Introduction to Programming in MATLAB and SCILAB

Transcription

1 Introduction to Programming in MATLAB and SCILAB By Dr. V. Madhusudanan Pillai Associate Professor Department of Mechanical Engineering National Institute of Technology Calicut Kozhikode , Kerala, India Content MATLAB as a programming language Introduction to Scilab 2 Department of Mechanical Engineering 1

2 What Is MATLAB? The name MATLAB is an abbreviation for MATrix LABoratory MATLAB is a high-performance language for technical computing Used mainly for algorithm development and data visualization Algorithms can be implemented and tested more quickly and easily than with traditional programming languages Provide quickly numerical and graphic answers to matrix and vector related math problems 3 Content of MATLAB system Development Environment MATLAB Mathematical Function Library MATLAB Language Graphics MATLAB Application Program Interface (API) 4 Department of Mechanical Engineering 2

3 Common Uses Developing Algorithms Data Analysis Data Visualization Numeric Computation 5 General Features of MATLAB The operations are designed to be as natural as possible Basic data element is an array that does not require dimensioning Consists a family of add-on application-specific solutions called toolboxes Toolboxes are comprehensive collections of MATLAB functions (M-files) to learn and apply specialized technology like signal processing, control systems, neural networks, fuzzy logic, wavelets, simulation, and many others. 6 Department of Mechanical Engineering 3

4 MATLAB Basics Starting MATLAB double-click the MATLAB icon, or in a terminal window, type matlab, and return In the Command Windowthe MATLAB prompt is >> The Desktop menu undocking command window tiling other windows (command history, workspace, current directory) 7 MATLAB Basics MATLAB as a calculator Type expressions at the >>, and press return Result is computed, and displayed as ans Use numbers, +, *, /, -, (), sin, cos, exp, abs, round, Precedence rules in expressions Left-to-right within a precedence group Precedence groups are (highest first) Highest precedence is parenthesis, then Power (^) Multiplication and division (*, /) Addition and subtraction (+, -) 8 Department of Mechanical Engineering 4

5 Examples of expressions Legal expressions >> 4 >> 5 + pi >> 6*sqrt(2)^4-12 >> 6 * sqrt( 2.0) ^ 4-12 >> sin(pi/3)^2 + cos(pi/3)^2 >> 1.0/0.0 # a number divided by zero is infinity (inf) >> -4/inf # This is equal to zero >> 0/0 # This is equal to infinity Illegal expressions >> 2 4 >> (2,4) 9 Variables Use name to assign result of an expression to a variable Variables do not need to be declared before assignment A single equal sign (=) is the assignment operator, LHS = RHS A semicolon at the end of the RHSexpression suppresses the display, but the assignment still takes place. Examples of Variables and Assignment Legal >> A = sqrt(13) >> B = exp(2); >> A = 2*B >> A = A + 1 >> C = tan(pi/4) Illegal (all for different reasons) >> D = sqrt(e) + 1; # if E is defined before then valid >> 3 = E >> 3*A = 14 >> F = Department of Mechanical Engineering 5

6 Creation of Vectors Colon notation to create a vector where x = s:d:f or x = (s:d:f) or x = [s:d:f] s = starting value, d = increment or decrement f = end or final value when d is omitted MatLab assumes d = 1. length(x) gives the number of terms in the vector. e.g. x = 0.2:0.1:1 11 Creation of Vectors and Operations Generation of n equally spaced values. x = linspace(s,f,n) The increment or decrement is calculated by MATLAB Increment or decrement, d = (f-s)/(n-1) e.g. x = linspace(-2,10,7) Vector can also be created with x = [-2,1,3,5,7,9,10]; or x = [-2,1:2:9,10]; z = x-1 results in z = z(1,3) = z(1,3)/2 results in z = z(3:5) = z(3:5)*3-1 results in z = y = z(3:5) results in y = Department of Mechanical Engineering 6

7 Array Operations y = [ ]; [ynew,indx] = sort(y) results in ynew= indx= Indxx= find(y<=9) and s = y(indxx) results in Indxx= and s= [ymax,indxmax]=max(y) [ymin,indxmin]=min(y) 13 Creation of Matrices A = [2 3 4;5 4 7; 7 6 9; 2 6 8]; or A = [ ]; [m,n] = size(a) results in m = 4 and n = 3 sl= length(a) results in S = 4 Special matrices x = ones(r,c) # creates ones matrix where, r and c are dimensions of matrix L = zeros(r,c) # creates the zeros matrix diag(a) # creates the (n x n) diagonal matrix whose elements are given by vector a of length n 14 Department of Mechanical Engineering 7

8 Manipulation of Matrices A=[ ]; A(3,4)=4 A(:,2) # Means all the rows of column 2 A(2,:) # Means all the columns of rows 2 A(1:3,3:5) results in [7 9 11;6 8 13;3 4 16]; x=a # Creates the transpose of A. 15 Manipulation of Matrices Addition/Substraction C = A+B and C = A-B # A & B have same dimensions Column augmentation C = [A,B] # A & B have same number of rows Row augmentation C = [A;B] # A & B have same number of columns Removing the row or column C(3,: ) = [] # 3 rd of C is removed Multiplication C=A*B # for multiplication matrix dimensions should match. i.e (m x k) (k x n) (m x n) 16 Department of Mechanical Engineering 8

9 Manipulation of Matrices Dot operations are used to do mathematical operations on element by element. C=A.*B C=A./B =A divided by B element by element C=A.\B =B divided by A element by element C=A.^B Also if x=1:8 and y=2.^x results in y= Functions Provides a large number of standard elementary mathematical functions, including abs, sqrt, exp, and sin Also provides many more advanced mathematical functions, including Bessel and gamma functions Most of these functions accept complex arguments For a list of the elementary mathematical functions, type help elfun For a list of more advanced mathematical and matrix functions, type help specfun help elmat 18 Department of Mechanical Engineering 9

10 The workspace It consists of the set of variables built up during a MATLABsession and stored in memory All variables that you create are accessible from the prompt >> Variables are accessed using their name as a reference Builtin Matlab commands >> who #list current variable >> whos #more information about current variable are used to see what is in the workspace. You can clear (ie, erase) variables with the clear command >> clear A # clears the variable A from the workspace 19 Saving the workspace When you quit MATLAB, the variables in the workspace are erased from memory. If you need them for later use, you must save them. You can save all variables (or just some of them) to a file using the command save >> save # saves all of the variables in the workspace into a file called matlab.mat(it is saved in the current directory).mat file is in binary format >> save Andy saves all of the variables in the workspace into a file called Andy.mat >> save Important A B C D* saves the variables A, B, Cand any variable beginning with Din the workspace into a file called Important.mat 20 Department of Mechanical Engineering 10

11 Loading from a.matfile loadis the opposite of save. It reads a.matfile, putting all variables contained in the.matfile into the workspace >> load # loads all of the variables from the file matlab.mat >> load Andy loads all of the variables from the file andy.mat 21 Script files Programming in Matlab A MATLAB script file (Called an M-file) is a text file that contains one or more MATLAB commands and, optionally, comments. The file is saved with the extension".m". When the filename (without the extension) is issued as a command in MATLAB, the file is opened, read, and the commands are executed as if input from the keyboard. TheresultissimilartorunningaprograminC. 22 Department of Mechanical Engineering 11

12 Script files factscript.m % FACTSCRIPT Compute n-factorial, n!=1*2*...*n y = prod(1:n); Executed by typing its name >> factscript Operates on variables in global workspace Variable n must exist in workspace Variable y is created (or over-written) Use comment lines (starting with %) to document file 23 Function files Functions describe subprograms Take inputs, generate outputs Have local variables (invisible in global workspace) Structure of Function files [output_arguments]= function_name(input_arguments) % Comment lines <function body> factfun.m function [z]=factfun(n) % FACTFUN Compute factorial z = prod(1:n); Execution of function file >> y = factfun(10); 24 Department of Mechanical Engineering 12

13 Script or function: when use what? Functions Take inputs, generate outputs, have internal variables Solve general problem for arbitrary parameters Scripts Operate on global workspace Document work, design experiment or test Solve a very specific problem once 25 Logical expressions Relational operators (compare arrays of same sizes) == (equal to) ~= (not equal) < (less than) <= (less than or equal to) > (greater than) >= (greater than or equal to) Logical operators (combinations of relational operators) & (and) if (x>=0) & (x<=10) (or) ~ (not) Logical functions xor # Logical EXCLUSIVE OR isempty # True for empty array any # True if any element of a vector is nonzero all # True if all elements of a vector are nonzero disp( x is in range 0,10 ) else end disp( x is out of range ) 26 Department of Mechanical Engineering 13

14 Flow control - selection The if-elseif-else-end construction if <logical expression> <commands> elseif <logical expression> <commands> else <commands> end if height>170 disp( tall ) elseif height<150 disp( small ) else disp( average ) end 27 Flow control - repetition Repeats a code segment a fixednumber of times for index = <vector> end <statements> The <statements> are executed repeatedly. At each iteration, the variable index is assigned a new value from <vector>. for k=1:12 kfac=prod(1:k); disp(['factorial of ',num2str(k),' is ',num2str(kfac)]); end 28 Department of Mechanical Engineering 14

15 Flow control conditional repetition while-loops while <logical expression> end <statements> <statements> are executed repeatedly as long as the <logical expression> evaluates to true 29 Scilab: The Free Platform for Numerical Computation Department of Mechanical Engineering 15

16 What is Scilab? Scilabis an open source scientific software package which can be used as a programming language. It can be used for numerical computations; providing a powerful open computing environment for engineering and scientific applications. It is a collection of collection of numerical algorithms covering many aspects of scientific computing problems. Since 1994 it has been distributed freely along with the source code via the Internet. It is currently used in educational and industrial environments around the world. 31 History Scilabwas created in 1990 by researchers from INRIA (French National Institute for Research in Computer Science and Control) and École nationaledes pontset chaussées(enpc) ScilabConsortium was formed in May 2003 to broaden contributions and promote Scilabas worldwide reference software in academia and industry In July 2008, the ScilabConsortium joined the Digiteo Foundation 32 Department of Mechanical Engineering 16

17 History Contd : Matlab written in Fortran and public domain 1984: creation of The MathWorks company Since 1990: Matlab is the standard and a monopoly Around 1980: Blaise then Basile built upon Matlab 1990: creation of Scilab at INRIA 1994: Scilab freely distributed on the net Courtesy: Claude Gomez (Scilab Consortium / Digiteo Director )and Bruno Jofret (Scilab Consortium / Digiteo Project Engineer), A ppt presentation on Scilab: The Platform for Numerical Computation 33 Scilab More than 1,700 functions Computation library Matrix computation, sparse matrices Polynomials and rational functions Interpolation, approximation Simulation: systems of differential equations Classic and robust control, LMI optimization Differentiable and non-differentiable optimization Signal processing Statistics Graphs and networks Scicos: block diagram simulator for dynamical systems Graphics, GUI, GUI builder 2-D and 3-D graphics, animation Ui controls, interface with TCL/TK User interface Language, interpreter Editor On line help Scilab Consortium Interface Services Toolboxes SIVP: image and video processing MIXMOD: cluster and discriminant Analysis OpenFEM: finite elements Wavelab: wavelet analysis OPC: data acquisition Grocer: econometric Modnum: communication systems in Scicos RTAI: real time Scicos CGAL: computational geometry GRID with ProActive GREENSCILAB: plant growth simulation Contributors Other Scientific Software Courtesy: Claude Gomez (Scilab Consortium / Digiteo Director )and Bruno Jofret (Scilab Consortium / Digiteo Project Engineer), A ppt presentation on Scilab: The Platform for Numerical Computation 34 Department of Mechanical Engineering 17

18 Websites Scilabbinaries can be downloaded directly from the Scilabhomepage for the platforms (Windows, Linux or Mac) Use the help provided on Scilabweb site A list of commercial books, free books, online tutorials and articles is presented on the Scilab homepage 35 Scilab in India A project on Scilabis currently going on in IITB This project is funded by MHRDas part of the National Mission on Education through ICT. Kannur, Mumbai and Puneuniversities have scilab as part of their syllabus 36 Department of Mechanical Engineering 18

19 Exercise Develop a program to sample a random value based on the given empirical distribution. For example, if the distribution is as follows Variable (d) Frequency(df) When we sample, the variable can have values as 1, 2, 7. The program has to give randomlyonevalue.wewanta generalised program so that for any empirical distribution it will give a random value. This value has to be used subsequently in some other program. 37 Approach Workout the problem yourself If the problem is very large work out a sample part of the problem and ensure that every distinct aspect are worked out Divide the problem into different distinct part Further consider dividing the distinct part again and again Write the program for each small part Put together some distinct parts to form function Put together these functions to form the final script file 38 Department of Mechanical Engineering 19

20 Working out Random Variable value (d) Frequency (df) Relative frequency (rf) Cumulative relative frequency (cf) Random number Total 50 Randomly generated variable value 39 Matlab features required Assignment Length Sum Rand Break Flow control for loop If Elseif else end Relational operator Logical operator Break Terminate the execution of WHILE or FOR loop Rand A function to generate uniformly distributed random number 40 Department of Mechanical Engineering 20

21 Breaking up the problem Step 0: The value of random variable and the frequency are stored in variables namely, d and df Step 1: Calculate the relative frequency (rf) Step 2: Calculate the cumulative relative frequency (cf) Step 3: Generate a random number 41 Breaking up the problem and program development contd Step 4: (i) Check where this random number is falling (ii) Once identified the upper and lower value in which it is falling, identify the random variable value corresponding to the upper cumulative value (iii)assign this value to a variable name (rd) which represent the randomly generated value from the empirical distribution 42 Department of Mechanical Engineering 21

22 Program development Step 0: Identification of name for input variables which has done at break up itself Step 1: rf = df/sum(df) Step 2: See the logic of how we have developed the cumulative frequency Logic: First value as such is appearing in the cumulative frequency and to get other values we repeatedly adding the relative frequency with the previous sum The first value also can be considered as a sum 43 Program development step 2 Let a variable be a and a =0 Add to a the first element of rf Now, a = rf(1) store this a to cf(1) Again add to this new a the second element of rf Now, a= rf(1) + rf(2) store this to cf(2) Repeat this step until the last element is added to a and stored 44 Department of Mechanical Engineering 22

23 Program development step 2 contd From the above logic we know that we want know the number of times to add to get the cumulative frequency The number of times is equal to the number of element of rfor dfor d That is, this is the length of the input vector Corresponding statement in MATLAB is ld = length(df) 45 Program development step 2 contd Repeated addition can be carried with FOR loop a = 0; For i= 1:ld a = a + rf(i); cf(i) = a; end Step 3: rn= rand() 46 Department of Mechanical Engineering 23

24 Program development step 4 Here, also a FOR loop is required as the rn generated may fall in any interval of the cf After the identification of range in which it is falling and assignment of upper value to rd, we can break from the loop Since we are checking the range in which it is falling, we have to use IF ELSE statement 47 Program development step 4 For j = 1: ld if j = =1 if rn<= cf(j) rd = d(j); break end elseifrn> cf(j-1) & rn<= cf(j) rd = d(j); break end end 48 Department of Mechanical Engineering 24

25 Develop the full program Above code can be used in both MATLABand Scilab Major difference in these systems Any comment line start with % in MATLAB and with // in Scilab For function file in MATLABthere is no endfunction statement at the end 49 References For Matlab 1. Rudra Pratap, Getting Started with MATLAB 7, First indian edition 2006, Oxford University Press Inc 2. E.B.Magrab, S.Azarm, B.Balachandran, J.H.Duncan, K.E.Herold and G.C.Walsh. An Engineer s Guide to MATLAB, second edition 2005, Pearson Prentice Hall For Scilab 50 Department of Mechanical Engineering 25