> rotate 3 d on Several other plot functions available >> surfl(F) Can change lightning and material properties >> cameramenu >> material metal 37

Introduction to Matlab 38 Graphics Bitmap images can also be visualized >> load mandrill >> image(X); colormap(map) >> axis image off 38

Introduction to Matlab 39 MATLAB - Reference: A Partial List of On-Line Matlab Tutorials and Matlab Books § http: //www. duke. edu/~hpgavin/matlab. html Getting started with Matlab § http: //www. engr. iupui. edu/ee/courses/matlab/tutorial_start. htm A quick reference to some of the key features of Matlab § http: //science. ntu. ac. uk/msor/ccb/matlab. html#MATLAB Matlab tutorial, with lots of links to other tutorials § http: //www. glue. umd. edu/~nsw/ench 250/matlab. htm Control Tutorial for Matlab § http: //www. engin. umich. edu/group/ctm/home. text. html A Practical Introduction to Matlab § http: //www. math. mtu. edu/~msgocken/intro. html Matlab Tutorial Information from UNH § http: //spicerack. sr. unh. edu/~mathadm/tutorial/software/matlab/ 39

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